2005-Developing a Theoretical Model to Investigate Thermal Performance of a Thin HP

8/2/2019 2005-Developing a Theoretical Model to Investigate Thermal Performance of a Thin HP

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Developing a theoretical model to investigate thermal

performance of a thin membrane heat-pipe solar collector

S.B. Riffat, X. Zhao *, P.S. Doherty

School of the Built Environment, The University of Nottingham, Nottingham, NG7 2RD, UK

Received 17 September 2003; accepted 7 August 2004

Abstract

A thin membrane heat-pipe solar collector was designed and constructed to allow heat from solar radi-

ation to be collected at a relatively high efficiency while keeping the capital cost low. A theoretical model

incorporating a set of heat balance equations was developed to analyse heat transfer processes occurring in

separate regions of the collector, i.e., the top cover, absorber and condenser/manifold areas, and examine

their relationship. The thermal performance of the collector was investigated using the theoretical model.The modelling predictions were validated using the experimental data from a referred source. The test effi-

ciency was found to be in the range 4070%, which is a bitter lower than the values predicted by modelling.

The factors influencing these results were investigated.

2004 Elsevier Ltd. All rights reserved.

Keywords: Heat pipes; Solar collector; Thin; Membrane; Efficiency; Testing; Simulation

1. Introduction

Solar collectors transform solar radiation into thermal energy. There are several types of solarcollector available for practical applications, including evacuated tubes, flat plate solar collectors

and parabolic dish collectors.

1359-4311/$ - see front matter 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.applthermaleng.2004.08.010

* Corresponding author. Tel.: +44 115 846 7873; fax: +44 115 951 3159.

E-mail address: [email protected] (X. Zhao).

www.elsevier.com/locate/apthermeng

Applied Thermal Engineering 25 (2005) 899915
mailto:[email protected]:[email protected]


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Nomenclature

A area (m2

)Cp specific heat (J/kg C)d diameter (m)Fv frictional resistance coefficient of the vapour flow in the heat pipe

h convection heat transfer coefficient (W/m2C)In global solar irradiation (W/m

2)k thermal conductivity (W/mC)V volume flow rate (m3/s)L length (m)m mass flow rate (kg/s)n number of the heat pipes includedNu Nusselt numberPr Prandtl numberQ heat (W)r radius (m)R heat resistance (m2C/W)t temperature (C)x general external parameterd thickness (m)q density of air (kg/m3)g collector thermal efficiencyterm 1

g collector thermal efficiencyterm 2

Subscripts

a ambientab absorber

abs absorptionadia adiabatic section

av averagecl cooling liquidcon condenser

cond condensation sectiondw downside walleq equivalent

evap evaporation sectionhp heat pipehy hydraulic

i insideinc incident radiation

ins insulation layer

900 S.B. Riffat et al. / Applied Thermal Engineering 25 (2005) 899915


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Heat pipes are devices of high thermal conductance, which transfer thermal energy by two-phase circulation of fluid, and can easily be integrated into most types of solar collector. The basic

difference in thermal performance between a heat-pipe solar collector and a conventional one liesin the heat-transfer processes from the absorber tube wall to the energy-transporting fluid. In the

case with a heat pipe, the process is evaporationcondensationconvection, while for conventionalsolar collectors, heat transfer occurs only in the absorber plate. Thus, solar collectors with heat

pipes have a lower thermal mass, resulting in a reduction of start-up time.A feature that makes heat pipes an attractive for use in solar collectors is their ability to operate

like a thermal-diode, i.e., the flow of the heat is in one direction only. This minimizes heat loss

from the transporting fluid, e.g., water, when incident radiation is low. Furthermore, when themaximum design temperature of the collector is reached, additional heat transfer can be pre-vented. This would prevent over-heating of the circulating fluid, a common problem in manyapplications of solar collectors [3,6].

