Comparative Study of the Performances of Four Photovoltaic-Thermal Solar Air Collectors

Comparative study of the performances of fourphotovoltaic/thermal solar air collectors

Adel A. Hegazy*

Mechanical Power Engineering and Energy Department, Faculty of Engineering, Minia University, Minia-61517, Egypt

Received 5 January 1999; accepted 17 August 1999

Abstract

An extensive investigation of the thermal, electrical, hydraulic and overall performances of flat platephotovoltaic/thermal (PV/T) air collectors has been made. Four popular designs are considered with theair flowing either over the absorber (Model I) or under it (Model II) and on both sides of the absorberin a single pass (Model III) or in a double pass fashion (Model IV). Heat balance equations are writtenfor each model and are numerically solved, incorporating measured climate data. The eects of airspecific flow rate and the selectivity of the absorber plate and PV cells on the performances have beenexamined. It is found that under similar operational conditions, the Model I collector has the lowestperformance, while the other models exhibit comparable thermal and electrical output gains.Nevertheless, the Model III collector demands the least fan power, followed by Models IV and II. It isalso shown that selective properties are inappropriate for these PV/T collectors due to the resultantreduction in the generated PV energy, especially at low flow rates. The study provides valuableinformation regarding the design and operation of such types of PV/T air collectors. # 2000 ElsevierScience Ltd. All rights reserved.

Keywords: Hybrid air collector; Flat PV modules system; Stand alone solar air heater; Performance analysis

1. Introduction

Solar energy is the cheapest source of energy available in the developing countries which are

Energy Conversion & Management 41 (2000) 861881

0196-8904/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.PII: S0196-8904(99)00136-3

www.elsevier.com/locate/enconman

* Tel.: +20-86-362083, ext. 237; fax: +20-86-346674.E-mail address: [email protected] (A.A. Hegazy).

Nomenclature

A area, m2

cp air specific heat, J/kg KD depth of air channel, mDh hydraulic diameter=4 flow area/p, mE electrical energy, Wf friction factorF packing factor=Ac/ApG specific mass rate=m

./Ap, kg/s m

2

h HTC=heat transfer coecient, W/m2 Kk thermal conductivity, W/m KI incident solar radiation intensity, W/m2

L length of absorber plate, mL length of air flow path, mm.

air mass flow rate, kg/sn number of collector elementsp channel wetted perimeter=2D+ 2W, mP pumping power, WQu rate of useful heat gain, WRe Reynolds number=4m

./mp

s air gap height in Model II collector, mS absorbed solar radiation intensity, W/m2

t thickness, mT temperature, KU heat loss coecient, W/m2 KV air mean velocity, m/sW width of absorber plate, mx distance from air inlet in flow direction, m

Greek symbolsa absorptivityDP pressure drop, N/m2

E emissivityZ eciency (%)m viscosity, kg/m sr density, kg/m3

s StefanBoltzmann constant, W/m2K4

t transmissivity

Subscriptsa ambientb bottom plate

A.A. Hegazy / Energy Conversion & Management 41 (2000) 861881862

mainly located on both sides of the equator. In these tropical and subtropical countries, theinsolation is considerably high, and therefore, solar energy has been traditionally used indrying and preservation of agricultural crops. The utility of solar air collectors for supplyingthe hot air required for this purpose, as well as the dehydration of industrial products andspace heating, has now become a common practice in these countries. However, electricalenergy is needed to operate the fan which forces the air throughout the system.The agriculture sector in most developing countries contains many isolated farms, small

remote villages and rural areas which experience diculties in connecting to electricity from thenational grid due to several technical and economical problems. However, this form of energydemand could be aorded by using photovoltaic/thermal (PV/T) air collectors in connectionwith storage batteries, which is an attractive alternative to grid extension. In fact, a few smallto medium PV/T collectors could provide the rural consumer with sucient electrical energy tocirculate the hot air and to run other domestic utilities.A PV/T air collector is simply a flat plate solar air heater with photovoltaic cells pasted on

the black absorber plate. It has the advantage of generating both thermal (low grade) andelectrical (high grade) energies from the same unit, and hence, it is less costly than twoseparate units. Flat plate air collectors exist in many designs, but the most common models areshown in Fig. 1. In these single glazing collectors, air may flow over the absorber (Model I) orbelow it (Model II), and even on both sides of the absorber in a single pass (Model III) or in adouble pass (Model IV) fashion. Although the Model I collector has the simplest design,Model II, of conventional design, is the PV/T collector which has been widely studied. Thearticles include those by Sopian et al. [1], Prakash [2], Bhargava et al. [3] and Cox andRaghuraman [4].Sopian et al. [1] also examined the performance of the Model IV PV/T collector and

