7232019 Passive Cooling of Buildings by Using Integrated Earth to Air Heat Exchanger
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Passive cooling of buildings by using integrated earth to air heat exchanger
and solar chimney
M Maerefat AP Haghighi
Department of Mechanical Engineering Faculty of Engineering Tarbiat Modares University Tehran 14115-143 Iran
a r t i c l e i n f o
Article history
Received 26 August 2009
Accepted 3 March 2010
Available online 26 March 2010
Keywords
Passive cooling
Earth to air heat exchanger
Solar chimney
a b s t r a c t
Passive cooling is being employed as a low-energy consuming technique to remove undesirable interiorheat from a building in the hot seasons There are numerous ways to promote this cooling technique and
in the present study the use of solar chimney (SC) together with earth to air heat exchanger (EAHE) is
introduced Consequently theoretical analyses have been conducted in order to investigate the cooling
and ventilation in a solar house through combined solar chimney and underground air channel The
1047297nding shows that the solar chimney can be perfectly used to power the underground cooling system
during the daytime without any need to electricity Moreover this system with a proper design may also
provide a thermally comfortable indoor environment for a large number of hours in the scorching
summer days Based on the required indoor thermal comfort conditions the numbers of required SCs
and EAHEs are calculated and some features of such a system is presented It is widely expected that the
proposed concept is useful enough to be incorporated with a stand-alone or a cluster of buildings
especially in some favorable climates
2010 Elsevier Ltd All rights reserved
1 Introduction
Environmental comfort economy and energy conservation are
some of the major functional considerations in the buildings So far
as institutional commercial and residential buildings are con-
cerned electrical air-conditioning systems are mainly employed for
the health and comfort of the occupants As matter of fact the
demand for air-conditioners is growing yearly However with the
increasing cost diminishing supply of nonrenewable energy and
environmental reasons there began a tremendous surge of interest
and research in solar and passive systems since the 1970s The use
of passive cooling techniques combined with a reduced cooling
load may not only result in a good thermal summer comfort but
they save cooling energy consumption too Here the two inter-
esting and promising passive cooling techniques are natural dayventilation and earth to air heat exchangers Natural ventilation is
usually employed in a region with mild climate and in spaces where
a little variation in indoor climate is tolerable A solar chimney on
the other hand is a good con1047297guration to implement natural
ventilation in buildings where solar energy is available
In the past decade solar chimneys had attracted much attention
of investigators and researchers As a matter of fact Bansal et al
analytically studied a solar chimney-assisted wind tower for
natural ventilation in buildings [1] The estimated effect of the solar
chimney was shown to be substantial in inducing natural ventila-
tion for low wind speeds Gan and Riffat also investigated solar-
assisted natural ventilation with heat-pipe heat recovery in natu-
rally ventilated buildings using a CFD technique [2] Hamdy and
Fikry examined theoptimum tiltangle of solar chimney system that
compromises between solar heat gain factor and stack high to
insure the best ventilation performance They also showed that the
air 1047298ow rate through roof solar chimney increases if the height
between inlet and outlet is increased [3] Khedari et al experi-
mentally investigated the feasibility of a solar chimney to reduce
heat gain in a house and the effect of openings on the ventilationrate The results showed that when the solar chimney was in use
room temperature was near that of the ambient air indicating
a good ability of the solar chimney to reduce house rsquos heat gain and
ensuring thermal comfort Opening a window or a door is less
ef 1047297cient than using solar chimneys [4] Mathur et al analytically
studied the effect of inclination of absorber on the air 1047298ow rate in
a solar induced ventilation system using roof solar chimney The
results showed that optimum absorber inclination varies from 40
to 60 depending upon the latitude of the location [5] Bassiouny
and Koura analytically and numerically studied the solar chimney
for improving room natural ventilation They found that the
Corresponding author Tel thorn98 21 8288 3360 fax thorn98 21 8288 3381
Mob thorn98 9123024381
E-mail address maerefatmodaresacir (M Maerefat)
Contents lists available at ScienceDirect
Renewable Energy
j o u r n a l h o m e p a g e w w w e l s e v i e r c o m l o c a t e r e n e n e
0960-1481$ e see front matter 2010 Elsevier Ltd All rights reserved
doi101016jrenene201003003
Renewable Energy 35 (2010) 2316e2324
7232019 Passive Cooling of Buildings by Using Integrated Earth to Air Heat Exchanger
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chimney width has a more signi1047297cant effect on ACH compared to
the chimney inlet size [6]
The earth to air heat exchanger is applicable for improving
natural ventilation through a cooling effect which can also
contribute to decrease temperature in the building The earth to air
heat exchanger is a pipe buried in the ground through which air is
sucked into a building Since the ground exhibits high thermal
inertia temperature at a certain depth is almost constant
throughout the year which allows for its use either as a heat sink
(in summer) or a heat source (in winter) [7] In the summer soil
temperature of a hot and arid region at a few meters deep is lower
than the mean daily outdoor air temperature and signi1047297cantly
lower than the usual outdoor daytime air temperature So it can be
used as a heat sink to cool the exterior warm air [8] The proper
designing of the earth to air heat exchanger requires deeper
understanding of the heat andmoisture dynamics in the earth to air
heat exchanger Various analytical and numerical models have
contributed to investigate the thermal behavior and cooling or
preheating potential of EAHE [9e12]
Krarti and Kreider [9] developed a simpli1047297ed analytical model to
determine the energy performance of an underground air tunnel
The model assumed that the air tunnel-ground system reaches
periodic and quasi-steady state behavior after some days of oper-ation Also parametric analysis was conducted to determine the
effect of tunnel hydraulic diameter and air 1047298ow rate on the heat
transfer between ground and air inside the tunnel Hollmuller [10]
considered a periodic input for the air in the buried pipe yielding
a physical interpretation of the amplitude-dampening and the
phase-shifting of the periodic input signal Al-Ajmi et al [11]
developed a theoretical model of an eartheair heat exchanger for
predicting the outlet air temperature and cooling potential of these
devices in a hot arid climate The results showed that the EAHE
have the potential for reducing cooling energy demand in a typical
house by 30 over the peak summer season Kumar et al [12] used
the concept of arti1047297cial neural network and goal oriented design to
propose a computer design tool that can help the designer to
evaluate any aspect of earth to air heat exchanger and behavior of
the 1047297nal con1047297guration The results showed that there are six vari-
ables in1047298uencing the thermal performance of the earth to air heat
exchangers These variables are length humidity ambient air
temperature ground surface temperature ground temperature at
burial depth and air mass 1047298ow rate
The technique for passive cooling that is introduced and inves-
tigated in the present paper is integrated earth to air heat
exchanger and solar chimney (EAHE-SC) system A schematic plan
of the passively cooled room is shown in Fig 1 This system realizes
both cooling and ventilation during daytime with the help of solar
energy thus it is natural day ventilating technique
The proposed solar system consists of two parts the solar
chimney and the earth to air heat exchanger The solar chimney
consisted of a glass surface oriented to the south and an absorber
wall that works as a capturing surface The air is heated up in the SC
by the solar energy and 1047298ows upward because of the stack effect It
causes driving force which sucks the outside air through the cool-
ing pipe
The EAHE consists of horizontal long pipes that areburied under
the bare surface at the speci1047297c depth The pipes are spread under
the ground in a parallel manner The pipe spacing is considered
more than the thickness of the heat penetrating depth to increasethe heat exchange between the soil and the air
It will be shown this system can provide good indoor condition
in accordance with the Adapted Comfort Standard (ACS) speci1047297ed
for thermal comfort in naturally ventilated buildings The required
indoor temperatures according to the adaptive comfort model are
shown in Fig 2 The 1047297gure only shows the acceptable temperature
of indoor air when the outdoor temperature is within the range of
0e40 C and it does not recommend the ventilation rate [13]
Ventilation standards require a minimum of 3 air changes per
hour for residential buildings in India [14] Therefore the minimum
ventilation rate is set approximately around 3 ACH It will be
consequently shown that how this ventilation rate suitably
provides the required cooling loads of a room
Fig 1 Schematic diagram of integrated earth to air heat exchanger and solar chimney
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 2324 2317
7232019 Passive Cooling of Buildings by Using Integrated Earth to Air Heat Exchanger
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2 Modeling the system
Themodeling includes models of solarchimney(Fig3) and earth
toair heat exchanger (Fig4) In estimating theventilationrateof theproposedsolarhouse as a wholeit is important to determine theair
1047298ow rate which can be handled under a particular design and
operating conditions For this an overall energy balance on the
chimney is considered This includes the energy balances of glass
cover wall the black absorber wall and the air in between Writing
energy balance equations for absorber surface glass surface and air
column and solving them for T g T abs and T f to calculate air 1047298ow rate
have sought a mathematical solution Chimney modeling has been
done in accordance with Ong model [15]
The EAHE system presented in this paper is modeled as two
coupled heat transfer processes namely convection heat transfer
between air 1047298owing in the pipe and the pipe inner surface and
conduction heat transfer between the pipe inner surface and the
surrounding soil
The major assumptions that are used in the modeling may be
summarized as follows
1 Air inlet to the chimney is considered to have the same room
air average temperature
2 Only buoyancy force is considered wind induced natural
ventilation is not included
3 The 1047298ows in the channels are hydrodynamically and thermally
fully developed
4 The glass cover is opaque for infrared radiation
5 Thermal capacities of glass and absorber wall are negligible
6 The air 1047298ow in the channel is radiative non-participating
media
7 All thermophysical properties are constant evaluated at an
average temperature
8 The soil is homogeneous and the soil type does not changealong the channel
9 The system is at steady-state condition
21 Mathematical modeling of solar chimney
An element of the model for SC is shown in Fig 3 In principle
and based on the energy conservation law a set of differential
equations are obtained along the length of SC The energy balance
equation for glass cover is
S g A g thorn hrabsg Aabs
T abs T g
frac14 hg Ag
T g T fsc
thorn U ga AgT g T fsc (1)
The overall top heat loss coef 1047297cient from glass cover to ambient
air U ga can be written as
U ga frac14 hwind thorn hr gsky thorn hga (2)
The convective heat transfer coef 1047297cient due to the wind hwind is
given by [16]
hwind frac14 28 thorn 30uwind (3)
The solar radiation heat 1047298ux absorbed by the glass cover S g is
given by
S g
frac14 ag
I (4)
Fig 2 Adaptive standard for naturally ventilated buildings
Fig 3 Schematic diagram of the heat transfer in the solar chimney
Fig 4 Cross section of an EAHE with heat penetration depth
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 23242318
7232019 Passive Cooling of Buildings by Using Integrated Earth to Air Heat Exchanger
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The radiative heat transfer coef 1047297cient from the outer glass
surface to the sky referred to the ambient temperature is obtained
from [15]
hr gsky frac14s3g
T g thorn T sky
T 2g thorn T 2
sky
T g T sky
T g T a
(5)
Where the sky temperature is T sky frac14 00552T a15[16]The radiation heat transfer coef 1047297cient between absorber plate
and glass cover may be obtained from [15]
hr absg frac14s
T 2g thorn T 2abs
T g thorn T abs
1=3g thorn 1=3abs 1 (6)
The convective heat transfer coef 1047297cient between the glass cover
and air 1047298ow in the chimney
hg frac14 Nugkfsc=Lg (7)
Where Nusselt number Nug frac14 06(Grgcos qPrfsc)02 Grashof
number Grg frac14
( g bS g
(Lg
)4(kfscn
fsc
2 )) [5] The convective heat transfer
coef 1047297cient between inclined absorber wall and the air 1047298ow in the
chimney is given by
habs frac14 Nuabskfsc=Lsc (8)
Where Nusselt number Nuabs frac14 06(Grabscos qPrfsc)02 and Grashof
number Grabs frac14 ( g bS abs(Labs)4(kfscnfsc2 )) All property values are
evaluated at average surfaceeair temperatures
The energy balance equation for air 1047298ow in the chimney is
habs Aabs
T abs T fsc
thorn hg Ag
T g T fsc
frac14 mC fsc
T fsc T r
g
(9)
The axial mean air temperature was experimentally determined
to follow the non-linear form [15]
T fsc frac14 gT fsco thorn eth1 gTHORNT fscin (10)
Value of the constantg is taken as 074 according to Ref [17] The
energy balance equation for the absorber plate is written as
S abs Aabs frac14 habs Aabs
T abs T fsc
thorn hr absg Aabs
T abs T g
thorn U absa AabsethT abs T aTHORN (11)
The overall heat transfer coef 1047297cient from the rear of the
absorber wall to the ambient U absa is given by
U absa frac14
1=eth
1=
ha thorn
t ins=
kinsTHORN
(12)
In the above equation ha has been taken as 28 Wm2 K [16]
22 Mathematical modeling of EAHE
In orderto determinethe system cooling capabilityone is mainly
interested in the cool air temperature supplied by the EAHE
Therefore detailed modeling of the EAHE is required The cross
section of EAHE used in the model and the thermal network of the
systemare shown in Figs 4 and5 respectively In order to impose the
ground thermal loads as boundary conditions at the EAHE wall the
undisturbed soil temperature (T su) has been used The soil temper-
ature is nearly constant at the penetration depth (Fig1) The pene-
tration depth is de1047297
ned when the surface of the soil is subjected to
a periodic temperature It depends on the soil diffusivity and the
temperature cycle frequency through equation (13) [10]
d frac14
ffiffiffiffiffiffiffi2ls
u
r (13)
Where ls frac14 ks(rsC s) for daily variation u frac14 (2pday) and for annualu frac14 (2p(year)) The penetration depths are used to calculate the
thermal resistance only and the rest of the analysis is carried out at
steady-state condition The model includes two equations one is
related to the energy balance of the circulating 1047298uid and the other
equation describes heat transfer in the soil region
The energy balance for d x a differential length of EAHE can be
expressed in the following form
T ft T su frac14 dQ Rtotal
d x (14)
Where Rtotal represents the overall thermal resistance which can
be de1047297ned by the resistance network as shown in Fig 5
Rtotal frac14 Rc thorn Rt thorn Rs (15)
Where Rc is the thermal resistance due to convection heat
transfer between air in the pipe and the pipe inner surface It may
be expressed as
Rc frac14 1
2pLt h ft (16)
The convection heat transfer coef 1047297cient inside the pipe is
de1047297ned by
hft frac14 Nutkft
2r ti(17)
The Nusselt number for air 1047298ow in pipe with smooth internalsurface depends on Reynolds number and it is given by [18]
Nu frac14 366 if Re lt 2300 (18a)
Nu frac14 x=8ethRe 1000THORNPr
1 thorn127 ffiffiffiffiffiffiffiffiffiffiffi
ethx=8THORNp
Pr2=3 1 if 2300 Relt5 106 (18b)
Where
x frac14 eth182log Re 164THORN2 if Re 2300 (19)
Rt is the thermal resistance of the pipe Steady-state analysis gives
the thermal resistance of the pipe annulus as
Fig 5 Thermal resistance between air 1047298ow and surrounding undisturbed soil
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 2324 2319
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Rt frac14 ln
r ti thorn t t
r ti
2pktLt (20)
Rs is the thermal resistance between EAHE and undisturbed soil
surface it is given by
Rs frac14 1
2pksLt
ln01 thorn d
r ti thorn t tthorn ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 thorn
d
r ti thorn t t
2
1s 1A (21)
The energy balance of the circulating 1047298uid is given by
dQ frac14 mC f dT ft
d x d x (22)
Eqs (14) and (22) give the differential overall energy balance
equation in the form8gtlt
gt
dT ft
d x thorn
T f t
mC ftRtotalfrac14 00
T ft frac14 T a x frac14 00
(23)
The solution of equation (23) can be expressed as
T fteth xTHORN frac14 T su thorn ethT a T suTHORNexp
x
mC ftRtotal
(24)
23 Room ventilation and temperature
Chimney effect causes the movement of air into and out of
buildings and is driven by buoyancy Buoyancy occurs due to
a difference in indoor-to-outdoor air density resulting from
temperature and moisture differences A chimney heated by solar
energy can be used to drive the chimney effect without increasing
room temperature The driving potential for the air 1047298ow through
the solar house is function of the pressure difference between the
inlet of the EAHE and the SC outlet The buoyancy pressure due to
increasing air temperature in SC sucks the cooled and heavy air
through the EAHE The friction losses due to 1047298uid 1047298ow through the
channels and across the 1047297ttings refrain from the 1047298uid 1047298ow If the
buoyancy pressure overcomes the sum of all 1047298ow pressure losses
the natural ventilation may take place
A mathematical model based on Bernoullirsquo s equation has been
used to estimate the system 1047298ow rate Thus the chimney net draft
Draftsccan be calculated by the following equation [19]
Draftsc frac14rfa rfsco
gLscsin q
0X7
j frac14 6
c j thorn xscLsc
dhyd
sc
1A
r
fscou
2
sc2
eth25THORN
Where the c j is the pressure loss coef 1047297cients at the locations which
are indicated in Fig 1
In right hand side of equation (25) the 1047297rstclause is thechimney
theoretical draft and the second one is the chimney pressure loss
The EAHE pressure loss DP EAHE is [20]
DP EAHE frac14
0X5
j frac14 1
c j thorn xtLEAHE
dti
1Arftu2
f t
2
(26)
The air temperature variation in the vertical pipe is ignored The air
temperature at the solar chimney inlet is assumed to be same as the
room air temperature which is higher than the cooled air
temperature at the pipe outlet So the chimney effects DraftEAHE
and DraftRoom can be expressed as
DraftEAHE frac14rfr rft
gH tr (27)
DraftRoom frac14
rfscin rfr
gH rinscin (28)
The required draft for cooling system DraftSystem is the sum of thepipe pressure loss and the negative pressure DraftEAHE and
DraftRoom
DraftSystem frac14 DP EAHE DraftEAHE thorn DraftRoom (29)
Under steady-state conditions we can write
DraftSystem frac14 Draftsc (30)
The air mass 1047298ow rate at the chimney and EAHE are the same if
there is no air in1047297ltration
m frac14 rAujChimney outlet frac14 r AujChimney inlet frac14 r AujEAHE (31)
By expanding equation (30) and use of equation (31) the airvelocity in the SC can be obtained as
usc frac14
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiBouyancy Terms
Friction Terms
r (32-a)
Where
Bouyancy Terms frac14 2
rfa rfsco
gLscSinethqTHORN
rfscin rfr
gH rinscin
rft rfr
gH tr
(32-b)
Friction Terms frac14 ethc THORN6rfsco Ascorfr Ascin
2
rfr thornn
ethc THORN7thornxsc Lsc
ethdhydTHORNsc
orfscothorn( P5
j frac14 1
c j thorn xtLtthornH trthornBurried depth of EAHE
dt
rfsco Asco
rft At
2)rft
(32-c)
The main criteria for thermal comfort condition are affected by two
factors the ACH and room air temperature The ACH is calculated
under steady-state conditions by the following equation [5]
ACH frac14 3600m
rfscV (33)
The room air temperature which depends on room heat gain is
obtained by the following equation
T r frac14 T ftot thorn Q rmC ft
(34)
Where Q r is sum of the heats that the room gains through the walls
and the heat generated by internal heat sources
3 Analysis
The system capability to provide the desired indoor condition
depends on parameters such as the ambient conditions (tempera-
ture solar radiation) dimensions of SC and EAHE and cooling
demand Parametric study is carried out to 1047297nd the effects of
geometrical dimensions of the SC and EAHE and outdoor envi-
ronmental conditions The following dimensions and speci1047297
cations
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 23242320
7232019 Passive Cooling of Buildings by Using Integrated Earth to Air Heat Exchanger
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are used in the modeling The room 40 40 3125 m in
dimensions without air in1047297ltration and has a minimum cooling
demand of Q frac14 116 W This is the demand of a room with adiabatic
walls which one person is resting in it The cooling demand is
changed at the range of 116e1500 W in the calculations
A solar chimney with the length of 40 m width of 10 m air gap
depth of 03 m and inlet of 04 04 m is considered These
dimensions are chosen based on studies of Ref [22] and may be
changed in the calculation A detailed study on a south facing solar
chimney in Tehran having 3544 N latitude position has found theoptimum angle of 50 to capture more radiation [5] Few numbers
of solar chimneys are adequate to provide the required stack effect
for the system
The cooling pipe of EAHE is a PVC pipe with 250 m length
001 m thickness and inside diameter of 05 m and is buried 30 m
below the soil surface According to the model developed by Bansal
et al [21] undisturbed soil temperature at a depth of 30 m is
approximated to be 19 C for a dry shaded soil surface condition
and it is considered to be the heat sink temperature These
dimensions have a decisive in1047298uence on cooling load and system
performance which will be investigated here Usually only one
EAHE suf 1047297cesto provide the necessarycooling load but in sever hot
conditions more cooling pipes may be employed
The EAHE outlet and the SC inlet are located on the oppositewalls (Fig 2) The SC inlet is lowered 07 m below the EAHE outlet
level The EAHE outlet is 3 m above the room 1047298oor thus it is 6 m
above the buried horizontal pipes of the EAHE The ambient
outdoor temperature is 34 C The thermophysical properties of the
materials included in the modeling are given in Table 1 The values
of the properties speci1047297ed in the table are kept constant in the
computation unless speci1047297cally noted otherwise
A computer program was written in MATLAB software to solve
the mathematical model The governing equations (1 9 11 24 and
32) have to be solved iteratively until convergence of the results
There is no experimental data to validate the results of theo-
retical model for the integrated system So the calculation has been
carried out for SC and EAHE separately under same conditions of
experimental studies of [22] and [23] to check the mathematical
model and to ensure the accuracy of computationsTable 2 shows the results of present model and the theoretical
and experimental results of Mathur et al [22] for different combi-
nations of solar radiation SC height and chimney inlet dimensions
The quantitative comparison shows a reasonable agreement
between the results obtained by the present study and the pub-
lished results of [22] The results of present study are closer to the
experimental results than the theoretical results of Ref [22] It
should be noted that the calculation carried out at the same
conditions of Ref [22] in which the roomvolume is 27 m3 and other
experimental conditions are given in Table 2
Fig 6 shows the air temperature variation along the cooling
pipe The results of the present work are calculated at the condi-
tions of experiments of Ref [23] given in Table 3 As the 1047297gure
shows there is good agreement between the present theoretical
results and the experimental results of Ref [23]
However it is reasonable to conclude that the mathematical
model can predict air temperature quite accurately and the calcu-
lated results are reliable