One of the first studies of heat pipes in solar applications was carried out by Bienert and Wol[3]. In this case, the evaporator end of a heat pipe was inserted in a flat-plate collector, and the

condenser protruded into a water manifold attached to the upper end of the collector. The resultsof this investigation were neither conclusive nor optimistic. Since then, numerous studies have

been carried out, including theoretical analysis and calculation [10,19,17,11], experimental testing[1,21,20,26,29,8,22], combined investigation involving theoretical analysis and experimental trials[9,12,13,15,16], as well as applications in practice [4,2,5,18]. Most of these studies involved the

investigation of the thermal performance of various types of heat-pipe solar collectors by analyt-ical, numerical or experimental methods with the aim of establishing suitable structures or systemlayouts, as well as optimum operating conditions for high efficiency.

Of the existing collector designs, evacuated tube and flat-plate collectors are most widely used,and the former is usually found to be more efficient for high temperature applications. Flat-plate

heat-pipe solar collectors, on the other hand, have their own set of advantages, including simplerstructure, lower cost, easier manufacture and simple operation.The lower efficiency of flat-plate collectors is mainly due to the heat loss via the cover surface

due to conduction and convection. Standard flat-plate collectors have typical efficiencies of 50%or less [22], while evacuated devices have efficiencies of about 5080% [21,20,29]. It would be desir-able to develop a new structure for flat plate collectors that would overcome heat loss problems

and allow a high efficiency to be achieved, while its capital cost still remains low.This paper introduces a novel flat plate heat pipe solar collector, termed as thin membrane heat

pipe solar collector. This collector is expected to achieve a higher efficiency, but with relativelylower capital cost, compared to normal flat plat heat pipe solar collectors. One prototype of such

lim limit

max maximum

o outsideref reflectiontc top covertra transmission

S.B. Riffat et al. / Applied Thermal Engineering 25 (2005) 899915 901


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kind of collector was constructed, and an analytical model that is able to simulate heat transfer

processes occurring in the collector and calculate its efficiency, was developed based at the proto-type structure. The model applied heat balance and heat resistance network method, which is a

new approach in collector thermal performance analyses. Simulation on the performance of thecollector was carried out, and the results were used to estimate its efficiency and determine the

relation between efficiency and general external parameter, (tmean ta)/In.

2. Prototype set-up

A prototype thin membrane heat-pipe solar collector was designed to collect and distribute heat

by means of vaporisation and condensation of a heat transfer fluid. It comprised mainly of anevacuated housing containing an absorber, a reservoir at the lower end of the collector and a con-

denser panel on the top end of the collector. A micro-pore insulation material, attained with analuminium/foam plastic tray, was fitted beneath the absorber panel to reduce downward heat loss.A clear acrylic cover was mounted on the top of the evacuated housing, creating an enclosed space

where a vacuum could be maintained to eliminate convection/conduction heat loss. Fig. 1 showsschematically the structure of such a prototype collector [23].

The main body of the collector comprised two plates separated by a thin evaporation gap.The plates were spot welded together creating mini-channels (ribs) running parallel across thewidth of the absorber, as shown in Fig. 2. Each mini-channel was considered to be a single

Fig. 1. Schematic diagram of the normal thin membrane heat pipe solar collector.



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miniature heat pipe, as has previously been investigated by Riffat et al. [24] using an analyt-ical and numerical model. The miniature heat pipes connected the evaporation section to the

condensation section of the collector to enable the flow of vapour refrigerant and condensedliquid refrigerant.

In this collector, the absorber comprised 22 mini-channels (ribs). The previous analytical

investigation showed such a single pipe had a heat transport capacity of 50W when it was oper-

ated at 80 C and installed with the inclination of 60 relative to the horizontal. Thus the wholepanel would have an overall heat transport capacity of 1100W, which is much higher than the

actual solar input (


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3. Analytical model set-up

The analytical model focused on heat transfer problems existed in the prototype heat pipe solarcollector. In fact, heat transfers exist in three major parts of the collector prototype, i.e., the topcover, the absorber (evaporator plate) and the condenser/manifold, as shown schematically in

Fig. 4. These heat transfers finally achieve balance themselves and are inter-linked by a distributed

Table 2

Parameters of the heat pipes and absorber panel

Absorpvity of absorber surface, aab 0.95 Thermal conductivity of bottom

plate, kdw, W/mK

0.0015

Reflectivity of absorber surface, refab 0.05 Thickness of bottom plate, ddw, m 0.0015

Emmitance of absorber surface, eab 0.1 Number of heat pipes 22

Absorber area, Aab 0.24 Equivalent diameter of

heat pipe (inner) dhp, m

0.002

Unshaded absorber area, Aab,r 0.233 Length of evaporator levap, m 1

Heat resistance of top cover

inner surface, Rtc,i, m2. K/W

0.12 Length of condenser lcon, m 0.1

Heat resistance of top cover

outer surface, Rtc,o, m2. K/W

0.06 Thermal conductivity of

heat pipe wall, khp, W/mK

43

Thermal conductivity of insulation

layer 1, kins1, W/mK

0.005 Thickness of heat pipe wall, dhp, m 0.001

Thickness of insulation

layer 1, dins1, m

0.025 Thermal conductivity of liquid film

on heat pipe inner wall, Kw, W/m K

0.68

Thermal conductivity of insulation

layer 2, kins2, W/mK

0.046 Equivalent diameter of vapour

column in evaporator dvap,evap, m

0.00196

Thickness of insulation

layer 2, dins2, m

0.005 Equivalent diameter of vapour

column in condenser dvap,con, m

0.0019

Fig. 3. The prototype thin membrane heat-pipe solar collector.



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temperature profile. In the modelling development, a few assumptions were made in order to sim-plify solution solving process, including:

A steady state condition has achieved and heat balance exists in each component and wholearea of the collector prototype.

The absorber has uniform temperature distribution over its surface area, supposed that a uni-

form heat input is exerted onto it.

There is no heat loss on the edge area of the absorber where the top cover and the bottomchamber are covered, due to a good insulation applied.

3.1. Heat transfer process in the top cover

For a given collector area and total solar irradiation, the heat striking the top cover surface ispart absorbed by the cover, part transmitting through the cover and reaching the absorber, andthe remaining is reflected to atmosphere. This heat transfer process can be expressed as

Qinc Qabc Qref Qtra 1

The absorbed heat will be dispersed to the surroundings or (and) absorber by ways of convection,conduction or radiation, to achieve a heat balance relative to the top cover. This balance may beexpressed as

Qabc Qtcab Qtca 2

Heat dissipation to the surroundings occurs mainly by the combined effect of conduction and con-vection. However, Heat transfer between the top cover and absorber may be complex. If the ab-sorber chamber were perfectly evacuated, heat transfer between the top cover and absorber would

only be induced by radiation. If the chamber were not evacuated, heat transfer between the topcover and the absorber will be a combined effect of conduction, convection and radiation.

Fig. 4. Schematic diagram showing relation of heat balances in different parts of a solar collector.



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The above items, i.e., Qabc, Qref, Qtra, Qtcab and Qtca, can be calculated using basic heat radi-

ation & convection equations given by Yang and Tao [28].

3.2. Heat transfer process in the absorber (evaporator) plate

Part of the heat reaching the absorber plate will be transferred to the working fluid through theminiature heat pipes formed by the spot welded flat plates, and this will cause the liquid to vapor-

ise. This is therefore termed the effective heat input. The remainder will be dispersed to the envi-ronment through the top cover and bottom casings, resulting in heat losses due to conduction,convection and radiation.