4 Result and discussion
41 Capability of the system to provide thermal comfort
Theoretical calculations are performed at various solar radia-
tions and room cooling demands The results are summarized in
Table 4 It is found that an integrated system of a few number of
solar chimneys with one (or at most two) EAHE cooling pipe can
Table 1
Thermophysical properties
Parameters Values
1 Transmissivity of glass 084 (d)
2 Absorptivity of glass 006 (d)
3 Emissivity of the glass 090 (d)
4 Absorptivity of absorber wall 095 (d)
5 Emissivity of the absorber wall 095 (d)
6 Thermal conductivity of the pipe (PVC) 023 (Wm K )7 Soil density 2050 (kgm3)
8 Thermal conductivity of the Soil 052 (Wm K)
9 Speci1047297c heat of soil 1840 (Jkg K)
Table 2
Comparison of experimental and theoretical results for solar chimney induced ACH number
Solar radiation
(Wm2)
Absorber
length (m)
Inlet chim dimens
(m m)
Ambient
temp (K)
ACH Errors of [22] Errors of present
studyEXP [22] Theo [22] Theo (present study)
300 07 10 03 295e302 4400 4173 4366 516 077
08 10 02 298e304 5330 4054 4757 2394 1075
09 10 01 294e296 2400 2704 2368 1266 133
500 07 10 03 295e302 4800 5160 4454 750 721
08 10 02 298e304 4530 4895 4816 806 631
09 10 01 294e296 2660 3461 2970 3011 1165
700 07 10 03 295e302 5600 5810 5404 375 35
08 10 02 298e304 5330 5175 5480 291 281
09 10 01 294e296 2930 3671 3217 2529 979
Fig 6 Comparison present results with experimental data
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 2324 2321
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provide the indoor thermal comfort conditions so the temperature
is retained at 2815e3194 C which is within the acceptable range
according to Ref [14] with 3e7 ACH which secures the required
ventilation rate As can be seen for higher cooling demands longer
and more cooling pipes of the EAHE are required
42 Effective dimensions of the system
There are many geometrical dimensions in the system that
affect its performance Some of them such as dimensions of the
inlet of the SC cross area of the SC etc have minor effects these
in1047298uence the 1047298ow rate slightly by changing the resistance to the
1047298ow While two geometrical dimensions have the substantial
effects i) absorbing surface area of the SC which provide the
energy for stack effect at the SC ii)cooling surface area of the EAHE
which facilitates heat removal from the air 1047298ow to soil
In the present study effects of variations of all dimensions are
investigated Based on the obtained results the dimensions
described in the section 3 have been chosen as suitable working
dimensions The details of the results are not given in the present
paper to save time However effects of changing the two ef 1047297cacious
dimensions are reported here
i) Absorber surface area is increased by increasing the length of
the chimney This increase results in higher ventilation rate or
higher ACH number On the other hand higher ventilation
rate with a constant cooling source results in higher indoor
temperature Thus more number of buried pipes are required
to cool the room and satisfy the thermal comfort require-
ments as shown in Table 5
ii) The lateral surface area of the buried pipe is serving as heat
exchange surface area of the heat sink of the system Gener-
ally larger cooling area provides more cooling effect to the
system In order to increase the cooling surface one may
increase the diameter andor the length of the pipe Table 6
shows the effect of EAHE length on system performance at
two different cooling demands For the length of EAHE less
than 20 m the comfort temperature may not be provided and
longer EAHE should be employed
Resultsof the study on thediameterof cooling pipes are shown in
Table 7 A comparative surveyshows that the required number of SCs
and EAHEs are minimums when the diameter is 05 m Therefore
this value is adopted as default valueof diameterand thevariation in
lateral area surfaces are made by increasing the length of the pipe
43 Effects of environmental conditions on the system performance
The environmental conditions are comprised of solar radiation
and outdoor ambient temperature in the present study Table 8
Table 3
Properties and conditions of experiment [23]
1 Length of EAHE 2500 (m)
2 Buried depth of EAHE 256 (m)
3 Radius of pipe 0305 (m)
4 Thickness of pipe 0002 (m)
5 Thermal conductivity of pipe 033 (Wm K)
6 Thermal conductivity of soil 116 (Wm K)
7 Thermal diffusivity of soil 645 107 (m2s)
8 Air velocity 147 (ms)
9 Air density 1214 (kgm3)
10 Air viscosity 178 107 (kgs m)
11 Speci1047297c heat of air 1205 103 (Jkg K)
12 Air Prandtl number 065 (d)
13 Thermal conductivity of air 028 (Wm K)
Table 4
Performance of the system at various cooling demands and solar radiations
Cooling
demand (W)
Solar radiation
(Wm2)
Length of
EAHE (m)
ACH
d
Room air
temp
( C)
Number
of SC
Number
of EAHE
116 400 25 634 2853 2 1
600 403 2814 1
800 506 2831 1
1000 584 2844 1
200 400 25 630 2935 2 1
600 356 2873 1
800 481 2935 1
1000 565 2933 1
400 400 30 569 2992 2 1
600 790 3015 2
800 388 2951 1
1000 487 3062 1
600 400 40 467 2827 2 1
600 721 3042 2
800 309 2777 1
1000 400 2902 1
800 400 40 520 2813 3 2
600 421 2764 2
800 533 2903 2
1000 627 3014 2
Note Ambient air temperature frac14 34 C
Table 5
Effects of absorber length on system performance
Cooling
demand (W)
Absorber
length (m)
ACH
d
Room air
temp (C)
Number
of SC
Number
of EAHE
116 30 440 2822 1 1
40 583 2844 1 1
50 706 2866 1 1
60 818 2886 1 1
800 30 236 2894 2 340 510 3098 2 3
50 662 3238 2 3
60 829 3363 2 3
800 30 312 2924 3 5
40 305 2941 2 4
50 351 2981 2 5
60 384 3019 2 6
Note Ambient air temperature frac14 34 C solar radiation frac14 1000 (Wm2)
Table 6
Effects of length of EAHE on system performance
Cooling
demand
(W)
Ambient
air temp
( C)
Solar
radiation
(Wm2)
Length of
EAHE
(m)
ACH
d
Room air
temp
( C)
Number
of SC
Number
of EAHE
116 40 400 150 347 2968 4 10
250 602 2972 3 2
350 517 2700 3 2450 579 2861 3 1
116 40 1000 150 347 2987 2 9
250 649 2872 2 3
350 465 2877 1 1
450 356 2633 1 1
800 40 400 150 Thermal comfort cannot be
provided
250 314 2900 3 5
350 454 2950 3 2
450 427 2700 3 2
800 40 1000 150 Thermal comfort cannot be
provided
250 335 2938 2 6
350 742 2952 2 3
450 559 2926 2 2
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shows the summary of results of the theoretical calculations fordifferent environmental conditions
The buoyancy driving force increases with an increase of solar
intensity and it causes higher ACH Thus less number of SCs are
required to drive the cool and heavy air through the EAHEs and to
compensate the pressure drops The results of calculations also
show that the required number of EAHEs should be increased to
retain the thermal comfort condition when the number of ACH and
indoor air temperature are increased at high solar radiation
The effect of ambient airtemperature on stack effect of SC is vice
versa The stack effect decreases when the ambient outdoor
temperature risesUnder these conditions more numberof SCs willbe required to ventilate the room
The results show that the system can provide the required
indoor temperature and ACH number even at harsh environmental
condition of high temperature of 45 C and low solar radiation of
100 Wm2 If the temperature is higher than 45 C the SC wonrsquot be
able to provide the stack effect and in this condition the use of
a small fan can help the cool air to 1047298ow from EAHE in to the room
and to realize thermal comfort condition
It should be noted that in this system all air 1047298ow is fresh air and
a reduction about 23 C in the inlet air is praiseful achievement of
the present passive cooling system
5 Conclusions
A passive solar system comprises of solar chimneys and earth to
air heat exchangers is proposed and studied in the present paper
The present study shows that the performance of the system
depends on solar radiation outdoor air temperature as well as
con1047297guration of both the SC and the EAHE
The results showed that the number of required SCs decreases
with the use of taller SCs The use of taller SCs lead to thermal
discomfort therefore more number of buried pipes should be
employed to cool air 1047298ow and satisfy the thermal needs
Results of the study on diameter of EAHE show that there is an
optimum diameter for cooling pipes (05 m) which gives the
minimum required number of SCs and EAHEs It has also been
found that the long EAHE with the length of more than 20 m should
be employed to provide the thermal comfort conditionThe results also show that when the ambient temperature and
cooling demand are high although providing thermal comfort is
dif 1047297cult proper con1047297gurations could provide good indoor condi-
tion even in the poor solar intensity of 100 Wm2 and high ambient
air temperature of 50 C
References
[1] Bansal NK Mathur R Bhandari MS A study of solar chimney assisted windtower system for natural ventilation in buildings Building and Environment199429(4)495e500
[2] Gan G Riffat SB A numerical study of solar chimney for natural ventilation of buildings with heat recovery Applied Thermal Engineering 1998181171e87
[3] Hamdy IF Fikry MA Passive solar ventilation Renewable Energy 199814
(1e
4)381e
6
Table 7
Effects of diameter of EAHE on system performance
Cooling
demand (W)
Ambient
air temp (C)
Solar radiation
(Wm2)
Diameter of
EAHE (m)
ACH
d
Room air
temp (C)
Number
of SC
Number
of EAHE
116 40 400 03 430 2996 3 2
05 602 2972 3 2
07 301 2989 3 4
09 476 2998 4 8
116 40 1000 03 507 2770 3 205 649 2872 2 3
07 867 2996 2 4
09 785 2980 2 8
800 40 400 03 Thermal comfort cannot be provided
05 314 2900 3 5
07 443 2986 4 7
09 Thermal comfort cannot be provided
800 40 1000 03 Thermal comfort cannot be provided
05 335 2938 2 6
07 321 2931 2 7
09 371 2994 2 12
Table 8
System performance at different indoor and outdoor conditions
Coolingdemand (W)
Ambient airtemp (C)
Solarradiation
(Wm2)
ACHd
Room airtemp (C)
Numberof SC
Numberof EAHE
500 40 100 328 2961 5 3
500 516 3113 3 3
900 483 3140 2 3
500 45 100 301 3092 6 4
500 430 3112 3 4
900 402 3127 2 4
500 50 100 305 3102 6 6
500 345 3162 3 5
900 306 3152 2 5
1000 40 100 498 3051 8 6
500 410 3195 2 2
900 363 3069 2 4
1000 45 100 415 3000 8 6500 327 3115 3 5
900 300 3090 2 5
1000 50 100 418 3195 8 7
500 305 3198 3 6
900 315 3153 3 12
1500 40 100 520 3136 8 4
500 329 3061 3 5
900 300 3035 2 5
1500 45 100 395 3100 9 9
500 362 3170 4 9
900 317 3160 3 12
1500 50 100
500 Thermal comfort cannot be provided
900
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[4] Khedari J Boonsri B Hirunlabh J Ventilation impact of a solar chimney onindoor temperature 1047298uctuation and air change in a school building Energyand Buildings 20003289e93
[5] Mathur J Mathur S Anupma Summer-performance of inclined roof solarchimney for natural ventilation Energy and Buildings 2006381156e63
[6] Bassiouny R Koura NSA An analytical and numerical study of solar chimneyuse for room natural ventilation Energy and Buildings 200840865e73
[7] Hollmuller P Lachal B Cooling and preheating with buried pipe systems moni-toring simulation and economic aspects Energy and Buildings 200133509e18
[8] Santamouris M Mihalakakou G Asimakoupolos D On the coupling of ther-
mostatically controlled buildings with ground and night ventilation passivedissipation techniques Solar Energy 199760(3e4)191e7
[9] Krarti M Kreider JF Analytical model for heat transfer in an underground airtunnel Energy Conversion and Management 199637(10)1561e74
[10] Hollmuller P Analytical characterization of amplitude-dampening and phase-shifting in airsoil heat exchangers International Journal of Heat and MassTransfer 2003464303e17
[11] Al-Ajmi F Loveday DL Hanby VI The cooling potential of eartheair heatexchangers for domestic buildings in a desert climate Building and Environ-ment 200641235e44
[12] Kumar R Kaushik SC Garg SN Heating and cooling potential of an earth-to-airheat exchanger using arti1047297cial neural network Renewable Energy2006311139e55
[13] Brager GS de Dear RJ A standard for natural ventilation ASHRAE Journal200042(10)21e8
[14] BIS Bureau of Indian Standards Handbook of functional requirements of buildings 1997 ISBN81-7061-011-7
[15] Ong KS A mathematical model of a solar chimney Renewable Energy2003281047e60
[16] Duf 1047297e JA Beckmann WA Solar engineering of thermal processes New YorkWiley Interscience ISBN 0-471-05066-0 1980
[17] Ong KS Chow CC Performance of solar chimney Solar Energy 2003741e17[18] VDI Waumlrmeatlas Springer Verlag 1994[19] ASHRAE handbook HVAC systems and equipment chimney gas vent and
1047297replace systems Atlanta GA American Society of Heating Refrigerating andAirconditioning Engineers Inc 2000 pp 301e3011
[20] ASHRAEhandbookfundamentals ductdesign AtlantaGAAmericanSociety of HeatingRefrigeratingand AirconditioningEngineers Inc 2000 pp341e346
[21] Bansal NK Sodha MS Bharadwi SS Performance of earth air tunnels Inter-national Journal of Energy Research 19837(4)333e45
[22] Mathur J Bansal NK Mathur S Jain M Anupma Experimental investigationson solar chimney for room ventilation Solar Energy 200680927e35
[23] Dhaliwal AS Goswami DY Heat transfer analysis in environmental controlusing an underground air tunnel Journal of Solar Energy Engineering1985107141e5
Nomenclature
A area ACH air change per hour (h1)C speci1047297c heat of air (JkgK)c pressure loss coef 1047297cient of 1047297ttingsD gap depth between absorber wall and glass (m)d diameter (m)H distance (m)h convective heat transfer coef 1047297cient (Wm2 K)hr radiative heat transfer coef 1047297cient (Wm2 K)
I total incident solar radiation on south facing inclined surface (Wm 2)k thermal conductivity (Wm K)L length (m)m mass 1047298ow rate of air (kgs)Q heat transfer to air stream (Wm2)R thermal resistance (m2 KW)r radius (m)S solar radiation heat 1047298ux absorbed by plate (Wm2)T temperature (K)t thickness (m)
U overall heat transfer coef 1047297cient (Wm2 K)u air velocity (ms)V volume of room (m3)W width of chimney (m)
xy coordinate system (m) Z height of chimney inlet (m)
Greek symbols
a absorbtion coef 1047297cientb volumetric coef 1047297cient of expansion (K1)g constant in Eqs(9) and(10)d heat penetration depth (m)3 emissivityq anglel thermal diffusivity (m2s)m Dynamic viscosity (kgs m)n Kinematic viscosity (m2s)x friction factor
r density (kgm
3
)s SteffaneBoltzmann constant (567 108Wm2 K4)u frequency of temperature oscillation (rads)
Dimensionless terms
Nu Nusselt number [hf L mf ]Pr Prandtl number [C f mf kf ]Gr Grashof number [ g bf (T T f )L3n 2]Ra Rayleigh number [GrPr]Re Reynolds number [uf dhydnf ]
Subscripts
a ambientabs absorber wallc convective
f air 1047298ow g glasshyd hydraulici internalin inletins insulation
j indexo outletr radius rooms soilsc solar chimneyst inner surface of tubesu undisturbed soilt pipe
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chimney width has a more signi1047297cant effect on ACH compared to
the chimney inlet size [6]
The earth to air heat exchanger is applicable for improving
natural ventilation through a cooling effect which can also
contribute to decrease temperature in the building The earth to air
heat exchanger is a pipe buried in the ground through which air is
sucked into a building Since the ground exhibits high thermal
inertia temperature at a certain depth is almost constant
throughout the year which allows for its use either as a heat sink
(in summer) or a heat source (in winter) [7] In the summer soil
temperature of a hot and arid region at a few meters deep is lower
than the mean daily outdoor air temperature and signi1047297cantly
lower than the usual outdoor daytime air temperature So it can be
used as a heat sink to cool the exterior warm air [8] The proper
designing of the earth to air heat exchanger requires deeper
understanding of the heat andmoisture dynamics in the earth to air
heat exchanger Various analytical and numerical models have
contributed to investigate the thermal behavior and cooling or
preheating potential of EAHE [9e12]
Krarti and Kreider [9] developed a simpli1047297ed analytical model to
determine the energy performance of an underground air tunnel
The model assumed that the air tunnel-ground system reaches
periodic and quasi-steady state behavior after some days of oper-ation Also parametric analysis was conducted to determine the
effect of tunnel hydraulic diameter and air 1047298ow rate on the heat
transfer between ground and air inside the tunnel Hollmuller [10]
considered a periodic input for the air in the buried pipe yielding
a physical interpretation of the amplitude-dampening and the
phase-shifting of the periodic input signal Al-Ajmi et al [11]
developed a theoretical model of an eartheair heat exchanger for
predicting the outlet air temperature and cooling potential of these
devices in a hot arid climate The results showed that the EAHE
have the potential for reducing cooling energy demand in a typical
house by 30 over the peak summer season Kumar et al [12] used
the concept of arti1047297cial neural network and goal oriented design to
propose a computer design tool that can help the designer to
evaluate any aspect of earth to air heat exchanger and behavior of
the 1047297nal con1047297guration The results showed that there are six vari-
ables in1047298uencing the thermal performance of the earth to air heat
exchangers These variables are length humidity ambient air
temperature ground surface temperature ground temperature at
burial depth and air mass 1047298ow rate
The technique for passive cooling that is introduced and inves-
tigated in the present paper is integrated earth to air heat
exchanger and solar chimney (EAHE-SC) system A schematic plan
of the passively cooled room is shown in Fig 1 This system realizes
both cooling and ventilation during daytime with the help of solar
energy thus it is natural day ventilating technique
The proposed solar system consists of two parts the solar
chimney and the earth to air heat exchanger The solar chimney
consisted of a glass surface oriented to the south and an absorber
wall that works as a capturing surface The air is heated up in the SC
by the solar energy and 1047298ows upward because of the stack effect It
causes driving force which sucks the outside air through the cool-
ing pipe
The EAHE consists of horizontal long pipes that areburied under
the bare surface at the speci1047297c depth The pipes are spread under
the ground in a parallel manner The pipe spacing is considered
more than the thickness of the heat penetrating depth to increasethe heat exchange between the soil and the air
It will be shown this system can provide good indoor condition
in accordance with the Adapted Comfort Standard (ACS) speci1047297ed
for thermal comfort in naturally ventilated buildings The required
indoor temperatures according to the adaptive comfort model are
shown in Fig 2 The 1047297gure only shows the acceptable temperature
of indoor air when the outdoor temperature is within the range of
0e40 C and it does not recommend the ventilation rate [13]
Ventilation standards require a minimum of 3 air changes per
hour for residential buildings in India [14] Therefore the minimum
ventilation rate is set approximately around 3 ACH It will be
consequently shown that how this ventilation rate suitably
provides the required cooling loads of a room
Fig 1 Schematic diagram of integrated earth to air heat exchanger and solar chimney
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2 Modeling the system
Themodeling includes models of solarchimney(Fig3) and earth
toair heat exchanger (Fig4) In estimating theventilationrateof theproposedsolarhouse as a wholeit is important to determine theair
1047298ow rate which can be handled under a particular design and
operating conditions For this an overall energy balance on the
chimney is considered This includes the energy balances of glass
cover wall the black absorber wall and the air in between Writing
energy balance equations for absorber surface glass surface and air
column and solving them for T g T abs and T f to calculate air 1047298ow rate
have sought a mathematical solution Chimney modeling has been
done in accordance with Ong model [15]
The EAHE system presented in this paper is modeled as two
coupled heat transfer processes namely convection heat transfer
between air 1047298owing in the pipe and the pipe inner surface and
conduction heat transfer between the pipe inner surface and the
surrounding soil
The major assumptions that are used in the modeling may be
summarized as follows
1 Air inlet to the chimney is considered to have the same room
air average temperature
2 Only buoyancy force is considered wind induced natural
ventilation is not included
3 The 1047298ows in the channels are hydrodynamically and thermally
fully developed
4 The glass cover is opaque for infrared radiation
5 Thermal capacities of glass and absorber wall are negligible
6 The air 1047298ow in the channel is radiative non-participating
media
7 All thermophysical properties are constant evaluated at an
average temperature
8 The soil is homogeneous and the soil type does not changealong the channel
9 The system is at steady-state condition
21 Mathematical modeling of solar chimney
An element of the model for SC is shown in Fig 3 In principle
and based on the energy conservation law a set of differential
equations are obtained along the length of SC The energy balance
equation for glass cover is
S g A g thorn hrabsg Aabs
T abs T g
frac14 hg Ag
T g T fsc
thorn U ga AgT g T fsc (1)
The overall top heat loss coef 1047297cient from glass cover to ambient
air U ga can be written as
U ga frac14 hwind thorn hr gsky thorn hga (2)
The convective heat transfer coef 1047297cient due to the wind hwind is
given by [16]
hwind frac14 28 thorn 30uwind (3)
The solar radiation heat 1047298ux absorbed by the glass cover S g is
given by
S g
frac14 ag
I (4)
Fig 2 Adaptive standard for naturally ventilated buildings
Fig 3 Schematic diagram of the heat transfer in the solar chimney
Fig 4 Cross section of an EAHE with heat penetration depth
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The radiative heat transfer coef 1047297cient from the outer glass
surface to the sky referred to the ambient temperature is obtained
from [15]
hr gsky frac14s3g
T g thorn T sky
T 2g thorn T 2
sky
T g T sky
T g T a
(5)
Where the sky temperature is T sky frac14 00552T a15[16]The radiation heat transfer coef 1047297cient between absorber plate
and glass cover may be obtained from [15]
hr absg frac14s
T 2g thorn T 2abs
T g thorn T abs
1=3g thorn 1=3abs 1 (6)
The convective heat transfer coef 1047297cient between the glass cover
and air 1047298ow in the chimney
hg frac14 Nugkfsc=Lg (7)
Where Nusselt number Nug frac14 06(Grgcos qPrfsc)02 Grashof
number Grg frac14
( g bS g
(Lg
)4(kfscn
fsc
2 )) [5] The convective heat transfer
coef 1047297cient between inclined absorber wall and the air 1047298ow in the
chimney is given by
habs frac14 Nuabskfsc=Lsc (8)
Where Nusselt number Nuabs frac14 06(Grabscos qPrfsc)02 and Grashof
number Grabs frac14 ( g bS abs(Labs)4(kfscnfsc2 )) All property values are
evaluated at average surfaceeair temperatures
The energy balance equation for air 1047298ow in the chimney is
habs Aabs
T abs T fsc
thorn hg Ag
T g T fsc
frac14 mC fsc
T fsc T r
g
(9)
The axial mean air temperature was experimentally determined
to follow the non-linear form [15]
T fsc frac14 gT fsco thorn eth1 gTHORNT fscin (10)
Value of the constantg is taken as 074 according to Ref [17] The
energy balance equation for the absorber plate is written as
S abs Aabs frac14 habs Aabs
T abs T fsc
thorn hr absg Aabs
T abs T g
thorn U absa AabsethT abs T aTHORN (11)
The overall heat transfer coef 1047297cient from the rear of the
absorber wall to the ambient U absa is given by
U absa frac14
1=eth
1=
ha thorn
t ins=
kinsTHORN
(12)
In the above equation ha has been taken as 28 Wm2 K [16]
22 Mathematical modeling of EAHE
In orderto determinethe system cooling capabilityone is mainly
interested in the cool air temperature supplied by the EAHE
Therefore detailed modeling of the EAHE is required The cross
section of EAHE used in the model and the thermal network of the
systemare shown in Figs 4 and5 respectively In order to impose the
ground thermal loads as boundary conditions at the EAHE wall the
undisturbed soil temperature (T su) has been used The soil temper-
ature is nearly constant at the penetration depth (Fig1) The pene-
tration depth is de1047297
ned when the surface of the soil is subjected to
a periodic temperature It depends on the soil diffusivity and the
temperature cycle frequency through equation (13) [10]
d frac14
ffiffiffiffiffiffiffi2ls
u
r (13)
Where ls frac14 ks(rsC s) for daily variation u frac14 (2pday) and for annualu frac14 (2p(year)) The penetration depths are used to calculate the
thermal resistance only and the rest of the analysis is carried out at
steady-state condition The model includes two equations one is