The heat losses include upward and downward losses. The upward loss refers to heat transferbetween the absorber and the top cover, which has been mentioned in Eq. (2), and the downward

loss can be expressed as

Qdwa Aabtab ta=dab=kab dins=kins ddw=kdw 1=ha 3

There are temperature differentials in the absorber area, which result in heat transmission fromthe plate area to the channels, or from one part to another part of the plate area. However, thesedifferentials are small as the plate and channels are made into an integrated body using stainless

steel, a good heat conductor. In order to simplify the thermal analysis, the differentials are con-sidered to be negligible and thus the absorber surface is assumed to be at the same temperature

over the whole area.In this situation, actual heat obtained by the absorber (evaporator) plate is then expressed

as

Qab Qtra Qabtc Qdwa 4

The heat obtained should be transferred to the heat pipes, causing evaporation of the operatingfluid inside the pipes. However, if the heat transport capacity of the heat pipes is not large enough

to transport such an amount of heat, then part of the heat will be dispersed to the surroundingsvia the top cover and the metal surface of the chamber, resulting in a change of temperature overthe absorber area.

To investigate the heat transfer of a heat pipe solar collector, it is necessary to determine its heattransport limitation. The limit of the heat transport capacity for a single heat pipe may be deter-

mined using the analytical model developed by Riffat et al. [24]. The maximum heat transportcapacity of the collector may then be obtained as

Qmax nQlim 5

Where n is the number of heat pipes included. IfQab is less than Qmax, then the heat obtained willbe transported without any restriction. However, if Qmax is less than Qab, then part of the ob-

tained heat will be dispersed to the surroundings, resulting in reduced heat transportation fromthe absorber to condenser. In this case, the temperature of the absorber surface would be adjusted

automatically until a new thermo-equilibrium is achieved.



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3.3. Heat transfer processes in the condensers and manifold

The heat obtained from the absorber, Qab, will be transported to the cooling fluid passing

across manifold through evaporation and condensation of the working fluid in the heat pipes.There are several heat resistances in this process, namely, the evaporator wall resistance, the

equivalent resistance of the working fluid and wick in the evaporator, the vapour flow resistance,the equivalent resistance of the working fluid and wick in the condenser, and the condenser wallresistance. These resistances can be calculated using the equations given by Dunn and Reay [7].

The total resistance would be the sum of the individual resistances.For a single heat pipe, heat transportation from the evaporator outer surface to the condenser

outer surface may be written as

Qhp;i pr2hpthp;evap thp;cond=Rhp 6

The heat will be transferred to the cooling liquid by heat conduction through the manifold wall,and heat convection between the manifold wall and the cooling liquid. The cooling liquid will beheated when flowing through the manifold channel, which is tightly fixed to the heat pipe con-

densers. For an inlet temperature given as t0, a temperature increase Dt1, (t1 t0), will be achievedafter the fluid passes around the first heat pipe due to heat absorption from the pipe. The fluid

temperature increases gradually along the flow direction due to continuous heat transfer fromthe parallel-array of heat pipes. The heat transfer between a single heat pipe and the cooling liquidmay be expressed as

Qcon;i Acon;ithp;cond ti1 ti=2

dcon

kcon

1

hcl

Cp;clmclti ti1 Qhp;i 7

hcl is the convective heat transfer coefficient of the cooling fluid, which is largely dependent on the

velocity of fluid passing over the surface, and the cross-sectional area, as well as the geometry ofthe flow channel. For the collector indicated above, the flow of the cooling liquid flow and the

manifold geometry are shown schematically in Fig. 5. The flow may be treated as half of the annu-lar flow. To solve for the convective heat transfer coefficient, hcon, the channel needs to be treatedas an annular geometry rather than a semi-annular one, and correspondingly, heat flow from the

inner wall needs to be doubled to comply with this treatment. Heat transfer through the outerwalls was negligible as a satisfactory insulation was provided. For both situations, calculationof hcl could be carried out using the annular flow model [14], as shown schematically in Fig. 6.

Nucl hclDhy;conkcon

8

Dhy;con Do;con Di;con 9

Di,con is the hydraulic diameter of the internal wall of the flow channel, and Do,con is that of theexternal wall of the flow channel. For the situation shown in Fig. 6, If b > (a2 a1), then:

Do;con a2

Di;con a1



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However, if b/(a2 a1) < 10 then:

Di;con 2a1b

a1 b

Do;con 2a2b

a2 b

Cooling liquid flow in the manifold is fully developed laminar flow, which has a Reynolds numberless than 400 due to its very low velocity and the relatively large cross-sectional area. For this case,Nuo may be obtained from Table 3 [14].

For a single heat pipe, given the inlet temperature ti1, the outlet temperature ti may be ob-tained by solving Eq. (7). For the whole condenser/manifold configuration, the overall heat trans-fer may be expressed as

Qcon Qcon;1 Qcon;2 Qcon;n Cp;clmcltn t0 10

Cooling fluid

Manifold

Heat pipe

panel

b

a2

a1

Fig. 5. Schematic diagram showing cooling liquid flow and manifold geometry in the thin membrane heat pipe solar

collector.

Qe

Di

Do

Fig. 6. Annular channel flow model.



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Qcon should be equal to Qob according to the principle of heat balance. Eqs. (6)(10) may be usedto obtain solutions for the outlet temperature and the mean temperature of the cooling water, aswell as the temperatures in different parts of the heat pipe panel.

3.4. Numerical procedure

The three heat processes described above are actually inter-linked by a well-developedtemperature layout. The numerical procedure used for the solution solving is indicated asfollows:

1. Given the collector configuration, geometrical and thermodynamic parameters of the collectorunit are determined;

2. Given the incident radiation and ambient temperature, the heat striking the absorber is

determined.3. Given the manifold configuration, as well as the cooling liquid flow condition, geometrical,

thermodynamic and flow parameters of the cooling fluid are determined;

4. Assuming an absorber temperature ts, heat analysis is carried out as follows: Heat balance of the top cover may be analysed using Eqs. (1) and (2), which results in solu-

tion solving of the inner surface temperature of top cover tci. Heat balance of the absorber (evaporator) plate may be analysed using Eqs. (3)(5), which

results in solution solving of the absorber heat gain, Qobt.

Heat balance of the heat pipes, and condenser/manifold pair may be analysed using Eqs.(6)(10), which results in solution solving of the heat gain of the cooling water passing

through the manifold, as well as the temperature layout in different areas of collector.5. If (Qobt Qcon)/Qobt > 0.5% (error allowance), then increase ts by 0.1C, and return to step 4for re-calculation.

6. If (Qobt Qcon)/Qobt < 0.5% (error allowance), then decrease ts by 0.1C, and return to step4 for a re-calculation.

7. If0.5% (Qobt Qcon)/Qobt 0.5%, heat balances in the whole system, as well as differentareas of the system, are achieved.

8. The cooling water temperature at the outlet and different points along the flow channel, as wellas the temperatures at different areas of the collector, may be calculated.

9. Program stops.

Table 3

Nusselt number

Di/Do Nuo

0 3.66

0.05 4.06

0.10 4.11

0.25 4.23

0.50 4.43

1.00 4.86



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4. Results and discussion

4.1. Efficiency calculation

The data obtained by running the computer program described in Section 3 could be used to

evaluate the thermal performance of a solar collector. For a solar collector, its performance is usu-ally evaluated using efficiency g, which is defined as the ratio of heat taken from the manifold bythe cooling liquid and the incident irradiation striking the collector absorber. g varies with a num-

ber of external parameters, including global solar irradiation In, ambient temperature ta, as well ascooling fluid inlet temperature t0 and mass flow rate m. These parameters may be grouped by aspecially-defined parameter, termed (tmean ta)/In, whereby tmean is the average temperature ofthe cooling fluid and may be written as

tmean

t0 tn

2 11

g is usually expressed as the function of (tmean ta)/In, as follows:

g g0 a1tmean ta

In

12

where g0,a1 are the collector character parameters.