related to the energy balance of the circulating 1047298uid and the other
equation describes heat transfer in the soil region
The energy balance for d x a differential length of EAHE can be
expressed in the following form
T ft T su frac14 dQ Rtotal
d x (14)
Where Rtotal represents the overall thermal resistance which can
be de1047297ned by the resistance network as shown in Fig 5
Rtotal frac14 Rc thorn Rt thorn Rs (15)
Where Rc is the thermal resistance due to convection heat
transfer between air in the pipe and the pipe inner surface It may
be expressed as
Rc frac14 1
2pLt h ft (16)
The convection heat transfer coef 1047297cient inside the pipe is
de1047297ned by
hft frac14 Nutkft
2r ti(17)
The Nusselt number for air 1047298ow in pipe with smooth internalsurface depends on Reynolds number and it is given by [18]
Nu frac14 366 if Re lt 2300 (18a)
Nu frac14 x=8ethRe 1000THORNPr
1 thorn127 ffiffiffiffiffiffiffiffiffiffiffi
ethx=8THORNp
Pr2=3 1 if 2300 Relt5 106 (18b)
Where
x frac14 eth182log Re 164THORN2 if Re 2300 (19)
Rt is the thermal resistance of the pipe Steady-state analysis gives
the thermal resistance of the pipe annulus as
Fig 5 Thermal resistance between air 1047298ow and surrounding undisturbed soil
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Rt frac14 ln
r ti thorn t t
r ti
2pktLt (20)
Rs is the thermal resistance between EAHE and undisturbed soil
surface it is given by
Rs frac14 1
2pksLt
ln01 thorn d
r ti thorn t tthorn ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 thorn
d
r ti thorn t t
2
1s 1A (21)
The energy balance of the circulating 1047298uid is given by
dQ frac14 mC f dT ft
d x d x (22)
Eqs (14) and (22) give the differential overall energy balance
equation in the form8gtlt
gt
dT ft
d x thorn
T f t
mC ftRtotalfrac14 00
T ft frac14 T a x frac14 00
(23)
The solution of equation (23) can be expressed as
T fteth xTHORN frac14 T su thorn ethT a T suTHORNexp
x
mC ftRtotal
(24)
23 Room ventilation and temperature
Chimney effect causes the movement of air into and out of
buildings and is driven by buoyancy Buoyancy occurs due to
a difference in indoor-to-outdoor air density resulting from
temperature and moisture differences A chimney heated by solar
energy can be used to drive the chimney effect without increasing
room temperature The driving potential for the air 1047298ow through
the solar house is function of the pressure difference between the
inlet of the EAHE and the SC outlet The buoyancy pressure due to
increasing air temperature in SC sucks the cooled and heavy air
through the EAHE The friction losses due to 1047298uid 1047298ow through the
channels and across the 1047297ttings refrain from the 1047298uid 1047298ow If the
buoyancy pressure overcomes the sum of all 1047298ow pressure losses
the natural ventilation may take place
A mathematical model based on Bernoullirsquo s equation has been
used to estimate the system 1047298ow rate Thus the chimney net draft
Draftsccan be calculated by the following equation [19]
Draftsc frac14rfa rfsco
gLscsin q
0X7
j frac14 6
c j thorn xscLsc
dhyd
sc
1A
r
fscou
2
sc2
eth25THORN
Where the c j is the pressure loss coef 1047297cients at the locations which
are indicated in Fig 1
In right hand side of equation (25) the 1047297rstclause is thechimney
theoretical draft and the second one is the chimney pressure loss
The EAHE pressure loss DP EAHE is [20]
DP EAHE frac14
0X5
j frac14 1
c j thorn xtLEAHE
dti
1Arftu2
f t
2
(26)
The air temperature variation in the vertical pipe is ignored The air
temperature at the solar chimney inlet is assumed to be same as the
room air temperature which is higher than the cooled air
temperature at the pipe outlet So the chimney effects DraftEAHE
and DraftRoom can be expressed as
DraftEAHE frac14rfr rft
gH tr (27)
DraftRoom frac14
rfscin rfr
gH rinscin (28)
The required draft for cooling system DraftSystem is the sum of thepipe pressure loss and the negative pressure DraftEAHE and
DraftRoom
DraftSystem frac14 DP EAHE DraftEAHE thorn DraftRoom (29)
Under steady-state conditions we can write
DraftSystem frac14 Draftsc (30)
The air mass 1047298ow rate at the chimney and EAHE are the same if
there is no air in1047297ltration
m frac14 rAujChimney outlet frac14 r AujChimney inlet frac14 r AujEAHE (31)
By expanding equation (30) and use of equation (31) the airvelocity in the SC can be obtained as
usc frac14
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiBouyancy Terms
Friction Terms
r (32-a)
Where
Bouyancy Terms frac14 2
rfa rfsco
gLscSinethqTHORN
rfscin rfr
gH rinscin
rft rfr
gH tr
(32-b)
Friction Terms frac14 ethc THORN6rfsco Ascorfr Ascin
2
rfr thornn
ethc THORN7thornxsc Lsc
ethdhydTHORNsc
orfscothorn( P5
j frac14 1
c j thorn xtLtthornH trthornBurried depth of EAHE
dt
rfsco Asco
rft At
2)rft
(32-c)
The main criteria for thermal comfort condition are affected by two
factors the ACH and room air temperature The ACH is calculated
under steady-state conditions by the following equation [5]
ACH frac14 3600m
rfscV (33)
The room air temperature which depends on room heat gain is
obtained by the following equation
T r frac14 T ftot thorn Q rmC ft
(34)
Where Q r is sum of the heats that the room gains through the walls
and the heat generated by internal heat sources
3 Analysis
The system capability to provide the desired indoor condition
depends on parameters such as the ambient conditions (tempera-
ture solar radiation) dimensions of SC and EAHE and cooling
demand Parametric study is carried out to 1047297nd the effects of
geometrical dimensions of the SC and EAHE and outdoor envi-
ronmental conditions The following dimensions and speci1047297
cations
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are used in the modeling The room 40 40 3125 m in
dimensions without air in1047297ltration and has a minimum cooling
demand of Q frac14 116 W This is the demand of a room with adiabatic
walls which one person is resting in it The cooling demand is
changed at the range of 116e1500 W in the calculations
A solar chimney with the length of 40 m width of 10 m air gap
depth of 03 m and inlet of 04 04 m is considered These
dimensions are chosen based on studies of Ref [22] and may be
changed in the calculation A detailed study on a south facing solar
chimney in Tehran having 3544 N latitude position has found theoptimum angle of 50 to capture more radiation [5] Few numbers
of solar chimneys are adequate to provide the required stack effect
for the system
The cooling pipe of EAHE is a PVC pipe with 250 m length
001 m thickness and inside diameter of 05 m and is buried 30 m
below the soil surface According to the model developed by Bansal
et al [21] undisturbed soil temperature at a depth of 30 m is
approximated to be 19 C for a dry shaded soil surface condition
and it is considered to be the heat sink temperature These
dimensions have a decisive in1047298uence on cooling load and system
performance which will be investigated here Usually only one
EAHE suf 1047297cesto provide the necessarycooling load but in sever hot
conditions more cooling pipes may be employed
The EAHE outlet and the SC inlet are located on the oppositewalls (Fig 2) The SC inlet is lowered 07 m below the EAHE outlet
level The EAHE outlet is 3 m above the room 1047298oor thus it is 6 m
above the buried horizontal pipes of the EAHE The ambient
outdoor temperature is 34 C The thermophysical properties of the
materials included in the modeling are given in Table 1 The values
of the properties speci1047297ed in the table are kept constant in the
computation unless speci1047297cally noted otherwise
A computer program was written in MATLAB software to solve
the mathematical model The governing equations (1 9 11 24 and
32) have to be solved iteratively until convergence of the results
There is no experimental data to validate the results of theo-
retical model for the integrated system So the calculation has been
carried out for SC and EAHE separately under same conditions of
experimental studies of [22] and [23] to check the mathematical
model and to ensure the accuracy of computationsTable 2 shows the results of present model and the theoretical
and experimental results of Mathur et al [22] for different combi-
nations of solar radiation SC height and chimney inlet dimensions
The quantitative comparison shows a reasonable agreement
between the results obtained by the present study and the pub-
lished results of [22] The results of present study are closer to the
experimental results than the theoretical results of Ref [22] It
should be noted that the calculation carried out at the same
conditions of Ref [22] in which the roomvolume is 27 m3 and other
experimental conditions are given in Table 2
Fig 6 shows the air temperature variation along the cooling
pipe The results of the present work are calculated at the condi-
tions of experiments of Ref [23] given in Table 3 As the 1047297gure
shows there is good agreement between the present theoretical
results and the experimental results of Ref [23]
However it is reasonable to conclude that the mathematical
model can predict air temperature quite accurately and the calcu-
lated results are reliable
4 Result and discussion
41 Capability of the system to provide thermal comfort
Theoretical calculations are performed at various solar radia-
tions and room cooling demands The results are summarized in
Table 4 It is found that an integrated system of a few number of
solar chimneys with one (or at most two) EAHE cooling pipe can
Table 1
Thermophysical properties
Parameters Values
1 Transmissivity of glass 084 (d)
2 Absorptivity of glass 006 (d)
3 Emissivity of the glass 090 (d)
4 Absorptivity of absorber wall 095 (d)
5 Emissivity of the absorber wall 095 (d)
6 Thermal conductivity of the pipe (PVC) 023 (Wm K )7 Soil density 2050 (kgm3)
8 Thermal conductivity of the Soil 052 (Wm K)
9 Speci1047297c heat of soil 1840 (Jkg K)
Table 2
Comparison of experimental and theoretical results for solar chimney induced ACH number
Solar radiation
(Wm2)
Absorber
length (m)
Inlet chim dimens
(m m)
Ambient
temp (K)
ACH Errors of [22] Errors of present
studyEXP [22] Theo [22] Theo (present study)
300 07 10 03 295e302 4400 4173 4366 516 077
08 10 02 298e304 5330 4054 4757 2394 1075
09 10 01 294e296 2400 2704 2368 1266 133
500 07 10 03 295e302 4800 5160 4454 750 721
08 10 02 298e304 4530 4895 4816 806 631
09 10 01 294e296 2660 3461 2970 3011 1165
700 07 10 03 295e302 5600 5810 5404 375 35
08 10 02 298e304 5330 5175 5480 291 281
09 10 01 294e296 2930 3671 3217 2529 979
Fig 6 Comparison present results with experimental data
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provide the indoor thermal comfort conditions so the temperature
is retained at 2815e3194 C which is within the acceptable range
according to Ref [14] with 3e7 ACH which secures the required
ventilation rate As can be seen for higher cooling demands longer
and more cooling pipes of the EAHE are required
42 Effective dimensions of the system
There are many geometrical dimensions in the system that
affect its performance Some of them such as dimensions of the
inlet of the SC cross area of the SC etc have minor effects these
in1047298uence the 1047298ow rate slightly by changing the resistance to the
1047298ow While two geometrical dimensions have the substantial
effects i) absorbing surface area of the SC which provide the
energy for stack effect at the SC ii)cooling surface area of the EAHE
which facilitates heat removal from the air 1047298ow to soil
In the present study effects of variations of all dimensions are
investigated Based on the obtained results the dimensions
described in the section 3 have been chosen as suitable working
dimensions The details of the results are not given in the present
paper to save time However effects of changing the two ef 1047297cacious
dimensions are reported here
i) Absorber surface area is increased by increasing the length of
the chimney This increase results in higher ventilation rate or
higher ACH number On the other hand higher ventilation
rate with a constant cooling source results in higher indoor
temperature Thus more number of buried pipes are required
to cool the room and satisfy the thermal comfort require-
ments as shown in Table 5
ii) The lateral surface area of the buried pipe is serving as heat
exchange surface area of the heat sink of the system Gener-
ally larger cooling area provides more cooling effect to the
system In order to increase the cooling surface one may
increase the diameter andor the length of the pipe Table 6
shows the effect of EAHE length on system performance at
two different cooling demands For the length of EAHE less
than 20 m the comfort temperature may not be provided and
longer EAHE should be employed
Resultsof the study on thediameterof cooling pipes are shown in
Table 7 A comparative surveyshows that the required number of SCs
and EAHEs are minimums when the diameter is 05 m Therefore
this value is adopted as default valueof diameterand thevariation in
lateral area surfaces are made by increasing the length of the pipe
43 Effects of environmental conditions on the system performance
The environmental conditions are comprised of solar radiation
and outdoor ambient temperature in the present study Table 8
Table 3
Properties and conditions of experiment [23]
1 Length of EAHE 2500 (m)
2 Buried depth of EAHE 256 (m)
3 Radius of pipe 0305 (m)
4 Thickness of pipe 0002 (m)
5 Thermal conductivity of pipe 033 (Wm K)
6 Thermal conductivity of soil 116 (Wm K)
7 Thermal diffusivity of soil 645 107 (m2s)
8 Air velocity 147 (ms)
9 Air density 1214 (kgm3)
10 Air viscosity 178 107 (kgs m)
11 Speci1047297c heat of air 1205 103 (Jkg K)
12 Air Prandtl number 065 (d)
13 Thermal conductivity of air 028 (Wm K)
Table 4
Performance of the system at various cooling demands and solar radiations
Cooling
demand (W)
Solar radiation
(Wm2)
Length of
EAHE (m)
ACH
d
Room air
temp
( C)
Number
of SC
Number
of EAHE
116 400 25 634 2853 2 1
600 403 2814 1
800 506 2831 1
1000 584 2844 1
200 400 25 630 2935 2 1
600 356 2873 1
800 481 2935 1
1000 565 2933 1
400 400 30 569 2992 2 1
600 790 3015 2
800 388 2951 1
1000 487 3062 1
600 400 40 467 2827 2 1
600 721 3042 2
800 309 2777 1
1000 400 2902 1
800 400 40 520 2813 3 2
600 421 2764 2
800 533 2903 2
1000 627 3014 2
Note Ambient air temperature frac14 34 C
Table 5
Effects of absorber length on system performance
Cooling
demand (W)
Absorber
length (m)
ACH
d
Room air
temp (C)
Number
of SC
Number
of EAHE
116 30 440 2822 1 1
40 583 2844 1 1
50 706 2866 1 1
60 818 2886 1 1
800 30 236 2894 2 340 510 3098 2 3
50 662 3238 2 3
60 829 3363 2 3
800 30 312 2924 3 5
40 305 2941 2 4
50 351 2981 2 5
60 384 3019 2 6
Note Ambient air temperature frac14 34 C solar radiation frac14 1000 (Wm2)
Table 6
Effects of length of EAHE on system performance
Cooling
demand
(W)
Ambient
air temp
( C)
Solar
radiation
(Wm2)
Length of
EAHE
(m)
ACH
d
Room air
temp
( C)
Number
of SC
Number
of EAHE
116 40 400 150 347 2968 4 10
250 602 2972 3 2
350 517 2700 3 2450 579 2861 3 1
116 40 1000 150 347 2987 2 9
250 649 2872 2 3
350 465 2877 1 1
450 356 2633 1 1
800 40 400 150 Thermal comfort cannot be
provided
250 314 2900 3 5
350 454 2950 3 2
450 427 2700 3 2
800 40 1000 150 Thermal comfort cannot be
provided
250 335 2938 2 6
350 742 2952 2 3
450 559 2926 2 2
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shows the summary of results of the theoretical calculations fordifferent environmental conditions
The buoyancy driving force increases with an increase of solar
intensity and it causes higher ACH Thus less number of SCs are
required to drive the cool and heavy air through the EAHEs and to
compensate the pressure drops The results of calculations also
show that the required number of EAHEs should be increased to
retain the thermal comfort condition when the number of ACH and
indoor air temperature are increased at high solar radiation
The effect of ambient airtemperature on stack effect of SC is vice
versa The stack effect decreases when the ambient outdoor
temperature risesUnder these conditions more numberof SCs willbe required to ventilate the room
The results show that the system can provide the required
indoor temperature and ACH number even at harsh environmental
condition of high temperature of 45 C and low solar radiation of
100 Wm2 If the temperature is higher than 45 C the SC wonrsquot be
able to provide the stack effect and in this condition the use of
a small fan can help the cool air to 1047298ow from EAHE in to the room
and to realize thermal comfort condition
It should be noted that in this system all air 1047298ow is fresh air and
a reduction about 23 C in the inlet air is praiseful achievement of
the present passive cooling system
5 Conclusions
A passive solar system comprises of solar chimneys and earth to
air heat exchangers is proposed and studied in the present paper
The present study shows that the performance of the system
depends on solar radiation outdoor air temperature as well as
con1047297guration of both the SC and the EAHE
The results showed that the number of required SCs decreases
with the use of taller SCs The use of taller SCs lead to thermal
discomfort therefore more number of buried pipes should be
employed to cool air 1047298ow and satisfy the thermal needs
Results of the study on diameter of EAHE show that there is an
optimum diameter for cooling pipes (05 m) which gives the
minimum required number of SCs and EAHEs It has also been
found that the long EAHE with the length of more than 20 m should
be employed to provide the thermal comfort conditionThe results also show that when the ambient temperature and
cooling demand are high although providing thermal comfort is
dif 1047297cult proper con1047297gurations could provide good indoor condi-
tion even in the poor solar intensity of 100 Wm2 and high ambient
air temperature of 50 C
References
[1] Bansal NK Mathur R Bhandari MS A study of solar chimney assisted windtower system for natural ventilation in buildings Building and Environment199429(4)495e500
[2] Gan G Riffat SB A numerical study of solar chimney for natural ventilation of buildings with heat recovery Applied Thermal Engineering 1998181171e87
[3] Hamdy IF Fikry MA Passive solar ventilation Renewable Energy 199814
(1e
4)381e
6
Table 7
Effects of diameter of EAHE on system performance
Cooling
demand (W)
Ambient
air temp (C)
Solar radiation
(Wm2)
Diameter of
EAHE (m)
ACH
d
Room air
temp (C)
Number
of SC
Number
of EAHE
116 40 400 03 430 2996 3 2
05 602 2972 3 2
07 301 2989 3 4
09 476 2998 4 8
116 40 1000 03 507 2770 3 205 649 2872 2 3
07 867 2996 2 4
09 785 2980 2 8
800 40 400 03 Thermal comfort cannot be provided
05 314 2900 3 5
07 443 2986 4 7
09 Thermal comfort cannot be provided
800 40 1000 03 Thermal comfort cannot be provided
05 335 2938 2 6
07 321 2931 2 7
09 371 2994 2 12
Table 8
System performance at different indoor and outdoor conditions
Coolingdemand (W)
Ambient airtemp (C)
Solarradiation
(Wm2)
ACHd
Room airtemp (C)
Numberof SC
Numberof EAHE
500 40 100 328 2961 5 3
500 516 3113 3 3
900 483 3140 2 3
500 45 100 301 3092 6 4
500 430 3112 3 4
900 402 3127 2 4
500 50 100 305 3102 6 6
500 345 3162 3 5
900 306 3152 2 5
1000 40 100 498 3051 8 6
500 410 3195 2 2
900 363 3069 2 4
1000 45 100 415 3000 8 6500 327 3115 3 5
900 300 3090 2 5
1000 50 100 418 3195 8 7
500 305 3198 3 6
900 315 3153 3 12
1500 40 100 520 3136 8 4
500 329 3061 3 5
900 300 3035 2 5
1500 45 100 395 3100 9 9
500 362 3170 4 9
900 317 3160 3 12
1500 50 100
500 Thermal comfort cannot be provided
900
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[4] Khedari J Boonsri B Hirunlabh J Ventilation impact of a solar chimney onindoor temperature 1047298uctuation and air change in a school building Energyand Buildings 20003289e93
[5] Mathur J Mathur S Anupma Summer-performance of inclined roof solarchimney for natural ventilation Energy and Buildings 2006381156e63
[6] Bassiouny R Koura NSA An analytical and numerical study of solar chimneyuse for room natural ventilation Energy and Buildings 200840865e73
[7] Hollmuller P Lachal B Cooling and preheating with buried pipe systems moni-toring simulation and economic aspects Energy and Buildings 200133509e18
[8] Santamouris M Mihalakakou G Asimakoupolos D On the coupling of ther-
mostatically controlled buildings with ground and night ventilation passivedissipation techniques Solar Energy 199760(3e4)191e7
[9] Krarti M Kreider JF Analytical model for heat transfer in an underground airtunnel Energy Conversion and Management 199637(10)1561e74
[10] Hollmuller P Analytical characterization of amplitude-dampening and phase-shifting in airsoil heat exchangers International Journal of Heat and MassTransfer 2003464303e17
[11] Al-Ajmi F Loveday DL Hanby VI The cooling potential of eartheair heatexchangers for domestic buildings in a desert climate Building and Environ-ment 200641235e44
[12] Kumar R Kaushik SC Garg SN Heating and cooling potential of an earth-to-airheat exchanger using arti1047297cial neural network Renewable Energy2006311139e55
[13] Brager GS de Dear RJ A standard for natural ventilation ASHRAE Journal200042(10)21e8
[14] BIS Bureau of Indian Standards Handbook of functional requirements of buildings 1997 ISBN81-7061-011-7
[15] Ong KS A mathematical model of a solar chimney Renewable Energy2003281047e60
[16] Duf 1047297e JA Beckmann WA Solar engineering of thermal processes New YorkWiley Interscience ISBN 0-471-05066-0 1980
[17] Ong KS Chow CC Performance of solar chimney Solar Energy 2003741e17[18] VDI Waumlrmeatlas Springer Verlag 1994[19] ASHRAE handbook HVAC systems and equipment chimney gas vent and
1047297replace systems Atlanta GA American Society of Heating Refrigerating andAirconditioning Engineers Inc 2000 pp 301e3011
[20] ASHRAEhandbookfundamentals ductdesign AtlantaGAAmericanSociety of HeatingRefrigeratingand AirconditioningEngineers Inc 2000 pp341e346
[21] Bansal NK Sodha MS Bharadwi SS Performance of earth air tunnels Inter-national Journal of Energy Research 19837(4)333e45
[22] Mathur J Bansal NK Mathur S Jain M Anupma Experimental investigationson solar chimney for room ventilation Solar Energy 200680927e35
[23] Dhaliwal AS Goswami DY Heat transfer analysis in environmental controlusing an underground air tunnel Journal of Solar Energy Engineering1985107141e5
Nomenclature
A area ACH air change per hour (h1)C speci1047297c heat of air (JkgK)c pressure loss coef 1047297cient of 1047297ttingsD gap depth between absorber wall and glass (m)d diameter (m)H distance (m)h convective heat transfer coef 1047297cient (Wm2 K)hr radiative heat transfer coef 1047297cient (Wm2 K)
I total incident solar radiation on south facing inclined surface (Wm 2)k thermal conductivity (Wm K)L length (m)m mass 1047298ow rate of air (kgs)Q heat transfer to air stream (Wm2)R thermal resistance (m2 KW)r radius (m)S solar radiation heat 1047298ux absorbed by plate (Wm2)T temperature (K)t thickness (m)
U overall heat transfer coef 1047297cient (Wm2 K)u air velocity (ms)V volume of room (m3)W width of chimney (m)
xy coordinate system (m) Z height of chimney inlet (m)
Greek symbols
a absorbtion coef 1047297cientb volumetric coef 1047297cient of expansion (K1)g constant in Eqs(9) and(10)d heat penetration depth (m)3 emissivityq anglel thermal diffusivity (m2s)m Dynamic viscosity (kgs m)n Kinematic viscosity (m2s)x friction factor
r density (kgm
3
)s SteffaneBoltzmann constant (567 108Wm2 K4)u frequency of temperature oscillation (rads)
Dimensionless terms
Nu Nusselt number [hf L mf ]Pr Prandtl number [C f mf kf ]Gr Grashof number [ g bf (T T f )L3n 2]Ra Rayleigh number [GrPr]Re Reynolds number [uf dhydnf ]
Subscripts
a ambientabs absorber wallc convective
f air 1047298ow g glasshyd hydraulici internalin inletins insulation
j indexo outletr radius rooms soilsc solar chimneyst inner surface of tubesu undisturbed soilt pipe
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2 Modeling the system
Themodeling includes models of solarchimney(Fig3) and earth
toair heat exchanger (Fig4) In estimating theventilationrateof theproposedsolarhouse as a wholeit is important to determine theair
1047298ow rate which can be handled under a particular design and
operating conditions For this an overall energy balance on the
chimney is considered This includes the energy balances of glass
cover wall the black absorber wall and the air in between Writing
energy balance equations for absorber surface glass surface and air
column and solving them for T g T abs and T f to calculate air 1047298ow rate
have sought a mathematical solution Chimney modeling has been
done in accordance with Ong model [15]
The EAHE system presented in this paper is modeled as two
coupled heat transfer processes namely convection heat transfer
between air 1047298owing in the pipe and the pipe inner surface and
conduction heat transfer between the pipe inner surface and the
surrounding soil