4.2. Simulation results

Simulation was carried out for the thin membrane heat pipe solar collector by assuming a cer-

tain operating parameters. The assumed parameters were coincident with the actual testing con-ditions in order to facilitate comparison between theoretical and experimental results, as shown inTable 4.

g(tmean ta)/In relations for the collector with/without evacuation treatment were investigatedusing the computer model developed, and the results are shown in Fig. 7. It was found that thesingle acrylic with an un-evacuated chamber has the much lower efficiency (6238%) than the

evacuated case (7568%). For the both cases, g decreased while (tmean ta)/In increased. The rela-tion ofg and (tmean ta)/In was approximately linear.

4.3. Experimental results

The prototype collector was tested at the laboratory of Fraunhofer Institute for Solar EnergySystem (ISE) in Germany, by complying with the European Standard of prEN 12975: 1999 [25].

Table 4

Summary of the external parameters

In, W/m2 1033 1033 1027 998 1031 949 962 968

ta, C 19.1 19.9 20.3 21.3 22.5 17.7 18.3 18.9

Mcl, kg/h 30.1 30 30 30.1 30.1 30.1 30.2 30

tin,cl, C 17.1 17.2 17.4 54.9 55.0 79.4 79.5 79.7



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The collector had a gross area of 0.4m2, of which 0.255m2 was the absorber area, and the rest wasthe condensation area. The absorber area was not completely utilised because of the edge effect,

and the un-shadowed area was only 0.233m2.

An outdoor climate was created in the laboratory. The wind speed was measured at the middlearea of the collector module, 5cm above the transparent cover, and adjusted to 3m/s using a ven-

tilator. Optical bulbs were scatter-distributed at the dome area to simulate the global solarirradiation.

Water was used as the cooling liquid, and passed through the collector manifold at a rate of

30kg/h during the test period.Test conditions and results were summarised in Table 5. The efficiencies were calculated using

the results obtained, and are shown in Fig. 8. The characteristic parameters indicating the collec-tor performance are given as: g0 = 0.70094; a1 = 4.604.

4.4. Comparison of the modelling and experimental results

Comparison was carried out between the modelling and experimental results for the thin mem-brane heat-pipe solar collector. The results of these comparisons are summarised in Fig. 9. It wasfound that the experimental efficiencies were lower than the predicted results for the evacuatedcase, but higher than those for the case of the single acrylic cover with an un-evacuated cham-

ber. The reason for this was investigated, and it was found that the evacuation of the chamberwas not well processed. This resulted in reduced efficiencies compared to the modelling results

because the theoretical analysis assumed that the chamber was completely evacuated. The topcover was deformed during processing an evacuation and to recover its shape, the chamber

Efficiency - (tmean -ta)/In relation - Comparison of different covers

30

35

40

45

50

55

60

65

70

75

80

-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

(tmean-ta)/In,oC.m

2/W

Efficiency,

%

Evacuated chamber

Un-evacuated chamber

Fig. 7. g(tmean ta)/In relationsimulation results.



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was filled with an inert gas, argon, after evacuation. Filling resulted in reduced efficiencies com-pared to the evacuated treatment, but still provide higher efficiency values than the un-evacuatedor un-filled cases.

5. Conclusions

A thin membrane heat-pipe solar collector was designed and constructed. The collector com-prised of two sheets of stainless steel spot welded along the length and parallel-arrayed at the

Table 5

Test results for the thin membrane heat pipe solar collector

In,

W/m2

Idiffuse,

W/m2

ta,

C

mcl,

kg/h

tin,cl,

C

tout,cl,

C

tout,cl tin,cl,

C

tmean,

C

(tmean ta)/In,

C m2

/W

g

1033 85 19.1 30.1 17.1 21.8 4.7 19.5 0.0003 0.6847

1033 87 19.9 30 17.2 22.1 4.9 19.7 0.0002 0.70731027 90 20.3 30 17.4 22.2 4.8 19.8 0.0005 0.7006998 121 21.3 30.1 54.9 58.6 3.7 56.7 0.0335 0.5561

1031 135 22.5 30.1 55 58.8 3.8 56.9 0.0333 0.5578

949 110 17.7 30.1 79.4 81.8 2.4 80.6 0.0663 0.3869

962 109 18.3 30.2 79.5 82.1 2.5 80.8 0.0649 0.3944

968 110 18.9 30 79.7 82.3 2.6 81.0 0.0642 0.4040

0

10

20

30

40

50

60

70

80

-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

(tmean-ta)/In,oC.m

2/W

Efficiency,

%

Efficiency - (tmean-ta)/Inrelation - test results

y = -460.4x + 70.094

R2 =0.9926

Fig. 8. g(tmean ta)/In relationtest results.



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width, creating mini-channels (ribs) running parallel along the width of the absorber. These were

termed miniature heat pipes. This design would reduce the capital cost of the heat pipe panelcompared to normal, flat-plate heat-pipe solar collectors. Furthermore, since the space betweenthe top cover and absorber plate was evacuated, or filled with an inert gas, the efficiency of this

type of collector was expected to be high.A theoretical model was developed to analyse the heat transfer occurring in the collector. The

heat processes in different areas of the collectors were investigated, and these were linked by a setof heat balance equations.

The thermal performance of the thin membrane heat-pipe solar collector was investigated using

the computer model developed. The simulation results were used to determine the collector effi-ciency g, which is defined as the ratio of heat taken from the manifold by the cooling liquid

and the incident irradiation striking the collector absorber. It was found that the efficiency varieswith the external conditions, i.e., global solar irradiation In, ambient temperature ta, as well ascooling fluid inlet temperature t0 and mass flow rate m, for the given collector structure. The exter-

nal conditions can be grouped by an item specified as (tmean ta)/In. Overall, g was found to de-crease with increasing of (tmean ta)/In. The relationship can be expressed by linear equations.

The modelling predictions were validated using the experimental data from a referred source.

The test efficiency was found to be in the range of 40%70%, which is lower than the values pre-dicted by modelling for the evacuated case, but higher than the values predicted for the case of asingle glass cover with an un-evacuated chamber. The reason for this was that the chamber was

filled with an inert gas, argon, after being evacuated, and this has a larger heat resistance than air,

0

10

20

30

40

50

60

70

80

-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Efficiency,

%

Comparison of testing and modelling results -

the thin membrane heat pipe solar collector

(tmean-ta)/In,oC.m2/W

single glass, unevacuated chamber

evacuated chamber

testing

Fig. 9. Comparison of testing and modelling results.



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but still gave rise to an extra conductive or/and convective heat loss compared to the evacuated

situation. This treatment was not taken into account in modelling development and processing.

Acknowledgment

The authors would like to acknowledge the financial support provided for this research by theEuropean Commission, under the Joule Craft Programme.

References

[1] R. Bairamov, K. Toiliev, Heat pipe in solar collectors, in: D.A. Ray (Ed.), Advances in Heat Pipe Technology,

Pergamon Press, Oxford, 1981.

[2] A. Balzar et al., A solar cooker using vacuum-tube collectors with integrated heat pipes, Solar Energy 58 (1996)

6368.

[3] W.B. Bienert, D.A. Wolf, Heat pipe applied to flat-plate solar collectors, Final Report COO/2604-76/1, 1976.

[4] T.Y. Bong et al., Thermal performance of a flat-plate heat pipe collector array, Solar Energy 50 (6) (1993) 491

498.

[5] W. Chun et al., An experimental study of the utilization of heat pipes for solar water heaters, Applied Thermal

Engineering 19 (1999) 807817.

[6] H.F.W. DeVriers, W. Kamminga, J.C. Franken, Fluid circulation control in conventional and heat pipe planar

solar collectors, Solar Energy 24 (1980) 209213.

[7] P.D. Dunn, D.A. Reay, Heat pipes, third ed., Pergamon Press, New York, 1982.

[8] M.A. El-nasr et al., Performance of a wickless heat pipe solar collector, Energy Source 15 (1993) 513522.