The major assumptions that are used in the modeling may be
summarized as follows
1 Air inlet to the chimney is considered to have the same room
air average temperature
2 Only buoyancy force is considered wind induced natural
ventilation is not included
3 The 1047298ows in the channels are hydrodynamically and thermally
fully developed
4 The glass cover is opaque for infrared radiation
5 Thermal capacities of glass and absorber wall are negligible
6 The air 1047298ow in the channel is radiative non-participating
media
7 All thermophysical properties are constant evaluated at an
average temperature
8 The soil is homogeneous and the soil type does not changealong the channel
9 The system is at steady-state condition
21 Mathematical modeling of solar chimney
An element of the model for SC is shown in Fig 3 In principle
and based on the energy conservation law a set of differential
equations are obtained along the length of SC The energy balance
equation for glass cover is
S g A g thorn hrabsg Aabs
T abs T g
frac14 hg Ag
T g T fsc
thorn U ga AgT g T fsc (1)
The overall top heat loss coef 1047297cient from glass cover to ambient
air U ga can be written as
U ga frac14 hwind thorn hr gsky thorn hga (2)
The convective heat transfer coef 1047297cient due to the wind hwind is
given by [16]
hwind frac14 28 thorn 30uwind (3)
The solar radiation heat 1047298ux absorbed by the glass cover S g is
given by
S g
frac14 ag
I (4)
Fig 2 Adaptive standard for naturally ventilated buildings
Fig 3 Schematic diagram of the heat transfer in the solar chimney
Fig 4 Cross section of an EAHE with heat penetration depth
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The radiative heat transfer coef 1047297cient from the outer glass
surface to the sky referred to the ambient temperature is obtained
from [15]
hr gsky frac14s3g
T g thorn T sky
T 2g thorn T 2
sky
T g T sky
T g T a
(5)
Where the sky temperature is T sky frac14 00552T a15[16]The radiation heat transfer coef 1047297cient between absorber plate
and glass cover may be obtained from [15]
hr absg frac14s
T 2g thorn T 2abs
T g thorn T abs
1=3g thorn 1=3abs 1 (6)
The convective heat transfer coef 1047297cient between the glass cover
and air 1047298ow in the chimney
hg frac14 Nugkfsc=Lg (7)
Where Nusselt number Nug frac14 06(Grgcos qPrfsc)02 Grashof
number Grg frac14
( g bS g
(Lg
)4(kfscn
fsc
2 )) [5] The convective heat transfer
coef 1047297cient between inclined absorber wall and the air 1047298ow in the
chimney is given by
habs frac14 Nuabskfsc=Lsc (8)
Where Nusselt number Nuabs frac14 06(Grabscos qPrfsc)02 and Grashof
number Grabs frac14 ( g bS abs(Labs)4(kfscnfsc2 )) All property values are
evaluated at average surfaceeair temperatures
The energy balance equation for air 1047298ow in the chimney is
habs Aabs
T abs T fsc
thorn hg Ag
T g T fsc
frac14 mC fsc
T fsc T r
g
(9)
The axial mean air temperature was experimentally determined
to follow the non-linear form [15]
T fsc frac14 gT fsco thorn eth1 gTHORNT fscin (10)
Value of the constantg is taken as 074 according to Ref [17] The
energy balance equation for the absorber plate is written as
S abs Aabs frac14 habs Aabs
T abs T fsc
thorn hr absg Aabs
T abs T g
thorn U absa AabsethT abs T aTHORN (11)
The overall heat transfer coef 1047297cient from the rear of the
absorber wall to the ambient U absa is given by
U absa frac14
1=eth
1=
ha thorn
t ins=
kinsTHORN
(12)
In the above equation ha has been taken as 28 Wm2 K [16]
22 Mathematical modeling of EAHE
In orderto determinethe system cooling capabilityone is mainly
interested in the cool air temperature supplied by the EAHE
Therefore detailed modeling of the EAHE is required The cross
section of EAHE used in the model and the thermal network of the
systemare shown in Figs 4 and5 respectively In order to impose the
ground thermal loads as boundary conditions at the EAHE wall the
undisturbed soil temperature (T su) has been used The soil temper-
ature is nearly constant at the penetration depth (Fig1) The pene-
tration depth is de1047297
ned when the surface of the soil is subjected to
a periodic temperature It depends on the soil diffusivity and the
temperature cycle frequency through equation (13) [10]
d frac14
ffiffiffiffiffiffiffi2ls
u
r (13)
Where ls frac14 ks(rsC s) for daily variation u frac14 (2pday) and for annualu frac14 (2p(year)) The penetration depths are used to calculate the
thermal resistance only and the rest of the analysis is carried out at
steady-state condition The model includes two equations one is
related to the energy balance of the circulating 1047298uid and the other
equation describes heat transfer in the soil region
The energy balance for d x a differential length of EAHE can be
expressed in the following form
T ft T su frac14 dQ Rtotal
d x (14)
Where Rtotal represents the overall thermal resistance which can
be de1047297ned by the resistance network as shown in Fig 5
Rtotal frac14 Rc thorn Rt thorn Rs (15)
Where Rc is the thermal resistance due to convection heat
transfer between air in the pipe and the pipe inner surface It may
be expressed as
Rc frac14 1
2pLt h ft (16)
The convection heat transfer coef 1047297cient inside the pipe is
de1047297ned by
hft frac14 Nutkft
2r ti(17)
The Nusselt number for air 1047298ow in pipe with smooth internalsurface depends on Reynolds number and it is given by [18]
Nu frac14 366 if Re lt 2300 (18a)
Nu frac14 x=8ethRe 1000THORNPr
1 thorn127 ffiffiffiffiffiffiffiffiffiffiffi
ethx=8THORNp
Pr2=3 1 if 2300 Relt5 106 (18b)
Where
x frac14 eth182log Re 164THORN2 if Re 2300 (19)
Rt is the thermal resistance of the pipe Steady-state analysis gives
the thermal resistance of the pipe annulus as
Fig 5 Thermal resistance between air 1047298ow and surrounding undisturbed soil
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Rt frac14 ln
r ti thorn t t
r ti
2pktLt (20)
Rs is the thermal resistance between EAHE and undisturbed soil
surface it is given by
Rs frac14 1
2pksLt
ln01 thorn d
r ti thorn t tthorn ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 thorn
d
r ti thorn t t
2
1s 1A (21)
The energy balance of the circulating 1047298uid is given by
dQ frac14 mC f dT ft
d x d x (22)
Eqs (14) and (22) give the differential overall energy balance
equation in the form8gtlt
gt
dT ft
d x thorn
T f t
mC ftRtotalfrac14 00
T ft frac14 T a x frac14 00
(23)
The solution of equation (23) can be expressed as
T fteth xTHORN frac14 T su thorn ethT a T suTHORNexp
x
mC ftRtotal
(24)
23 Room ventilation and temperature
Chimney effect causes the movement of air into and out of
buildings and is driven by buoyancy Buoyancy occurs due to
a difference in indoor-to-outdoor air density resulting from
temperature and moisture differences A chimney heated by solar
energy can be used to drive the chimney effect without increasing
room temperature The driving potential for the air 1047298ow through
the solar house is function of the pressure difference between the
inlet of the EAHE and the SC outlet The buoyancy pressure due to
increasing air temperature in SC sucks the cooled and heavy air
through the EAHE The friction losses due to 1047298uid 1047298ow through the
channels and across the 1047297ttings refrain from the 1047298uid 1047298ow If the
buoyancy pressure overcomes the sum of all 1047298ow pressure losses
the natural ventilation may take place
A mathematical model based on Bernoullirsquo s equation has been
used to estimate the system 1047298ow rate Thus the chimney net draft
Draftsccan be calculated by the following equation [19]
Draftsc frac14rfa rfsco
gLscsin q
0X7
j frac14 6
c j thorn xscLsc
dhyd
sc
1A
r
fscou
2
sc2
eth25THORN
Where the c j is the pressure loss coef 1047297cients at the locations which
are indicated in Fig 1
In right hand side of equation (25) the 1047297rstclause is thechimney
theoretical draft and the second one is the chimney pressure loss
The EAHE pressure loss DP EAHE is [20]
DP EAHE frac14
0X5
j frac14 1
c j thorn xtLEAHE
dti
1Arftu2
f t
2
(26)
The air temperature variation in the vertical pipe is ignored The air
temperature at the solar chimney inlet is assumed to be same as the
room air temperature which is higher than the cooled air
temperature at the pipe outlet So the chimney effects DraftEAHE
and DraftRoom can be expressed as
DraftEAHE frac14rfr rft
gH tr (27)
DraftRoom frac14
rfscin rfr
gH rinscin (28)
The required draft for cooling system DraftSystem is the sum of thepipe pressure loss and the negative pressure DraftEAHE and
DraftRoom
DraftSystem frac14 DP EAHE DraftEAHE thorn DraftRoom (29)
Under steady-state conditions we can write
DraftSystem frac14 Draftsc (30)
The air mass 1047298ow rate at the chimney and EAHE are the same if
there is no air in1047297ltration
m frac14 rAujChimney outlet frac14 r AujChimney inlet frac14 r AujEAHE (31)
By expanding equation (30) and use of equation (31) the airvelocity in the SC can be obtained as
usc frac14
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiBouyancy Terms
Friction Terms
r (32-a)
Where
Bouyancy Terms frac14 2
rfa rfsco
gLscSinethqTHORN
rfscin rfr
gH rinscin
rft rfr
gH tr
(32-b)
Friction Terms frac14 ethc THORN6rfsco Ascorfr Ascin
2
rfr thornn
ethc THORN7thornxsc Lsc
ethdhydTHORNsc
orfscothorn( P5
j frac14 1
c j thorn xtLtthornH trthornBurried depth of EAHE
dt
rfsco Asco
rft At
2)rft
(32-c)
The main criteria for thermal comfort condition are affected by two
factors the ACH and room air temperature The ACH is calculated
under steady-state conditions by the following equation [5]
ACH frac14 3600m
rfscV (33)
The room air temperature which depends on room heat gain is
obtained by the following equation
T r frac14 T ftot thorn Q rmC ft
(34)
Where Q r is sum of the heats that the room gains through the walls
and the heat generated by internal heat sources
3 Analysis
The system capability to provide the desired indoor condition
depends on parameters such as the ambient conditions (tempera-
ture solar radiation) dimensions of SC and EAHE and cooling
demand Parametric study is carried out to 1047297nd the effects of
geometrical dimensions of the SC and EAHE and outdoor envi-
ronmental conditions The following dimensions and speci1047297
cations
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are used in the modeling The room 40 40 3125 m in
dimensions without air in1047297ltration and has a minimum cooling
demand of Q frac14 116 W This is the demand of a room with adiabatic
walls which one person is resting in it The cooling demand is
changed at the range of 116e1500 W in the calculations
A solar chimney with the length of 40 m width of 10 m air gap
depth of 03 m and inlet of 04 04 m is considered These
dimensions are chosen based on studies of Ref [22] and may be
changed in the calculation A detailed study on a south facing solar
chimney in Tehran having 3544 N latitude position has found theoptimum angle of 50 to capture more radiation [5] Few numbers
of solar chimneys are adequate to provide the required stack effect
for the system
The cooling pipe of EAHE is a PVC pipe with 250 m length
001 m thickness and inside diameter of 05 m and is buried 30 m
below the soil surface According to the model developed by Bansal
et al [21] undisturbed soil temperature at a depth of 30 m is
approximated to be 19 C for a dry shaded soil surface condition
and it is considered to be the heat sink temperature These
dimensions have a decisive in1047298uence on cooling load and system
performance which will be investigated here Usually only one
EAHE suf 1047297cesto provide the necessarycooling load but in sever hot
conditions more cooling pipes may be employed
The EAHE outlet and the SC inlet are located on the oppositewalls (Fig 2) The SC inlet is lowered 07 m below the EAHE outlet
level The EAHE outlet is 3 m above the room 1047298oor thus it is 6 m
above the buried horizontal pipes of the EAHE The ambient
outdoor temperature is 34 C The thermophysical properties of the
materials included in the modeling are given in Table 1 The values
of the properties speci1047297ed in the table are kept constant in the
computation unless speci1047297cally noted otherwise
A computer program was written in MATLAB software to solve
the mathematical model The governing equations (1 9 11 24 and
32) have to be solved iteratively until convergence of the results
There is no experimental data to validate the results of theo-
retical model for the integrated system So the calculation has been
carried out for SC and EAHE separately under same conditions of
experimental studies of [22] and [23] to check the mathematical
model and to ensure the accuracy of computationsTable 2 shows the results of present model and the theoretical
and experimental results of Mathur et al [22] for different combi-
nations of solar radiation SC height and chimney inlet dimensions
The quantitative comparison shows a reasonable agreement
between the results obtained by the present study and the pub-
lished results of [22] The results of present study are closer to the
experimental results than the theoretical results of Ref [22] It
should be noted that the calculation carried out at the same
conditions of Ref [22] in which the roomvolume is 27 m3 and other
experimental conditions are given in Table 2
Fig 6 shows the air temperature variation along the cooling
pipe The results of the present work are calculated at the condi-
tions of experiments of Ref [23] given in Table 3 As the 1047297gure
shows there is good agreement between the present theoretical
results and the experimental results of Ref [23]
However it is reasonable to conclude that the mathematical
model can predict air temperature quite accurately and the calcu-
lated results are reliable
4 Result and discussion
41 Capability of the system to provide thermal comfort
Theoretical calculations are performed at various solar radia-
tions and room cooling demands The results are summarized in
Table 4 It is found that an integrated system of a few number of
solar chimneys with one (or at most two) EAHE cooling pipe can
Table 1
Thermophysical properties
Parameters Values
1 Transmissivity of glass 084 (d)
2 Absorptivity of glass 006 (d)
3 Emissivity of the glass 090 (d)
4 Absorptivity of absorber wall 095 (d)
5 Emissivity of the absorber wall 095 (d)
6 Thermal conductivity of the pipe (PVC) 023 (Wm K )7 Soil density 2050 (kgm3)
8 Thermal conductivity of the Soil 052 (Wm K)
9 Speci1047297c heat of soil 1840 (Jkg K)
Table 2
Comparison of experimental and theoretical results for solar chimney induced ACH number
Solar radiation
(Wm2)
Absorber
length (m)
Inlet chim dimens
(m m)
Ambient
temp (K)
ACH Errors of [22] Errors of present
studyEXP [22] Theo [22] Theo (present study)
300 07 10 03 295e302 4400 4173 4366 516 077
08 10 02 298e304 5330 4054 4757 2394 1075
09 10 01 294e296 2400 2704 2368 1266 133
500 07 10 03 295e302 4800 5160 4454 750 721
08 10 02 298e304 4530 4895 4816 806 631
09 10 01 294e296 2660 3461 2970 3011 1165
700 07 10 03 295e302 5600 5810 5404 375 35
08 10 02 298e304 5330 5175 5480 291 281
09 10 01 294e296 2930 3671 3217 2529 979
Fig 6 Comparison present results with experimental data
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provide the indoor thermal comfort conditions so the temperature
is retained at 2815e3194 C which is within the acceptable range
according to Ref [14] with 3e7 ACH which secures the required
ventilation rate As can be seen for higher cooling demands longer
and more cooling pipes of the EAHE are required
42 Effective dimensions of the system
There are many geometrical dimensions in the system that
affect its performance Some of them such as dimensions of the
inlet of the SC cross area of the SC etc have minor effects these
in1047298uence the 1047298ow rate slightly by changing the resistance to the
1047298ow While two geometrical dimensions have the substantial
effects i) absorbing surface area of the SC which provide the
energy for stack effect at the SC ii)cooling surface area of the EAHE
which facilitates heat removal from the air 1047298ow to soil
In the present study effects of variations of all dimensions are
investigated Based on the obtained results the dimensions
described in the section 3 have been chosen as suitable working
dimensions The details of the results are not given in the present
paper to save time However effects of changing the two ef 1047297cacious
dimensions are reported here
i) Absorber surface area is increased by increasing the length of
the chimney This increase results in higher ventilation rate or
higher ACH number On the other hand higher ventilation
rate with a constant cooling source results in higher indoor
temperature Thus more number of buried pipes are required
to cool the room and satisfy the thermal comfort require-
ments as shown in Table 5
ii) The lateral surface area of the buried pipe is serving as heat
exchange surface area of the heat sink of the system Gener-
ally larger cooling area provides more cooling effect to the
system In order to increase the cooling surface one may
increase the diameter andor the length of the pipe Table 6
shows the effect of EAHE length on system performance at
two different cooling demands For the length of EAHE less
than 20 m the comfort temperature may not be provided and
longer EAHE should be employed
Resultsof the study on thediameterof cooling pipes are shown in
Table 7 A comparative surveyshows that the required number of SCs
and EAHEs are minimums when the diameter is 05 m Therefore
this value is adopted as default valueof diameterand thevariation in
lateral area surfaces are made by increasing the length of the pipe
43 Effects of environmental conditions on the system performance
The environmental conditions are comprised of solar radiation
and outdoor ambient temperature in the present study Table 8
Table 3
Properties and conditions of experiment [23]
1 Length of EAHE 2500 (m)
2 Buried depth of EAHE 256 (m)
3 Radius of pipe 0305 (m)
4 Thickness of pipe 0002 (m)
5 Thermal conductivity of pipe 033 (Wm K)
6 Thermal conductivity of soil 116 (Wm K)
7 Thermal diffusivity of soil 645 107 (m2s)
8 Air velocity 147 (ms)
9 Air density 1214 (kgm3)
10 Air viscosity 178 107 (kgs m)
11 Speci1047297c heat of air 1205 103 (Jkg K)
12 Air Prandtl number 065 (d)
13 Thermal conductivity of air 028 (Wm K)
Table 4
Performance of the system at various cooling demands and solar radiations
Cooling
demand (W)
Solar radiation
(Wm2)
Length of
EAHE (m)
ACH
d
Room air
temp
( C)
Number
of SC
Number
of EAHE
116 400 25 634 2853 2 1
600 403 2814 1
800 506 2831 1
1000 584 2844 1
200 400 25 630 2935 2 1
600 356 2873 1
800 481 2935 1
1000 565 2933 1
400 400 30 569 2992 2 1
600 790 3015 2
800 388 2951 1
1000 487 3062 1
600 400 40 467 2827 2 1
600 721 3042 2
800 309 2777 1
1000 400 2902 1
800 400 40 520 2813 3 2
600 421 2764 2
800 533 2903 2
1000 627 3014 2
Note Ambient air temperature frac14 34 C
Table 5
Effects of absorber length on system performance
Cooling
demand (W)
Absorber
length (m)
ACH
d
Room air
temp (C)
Number
of SC
Number
of EAHE
116 30 440 2822 1 1
40 583 2844 1 1
50 706 2866 1 1
60 818 2886 1 1
800 30 236 2894 2 340 510 3098 2 3
50 662 3238 2 3
60 829 3363 2 3
800 30 312 2924 3 5
40 305 2941 2 4
50 351 2981 2 5
60 384 3019 2 6
Note Ambient air temperature frac14 34 C solar radiation frac14 1000 (Wm2)
Table 6
Effects of length of EAHE on system performance
Cooling
demand
(W)
Ambient
air temp
( C)
Solar
radiation
(Wm2)
Length of
EAHE
(m)
ACH
d
Room air
temp
( C)
Number
of SC
Number
of EAHE
116 40 400 150 347 2968 4 10
250 602 2972 3 2
350 517 2700 3 2450 579 2861 3 1
116 40 1000 150 347 2987 2 9
250 649 2872 2 3
350 465 2877 1 1
450 356 2633 1 1
800 40 400 150 Thermal comfort cannot be
provided
250 314 2900 3 5
350 454 2950 3 2
450 427 2700 3 2
800 40 1000 150 Thermal comfort cannot be
provided
250 335 2938 2 6
350 742 2952 2 3
450 559 2926 2 2
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shows the summary of results of the theoretical calculations fordifferent environmental conditions
The buoyancy driving force increases with an increase of solar
intensity and it causes higher ACH Thus less number of SCs are
required to drive the cool and heavy air through the EAHEs and to
compensate the pressure drops The results of calculations also
show that the required number of EAHEs should be increased to
retain the thermal comfort condition when the number of ACH and
indoor air temperature are increased at high solar radiation
The effect of ambient airtemperature on stack effect of SC is vice
versa The stack effect decreases when the ambient outdoor
temperature risesUnder these conditions more numberof SCs willbe required to ventilate the room
The results show that the system can provide the required
indoor temperature and ACH number even at harsh environmental
condition of high temperature of 45 C and low solar radiation of
100 Wm2 If the temperature is higher than 45 C the SC wonrsquot be
able to provide the stack effect and in this condition the use of
a small fan can help the cool air to 1047298ow from EAHE in to the room
and to realize thermal comfort condition
It should be noted that in this system all air 1047298ow is fresh air and
a reduction about 23 C in the inlet air is praiseful achievement of
the present passive cooling system
5 Conclusions
A passive solar system comprises of solar chimneys and earth to
air heat exchangers is proposed and studied in the present paper
The present study shows that the performance of the system
depends on solar radiation outdoor air temperature as well as
con1047297guration of both the SC and the EAHE
The results showed that the number of required SCs decreases
with the use of taller SCs The use of taller SCs lead to thermal
discomfort therefore more number of buried pipes should be
employed to cool air 1047298ow and satisfy the thermal needs
Results of the study on diameter of EAHE show that there is an
optimum diameter for cooling pipes (05 m) which gives the
minimum required number of SCs and EAHEs It has also been
found that the long EAHE with the length of more than 20 m should
be employed to provide the thermal comfort conditionThe results also show that when the ambient temperature and
cooling demand are high although providing thermal comfort is
dif 1047297cult proper con1047297gurations could provide good indoor condi-
tion even in the poor solar intensity of 100 Wm2 and high ambient
air temperature of 50 C
References
[1] Bansal NK Mathur R Bhandari MS A study of solar chimney assisted windtower system for natural ventilation in buildings Building and Environment199429(4)495e500
[2] Gan G Riffat SB A numerical study of solar chimney for natural ventilation of buildings with heat recovery Applied Thermal Engineering 1998181171e87
[3] Hamdy IF Fikry MA Passive solar ventilation Renewable Energy 199814
(1e
4)381e
6
Table 7
Effects of diameter of EAHE on system performance
Cooling
demand (W)
Ambient
air temp (C)
Solar radiation
(Wm2)
Diameter of
EAHE (m)
ACH
d
Room air
temp (C)
Number
of SC
Number
of EAHE
116 40 400 03 430 2996 3 2
05 602 2972 3 2
07 301 2989 3 4
09 476 2998 4 8
116 40 1000 03 507 2770 3 205 649 2872 2 3
07 867 2996 2 4
09 785 2980 2 8
800 40 400 03 Thermal comfort cannot be provided
05 314 2900 3 5
07 443 2986 4 7
09 Thermal comfort cannot be provided
800 40 1000 03 Thermal comfort cannot be provided
05 335 2938 2 6
07 321 2931 2 7
09 371 2994 2 12
Table 8
System performance at different indoor and outdoor conditions
Coolingdemand (W)
Ambient airtemp (C)
Solarradiation
(Wm2)
ACHd
Room airtemp (C)
Numberof SC
Numberof EAHE
500 40 100 328 2961 5 3
500 516 3113 3 3
900 483 3140 2 3
500 45 100 301 3092 6 4
500 430 3112 3 4
900 402 3127 2 4
500 50 100 305 3102 6 6
500 345 3162 3 5
900 306 3152 2 5
1000 40 100 498 3051 8 6
500 410 3195 2 2
900 363 3069 2 4
1000 45 100 415 3000 8 6500 327 3115 3 5
900 300 3090 2 5
1000 50 100 418 3195 8 7
500 305 3198 3 6
900 315 3153 3 12
1500 40 100 520 3136 8 4
500 329 3061 3 5
900 300 3035 2 5
1500 45 100 395 3100 9 9
500 362 3170 4 9
900 317 3160 3 12
1500 50 100
500 Thermal comfort cannot be provided
900
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[4] Khedari J Boonsri B Hirunlabh J Ventilation impact of a solar chimney onindoor temperature 1047298uctuation and air change in a school building Energyand Buildings 20003289e93
[5] Mathur J Mathur S Anupma Summer-performance of inclined roof solarchimney for natural ventilation Energy and Buildings 2006381156e63
[6] Bassiouny R Koura NSA An analytical and numerical study of solar chimneyuse for room natural ventilation Energy and Buildings 200840865e73
[7] Hollmuller P Lachal B Cooling and preheating with buried pipe systems moni-toring simulation and economic aspects Energy and Buildings 200133509e18
[8] Santamouris M Mihalakakou G Asimakoupolos D On the coupling of ther-
mostatically controlled buildings with ground and night ventilation passivedissipation techniques Solar Energy 199760(3e4)191e7
[9] Krarti M Kreider JF Analytical model for heat transfer in an underground airtunnel Energy Conversion and Management 199637(10)1561e74
[10] Hollmuller P Analytical characterization of amplitude-dampening and phase-shifting in airsoil heat exchangers International Journal of Heat and MassTransfer 2003464303e17
[11] Al-Ajmi F Loveday DL Hanby VI The cooling potential of eartheair heatexchangers for domestic buildings in a desert climate Building and Environ-ment 200641235e44
[12] Kumar R Kaushik SC Garg SN Heating and cooling potential of an earth-to-airheat exchanger using arti1047297cial neural network Renewable Energy2006311139e55
[13] Brager GS de Dear RJ A standard for natural ventilation ASHRAE Journal200042(10)21e8
[14] BIS Bureau of Indian Standards Handbook of functional requirements of buildings 1997 ISBN81-7061-011-7
[15] Ong KS A mathematical model of a solar chimney Renewable Energy2003281047e60
[16] Duf 1047297e JA Beckmann WA Solar engineering of thermal processes New YorkWiley Interscience ISBN 0-471-05066-0 1980
[17] Ong KS Chow CC Performance of solar chimney Solar Energy 2003741e17[18] VDI Waumlrmeatlas Springer Verlag 1994[19] ASHRAE handbook HVAC systems and equipment chimney gas vent and
1047297replace systems Atlanta GA American Society of Heating Refrigerating andAirconditioning Engineers Inc 2000 pp 301e3011
[20] ASHRAEhandbookfundamentals ductdesign AtlantaGAAmericanSociety of HeatingRefrigeratingand AirconditioningEngineers Inc 2000 pp341e346
[21] Bansal NK Sodha MS Bharadwi SS Performance of earth air tunnels Inter-national Journal of Energy Research 19837(4)333e45
[22] Mathur J Bansal NK Mathur S Jain M Anupma Experimental investigationson solar chimney for room ventilation Solar Energy 200680927e35
[23] Dhaliwal AS Goswami DY Heat transfer analysis in environmental controlusing an underground air tunnel Journal of Solar Energy Engineering1985107141e5
Nomenclature
A area ACH air change per hour (h1)C speci1047297c heat of air (JkgK)c pressure loss coef 1047297cient of 1047297ttingsD gap depth between absorber wall and glass (m)d diameter (m)H distance (m)h convective heat transfer coef 1047297cient (Wm2 K)hr radiative heat transfer coef 1047297cient (Wm2 K)
I total incident solar radiation on south facing inclined surface (Wm 2)k thermal conductivity (Wm K)L length (m)m mass 1047298ow rate of air (kgs)Q heat transfer to air stream (Wm2)R thermal resistance (m2 KW)r radius (m)S solar radiation heat 1047298ux absorbed by plate (Wm2)T temperature (K)t thickness (m)
U overall heat transfer coef 1047297cient (Wm2 K)u air velocity (ms)V volume of room (m3)W width of chimney (m)
xy coordinate system (m) Z height of chimney inlet (m)
Greek symbols
a absorbtion coef 1047297cientb volumetric coef 1047297cient of expansion (K1)g constant in Eqs(9) and(10)d heat penetration depth (m)3 emissivityq anglel thermal diffusivity (m2s)m Dynamic viscosity (kgs m)n Kinematic viscosity (m2s)x friction factor
r density (kgm
3
)s SteffaneBoltzmann constant (567 108Wm2 K4)u frequency of temperature oscillation (rads)
Dimensionless terms
Nu Nusselt number [hf L mf ]Pr Prandtl number [C f mf kf ]Gr Grashof number [ g bf (T T f )L3n 2]Ra Rayleigh number [GrPr]Re Reynolds number [uf dhydnf ]
Subscripts
a ambientabs absorber wallc convective
f air 1047298ow g glasshyd hydraulici internalin inletins insulation
j indexo outletr radius rooms soilsc solar chimneyst inner surface of tubesu undisturbed soilt pipe
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The radiative heat transfer coef 1047297cient from the outer glass
surface to the sky referred to the ambient temperature is obtained
from [15]
hr gsky frac14s3g
T g thorn T sky
T 2g thorn T 2
sky
T g T sky
T g T a
(5)
Where the sky temperature is T sky frac14 00552T a15[16]The radiation heat transfer coef 1047297cient between absorber plate
and glass cover may be obtained from [15]
hr absg frac14s
T 2g thorn T 2abs
T g thorn T abs
1=3g thorn 1=3abs 1 (6)
The convective heat transfer coef 1047297cient between the glass cover
and air 1047298ow in the chimney
hg frac14 Nugkfsc=Lg (7)
Where Nusselt number Nug frac14 06(Grgcos qPrfsc)02 Grashof
number Grg frac14
( g bS g
(Lg
)4(kfscn
fsc
2 )) [5] The convective heat transfer
coef 1047297cient between inclined absorber wall and the air 1047298ow in the
chimney is given by
habs frac14 Nuabskfsc=Lsc (8)
Where Nusselt number Nuabs frac14 06(Grabscos qPrfsc)02 and Grashof
number Grabs frac14 ( g bS abs(Labs)4(kfscnfsc2 )) All property values are
evaluated at average surfaceeair temperatures
The energy balance equation for air 1047298ow in the chimney is
habs Aabs
T abs T fsc
thorn hg Ag
T g T fsc
frac14 mC fsc
T fsc T r
g
(9)
The axial mean air temperature was experimentally determined
to follow the non-linear form [15]
T fsc frac14 gT fsco thorn eth1 gTHORNT fscin (10)
Value of the constantg is taken as 074 according to Ref [17] The
energy balance equation for the absorber plate is written as
S abs Aabs frac14 habs Aabs
T abs T fsc
thorn hr absg Aabs
T abs T g
thorn U absa AabsethT abs T aTHORN (11)
The overall heat transfer coef 1047297cient from the rear of the
absorber wall to the ambient U absa is given by
U absa frac14
1=eth
1=
ha thorn
t ins=
kinsTHORN
(12)
In the above equation ha has been taken as 28 Wm2 K [16]
22 Mathematical modeling of EAHE
In orderto determinethe system cooling capabilityone is mainly
interested in the cool air temperature supplied by the EAHE
Therefore detailed modeling of the EAHE is required The cross
section of EAHE used in the model and the thermal network of the
systemare shown in Figs 4 and5 respectively In order to impose the
ground thermal loads as boundary conditions at the EAHE wall the
undisturbed soil temperature (T su) has been used The soil temper-
ature is nearly constant at the penetration depth (Fig1) The pene-
tration depth is de1047297
ned when the surface of the soil is subjected to
a periodic temperature It depends on the soil diffusivity and the
temperature cycle frequency through equation (13) [10]
d frac14
ffiffiffiffiffiffiffi2ls
u
r (13)
Where ls frac14 ks(rsC s) for daily variation u frac14 (2pday) and for annualu frac14 (2p(year)) The penetration depths are used to calculate the
thermal resistance only and the rest of the analysis is carried out at
steady-state condition The model includes two equations one is
related to the energy balance of the circulating 1047298uid and the other
equation describes heat transfer in the soil region
The energy balance for d x a differential length of EAHE can be
expressed in the following form
T ft T su frac14 dQ Rtotal
d x (14)
Where Rtotal represents the overall thermal resistance which can
be de1047297ned by the resistance network as shown in Fig 5
Rtotal frac14 Rc thorn Rt thorn Rs (15)
Where Rc is the thermal resistance due to convection heat
transfer between air in the pipe and the pipe inner surface It may
be expressed as
Rc frac14 1
2pLt h ft (16)
The convection heat transfer coef 1047297cient inside the pipe is
de1047297ned by
hft frac14 Nutkft
2r ti(17)
The Nusselt number for air 1047298ow in pipe with smooth internalsurface depends on Reynolds number and it is given by [18]
Nu frac14 366 if Re lt 2300 (18a)
Nu frac14 x=8ethRe 1000THORNPr
1 thorn127 ffiffiffiffiffiffiffiffiffiffiffi
ethx=8THORNp
Pr2=3 1 if 2300 Relt5 106 (18b)
Where
x frac14 eth182log Re 164THORN2 if Re 2300 (19)
Rt is the thermal resistance of the pipe Steady-state analysis gives
the thermal resistance of the pipe annulus as
Fig 5 Thermal resistance between air 1047298ow and surrounding undisturbed soil
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Rt frac14 ln
r ti thorn t t
r ti
2pktLt (20)
Rs is the thermal resistance between EAHE and undisturbed soil
surface it is given by
Rs frac14 1
2pksLt
ln01 thorn d
r ti thorn t tthorn ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 thorn
d
r ti thorn t t
2
1s 1A (21)
The energy balance of the circulating 1047298uid is given by
dQ frac14 mC f dT ft
d x d x (22)
Eqs (14) and (22) give the differential overall energy balance
equation in the form8gtlt
gt
dT ft
d x thorn
T f t
mC ftRtotalfrac14 00
T ft frac14 T a x frac14 00
(23)
The solution of equation (23) can be expressed as
T fteth xTHORN frac14 T su thorn ethT a T suTHORNexp
x
mC ftRtotal
(24)
23 Room ventilation and temperature
Chimney effect causes the movement of air into and out of
buildings and is driven by buoyancy Buoyancy occurs due to
a difference in indoor-to-outdoor air density resulting from
temperature and moisture differences A chimney heated by solar
energy can be used to drive the chimney effect without increasing
room temperature The driving potential for the air 1047298ow through
the solar house is function of the pressure difference between the
inlet of the EAHE and the SC outlet The buoyancy pressure due to
increasing air temperature in SC sucks the cooled and heavy air
through the EAHE The friction losses due to 1047298uid 1047298ow through the
channels and across the 1047297ttings refrain from the 1047298uid 1047298ow If the
buoyancy pressure overcomes the sum of all 1047298ow pressure losses
the natural ventilation may take place
A mathematical model based on Bernoullirsquo s equation has been
used to estimate the system 1047298ow rate Thus the chimney net draft
Draftsccan be calculated by the following equation [19]
Draftsc frac14rfa rfsco
gLscsin q
0X7
j frac14 6
c j thorn xscLsc
dhyd
sc
1A
r
fscou
2
sc2
eth25THORN
Where the c j is the pressure loss coef 1047297cients at the locations which
are indicated in Fig 1
In right hand side of equation (25) the 1047297rstclause is thechimney
theoretical draft and the second one is the chimney pressure loss
The EAHE pressure loss DP EAHE is [20]
DP EAHE frac14
0X5
j frac14 1
c j thorn xtLEAHE
dti
1Arftu2
f t
2
(26)
The air temperature variation in the vertical pipe is ignored The air
temperature at the solar chimney inlet is assumed to be same as the
room air temperature which is higher than the cooled air
temperature at the pipe outlet So the chimney effects DraftEAHE
and DraftRoom can be expressed as
DraftEAHE frac14rfr rft
gH tr (27)
DraftRoom frac14
rfscin rfr
gH rinscin (28)
The required draft for cooling system DraftSystem is the sum of thepipe pressure loss and the negative pressure DraftEAHE and
DraftRoom
DraftSystem frac14 DP EAHE DraftEAHE thorn DraftRoom (29)
Under steady-state conditions we can write
DraftSystem frac14 Draftsc (30)
The air mass 1047298ow rate at the chimney and EAHE are the same if
there is no air in1047297ltration
m frac14 rAujChimney outlet frac14 r AujChimney inlet frac14 r AujEAHE (31)
By expanding equation (30) and use of equation (31) the airvelocity in the SC can be obtained as
usc frac14
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiBouyancy Terms
Friction Terms
r (32-a)
Where
Bouyancy Terms frac14 2
rfa rfsco
gLscSinethqTHORN
rfscin rfr
gH rinscin
rft rfr
gH tr
(32-b)
Friction Terms frac14 ethc THORN6rfsco Ascorfr Ascin
2
rfr thornn
ethc THORN7thornxsc Lsc
ethdhydTHORNsc
orfscothorn( P5
j frac14 1
c j thorn xtLtthornH trthornBurried depth of EAHE
dt
rfsco Asco
rft At
2)rft
(32-c)
The main criteria for thermal comfort condition are affected by two
factors the ACH and room air temperature The ACH is calculated
under steady-state conditions by the following equation [5]
ACH frac14 3600m
rfscV (33)
The room air temperature which depends on room heat gain is
obtained by the following equation
T r frac14 T ftot thorn Q rmC ft
(34)
Where Q r is sum of the heats that the room gains through the walls
and the heat generated by internal heat sources
3 Analysis
The system capability to provide the desired indoor condition
depends on parameters such as the ambient conditions (tempera-
ture solar radiation) dimensions of SC and EAHE and cooling
demand Parametric study is carried out to 1047297nd the effects of
geometrical dimensions of the SC and EAHE and outdoor envi-
ronmental conditions The following dimensions and speci1047297
cations
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are used in the modeling The room 40 40 3125 m in
dimensions without air in1047297ltration and has a minimum cooling
demand of Q frac14 116 W This is the demand of a room with adiabatic
walls which one person is resting in it The cooling demand is
changed at the range of 116e1500 W in the calculations
A solar chimney with the length of 40 m width of 10 m air gap
depth of 03 m and inlet of 04 04 m is considered These
dimensions are chosen based on studies of Ref [22] and may be
changed in the calculation A detailed study on a south facing solar
chimney in Tehran having 3544 N latitude position has found theoptimum angle of 50 to capture more radiation [5] Few numbers
of solar chimneys are adequate to provide the required stack effect
for the system
The cooling pipe of EAHE is a PVC pipe with 250 m length
001 m thickness and inside diameter of 05 m and is buried 30 m
below the soil surface According to the model developed by Bansal
et al [21] undisturbed soil temperature at a depth of 30 m is
approximated to be 19 C for a dry shaded soil surface condition
and it is considered to be the heat sink temperature These
dimensions have a decisive in1047298uence on cooling load and system
performance which will be investigated here Usually only one
EAHE suf 1047297cesto provide the necessarycooling load but in sever hot
conditions more cooling pipes may be employed
The EAHE outlet and the SC inlet are located on the oppositewalls (Fig 2) The SC inlet is lowered 07 m below the EAHE outlet
level The EAHE outlet is 3 m above the room 1047298oor thus it is 6 m
above the buried horizontal pipes of the EAHE The ambient
outdoor temperature is 34 C The thermophysical properties of the
materials included in the modeling are given in Table 1 The values
of the properties speci1047297ed in the table are kept constant in the
computation unless speci1047297cally noted otherwise
A computer program was written in MATLAB software to solve
the mathematical model The governing equations (1 9 11 24 and
32) have to be solved iteratively until convergence of the results
There is no experimental data to validate the results of theo-
retical model for the integrated system So the calculation has been
carried out for SC and EAHE separately under same conditions of
experimental studies of [22] and [23] to check the mathematical
model and to ensure the accuracy of computationsTable 2 shows the results of present model and the theoretical
and experimental results of Mathur et al [22] for different combi-
nations of solar radiation SC height and chimney inlet dimensions
The quantitative comparison shows a reasonable agreement
between the results obtained by the present study and the pub-
lished results of [22] The results of present study are closer to the
experimental results than the theoretical results of Ref [22] It
should be noted that the calculation carried out at the same
conditions of Ref [22] in which the roomvolume is 27 m3 and other
experimental conditions are given in Table 2
Fig 6 shows the air temperature variation along the cooling
pipe The results of the present work are calculated at the condi-
tions of experiments of Ref [23] given in Table 3 As the 1047297gure
shows there is good agreement between the present theoretical
results and the experimental results of Ref [23]
However it is reasonable to conclude that the mathematical
model can predict air temperature quite accurately and the calcu-
lated results are reliable
4 Result and discussion
41 Capability of the system to provide thermal comfort
Theoretical calculations are performed at various solar radia-
tions and room cooling demands The results are summarized in
Table 4 It is found that an integrated system of a few number of
solar chimneys with one (or at most two) EAHE cooling pipe can
Table 1
Thermophysical properties
Parameters Values
1 Transmissivity of glass 084 (d)
2 Absorptivity of glass 006 (d)
3 Emissivity of the glass 090 (d)
4 Absorptivity of absorber wall 095 (d)
5 Emissivity of the absorber wall 095 (d)
6 Thermal conductivity of the pipe (PVC) 023 (Wm K )7 Soil density 2050 (kgm3)
8 Thermal conductivity of the Soil 052 (Wm K)
9 Speci1047297c heat of soil 1840 (Jkg K)
Table 2
Comparison of experimental and theoretical results for solar chimney induced ACH number
Solar radiation
(Wm2)
Absorber
length (m)
Inlet chim dimens
(m m)
Ambient
temp (K)
ACH Errors of [22] Errors of present
studyEXP [22] Theo [22] Theo (present study)
300 07 10 03 295e302 4400 4173 4366 516 077
08 10 02 298e304 5330 4054 4757 2394 1075
09 10 01 294e296 2400 2704 2368 1266 133
500 07 10 03 295e302 4800 5160 4454 750 721
08 10 02 298e304 4530 4895 4816 806 631
09 10 01 294e296 2660 3461 2970 3011 1165
700 07 10 03 295e302 5600 5810 5404 375 35
08 10 02 298e304 5330 5175 5480 291 281
09 10 01 294e296 2930 3671 3217 2529 979
Fig 6 Comparison present results with experimental data
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provide the indoor thermal comfort conditions so the temperature
is retained at 2815e3194 C which is within the acceptable range
according to Ref [14] with 3e7 ACH which secures the required
ventilation rate As can be seen for higher cooling demands longer
and more cooling pipes of the EAHE are required
42 Effective dimensions of the system
There are many geometrical dimensions in the system that
affect its performance Some of them such as dimensions of the
inlet of the SC cross area of the SC etc have minor effects these
in1047298uence the 1047298ow rate slightly by changing the resistance to the
1047298ow While two geometrical dimensions have the substantial
effects i) absorbing surface area of the SC which provide the
energy for stack effect at the SC ii)cooling surface area of the EAHE
which facilitates heat removal from the air 1047298ow to soil
In the present study effects of variations of all dimensions are
investigated Based on the obtained results the dimensions
described in the section 3 have been chosen as suitable working
dimensions The details of the results are not given in the present
paper to save time However effects of changing the two ef 1047297cacious
dimensions are reported here
i) Absorber surface area is increased by increasing the length of
the chimney This increase results in higher ventilation rate or
higher ACH number On the other hand higher ventilation
rate with a constant cooling source results in higher indoor
temperature Thus more number of buried pipes are required
to cool the room and satisfy the thermal comfort require-
ments as shown in Table 5
ii) The lateral surface area of the buried pipe is serving as heat
exchange surface area of the heat sink of the system Gener-
ally larger cooling area provides more cooling effect to the
system In order to increase the cooling surface one may
increase the diameter andor the length of the pipe Table 6
shows the effect of EAHE length on system performance at
two different cooling demands For the length of EAHE less
than 20 m the comfort temperature may not be provided and
longer EAHE should be employed
Resultsof the study on thediameterof cooling pipes are shown in
Table 7 A comparative surveyshows that the required number of SCs
and EAHEs are minimums when the diameter is 05 m Therefore
this value is adopted as default valueof diameterand thevariation in
lateral area surfaces are made by increasing the length of the pipe
43 Effects of environmental conditions on the system performance
The environmental conditions are comprised of solar radiation
and outdoor ambient temperature in the present study Table 8
Table 3
Properties and conditions of experiment [23]
1 Length of EAHE 2500 (m)
2 Buried depth of EAHE 256 (m)
3 Radius of pipe 0305 (m)
4 Thickness of pipe 0002 (m)
5 Thermal conductivity of pipe 033 (Wm K)
6 Thermal conductivity of soil 116 (Wm K)
7 Thermal diffusivity of soil 645 107 (m2s)
8 Air velocity 147 (ms)
9 Air density 1214 (kgm3)
10 Air viscosity 178 107 (kgs m)
11 Speci1047297c heat of air 1205 103 (Jkg K)
12 Air Prandtl number 065 (d)
13 Thermal conductivity of air 028 (Wm K)
Table 4
Performance of the system at various cooling demands and solar radiations
Cooling
demand (W)
Solar radiation
(Wm2)
Length of
EAHE (m)
ACH
d
Room air
temp
( C)
Number
of SC
Number
of EAHE
116 400 25 634 2853 2 1
600 403 2814 1
800 506 2831 1
1000 584 2844 1
200 400 25 630 2935 2 1
600 356 2873 1
800 481 2935 1
1000 565 2933 1
400 400 30 569 2992 2 1
600 790 3015 2
800 388 2951 1
1000 487 3062 1
600 400 40 467 2827 2 1
600 721 3042 2
800 309 2777 1
1000 400 2902 1
800 400 40 520 2813 3 2
600 421 2764 2
800 533 2903 2
1000 627 3014 2
Note Ambient air temperature frac14 34 C
Table 5
Effects of absorber length on system performance
Cooling
demand (W)
Absorber
length (m)
ACH
d
Room air
temp (C)
Number
of SC
Number
of EAHE
116 30 440 2822 1 1
40 583 2844 1 1
50 706 2866 1 1
60 818 2886 1 1
800 30 236 2894 2 340 510 3098 2 3
50 662 3238 2 3
60 829 3363 2 3
800 30 312 2924 3 5
40 305 2941 2 4
50 351 2981 2 5
60 384 3019 2 6
Note Ambient air temperature frac14 34 C solar radiation frac14 1000 (Wm2)
Table 6
Effects of length of EAHE on system performance
Cooling
demand
(W)
Ambient
air temp
( C)
Solar
radiation
(Wm2)
Length of
EAHE
(m)
ACH
d
Room air
temp
( C)
Number
of SC
Number
of EAHE
116 40 400 150 347 2968 4 10
250 602 2972 3 2
350 517 2700 3 2450 579 2861 3 1
116 40 1000 150 347 2987 2 9
250 649 2872 2 3
350 465 2877 1 1
450 356 2633 1 1
800 40 400 150 Thermal comfort cannot be
provided
250 314 2900 3 5
350 454 2950 3 2
450 427 2700 3 2
800 40 1000 150 Thermal comfort cannot be
provided
250 335 2938 2 6
350 742 2952 2 3
450 559 2926 2 2
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shows the summary of results of the theoretical calculations fordifferent environmental conditions
The buoyancy driving force increases with an increase of solar
intensity and it causes higher ACH Thus less number of SCs are
required to drive the cool and heavy air through the EAHEs and to
compensate the pressure drops The results of calculations also
show that the required number of EAHEs should be increased to
retain the thermal comfort condition when the number of ACH and
indoor air temperature are increased at high solar radiation
The effect of ambient airtemperature on stack effect of SC is vice
versa The stack effect decreases when the ambient outdoor
temperature risesUnder these conditions more numberof SCs willbe required to ventilate the room
The results show that the system can provide the required
indoor temperature and ACH number even at harsh environmental
condition of high temperature of 45 C and low solar radiation of
100 Wm2 If the temperature is higher than 45 C the SC wonrsquot be
able to provide the stack effect and in this condition the use of
a small fan can help the cool air to 1047298ow from EAHE in to the room
and to realize thermal comfort condition
It should be noted that in this system all air 1047298ow is fresh air and
a reduction about 23 C in the inlet air is praiseful achievement of
the present passive cooling system
5 Conclusions
A passive solar system comprises of solar chimneys and earth to
air heat exchangers is proposed and studied in the present paper
The present study shows that the performance of the system
depends on solar radiation outdoor air temperature as well as
con1047297guration of both the SC and the EAHE
The results showed that the number of required SCs decreases
with the use of taller SCs The use of taller SCs lead to thermal
discomfort therefore more number of buried pipes should be
employed to cool air 1047298ow and satisfy the thermal needs
Results of the study on diameter of EAHE show that there is an
optimum diameter for cooling pipes (05 m) which gives the
minimum required number of SCs and EAHEs It has also been
found that the long EAHE with the length of more than 20 m should
be employed to provide the thermal comfort conditionThe results also show that when the ambient temperature and
cooling demand are high although providing thermal comfort is
dif 1047297cult proper con1047297gurations could provide good indoor condi-
tion even in the poor solar intensity of 100 Wm2 and high ambient
air temperature of 50 C
References
[1] Bansal NK Mathur R Bhandari MS A study of solar chimney assisted windtower system for natural ventilation in buildings Building and Environment199429(4)495e500
[2] Gan G Riffat SB A numerical study of solar chimney for natural ventilation of buildings with heat recovery Applied Thermal Engineering 1998181171e87
[3] Hamdy IF Fikry MA Passive solar ventilation Renewable Energy 199814
(1e
4)381e
6
Table 7
Effects of diameter of EAHE on system performance
Cooling
demand (W)
Ambient
air temp (C)
Solar radiation
(Wm2)
Diameter of
EAHE (m)
ACH
d
Room air
temp (C)
Number
of SC
Number
of EAHE
116 40 400 03 430 2996 3 2
05 602 2972 3 2
07 301 2989 3 4
09 476 2998 4 8