[9] D.M. Ernst, Cost-effective solar collectors using heat pipes, Final Technical Report, DOE/CS/34099-4, 1981.

[10] R.D. Franken, in: Proc. ISES. New Delhi, 1979, pp. 885.[11] H.M.S. Hussein, et al., Optimisation of a wickless heat pipe flat plate solar collector, Energy Converstion and

Management 40 (1999) 19491961.

[12] K.A.R. Ismail, M.M. Abogderah, Comparative study between flat plate solar collector with heat pipes and

commercial conventional unit, IV congresso latino americano de transferencia de calor y material, La Serena,

Chile, 1991, pp. 229332.

[13] K.A.R. Ismail, M.M. Abogderah, Thermal and numerical analysis of heat pipe solar collector, in: Proceedings of

the Second Renewable Energy Congress, Reading, UK, vol. 2, 1992, pp. 862866.

[14] P. Incropera Frank, P. De Witt David, Fundamentals of Heat and Mass Transfer, third ed., John Wiley & Sons,

Inc., Singapore, 1997, pp. 502503.

[15] K.A.R. Ismail, M.M. Abogderah, Residential solar collector with heat pipes, 8th Heat Pipe Conference, Beijing,

China, 1992, pp. 531534.

[16] K.A.R. Ismail, M.M. Abogderah, Performance of a heat pipe solar collector, Journal of Solar Energy Engineering

120 (1998) 5159.

[17] W.D. Lu, H.F. Guo, Performance of a gravity assisted heat pipe solar collector, International Journal of Solar

Energy 3 (1984) 111.

[18] E. Mathioulakis et al., A new heat-pipe type solar domestic hot water system, Solar Energy 72 (1) (2002) 1320.

[19] U. Ortabasi, F. Fehlner, Cusp mirror-heat-pipe evacuated tubular solar thermal collector, Solar Energy 24 (1979)

477489.

[20] J.W. Ramsey, Experimental evaluation of a cylindrical parabolic solar collector. ASME paper 76-WA/HT-13 8,

1986.

[21] J. Ribot, R.D. McConnell, Testing and analysis of a heat pipe solar collector, ASME Journal of Solar Energy

Engineering 105 (1983) 440445.



17/17

[22] S.B. Riffat, P.S. Doherty, E.I. Abdel Aziz, Performance testing of different types of liquid flat plate collectors,

International Journal of Energy Research 24 (2000) 12031215.

[23] S.B. Riffat, X. Zhao, P.S. Doherty, Structure optimisation and performance simulation of a novel thin membrane

heat pipe solar collector using a mathematical model, International Journal of Ambient Energy 23 (1) (2002) 316.[24] S.B. Riffat, X. Zhao, P.S. Doherty, Analytical and numerical simulation of the thermal performance of mini

gravitational and micro gravitational heat pipes, Applied Thermal Engineering 22 (2002) 10471068.

[25] Rommel Matthias, Tests of the thin membrane heat pipe solar collector, Fraunhofer Institut Solare Energies-

ysteme, November 2000.

[26] M. Terpstra, J. Van Veen, Heat Pipes: Construction and Application. A Study of Patents and Patent Applications,

Elsevier Applied Science, New York, 1987.

[27] W.K.A. Yagoub, A review of coating materials for a novel membrane heat pipe solar panel, Report to project

coordinator, University of Nottingham, May 1999.

[28] S. Yang, W. Tao, in: Heat Transfer, China High Education Press, Beijing, China, 1998, pp. 162165.

[29] M.A. Zanardi, Numerical and experimental analysis of a cylindrical parabolic solar collector with a heat pipe.

Ph.D dissertation, Department of Mechanical Engineering, Campinas State University, Brazil, 1989.

[30] X. Zhao, Investigation of a Novel Heat Pipe Solar Collector/CHP System, Ph.D thesis, The University of

Nottingham, UK, 2003, pp. 4762.


Documents

2005-Developing a Theoretical Model to Investigate Thermal Performance of a Thin HP