116 40 1000 03 507 2770 3 205 649 2872 2 3
07 867 2996 2 4
09 785 2980 2 8
800 40 400 03 Thermal comfort cannot be provided
05 314 2900 3 5
07 443 2986 4 7
09 Thermal comfort cannot be provided
800 40 1000 03 Thermal comfort cannot be provided
05 335 2938 2 6
07 321 2931 2 7
09 371 2994 2 12
Table 8
System performance at different indoor and outdoor conditions
Coolingdemand (W)
Ambient airtemp (C)
Solarradiation
(Wm2)
ACHd
Room airtemp (C)
Numberof SC
Numberof EAHE
500 40 100 328 2961 5 3
500 516 3113 3 3
900 483 3140 2 3
500 45 100 301 3092 6 4
500 430 3112 3 4
900 402 3127 2 4
500 50 100 305 3102 6 6
500 345 3162 3 5
900 306 3152 2 5
1000 40 100 498 3051 8 6
500 410 3195 2 2
900 363 3069 2 4
1000 45 100 415 3000 8 6500 327 3115 3 5
900 300 3090 2 5
1000 50 100 418 3195 8 7
500 305 3198 3 6
900 315 3153 3 12
1500 40 100 520 3136 8 4
500 329 3061 3 5
900 300 3035 2 5
1500 45 100 395 3100 9 9
500 362 3170 4 9
900 317 3160 3 12
1500 50 100
500 Thermal comfort cannot be provided
900
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[4] Khedari J Boonsri B Hirunlabh J Ventilation impact of a solar chimney onindoor temperature 1047298uctuation and air change in a school building Energyand Buildings 20003289e93
[5] Mathur J Mathur S Anupma Summer-performance of inclined roof solarchimney for natural ventilation Energy and Buildings 2006381156e63
[6] Bassiouny R Koura NSA An analytical and numerical study of solar chimneyuse for room natural ventilation Energy and Buildings 200840865e73
[7] Hollmuller P Lachal B Cooling and preheating with buried pipe systems moni-toring simulation and economic aspects Energy and Buildings 200133509e18
[8] Santamouris M Mihalakakou G Asimakoupolos D On the coupling of ther-
mostatically controlled buildings with ground and night ventilation passivedissipation techniques Solar Energy 199760(3e4)191e7
[9] Krarti M Kreider JF Analytical model for heat transfer in an underground airtunnel Energy Conversion and Management 199637(10)1561e74
[10] Hollmuller P Analytical characterization of amplitude-dampening and phase-shifting in airsoil heat exchangers International Journal of Heat and MassTransfer 2003464303e17
[11] Al-Ajmi F Loveday DL Hanby VI The cooling potential of eartheair heatexchangers for domestic buildings in a desert climate Building and Environ-ment 200641235e44
[12] Kumar R Kaushik SC Garg SN Heating and cooling potential of an earth-to-airheat exchanger using arti1047297cial neural network Renewable Energy2006311139e55
[13] Brager GS de Dear RJ A standard for natural ventilation ASHRAE Journal200042(10)21e8
[14] BIS Bureau of Indian Standards Handbook of functional requirements of buildings 1997 ISBN81-7061-011-7
[15] Ong KS A mathematical model of a solar chimney Renewable Energy2003281047e60
[16] Duf 1047297e JA Beckmann WA Solar engineering of thermal processes New YorkWiley Interscience ISBN 0-471-05066-0 1980
[17] Ong KS Chow CC Performance of solar chimney Solar Energy 2003741e17[18] VDI Waumlrmeatlas Springer Verlag 1994[19] ASHRAE handbook HVAC systems and equipment chimney gas vent and
1047297replace systems Atlanta GA American Society of Heating Refrigerating andAirconditioning Engineers Inc 2000 pp 301e3011
[20] ASHRAEhandbookfundamentals ductdesign AtlantaGAAmericanSociety of HeatingRefrigeratingand AirconditioningEngineers Inc 2000 pp341e346
[21] Bansal NK Sodha MS Bharadwi SS Performance of earth air tunnels Inter-national Journal of Energy Research 19837(4)333e45
[22] Mathur J Bansal NK Mathur S Jain M Anupma Experimental investigationson solar chimney for room ventilation Solar Energy 200680927e35
[23] Dhaliwal AS Goswami DY Heat transfer analysis in environmental controlusing an underground air tunnel Journal of Solar Energy Engineering1985107141e5
Nomenclature
A area ACH air change per hour (h1)C speci1047297c heat of air (JkgK)c pressure loss coef 1047297cient of 1047297ttingsD gap depth between absorber wall and glass (m)d diameter (m)H distance (m)h convective heat transfer coef 1047297cient (Wm2 K)hr radiative heat transfer coef 1047297cient (Wm2 K)
I total incident solar radiation on south facing inclined surface (Wm 2)k thermal conductivity (Wm K)L length (m)m mass 1047298ow rate of air (kgs)Q heat transfer to air stream (Wm2)R thermal resistance (m2 KW)r radius (m)S solar radiation heat 1047298ux absorbed by plate (Wm2)T temperature (K)t thickness (m)
U overall heat transfer coef 1047297cient (Wm2 K)u air velocity (ms)V volume of room (m3)W width of chimney (m)
xy coordinate system (m) Z height of chimney inlet (m)
Greek symbols
a absorbtion coef 1047297cientb volumetric coef 1047297cient of expansion (K1)g constant in Eqs(9) and(10)d heat penetration depth (m)3 emissivityq anglel thermal diffusivity (m2s)m Dynamic viscosity (kgs m)n Kinematic viscosity (m2s)x friction factor
r density (kgm
3
)s SteffaneBoltzmann constant (567 108Wm2 K4)u frequency of temperature oscillation (rads)
Dimensionless terms
Nu Nusselt number [hf L mf ]Pr Prandtl number [C f mf kf ]Gr Grashof number [ g bf (T T f )L3n 2]Ra Rayleigh number [GrPr]Re Reynolds number [uf dhydnf ]
Subscripts
a ambientabs absorber wallc convective
f air 1047298ow g glasshyd hydraulici internalin inletins insulation
j indexo outletr radius rooms soilsc solar chimneyst inner surface of tubesu undisturbed soilt pipe
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Rt frac14 ln
r ti thorn t t
r ti
2pktLt (20)
Rs is the thermal resistance between EAHE and undisturbed soil
surface it is given by
Rs frac14 1
2pksLt
ln01 thorn d
r ti thorn t tthorn ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 thorn
d
r ti thorn t t
2
1s 1A (21)
The energy balance of the circulating 1047298uid is given by
dQ frac14 mC f dT ft
d x d x (22)
Eqs (14) and (22) give the differential overall energy balance
equation in the form8gtlt
gt
dT ft
d x thorn
T f t
mC ftRtotalfrac14 00
T ft frac14 T a x frac14 00
(23)
The solution of equation (23) can be expressed as
T fteth xTHORN frac14 T su thorn ethT a T suTHORNexp
x
mC ftRtotal
(24)
23 Room ventilation and temperature
Chimney effect causes the movement of air into and out of
buildings and is driven by buoyancy Buoyancy occurs due to
a difference in indoor-to-outdoor air density resulting from
temperature and moisture differences A chimney heated by solar
energy can be used to drive the chimney effect without increasing
room temperature The driving potential for the air 1047298ow through
the solar house is function of the pressure difference between the
inlet of the EAHE and the SC outlet The buoyancy pressure due to
increasing air temperature in SC sucks the cooled and heavy air
through the EAHE The friction losses due to 1047298uid 1047298ow through the
channels and across the 1047297ttings refrain from the 1047298uid 1047298ow If the
buoyancy pressure overcomes the sum of all 1047298ow pressure losses
the natural ventilation may take place
A mathematical model based on Bernoullirsquo s equation has been
used to estimate the system 1047298ow rate Thus the chimney net draft
Draftsccan be calculated by the following equation [19]
Draftsc frac14rfa rfsco
gLscsin q
0X7
j frac14 6
c j thorn xscLsc
dhyd
sc
1A
r
fscou
2
sc2
eth25THORN
Where the c j is the pressure loss coef 1047297cients at the locations which
are indicated in Fig 1
In right hand side of equation (25) the 1047297rstclause is thechimney
theoretical draft and the second one is the chimney pressure loss
The EAHE pressure loss DP EAHE is [20]
DP EAHE frac14
0X5
j frac14 1
c j thorn xtLEAHE
dti
1Arftu2
f t
2
(26)
The air temperature variation in the vertical pipe is ignored The air
temperature at the solar chimney inlet is assumed to be same as the
room air temperature which is higher than the cooled air
temperature at the pipe outlet So the chimney effects DraftEAHE
and DraftRoom can be expressed as
DraftEAHE frac14rfr rft
gH tr (27)
DraftRoom frac14
rfscin rfr
gH rinscin (28)
The required draft for cooling system DraftSystem is the sum of thepipe pressure loss and the negative pressure DraftEAHE and
DraftRoom
DraftSystem frac14 DP EAHE DraftEAHE thorn DraftRoom (29)
Under steady-state conditions we can write
DraftSystem frac14 Draftsc (30)
The air mass 1047298ow rate at the chimney and EAHE are the same if
there is no air in1047297ltration
m frac14 rAujChimney outlet frac14 r AujChimney inlet frac14 r AujEAHE (31)
By expanding equation (30) and use of equation (31) the airvelocity in the SC can be obtained as
usc frac14
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiBouyancy Terms
Friction Terms
r (32-a)
Where
Bouyancy Terms frac14 2
rfa rfsco
gLscSinethqTHORN
rfscin rfr
gH rinscin
rft rfr
gH tr
(32-b)
Friction Terms frac14 ethc THORN6rfsco Ascorfr Ascin
2
rfr thornn
ethc THORN7thornxsc Lsc
ethdhydTHORNsc
orfscothorn( P5
j frac14 1
c j thorn xtLtthornH trthornBurried depth of EAHE
dt
rfsco Asco
rft At
2)rft
(32-c)
The main criteria for thermal comfort condition are affected by two
factors the ACH and room air temperature The ACH is calculated
under steady-state conditions by the following equation [5]
ACH frac14 3600m
rfscV (33)
The room air temperature which depends on room heat gain is
obtained by the following equation
T r frac14 T ftot thorn Q rmC ft
(34)
Where Q r is sum of the heats that the room gains through the walls
and the heat generated by internal heat sources
3 Analysis
The system capability to provide the desired indoor condition
depends on parameters such as the ambient conditions (tempera-
ture solar radiation) dimensions of SC and EAHE and cooling
demand Parametric study is carried out to 1047297nd the effects of
geometrical dimensions of the SC and EAHE and outdoor envi-
ronmental conditions The following dimensions and speci1047297
cations
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 23242320
7232019 Passive Cooling of Buildings by Using Integrated Earth to Air Heat Exchanger
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are used in the modeling The room 40 40 3125 m in
dimensions without air in1047297ltration and has a minimum cooling
demand of Q frac14 116 W This is the demand of a room with adiabatic
walls which one person is resting in it The cooling demand is
changed at the range of 116e1500 W in the calculations
A solar chimney with the length of 40 m width of 10 m air gap
depth of 03 m and inlet of 04 04 m is considered These
dimensions are chosen based on studies of Ref [22] and may be
changed in the calculation A detailed study on a south facing solar
chimney in Tehran having 3544 N latitude position has found theoptimum angle of 50 to capture more radiation [5] Few numbers
of solar chimneys are adequate to provide the required stack effect
for the system
The cooling pipe of EAHE is a PVC pipe with 250 m length
001 m thickness and inside diameter of 05 m and is buried 30 m
below the soil surface According to the model developed by Bansal
et al [21] undisturbed soil temperature at a depth of 30 m is
approximated to be 19 C for a dry shaded soil surface condition
and it is considered to be the heat sink temperature These
dimensions have a decisive in1047298uence on cooling load and system
performance which will be investigated here Usually only one
EAHE suf 1047297cesto provide the necessarycooling load but in sever hot
conditions more cooling pipes may be employed
The EAHE outlet and the SC inlet are located on the oppositewalls (Fig 2) The SC inlet is lowered 07 m below the EAHE outlet
level The EAHE outlet is 3 m above the room 1047298oor thus it is 6 m
above the buried horizontal pipes of the EAHE The ambient
outdoor temperature is 34 C The thermophysical properties of the
materials included in the modeling are given in Table 1 The values
of the properties speci1047297ed in the table are kept constant in the
computation unless speci1047297cally noted otherwise
A computer program was written in MATLAB software to solve
the mathematical model The governing equations (1 9 11 24 and
32) have to be solved iteratively until convergence of the results
There is no experimental data to validate the results of theo-
retical model for the integrated system So the calculation has been
carried out for SC and EAHE separately under same conditions of
experimental studies of [22] and [23] to check the mathematical
model and to ensure the accuracy of computationsTable 2 shows the results of present model and the theoretical
and experimental results of Mathur et al [22] for different combi-
nations of solar radiation SC height and chimney inlet dimensions
The quantitative comparison shows a reasonable agreement
between the results obtained by the present study and the pub-
lished results of [22] The results of present study are closer to the
experimental results than the theoretical results of Ref [22] It
should be noted that the calculation carried out at the same
conditions of Ref [22] in which the roomvolume is 27 m3 and other
experimental conditions are given in Table 2
Fig 6 shows the air temperature variation along the cooling
pipe The results of the present work are calculated at the condi-
tions of experiments of Ref [23] given in Table 3 As the 1047297gure
shows there is good agreement between the present theoretical
results and the experimental results of Ref [23]
However it is reasonable to conclude that the mathematical
model can predict air temperature quite accurately and the calcu-
lated results are reliable
4 Result and discussion
41 Capability of the system to provide thermal comfort
Theoretical calculations are performed at various solar radia-
tions and room cooling demands The results are summarized in
Table 4 It is found that an integrated system of a few number of
solar chimneys with one (or at most two) EAHE cooling pipe can
Table 1
Thermophysical properties
Parameters Values
1 Transmissivity of glass 084 (d)
2 Absorptivity of glass 006 (d)
3 Emissivity of the glass 090 (d)
4 Absorptivity of absorber wall 095 (d)
5 Emissivity of the absorber wall 095 (d)
6 Thermal conductivity of the pipe (PVC) 023 (Wm K )7 Soil density 2050 (kgm3)
8 Thermal conductivity of the Soil 052 (Wm K)
9 Speci1047297c heat of soil 1840 (Jkg K)
Table 2
Comparison of experimental and theoretical results for solar chimney induced ACH number
Solar radiation
(Wm2)
Absorber
length (m)
Inlet chim dimens
(m m)
Ambient
temp (K)
ACH Errors of [22] Errors of present
studyEXP [22] Theo [22] Theo (present study)
300 07 10 03 295e302 4400 4173 4366 516 077
08 10 02 298e304 5330 4054 4757 2394 1075
09 10 01 294e296 2400 2704 2368 1266 133
500 07 10 03 295e302 4800 5160 4454 750 721
08 10 02 298e304 4530 4895 4816 806 631
09 10 01 294e296 2660 3461 2970 3011 1165
700 07 10 03 295e302 5600 5810 5404 375 35
08 10 02 298e304 5330 5175 5480 291 281
09 10 01 294e296 2930 3671 3217 2529 979
Fig 6 Comparison present results with experimental data
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 2324 2321
7232019 Passive Cooling of Buildings by Using Integrated Earth to Air Heat Exchanger
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provide the indoor thermal comfort conditions so the temperature
is retained at 2815e3194 C which is within the acceptable range
according to Ref [14] with 3e7 ACH which secures the required
ventilation rate As can be seen for higher cooling demands longer
and more cooling pipes of the EAHE are required
42 Effective dimensions of the system
There are many geometrical dimensions in the system that
affect its performance Some of them such as dimensions of the
inlet of the SC cross area of the SC etc have minor effects these
in1047298uence the 1047298ow rate slightly by changing the resistance to the
1047298ow While two geometrical dimensions have the substantial
effects i) absorbing surface area of the SC which provide the
energy for stack effect at the SC ii)cooling surface area of the EAHE
which facilitates heat removal from the air 1047298ow to soil
In the present study effects of variations of all dimensions are
investigated Based on the obtained results the dimensions
described in the section 3 have been chosen as suitable working
dimensions The details of the results are not given in the present
paper to save time However effects of changing the two ef 1047297cacious
dimensions are reported here
i) Absorber surface area is increased by increasing the length of
the chimney This increase results in higher ventilation rate or
higher ACH number On the other hand higher ventilation
rate with a constant cooling source results in higher indoor
temperature Thus more number of buried pipes are required
to cool the room and satisfy the thermal comfort require-
ments as shown in Table 5
ii) The lateral surface area of the buried pipe is serving as heat
exchange surface area of the heat sink of the system Gener-
ally larger cooling area provides more cooling effect to the
system In order to increase the cooling surface one may
increase the diameter andor the length of the pipe Table 6
shows the effect of EAHE length on system performance at
two different cooling demands For the length of EAHE less
than 20 m the comfort temperature may not be provided and
longer EAHE should be employed
Resultsof the study on thediameterof cooling pipes are shown in
Table 7 A comparative surveyshows that the required number of SCs
and EAHEs are minimums when the diameter is 05 m Therefore
this value is adopted as default valueof diameterand thevariation in
lateral area surfaces are made by increasing the length of the pipe
43 Effects of environmental conditions on the system performance
The environmental conditions are comprised of solar radiation
and outdoor ambient temperature in the present study Table 8
Table 3
Properties and conditions of experiment [23]
1 Length of EAHE 2500 (m)
2 Buried depth of EAHE 256 (m)
3 Radius of pipe 0305 (m)
4 Thickness of pipe 0002 (m)
5 Thermal conductivity of pipe 033 (Wm K)
6 Thermal conductivity of soil 116 (Wm K)
7 Thermal diffusivity of soil 645 107 (m2s)
8 Air velocity 147 (ms)
9 Air density 1214 (kgm3)
10 Air viscosity 178 107 (kgs m)
11 Speci1047297c heat of air 1205 103 (Jkg K)
12 Air Prandtl number 065 (d)
13 Thermal conductivity of air 028 (Wm K)
Table 4
Performance of the system at various cooling demands and solar radiations
Cooling
demand (W)
Solar radiation
(Wm2)
Length of
EAHE (m)
ACH
d
Room air
temp
( C)
Number
of SC
Number
of EAHE
116 400 25 634 2853 2 1
600 403 2814 1
800 506 2831 1
1000 584 2844 1
200 400 25 630 2935 2 1
600 356 2873 1
800 481 2935 1
1000 565 2933 1
400 400 30 569 2992 2 1
600 790 3015 2
800 388 2951 1
1000 487 3062 1
600 400 40 467 2827 2 1
600 721 3042 2
800 309 2777 1
1000 400 2902 1
800 400 40 520 2813 3 2
600 421 2764 2
800 533 2903 2
1000 627 3014 2
Note Ambient air temperature frac14 34 C
Table 5
Effects of absorber length on system performance
Cooling
demand (W)
Absorber
length (m)
ACH
d
Room air
temp (C)
Number
of SC
Number
of EAHE
116 30 440 2822 1 1
40 583 2844 1 1
50 706 2866 1 1
60 818 2886 1 1
800 30 236 2894 2 340 510 3098 2 3
50 662 3238 2 3
60 829 3363 2 3
800 30 312 2924 3 5
40 305 2941 2 4
50 351 2981 2 5
60 384 3019 2 6
Note Ambient air temperature frac14 34 C solar radiation frac14 1000 (Wm2)
Table 6
Effects of length of EAHE on system performance
Cooling
demand
(W)
Ambient
air temp
( C)
Solar
radiation
(Wm2)
Length of
EAHE
(m)
ACH
d
Room air
temp
( C)
Number
of SC
Number
of EAHE
116 40 400 150 347 2968 4 10
250 602 2972 3 2
350 517 2700 3 2450 579 2861 3 1
116 40 1000 150 347 2987 2 9
250 649 2872 2 3
350 465 2877 1 1
450 356 2633 1 1
800 40 400 150 Thermal comfort cannot be
provided
250 314 2900 3 5
350 454 2950 3 2
450 427 2700 3 2
800 40 1000 150 Thermal comfort cannot be
provided
250 335 2938 2 6
350 742 2952 2 3
450 559 2926 2 2
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 23242322
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shows the summary of results of the theoretical calculations fordifferent environmental conditions
The buoyancy driving force increases with an increase of solar
intensity and it causes higher ACH Thus less number of SCs are
required to drive the cool and heavy air through the EAHEs and to
compensate the pressure drops The results of calculations also
show that the required number of EAHEs should be increased to
retain the thermal comfort condition when the number of ACH and
indoor air temperature are increased at high solar radiation
The effect of ambient airtemperature on stack effect of SC is vice
versa The stack effect decreases when the ambient outdoor
temperature risesUnder these conditions more numberof SCs willbe required to ventilate the room
The results show that the system can provide the required
indoor temperature and ACH number even at harsh environmental
condition of high temperature of 45 C and low solar radiation of
100 Wm2 If the temperature is higher than 45 C the SC wonrsquot be
able to provide the stack effect and in this condition the use of
a small fan can help the cool air to 1047298ow from EAHE in to the room
and to realize thermal comfort condition
It should be noted that in this system all air 1047298ow is fresh air and
a reduction about 23 C in the inlet air is praiseful achievement of
the present passive cooling system
5 Conclusions
A passive solar system comprises of solar chimneys and earth to
air heat exchangers is proposed and studied in the present paper
The present study shows that the performance of the system
depends on solar radiation outdoor air temperature as well as
con1047297guration of both the SC and the EAHE
The results showed that the number of required SCs decreases
with the use of taller SCs The use of taller SCs lead to thermal
discomfort therefore more number of buried pipes should be
employed to cool air 1047298ow and satisfy the thermal needs
Results of the study on diameter of EAHE show that there is an
optimum diameter for cooling pipes (05 m) which gives the
minimum required number of SCs and EAHEs It has also been
found that the long EAHE with the length of more than 20 m should
be employed to provide the thermal comfort conditionThe results also show that when the ambient temperature and
cooling demand are high although providing thermal comfort is
dif 1047297cult proper con1047297gurations could provide good indoor condi-
tion even in the poor solar intensity of 100 Wm2 and high ambient
air temperature of 50 C
References
[1] Bansal NK Mathur R Bhandari MS A study of solar chimney assisted windtower system for natural ventilation in buildings Building and Environment199429(4)495e500
[2] Gan G Riffat SB A numerical study of solar chimney for natural ventilation of buildings with heat recovery Applied Thermal Engineering 1998181171e87
[3] Hamdy IF Fikry MA Passive solar ventilation Renewable Energy 199814
(1e
4)381e
6
Table 7
Effects of diameter of EAHE on system performance
Cooling
demand (W)
Ambient
air temp (C)
Solar radiation
(Wm2)
Diameter of
EAHE (m)
ACH
d
Room air
temp (C)
Number
of SC
Number
of EAHE
116 40 400 03 430 2996 3 2
05 602 2972 3 2
07 301 2989 3 4
09 476 2998 4 8
116 40 1000 03 507 2770 3 205 649 2872 2 3
07 867 2996 2 4
09 785 2980 2 8
800 40 400 03 Thermal comfort cannot be provided
05 314 2900 3 5
07 443 2986 4 7
09 Thermal comfort cannot be provided
800 40 1000 03 Thermal comfort cannot be provided
05 335 2938 2 6
07 321 2931 2 7
09 371 2994 2 12
Table 8
System performance at different indoor and outdoor conditions
Coolingdemand (W)
Ambient airtemp (C)
Solarradiation
(Wm2)
ACHd
Room airtemp (C)
Numberof SC
Numberof EAHE
500 40 100 328 2961 5 3
500 516 3113 3 3
900 483 3140 2 3
500 45 100 301 3092 6 4
500 430 3112 3 4
900 402 3127 2 4
500 50 100 305 3102 6 6
500 345 3162 3 5
900 306 3152 2 5
1000 40 100 498 3051 8 6
500 410 3195 2 2
900 363 3069 2 4
1000 45 100 415 3000 8 6500 327 3115 3 5
900 300 3090 2 5
1000 50 100 418 3195 8 7
500 305 3198 3 6
900 315 3153 3 12
1500 40 100 520 3136 8 4
500 329 3061 3 5
900 300 3035 2 5
1500 45 100 395 3100 9 9
500 362 3170 4 9
900 317 3160 3 12
1500 50 100
500 Thermal comfort cannot be provided
900
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 2324 2323
7232019 Passive Cooling of Buildings by Using Integrated Earth to Air Heat Exchanger
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[4] Khedari J Boonsri B Hirunlabh J Ventilation impact of a solar chimney onindoor temperature 1047298uctuation and air change in a school building Energyand Buildings 20003289e93
[5] Mathur J Mathur S Anupma Summer-performance of inclined roof solarchimney for natural ventilation Energy and Buildings 2006381156e63
[6] Bassiouny R Koura NSA An analytical and numerical study of solar chimneyuse for room natural ventilation Energy and Buildings 200840865e73
[7] Hollmuller P Lachal B Cooling and preheating with buried pipe systems moni-toring simulation and economic aspects Energy and Buildings 200133509e18
[8] Santamouris M Mihalakakou G Asimakoupolos D On the coupling of ther-
mostatically controlled buildings with ground and night ventilation passivedissipation techniques Solar Energy 199760(3e4)191e7
[9] Krarti M Kreider JF Analytical model for heat transfer in an underground airtunnel Energy Conversion and Management 199637(10)1561e74
[10] Hollmuller P Analytical characterization of amplitude-dampening and phase-shifting in airsoil heat exchangers International Journal of Heat and MassTransfer 2003464303e17
[11] Al-Ajmi F Loveday DL Hanby VI The cooling potential of eartheair heatexchangers for domestic buildings in a desert climate Building and Environ-ment 200641235e44
[12] Kumar R Kaushik SC Garg SN Heating and cooling potential of an earth-to-airheat exchanger using arti1047297cial neural network Renewable Energy2006311139e55
[13] Brager GS de Dear RJ A standard for natural ventilation ASHRAE Journal200042(10)21e8
[14] BIS Bureau of Indian Standards Handbook of functional requirements of buildings 1997 ISBN81-7061-011-7
[15] Ong KS A mathematical model of a solar chimney Renewable Energy2003281047e60
[16] Duf 1047297e JA Beckmann WA Solar engineering of thermal processes New YorkWiley Interscience ISBN 0-471-05066-0 1980
[17] Ong KS Chow CC Performance of solar chimney Solar Energy 2003741e17[18] VDI Waumlrmeatlas Springer Verlag 1994[19] ASHRAE handbook HVAC systems and equipment chimney gas vent and
1047297replace systems Atlanta GA American Society of Heating Refrigerating andAirconditioning Engineers Inc 2000 pp 301e3011
[20] ASHRAEhandbookfundamentals ductdesign AtlantaGAAmericanSociety of HeatingRefrigeratingand AirconditioningEngineers Inc 2000 pp341e346
[21] Bansal NK Sodha MS Bharadwi SS Performance of earth air tunnels Inter-national Journal of Energy Research 19837(4)333e45
[22] Mathur J Bansal NK Mathur S Jain M Anupma Experimental investigationson solar chimney for room ventilation Solar Energy 200680927e35
[23] Dhaliwal AS Goswami DY Heat transfer analysis in environmental controlusing an underground air tunnel Journal of Solar Energy Engineering1985107141e5
Nomenclature
A area ACH air change per hour (h1)C speci1047297c heat of air (JkgK)c pressure loss coef 1047297cient of 1047297ttingsD gap depth between absorber wall and glass (m)d diameter (m)H distance (m)h convective heat transfer coef 1047297cient (Wm2 K)hr radiative heat transfer coef 1047297cient (Wm2 K)
I total incident solar radiation on south facing inclined surface (Wm 2)k thermal conductivity (Wm K)L length (m)m mass 1047298ow rate of air (kgs)Q heat transfer to air stream (Wm2)R thermal resistance (m2 KW)r radius (m)S solar radiation heat 1047298ux absorbed by plate (Wm2)T temperature (K)t thickness (m)
U overall heat transfer coef 1047297cient (Wm2 K)u air velocity (ms)V volume of room (m3)W width of chimney (m)
xy coordinate system (m) Z height of chimney inlet (m)
Greek symbols
a absorbtion coef 1047297cientb volumetric coef 1047297cient of expansion (K1)g constant in Eqs(9) and(10)d heat penetration depth (m)3 emissivityq anglel thermal diffusivity (m2s)m Dynamic viscosity (kgs m)n Kinematic viscosity (m2s)x friction factor
r density (kgm
3
)s SteffaneBoltzmann constant (567 108Wm2 K4)u frequency of temperature oscillation (rads)
Dimensionless terms
Nu Nusselt number [hf L mf ]Pr Prandtl number [C f mf kf ]Gr Grashof number [ g bf (T T f )L3n 2]Ra Rayleigh number [GrPr]Re Reynolds number [uf dhydnf ]
Subscripts
a ambientabs absorber wallc convective
f air 1047298ow g glasshyd hydraulici internalin inletins insulation
j indexo outletr radius rooms soilsc solar chimneyst inner surface of tubesu undisturbed soilt pipe
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 23242324
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are used in the modeling The room 40 40 3125 m in
dimensions without air in1047297ltration and has a minimum cooling
demand of Q frac14 116 W This is the demand of a room with adiabatic
walls which one person is resting in it The cooling demand is
changed at the range of 116e1500 W in the calculations
A solar chimney with the length of 40 m width of 10 m air gap
depth of 03 m and inlet of 04 04 m is considered These
dimensions are chosen based on studies of Ref [22] and may be
changed in the calculation A detailed study on a south facing solar
chimney in Tehran having 3544 N latitude position has found theoptimum angle of 50 to capture more radiation [5] Few numbers
of solar chimneys are adequate to provide the required stack effect
for the system
The cooling pipe of EAHE is a PVC pipe with 250 m length
001 m thickness and inside diameter of 05 m and is buried 30 m
below the soil surface According to the model developed by Bansal
et al [21] undisturbed soil temperature at a depth of 30 m is
approximated to be 19 C for a dry shaded soil surface condition
and it is considered to be the heat sink temperature These
dimensions have a decisive in1047298uence on cooling load and system
performance which will be investigated here Usually only one
EAHE suf 1047297cesto provide the necessarycooling load but in sever hot
conditions more cooling pipes may be employed
The EAHE outlet and the SC inlet are located on the oppositewalls (Fig 2) The SC inlet is lowered 07 m below the EAHE outlet
level The EAHE outlet is 3 m above the room 1047298oor thus it is 6 m
above the buried horizontal pipes of the EAHE The ambient
outdoor temperature is 34 C The thermophysical properties of the
materials included in the modeling are given in Table 1 The values
of the properties speci1047297ed in the table are kept constant in the
computation unless speci1047297cally noted otherwise
A computer program was written in MATLAB software to solve
the mathematical model The governing equations (1 9 11 24 and
32) have to be solved iteratively until convergence of the results
There is no experimental data to validate the results of theo-
retical model for the integrated system So the calculation has been
carried out for SC and EAHE separately under same conditions of
experimental studies of [22] and [23] to check the mathematical
model and to ensure the accuracy of computationsTable 2 shows the results of present model and the theoretical
and experimental results of Mathur et al [22] for different combi-
nations of solar radiation SC height and chimney inlet dimensions
The quantitative comparison shows a reasonable agreement
between the results obtained by the present study and the pub-
lished results of [22] The results of present study are closer to the
experimental results than the theoretical results of Ref [22] It
should be noted that the calculation carried out at the same
conditions of Ref [22] in which the roomvolume is 27 m3 and other
experimental conditions are given in Table 2
Fig 6 shows the air temperature variation along the cooling
pipe The results of the present work are calculated at the condi-
tions of experiments of Ref [23] given in Table 3 As the 1047297gure
shows there is good agreement between the present theoretical
results and the experimental results of Ref [23]
However it is reasonable to conclude that the mathematical
model can predict air temperature quite accurately and the calcu-
lated results are reliable
4 Result and discussion
41 Capability of the system to provide thermal comfort
Theoretical calculations are performed at various solar radia-
tions and room cooling demands The results are summarized in
Table 4 It is found that an integrated system of a few number of
solar chimneys with one (or at most two) EAHE cooling pipe can
Table 1
Thermophysical properties
Parameters Values
1 Transmissivity of glass 084 (d)
2 Absorptivity of glass 006 (d)
3 Emissivity of the glass 090 (d)
4 Absorptivity of absorber wall 095 (d)
5 Emissivity of the absorber wall 095 (d)
6 Thermal conductivity of the pipe (PVC) 023 (Wm K )7 Soil density 2050 (kgm3)
8 Thermal conductivity of the Soil 052 (Wm K)
9 Speci1047297c heat of soil 1840 (Jkg K)
Table 2
Comparison of experimental and theoretical results for solar chimney induced ACH number
Solar radiation
(Wm2)
Absorber
length (m)
Inlet chim dimens
(m m)
Ambient
temp (K)
ACH Errors of [22] Errors of present
studyEXP [22] Theo [22] Theo (present study)
300 07 10 03 295e302 4400 4173 4366 516 077
08 10 02 298e304 5330 4054 4757 2394 1075
09 10 01 294e296 2400 2704 2368 1266 133
500 07 10 03 295e302 4800 5160 4454 750 721
08 10 02 298e304 4530 4895 4816 806 631
09 10 01 294e296 2660 3461 2970 3011 1165
700 07 10 03 295e302 5600 5810 5404 375 35
08 10 02 298e304 5330 5175 5480 291 281
09 10 01 294e296 2930 3671 3217 2529 979
Fig 6 Comparison present results with experimental data
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 2324 2321
7232019 Passive Cooling of Buildings by Using Integrated Earth to Air Heat Exchanger
httpslidepdfcomreaderfullpassive-cooling-of-buildings-by-using-integrated-earth-to-air-heat-exchanger 79
provide the indoor thermal comfort conditions so the temperature
is retained at 2815e3194 C which is within the acceptable range
according to Ref [14] with 3e7 ACH which secures the required
ventilation rate As can be seen for higher cooling demands longer
and more cooling pipes of the EAHE are required
42 Effective dimensions of the system
There are many geometrical dimensions in the system that
affect its performance Some of them such as dimensions of the
inlet of the SC cross area of the SC etc have minor effects these
in1047298uence the 1047298ow rate slightly by changing the resistance to the
1047298ow While two geometrical dimensions have the substantial
effects i) absorbing surface area of the SC which provide the
energy for stack effect at the SC ii)cooling surface area of the EAHE
which facilitates heat removal from the air 1047298ow to soil
In the present study effects of variations of all dimensions are
investigated Based on the obtained results the dimensions
described in the section 3 have been chosen as suitable working
dimensions The details of the results are not given in the present
paper to save time However effects of changing the two ef 1047297cacious
dimensions are reported here
i) Absorber surface area is increased by increasing the length of
the chimney This increase results in higher ventilation rate or
higher ACH number On the other hand higher ventilation
rate with a constant cooling source results in higher indoor
temperature Thus more number of buried pipes are required
to cool the room and satisfy the thermal comfort require-
ments as shown in Table 5
ii) The lateral surface area of the buried pipe is serving as heat
exchange surface area of the heat sink of the system Gener-
ally larger cooling area provides more cooling effect to the
system In order to increase the cooling surface one may
increase the diameter andor the length of the pipe Table 6
shows the effect of EAHE length on system performance at
two different cooling demands For the length of EAHE less
than 20 m the comfort temperature may not be provided and
longer EAHE should be employed
Resultsof the study on thediameterof cooling pipes are shown in
Table 7 A comparative surveyshows that the required number of SCs
and EAHEs are minimums when the diameter is 05 m Therefore
this value is adopted as default valueof diameterand thevariation in
lateral area surfaces are made by increasing the length of the pipe
43 Effects of environmental conditions on the system performance
The environmental conditions are comprised of solar radiation
and outdoor ambient temperature in the present study Table 8
Table 3
Properties and conditions of experiment [23]
1 Length of EAHE 2500 (m)
2 Buried depth of EAHE 256 (m)
3 Radius of pipe 0305 (m)
4 Thickness of pipe 0002 (m)
5 Thermal conductivity of pipe 033 (Wm K)
6 Thermal conductivity of soil 116 (Wm K)
7 Thermal diffusivity of soil 645 107 (m2s)
8 Air velocity 147 (ms)
9 Air density 1214 (kgm3)
10 Air viscosity 178 107 (kgs m)
11 Speci1047297c heat of air 1205 103 (Jkg K)
12 Air Prandtl number 065 (d)
13 Thermal conductivity of air 028 (Wm K)
Table 4
Performance of the system at various cooling demands and solar radiations
Cooling
demand (W)
Solar radiation
(Wm2)
Length of
EAHE (m)
ACH
d
Room air
temp
( C)
Number
of SC
Number
of EAHE
116 400 25 634 2853 2 1
600 403 2814 1
800 506 2831 1
1000 584 2844 1
200 400 25 630 2935 2 1
600 356 2873 1
800 481 2935 1
1000 565 2933 1
400 400 30 569 2992 2 1
600 790 3015 2
800 388 2951 1
1000 487 3062 1
600 400 40 467 2827 2 1
600 721 3042 2
800 309 2777 1
1000 400 2902 1
800 400 40 520 2813 3 2
600 421 2764 2
800 533 2903 2
1000 627 3014 2
Note Ambient air temperature frac14 34 C
Table 5
Effects of absorber length on system performance
Cooling
demand (W)
Absorber
length (m)
ACH
d
Room air
temp (C)
Number
of SC
Number
of EAHE
116 30 440 2822 1 1
40 583 2844 1 1
50 706 2866 1 1
60 818 2886 1 1
800 30 236 2894 2 340 510 3098 2 3
50 662 3238 2 3
60 829 3363 2 3
800 30 312 2924 3 5
40 305 2941 2 4
50 351 2981 2 5
60 384 3019 2 6
Note Ambient air temperature frac14 34 C solar radiation frac14 1000 (Wm2)
Table 6
Effects of length of EAHE on system performance
Cooling
demand
(W)
Ambient
air temp
( C)
Solar
radiation
(Wm2)
Length of
EAHE
(m)
ACH
d
Room air
temp
( C)
Number
of SC
Number
of EAHE
116 40 400 150 347 2968 4 10
250 602 2972 3 2
350 517 2700 3 2450 579 2861 3 1
116 40 1000 150 347 2987 2 9
250 649 2872 2 3
350 465 2877 1 1
450 356 2633 1 1
800 40 400 150 Thermal comfort cannot be
provided
250 314 2900 3 5
350 454 2950 3 2
450 427 2700 3 2
800 40 1000 150 Thermal comfort cannot be
provided
250 335 2938 2 6
350 742 2952 2 3
450 559 2926 2 2
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 23242322
7232019 Passive Cooling of Buildings by Using Integrated Earth to Air Heat Exchanger
httpslidepdfcomreaderfullpassive-cooling-of-buildings-by-using-integrated-earth-to-air-heat-exchanger 89
shows the summary of results of the theoretical calculations fordifferent environmental conditions
The buoyancy driving force increases with an increase of solar
intensity and it causes higher ACH Thus less number of SCs are
required to drive the cool and heavy air through the EAHEs and to
compensate the pressure drops The results of calculations also
show that the required number of EAHEs should be increased to
retain the thermal comfort condition when the number of ACH and
indoor air temperature are increased at high solar radiation
The effect of ambient airtemperature on stack effect of SC is vice
versa The stack effect decreases when the ambient outdoor
temperature risesUnder these conditions more numberof SCs willbe required to ventilate the room
The results show that the system can provide the required
indoor temperature and ACH number even at harsh environmental
condition of high temperature of 45 C and low solar radiation of
100 Wm2 If the temperature is higher than 45 C the SC wonrsquot be
able to provide the stack effect and in this condition the use of
a small fan can help the cool air to 1047298ow from EAHE in to the room
and to realize thermal comfort condition
It should be noted that in this system all air 1047298ow is fresh air and
a reduction about 23 C in the inlet air is praiseful achievement of
the present passive cooling system
5 Conclusions
A passive solar system comprises of solar chimneys and earth to
air heat exchangers is proposed and studied in the present paper
The present study shows that the performance of the system
depends on solar radiation outdoor air temperature as well as
con1047297guration of both the SC and the EAHE
The results showed that the number of required SCs decreases
with the use of taller SCs The use of taller SCs lead to thermal
discomfort therefore more number of buried pipes should be
employed to cool air 1047298ow and satisfy the thermal needs
Results of the study on diameter of EAHE show that there is an
optimum diameter for cooling pipes (05 m) which gives the
minimum required number of SCs and EAHEs It has also been
found that the long EAHE with the length of more than 20 m should
be employed to provide the thermal comfort conditionThe results also show that when the ambient temperature and
cooling demand are high although providing thermal comfort is
dif 1047297cult proper con1047297gurations could provide good indoor condi-
tion even in the poor solar intensity of 100 Wm2 and high ambient
air temperature of 50 C
References
[1] Bansal NK Mathur R Bhandari MS A study of solar chimney assisted windtower system for natural ventilation in buildings Building and Environment199429(4)495e500
[2] Gan G Riffat SB A numerical study of solar chimney for natural ventilation of buildings with heat recovery Applied Thermal Engineering 1998181171e87
[3] Hamdy IF Fikry MA Passive solar ventilation Renewable Energy 199814
(1e
4)381e
6
Table 7
Effects of diameter of EAHE on system performance
Cooling
demand (W)
Ambient
air temp (C)
Solar radiation
(Wm2)
Diameter of
EAHE (m)
ACH
d
Room air
temp (C)
Number
of SC
Number
of EAHE
116 40 400 03 430 2996 3 2
05 602 2972 3 2
07 301 2989 3 4
09 476 2998 4 8
116 40 1000 03 507 2770 3 205 649 2872 2 3
07 867 2996 2 4
09 785 2980 2 8
800 40 400 03 Thermal comfort cannot be provided
05 314 2900 3 5
07 443 2986 4 7
09 Thermal comfort cannot be provided
800 40 1000 03 Thermal comfort cannot be provided
05 335 2938 2 6
07 321 2931 2 7
09 371 2994 2 12
Table 8
System performance at different indoor and outdoor conditions
Coolingdemand (W)
Ambient airtemp (C)
Solarradiation
(Wm2)
ACHd
Room airtemp (C)
Numberof SC
Numberof EAHE
500 40 100 328 2961 5 3
500 516 3113 3 3
900 483 3140 2 3
500 45 100 301 3092 6 4
500 430 3112 3 4
900 402 3127 2 4
500 50 100 305 3102 6 6
500 345 3162 3 5
900 306 3152 2 5
1000 40 100 498 3051 8 6
500 410 3195 2 2
900 363 3069 2 4
1000 45 100 415 3000 8 6500 327 3115 3 5
900 300 3090 2 5
1000 50 100 418 3195 8 7
500 305 3198 3 6
900 315 3153 3 12
1500 40 100 520 3136 8 4
500 329 3061 3 5
900 300 3035 2 5
1500 45 100 395 3100 9 9
500 362 3170 4 9
900 317 3160 3 12
1500 50 100
500 Thermal comfort cannot be provided
900
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 2324 2323
7232019 Passive Cooling of Buildings by Using Integrated Earth to Air Heat Exchanger
httpslidepdfcomreaderfullpassive-cooling-of-buildings-by-using-integrated-earth-to-air-heat-exchanger 99
[4] Khedari J Boonsri B Hirunlabh J Ventilation impact of a solar chimney onindoor temperature 1047298uctuation and air change in a school building Energyand Buildings 20003289e93
[5] Mathur J Mathur S Anupma Summer-performance of inclined roof solarchimney for natural ventilation Energy and Buildings 2006381156e63
[6] Bassiouny R Koura NSA An analytical and numerical study of solar chimneyuse for room natural ventilation Energy and Buildings 200840865e73
[7] Hollmuller P Lachal B Cooling and preheating with buried pipe systems moni-toring simulation and economic aspects Energy and Buildings 200133509e18
[8] Santamouris M Mihalakakou G Asimakoupolos D On the coupling of ther-
mostatically controlled buildings with ground and night ventilation passivedissipation techniques Solar Energy 199760(3e4)191e7
[9] Krarti M Kreider JF Analytical model for heat transfer in an underground airtunnel Energy Conversion and Management 199637(10)1561e74
[10] Hollmuller P Analytical characterization of amplitude-dampening and phase-shifting in airsoil heat exchangers International Journal of Heat and MassTransfer 2003464303e17
[11] Al-Ajmi F Loveday DL Hanby VI The cooling potential of eartheair heatexchangers for domestic buildings in a desert climate Building and Environ-ment 200641235e44
[12] Kumar R Kaushik SC Garg SN Heating and cooling potential of an earth-to-airheat exchanger using arti1047297cial neural network Renewable Energy2006311139e55
[13] Brager GS de Dear RJ A standard for natural ventilation ASHRAE Journal200042(10)21e8
[14] BIS Bureau of Indian Standards Handbook of functional requirements of buildings 1997 ISBN81-7061-011-7
[15] Ong KS A mathematical model of a solar chimney Renewable Energy2003281047e60
[16] Duf 1047297e JA Beckmann WA Solar engineering of thermal processes New YorkWiley Interscience ISBN 0-471-05066-0 1980
[17] Ong KS Chow CC Performance of solar chimney Solar Energy 2003741e17[18] VDI Waumlrmeatlas Springer Verlag 1994[19] ASHRAE handbook HVAC systems and equipment chimney gas vent and
1047297replace systems Atlanta GA American Society of Heating Refrigerating andAirconditioning Engineers Inc 2000 pp 301e3011
[20] ASHRAEhandbookfundamentals ductdesign AtlantaGAAmericanSociety of HeatingRefrigeratingand AirconditioningEngineers Inc 2000 pp341e346
[21] Bansal NK Sodha MS Bharadwi SS Performance of earth air tunnels Inter-national Journal of Energy Research 19837(4)333e45
[22] Mathur J Bansal NK Mathur S Jain M Anupma Experimental investigationson solar chimney for room ventilation Solar Energy 200680927e35
[23] Dhaliwal AS Goswami DY Heat transfer analysis in environmental controlusing an underground air tunnel Journal of Solar Energy Engineering1985107141e5
Nomenclature
A area ACH air change per hour (h1)C speci1047297c heat of air (JkgK)c pressure loss coef 1047297cient of 1047297ttingsD gap depth between absorber wall and glass (m)d diameter (m)H distance (m)h convective heat transfer coef 1047297cient (Wm2 K)hr radiative heat transfer coef 1047297cient (Wm2 K)
I total incident solar radiation on south facing inclined surface (Wm 2)k thermal conductivity (Wm K)L length (m)m mass 1047298ow rate of air (kgs)Q heat transfer to air stream (Wm2)R thermal resistance (m2 KW)r radius (m)S solar radiation heat 1047298ux absorbed by plate (Wm2)T temperature (K)t thickness (m)
U overall heat transfer coef 1047297cient (Wm2 K)u air velocity (ms)V volume of room (m3)W width of chimney (m)
xy coordinate system (m) Z height of chimney inlet (m)
Greek symbols
a absorbtion coef 1047297cientb volumetric coef 1047297cient of expansion (K1)g constant in Eqs(9) and(10)d heat penetration depth (m)3 emissivityq anglel thermal diffusivity (m2s)m Dynamic viscosity (kgs m)n Kinematic viscosity (m2s)x friction factor
r density (kgm
3
)s SteffaneBoltzmann constant (567 108Wm2 K4)u frequency of temperature oscillation (rads)
Dimensionless terms
Nu Nusselt number [hf L mf ]Pr Prandtl number [C f mf kf ]Gr Grashof number [ g bf (T T f )L3n 2]Ra Rayleigh number [GrPr]Re Reynolds number [uf dhydnf ]
Subscripts
a ambientabs absorber wallc convective
f air 1047298ow g glasshyd hydraulici internalin inletins insulation
j indexo outletr radius rooms soilsc solar chimneyst inner surface of tubesu undisturbed soilt pipe
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 23242324
7232019 Passive Cooling of Buildings by Using Integrated Earth to Air Heat Exchanger
httpslidepdfcomreaderfullpassive-cooling-of-buildings-by-using-integrated-earth-to-air-heat-exchanger 79
provide the indoor thermal comfort conditions so the temperature
is retained at 2815e3194 C which is within the acceptable range
according to Ref [14] with 3e7 ACH which secures the required
ventilation rate As can be seen for higher cooling demands longer
and more cooling pipes of the EAHE are required
42 Effective dimensions of the system
There are many geometrical dimensions in the system that
affect its performance Some of them such as dimensions of the
inlet of the SC cross area of the SC etc have minor effects these
in1047298uence the 1047298ow rate slightly by changing the resistance to the
1047298ow While two geometrical dimensions have the substantial
effects i) absorbing surface area of the SC which provide the
energy for stack effect at the SC ii)cooling surface area of the EAHE
which facilitates heat removal from the air 1047298ow to soil
In the present study effects of variations of all dimensions are
investigated Based on the obtained results the dimensions
described in the section 3 have been chosen as suitable working
dimensions The details of the results are not given in the present
paper to save time However effects of changing the two ef 1047297cacious
dimensions are reported here
i) Absorber surface area is increased by increasing the length of
the chimney This increase results in higher ventilation rate or
higher ACH number On the other hand higher ventilation
rate with a constant cooling source results in higher indoor
temperature Thus more number of buried pipes are required
to cool the room and satisfy the thermal comfort require-
ments as shown in Table 5
ii) The lateral surface area of the buried pipe is serving as heat
exchange surface area of the heat sink of the system Gener-
ally larger cooling area provides more cooling effect to the
system In order to increase the cooling surface one may
increase the diameter andor the length of the pipe Table 6
shows the effect of EAHE length on system performance at
two different cooling demands For the length of EAHE less
than 20 m the comfort temperature may not be provided and
longer EAHE should be employed
Resultsof the study on thediameterof cooling pipes are shown in
Table 7 A comparative surveyshows that the required number of SCs
and EAHEs are minimums when the diameter is 05 m Therefore
this value is adopted as default valueof diameterand thevariation in
lateral area surfaces are made by increasing the length of the pipe
43 Effects of environmental conditions on the system performance
The environmental conditions are comprised of solar radiation
and outdoor ambient temperature in the present study Table 8
Table 3
Properties and conditions of experiment [23]
1 Length of EAHE 2500 (m)
2 Buried depth of EAHE 256 (m)
3 Radius of pipe 0305 (m)
4 Thickness of pipe 0002 (m)
5 Thermal conductivity of pipe 033 (Wm K)
6 Thermal conductivity of soil 116 (Wm K)
7 Thermal diffusivity of soil 645 107 (m2s)
8 Air velocity 147 (ms)
9 Air density 1214 (kgm3)
10 Air viscosity 178 107 (kgs m)
11 Speci1047297c heat of air 1205 103 (Jkg K)
12 Air Prandtl number 065 (d)
13 Thermal conductivity of air 028 (Wm K)
Table 4
Performance of the system at various cooling demands and solar radiations
Cooling
demand (W)
Solar radiation
(Wm2)
Length of
EAHE (m)
ACH
d
Room air
temp
( C)
Number
of SC
Number
of EAHE
116 400 25 634 2853 2 1
600 403 2814 1
800 506 2831 1
1000 584 2844 1
200 400 25 630 2935 2 1
600 356 2873 1
800 481 2935 1
1000 565 2933 1
400 400 30 569 2992 2 1
600 790 3015 2
800 388 2951 1
1000 487 3062 1
600 400 40 467 2827 2 1
600 721 3042 2
800 309 2777 1
1000 400 2902 1
800 400 40 520 2813 3 2
600 421 2764 2
800 533 2903 2
1000 627 3014 2
Note Ambient air temperature frac14 34 C
Table 5
Effects of absorber length on system performance
Cooling
demand (W)
Absorber
length (m)
ACH
d
Room air
temp (C)
Number
of SC
Number
of EAHE
116 30 440 2822 1 1
40 583 2844 1 1
50 706 2866 1 1
60 818 2886 1 1
800 30 236 2894 2 340 510 3098 2 3
50 662 3238 2 3
60 829 3363 2 3
800 30 312 2924 3 5
40 305 2941 2 4
50 351 2981 2 5
60 384 3019 2 6
Note Ambient air temperature frac14 34 C solar radiation frac14 1000 (Wm2)
Table 6
Effects of length of EAHE on system performance
Cooling
demand
(W)
Ambient
air temp
( C)
Solar
radiation
(Wm2)
Length of
EAHE
(m)
ACH
d
Room air
temp
( C)
Number
of SC
Number
of EAHE
116 40 400 150 347 2968 4 10
250 602 2972 3 2
350 517 2700 3 2450 579 2861 3 1
116 40 1000 150 347 2987 2 9
250 649 2872 2 3
350 465 2877 1 1
450 356 2633 1 1
800 40 400 150 Thermal comfort cannot be
provided
250 314 2900 3 5
350 454 2950 3 2
450 427 2700 3 2
800 40 1000 150 Thermal comfort cannot be
provided
250 335 2938 2 6
350 742 2952 2 3
450 559 2926 2 2
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 23242322
7232019 Passive Cooling of Buildings by Using Integrated Earth to Air Heat Exchanger
httpslidepdfcomreaderfullpassive-cooling-of-buildings-by-using-integrated-earth-to-air-heat-exchanger 89
shows the summary of results of the theoretical calculations fordifferent environmental conditions
The buoyancy driving force increases with an increase of solar
intensity and it causes higher ACH Thus less number of SCs are
required to drive the cool and heavy air through the EAHEs and to
compensate the pressure drops The results of calculations also
show that the required number of EAHEs should be increased to
retain the thermal comfort condition when the number of ACH and
indoor air temperature are increased at high solar radiation
The effect of ambient airtemperature on stack effect of SC is vice
versa The stack effect decreases when the ambient outdoor
temperature risesUnder these conditions more numberof SCs willbe required to ventilate the room
The results show that the system can provide the required
indoor temperature and ACH number even at harsh environmental
condition of high temperature of 45 C and low solar radiation of
100 Wm2 If the temperature is higher than 45 C the SC wonrsquot be
able to provide the stack effect and in this condition the use of
a small fan can help the cool air to 1047298ow from EAHE in to the room
and to realize thermal comfort condition
It should be noted that in this system all air 1047298ow is fresh air and
a reduction about 23 C in the inlet air is praiseful achievement of
the present passive cooling system
5 Conclusions
A passive solar system comprises of solar chimneys and earth to
air heat exchangers is proposed and studied in the present paper
The present study shows that the performance of the system
depends on solar radiation outdoor air temperature as well as
con1047297guration of both the SC and the EAHE
The results showed that the number of required SCs decreases
with the use of taller SCs The use of taller SCs lead to thermal
discomfort therefore more number of buried pipes should be
employed to cool air 1047298ow and satisfy the thermal needs
Results of the study on diameter of EAHE show that there is an
optimum diameter for cooling pipes (05 m) which gives the
minimum required number of SCs and EAHEs It has also been
found that the long EAHE with the length of more than 20 m should
be employed to provide the thermal comfort conditionThe results also show that when the ambient temperature and
cooling demand are high although providing thermal comfort is
dif 1047297cult proper con1047297gurations could provide good indoor condi-
tion even in the poor solar intensity of 100 Wm2 and high ambient
air temperature of 50 C
References
[1] Bansal NK Mathur R Bhandari MS A study of solar chimney assisted windtower system for natural ventilation in buildings Building and Environment199429(4)495e500
[2] Gan G Riffat SB A numerical study of solar chimney for natural ventilation of buildings with heat recovery Applied Thermal Engineering 1998181171e87
[3] Hamdy IF Fikry MA Passive solar ventilation Renewable Energy 199814
(1e
4)381e
6
Table 7
Effects of diameter of EAHE on system performance
Cooling
demand (W)
Ambient
air temp (C)
Solar radiation
(Wm2)
Diameter of
EAHE (m)
ACH
d
Room air
temp (C)
Number
of SC
Number
of EAHE
116 40 400 03 430 2996 3 2
05 602 2972 3 2
07 301 2989 3 4
09 476 2998 4 8
116 40 1000 03 507 2770 3 205 649 2872 2 3
07 867 2996 2 4
09 785 2980 2 8
800 40 400 03 Thermal comfort cannot be provided
05 314 2900 3 5
07 443 2986 4 7
09 Thermal comfort cannot be provided
800 40 1000 03 Thermal comfort cannot be provided
05 335 2938 2 6
07 321 2931 2 7
09 371 2994 2 12
Table 8
System performance at different indoor and outdoor conditions
Coolingdemand (W)
Ambient airtemp (C)
Solarradiation
(Wm2)
ACHd
Room airtemp (C)
Numberof SC
Numberof EAHE
500 40 100 328 2961 5 3
500 516 3113 3 3
900 483 3140 2 3
500 45 100 301 3092 6 4
500 430 3112 3 4
900 402 3127 2 4
500 50 100 305 3102 6 6
500 345 3162 3 5
900 306 3152 2 5
1000 40 100 498 3051 8 6
500 410 3195 2 2
900 363 3069 2 4
1000 45 100 415 3000 8 6500 327 3115 3 5
900 300 3090 2 5
1000 50 100 418 3195 8 7
500 305 3198 3 6
900 315 3153 3 12
1500 40 100 520 3136 8 4
500 329 3061 3 5
900 300 3035 2 5
1500 45 100 395 3100 9 9
500 362 3170 4 9
900 317 3160 3 12
1500 50 100
500 Thermal comfort cannot be provided
900
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 2324 2323
7232019 Passive Cooling of Buildings by Using Integrated Earth to Air Heat Exchanger
httpslidepdfcomreaderfullpassive-cooling-of-buildings-by-using-integrated-earth-to-air-heat-exchanger 99
[4] Khedari J Boonsri B Hirunlabh J Ventilation impact of a solar chimney onindoor temperature 1047298uctuation and air change in a school building Energyand Buildings 20003289e93
[5] Mathur J Mathur S Anupma Summer-performance of inclined roof solarchimney for natural ventilation Energy and Buildings 2006381156e63
[6] Bassiouny R Koura NSA An analytical and numerical study of solar chimneyuse for room natural ventilation Energy and Buildings 200840865e73
[7] Hollmuller P Lachal B Cooling and preheating with buried pipe systems moni-toring simulation and economic aspects Energy and Buildings 200133509e18
[8] Santamouris M Mihalakakou G Asimakoupolos D On the coupling of ther-
mostatically controlled buildings with ground and night ventilation passivedissipation techniques Solar Energy 199760(3e4)191e7
[9] Krarti M Kreider JF Analytical model for heat transfer in an underground airtunnel Energy Conversion and Management 199637(10)1561e74
[10] Hollmuller P Analytical characterization of amplitude-dampening and phase-shifting in airsoil heat exchangers International Journal of Heat and MassTransfer 2003464303e17
[11] Al-Ajmi F Loveday DL Hanby VI The cooling potential of eartheair heatexchangers for domestic buildings in a desert climate Building and Environ-ment 200641235e44
[12] Kumar R Kaushik SC Garg SN Heating and cooling potential of an earth-to-airheat exchanger using arti1047297cial neural network Renewable Energy2006311139e55
[13] Brager GS de Dear RJ A standard for natural ventilation ASHRAE Journal200042(10)21e8
[14] BIS Bureau of Indian Standards Handbook of functional requirements of buildings 1997 ISBN81-7061-011-7
[15] Ong KS A mathematical model of a solar chimney Renewable Energy2003281047e60
[16] Duf 1047297e JA Beckmann WA Solar engineering of thermal processes New YorkWiley Interscience ISBN 0-471-05066-0 1980
[17] Ong KS Chow CC Performance of solar chimney Solar Energy 2003741e17[18] VDI Waumlrmeatlas Springer Verlag 1994[19] ASHRAE handbook HVAC systems and equipment chimney gas vent and
1047297replace systems Atlanta GA American Society of Heating Refrigerating andAirconditioning Engineers Inc 2000 pp 301e3011
[20] ASHRAEhandbookfundamentals ductdesign AtlantaGAAmericanSociety of HeatingRefrigeratingand AirconditioningEngineers Inc 2000 pp341e346
[21] Bansal NK Sodha MS Bharadwi SS Performance of earth air tunnels Inter-national Journal of Energy Research 19837(4)333e45
[22] Mathur J Bansal NK Mathur S Jain M Anupma Experimental investigationson solar chimney for room ventilation Solar Energy 200680927e35
[23] Dhaliwal AS Goswami DY Heat transfer analysis in environmental controlusing an underground air tunnel Journal of Solar Energy Engineering1985107141e5
Nomenclature
A area ACH air change per hour (h1)C speci1047297c heat of air (JkgK)c pressure loss coef 1047297cient of 1047297ttingsD gap depth between absorber wall and glass (m)d diameter (m)H distance (m)h convective heat transfer coef 1047297cient (Wm2 K)hr radiative heat transfer coef 1047297cient (Wm2 K)
I total incident solar radiation on south facing inclined surface (Wm 2)k thermal conductivity (Wm K)L length (m)m mass 1047298ow rate of air (kgs)Q heat transfer to air stream (Wm2)R thermal resistance (m2 KW)r radius (m)S solar radiation heat 1047298ux absorbed by plate (Wm2)T temperature (K)t thickness (m)
U overall heat transfer coef 1047297cient (Wm2 K)u air velocity (ms)V volume of room (m3)W width of chimney (m)
xy coordinate system (m) Z height of chimney inlet (m)
Greek symbols
a absorbtion coef 1047297cientb volumetric coef 1047297cient of expansion (K1)g constant in Eqs(9) and(10)d heat penetration depth (m)3 emissivityq anglel thermal diffusivity (m2s)m Dynamic viscosity (kgs m)n Kinematic viscosity (m2s)x friction factor
r density (kgm
3
)s SteffaneBoltzmann constant (567 108Wm2 K4)u frequency of temperature oscillation (rads)
Dimensionless terms
Nu Nusselt number [hf L mf ]Pr Prandtl number [C f mf kf ]Gr Grashof number [ g bf (T T f )L3n 2]Ra Rayleigh number [GrPr]Re Reynolds number [uf dhydnf ]
Subscripts
a ambientabs absorber wallc convective
f air 1047298ow g glasshyd hydraulici internalin inletins insulation
j indexo outletr radius rooms soilsc solar chimneyst inner surface of tubesu undisturbed soilt pipe
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 23242324
7232019 Passive Cooling of Buildings by Using Integrated Earth to Air Heat Exchanger
httpslidepdfcomreaderfullpassive-cooling-of-buildings-by-using-integrated-earth-to-air-heat-exchanger 89
shows the summary of results of the theoretical calculations fordifferent environmental conditions
The buoyancy driving force increases with an increase of solar
intensity and it causes higher ACH Thus less number of SCs are
required to drive the cool and heavy air through the EAHEs and to
compensate the pressure drops The results of calculations also
show that the required number of EAHEs should be increased to
retain the thermal comfort condition when the number of ACH and
indoor air temperature are increased at high solar radiation
The effect of ambient airtemperature on stack effect of SC is vice
versa The stack effect decreases when the ambient outdoor
temperature risesUnder these conditions more numberof SCs willbe required to ventilate the room
The results show that the system can provide the required
indoor temperature and ACH number even at harsh environmental
condition of high temperature of 45 C and low solar radiation of
100 Wm2 If the temperature is higher than 45 C the SC wonrsquot be
able to provide the stack effect and in this condition the use of
a small fan can help the cool air to 1047298ow from EAHE in to the room
and to realize thermal comfort condition
It should be noted that in this system all air 1047298ow is fresh air and
a reduction about 23 C in the inlet air is praiseful achievement of
the present passive cooling system
5 Conclusions
A passive solar system comprises of solar chimneys and earth to
air heat exchangers is proposed and studied in the present paper
The present study shows that the performance of the system
depends on solar radiation outdoor air temperature as well as
con1047297guration of both the SC and the EAHE
The results showed that the number of required SCs decreases
with the use of taller SCs The use of taller SCs lead to thermal
discomfort therefore more number of buried pipes should be
employed to cool air 1047298ow and satisfy the thermal needs
Results of the study on diameter of EAHE show that there is an
optimum diameter for cooling pipes (05 m) which gives the
minimum required number of SCs and EAHEs It has also been
found that the long EAHE with the length of more than 20 m should
be employed to provide the thermal comfort conditionThe results also show that when the ambient temperature and
cooling demand are high although providing thermal comfort is
dif 1047297cult proper con1047297gurations could provide good indoor condi-
tion even in the poor solar intensity of 100 Wm2 and high ambient
air temperature of 50 C
References
[1] Bansal NK Mathur R Bhandari MS A study of solar chimney assisted windtower system for natural ventilation in buildings Building and Environment199429(4)495e500
[2] Gan G Riffat SB A numerical study of solar chimney for natural ventilation of buildings with heat recovery Applied Thermal Engineering 1998181171e87
[3] Hamdy IF Fikry MA Passive solar ventilation Renewable Energy 199814
(1e
4)381e
6
Table 7
Effects of diameter of EAHE on system performance
Cooling
demand (W)
Ambient
air temp (C)
Solar radiation
(Wm2)
Diameter of
EAHE (m)
ACH
d
Room air
temp (C)
Number
of SC
Number
of EAHE
116 40 400 03 430 2996 3 2
05 602 2972 3 2
07 301 2989 3 4
09 476 2998 4 8
116 40 1000 03 507 2770 3 205 649 2872 2 3
07 867 2996 2 4
09 785 2980 2 8
800 40 400 03 Thermal comfort cannot be provided
05 314 2900 3 5
07 443 2986 4 7
09 Thermal comfort cannot be provided
800 40 1000 03 Thermal comfort cannot be provided
05 335 2938 2 6
07 321 2931 2 7
09 371 2994 2 12
Table 8
System performance at different indoor and outdoor conditions
Coolingdemand (W)
Ambient airtemp (C)
Solarradiation
(Wm2)
ACHd
Room airtemp (C)
Numberof SC
Numberof EAHE
500 40 100 328 2961 5 3
500 516 3113 3 3
900 483 3140 2 3
500 45 100 301 3092 6 4
500 430 3112 3 4
900 402 3127 2 4
500 50 100 305 3102 6 6
500 345 3162 3 5
900 306 3152 2 5
1000 40 100 498 3051 8 6
500 410 3195 2 2
900 363 3069 2 4
1000 45 100 415 3000 8 6500 327 3115 3 5
900 300 3090 2 5
1000 50 100 418 3195 8 7
500 305 3198 3 6
900 315 3153 3 12
1500 40 100 520 3136 8 4
500 329 3061 3 5
900 300 3035 2 5
1500 45 100 395 3100 9 9
500 362 3170 4 9
900 317 3160 3 12
1500 50 100
500 Thermal comfort cannot be provided
900
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 2324 2323
7232019 Passive Cooling of Buildings by Using Integrated Earth to Air Heat Exchanger
httpslidepdfcomreaderfullpassive-cooling-of-buildings-by-using-integrated-earth-to-air-heat-exchanger 99
[4] Khedari J Boonsri B Hirunlabh J Ventilation impact of a solar chimney onindoor temperature 1047298uctuation and air change in a school building Energyand Buildings 20003289e93
[5] Mathur J Mathur S Anupma Summer-performance of inclined roof solarchimney for natural ventilation Energy and Buildings 2006381156e63
[6] Bassiouny R Koura NSA An analytical and numerical study of solar chimneyuse for room natural ventilation Energy and Buildings 200840865e73
[7] Hollmuller P Lachal B Cooling and preheating with buried pipe systems moni-toring simulation and economic aspects Energy and Buildings 200133509e18
[8] Santamouris M Mihalakakou G Asimakoupolos D On the coupling of ther-
mostatically controlled buildings with ground and night ventilation passivedissipation techniques Solar Energy 199760(3e4)191e7
[9] Krarti M Kreider JF Analytical model for heat transfer in an underground airtunnel Energy Conversion and Management 199637(10)1561e74
[10] Hollmuller P Analytical characterization of amplitude-dampening and phase-shifting in airsoil heat exchangers International Journal of Heat and MassTransfer 2003464303e17
[11] Al-Ajmi F Loveday DL Hanby VI The cooling potential of eartheair heatexchangers for domestic buildings in a desert climate Building and Environ-ment 200641235e44
[12] Kumar R Kaushik SC Garg SN Heating and cooling potential of an earth-to-airheat exchanger using arti1047297cial neural network Renewable Energy2006311139e55
[13] Brager GS de Dear RJ A standard for natural ventilation ASHRAE Journal200042(10)21e8
[14] BIS Bureau of Indian Standards Handbook of functional requirements of buildings 1997 ISBN81-7061-011-7
[15] Ong KS A mathematical model of a solar chimney Renewable Energy2003281047e60
[16] Duf 1047297e JA Beckmann WA Solar engineering of thermal processes New YorkWiley Interscience ISBN 0-471-05066-0 1980
[17] Ong KS Chow CC Performance of solar chimney Solar Energy 2003741e17[18] VDI Waumlrmeatlas Springer Verlag 1994[19] ASHRAE handbook HVAC systems and equipment chimney gas vent and
1047297replace systems Atlanta GA American Society of Heating Refrigerating andAirconditioning Engineers Inc 2000 pp 301e3011
[20] ASHRAEhandbookfundamentals ductdesign AtlantaGAAmericanSociety of HeatingRefrigeratingand AirconditioningEngineers Inc 2000 pp341e346
[21] Bansal NK Sodha MS Bharadwi SS Performance of earth air tunnels Inter-national Journal of Energy Research 19837(4)333e45
[22] Mathur J Bansal NK Mathur S Jain M Anupma Experimental investigationson solar chimney for room ventilation Solar Energy 200680927e35
[23] Dhaliwal AS Goswami DY Heat transfer analysis in environmental controlusing an underground air tunnel Journal of Solar Energy Engineering1985107141e5
Nomenclature
A area ACH air change per hour (h1)C speci1047297c heat of air (JkgK)c pressure loss coef 1047297cient of 1047297ttingsD gap depth between absorber wall and glass (m)d diameter (m)H distance (m)h convective heat transfer coef 1047297cient (Wm2 K)hr radiative heat transfer coef 1047297cient (Wm2 K)
I total incident solar radiation on south facing inclined surface (Wm 2)k thermal conductivity (Wm K)L length (m)m mass 1047298ow rate of air (kgs)Q heat transfer to air stream (Wm2)R thermal resistance (m2 KW)r radius (m)S solar radiation heat 1047298ux absorbed by plate (Wm2)T temperature (K)t thickness (m)
U overall heat transfer coef 1047297cient (Wm2 K)u air velocity (ms)V volume of room (m3)W width of chimney (m)
xy coordinate system (m) Z height of chimney inlet (m)
Greek symbols
a absorbtion coef 1047297cientb volumetric coef 1047297cient of expansion (K1)g constant in Eqs(9) and(10)d heat penetration depth (m)3 emissivityq anglel thermal diffusivity (m2s)m Dynamic viscosity (kgs m)n Kinematic viscosity (m2s)x friction factor
r density (kgm
3
)s SteffaneBoltzmann constant (567 108Wm2 K4)u frequency of temperature oscillation (rads)
Dimensionless terms
Nu Nusselt number [hf L mf ]Pr Prandtl number [C f mf kf ]Gr Grashof number [ g bf (T T f )L3n 2]Ra Rayleigh number [GrPr]Re Reynolds number [uf dhydnf ]
Subscripts
a ambientabs absorber wallc convective
f air 1047298ow g glasshyd hydraulici internalin inletins insulation
j indexo outletr radius rooms soilsc solar chimneyst inner surface of tubesu undisturbed soilt pipe
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 23242324
7232019 Passive Cooling of Buildings by Using Integrated Earth to Air Heat Exchanger
httpslidepdfcomreaderfullpassive-cooling-of-buildings-by-using-integrated-earth-to-air-heat-exchanger 99
[4] Khedari J Boonsri B Hirunlabh J Ventilation impact of a solar chimney onindoor temperature 1047298uctuation and air change in a school building Energyand Buildings 20003289e93
[5] Mathur J Mathur S Anupma Summer-performance of inclined roof solarchimney for natural ventilation Energy and Buildings 2006381156e63
[6] Bassiouny R Koura NSA An analytical and numerical study of solar chimneyuse for room natural ventilation Energy and Buildings 200840865e73
[7] Hollmuller P Lachal B Cooling and preheating with buried pipe systems moni-toring simulation and economic aspects Energy and Buildings 200133509e18
[8] Santamouris M Mihalakakou G Asimakoupolos D On the coupling of ther-
mostatically controlled buildings with ground and night ventilation passivedissipation techniques Solar Energy 199760(3e4)191e7
[9] Krarti M Kreider JF Analytical model for heat transfer in an underground airtunnel Energy Conversion and Management 199637(10)1561e74
[10] Hollmuller P Analytical characterization of amplitude-dampening and phase-shifting in airsoil heat exchangers International Journal of Heat and MassTransfer 2003464303e17
[11] Al-Ajmi F Loveday DL Hanby VI The cooling potential of eartheair heatexchangers for domestic buildings in a desert climate Building and Environ-ment 200641235e44
[12] Kumar R Kaushik SC Garg SN Heating and cooling potential of an earth-to-airheat exchanger using arti1047297cial neural network Renewable Energy2006311139e55
[13] Brager GS de Dear RJ A standard for natural ventilation ASHRAE Journal200042(10)21e8
[14] BIS Bureau of Indian Standards Handbook of functional requirements of buildings 1997 ISBN81-7061-011-7
[15] Ong KS A mathematical model of a solar chimney Renewable Energy2003281047e60
[16] Duf 1047297e JA Beckmann WA Solar engineering of thermal processes New YorkWiley Interscience ISBN 0-471-05066-0 1980
[17] Ong KS Chow CC Performance of solar chimney Solar Energy 2003741e17[18] VDI Waumlrmeatlas Springer Verlag 1994[19] ASHRAE handbook HVAC systems and equipment chimney gas vent and
1047297replace systems Atlanta GA American Society of Heating Refrigerating andAirconditioning Engineers Inc 2000 pp 301e3011
[20] ASHRAEhandbookfundamentals ductdesign AtlantaGAAmericanSociety of HeatingRefrigeratingand AirconditioningEngineers Inc 2000 pp341e346
[21] Bansal NK Sodha MS Bharadwi SS Performance of earth air tunnels Inter-national Journal of Energy Research 19837(4)333e45
[22] Mathur J Bansal NK Mathur S Jain M Anupma Experimental investigationson solar chimney for room ventilation Solar Energy 200680927e35
[23] Dhaliwal AS Goswami DY Heat transfer analysis in environmental controlusing an underground air tunnel Journal of Solar Energy Engineering1985107141e5
Nomenclature
A area ACH air change per hour (h1)C speci1047297c heat of air (JkgK)c pressure loss coef 1047297cient of 1047297ttingsD gap depth between absorber wall and glass (m)d diameter (m)H distance (m)h convective heat transfer coef 1047297cient (Wm2 K)hr radiative heat transfer coef 1047297cient (Wm2 K)
I total incident solar radiation on south facing inclined surface (Wm 2)k thermal conductivity (Wm K)L length (m)m mass 1047298ow rate of air (kgs)Q heat transfer to air stream (Wm2)R thermal resistance (m2 KW)r radius (m)S solar radiation heat 1047298ux absorbed by plate (Wm2)T temperature (K)t thickness (m)
U overall heat transfer coef 1047297cient (Wm2 K)u air velocity (ms)V volume of room (m3)W width of chimney (m)
xy coordinate system (m) Z height of chimney inlet (m)
Greek symbols
a absorbtion coef 1047297cientb volumetric coef 1047297cient of expansion (K1)g constant in Eqs(9) and(10)d heat penetration depth (m)3 emissivityq anglel thermal diffusivity (m2s)m Dynamic viscosity (kgs m)n Kinematic viscosity (m2s)x friction factor
r density (kgm
3
)s SteffaneBoltzmann constant (567 108Wm2 K4)u frequency of temperature oscillation (rads)
Dimensionless terms
Nu Nusselt number [hf L mf ]Pr Prandtl number [C f mf kf ]Gr Grashof number [ g bf (T T f )L3n 2]Ra Rayleigh number [GrPr]Re Reynolds number [uf dhydnf ]
Subscripts
a ambientabs absorber wallc convective
f air 1047298ow g glasshyd hydraulici internalin inletins insulation
j indexo outletr radius rooms soilsc solar chimneyst inner surface of tubesu undisturbed soilt pipe
M Maerefat AP Haghighi Renewable Energy 35 (2010) 2316 e 23242324