concluded that it has a superior performance over Model II. However, they did not considerthe extra increase in energy demand for pumping the air through Model IV in comparison withthat of the Model II collector. The aim of the present investigation is, thus, to comparecritically the overall performances of these two collectors in addition to those of Models I and

c PV cellsd dailyg glass coveri inletin insulationm meano outletp absorber platepo pottantr radiatives skyw wind1 air stream 12 air stream 2

A.A. Hegazy / Energy Conversion & Management 41 (2000) 861881 863

Fig. 1. Schematics of the various PV/T models along with heat transfer coecients.


III, Fig. 1. This includes both kinds of energy, i.e. thermal and electrical, as well as pumpingpower requirements and the net available electrical energy after taking into account the energyloss in the storage and the power consumed by the fan. The eects of mass flow rate and theradiative properties of the absorber plate and PV cells on the performances are alsoinvestigated.

2. Design of PV/T collectors

The various designs of PV/T collectors are shown in Fig. 1. Each collector is covered with a3 mm thick (tg) glass plate and has an eective absorber area of length L= 9 m and widthW= 1 m. There is only a single rectangular flow channel inside Models I and II, while theother models exhibit two identical channels above and under the absorber; separated in ModelIII but interconnected by a 1808 close return bend in Model IV. The depth of a particularchannel (D ) is chosen as to satisfy the optimization criterion proposed by Hegazy [5,15] forvariable mass flow operation:

D=Loptimum 2:5 103: 1In this criterion, L is the length of the flow path traversed by the turbulent airflow from inletto exit, and therefore, L=L for Models I, II and III, but L=2L for the Model IV collector.Ambient air enters the various channels at x= 0 and the hot air emerges at x=L except forModel IV, where air first flows in the channel above the absorber and returns through the oneunder it, i.e. air also exits at x= 0. To minimize heat loss to the ambient, the side walls andback plate of each collector are adequately insulated (tin=50 mm, kin=0.045 W/m K) andsuitably enclosed.The photovoltaic system consists basically of PV modules, storage batteries with a charge

regulator and an inverter to convert D.C. to A.C. for domestic supplies. Commercial PVmodules are constructed from monocrystalline silicon cells which are encapsulated between aprotective transparent layer (pottant) and a moisture-proof backing. A typically available50Wp, 16.5 V module contains 36 series connected cells (each 10 cm diameter) with overalldimensions of 98.2 43.6 3.85 cm, Ref. [6]. Hence, 20 PV modules are required to cover theabsorber eective area of 9 m2 so hat the fraction of area occupied by the solar cells, i.e.packing factor F, is 62.8%. The PV modules are commonly pasted on the absorber plate usinga silicon dielectric heat transfer compound to ensure good electrical insulation along with goodthermal contact. A series parallel arrangement is usually used to connect the PV modules inorder to provide the desired voltage and current.

3. Mathematical formulation

Fig. 1 also shows the various heat transfer coecients (HTCs) along the surfaces of the fourPV/T collectors considered in this study. For each model, an energy balance analysis isperformed over a dierential element having a surface area (width length) W dx after


making the following assumptions: (a) heat transfer is quasi-steady and one dimensional; (b)there is no air leakage from the hydraulically smooth flow channels; (c) heat capacity eects ofthe glass cover, enclosed air, PV modules, absorber and bottom plates are negligible; (d) thepart of solar radiation which is not converted into electrical energy is absorbed by the PV cellsand the plates as thermal energy; (e) the temperatures of the PV modules, glass, absorber andbottom plates vary only along the x-direction of the airflow; (f) each collector consists of anumber of small elements so that the temperatures of the element surfaces are uniform, whilethat of the turbulent airflow inside varies linearly along its small length dx; (g) the PV modulesare in perfect thermal contact with the absorber plate of a particular element and both havethe same uniform temperature. Accordingly, the energy balance equations for the jth elementof a particular collector are as follows after dropping the subscript ( j ) for the sake ofsimplicity.

3.1. Model I PV/T collector

For glass cover:

Sg hgTm Tg hrpgTp Tg hw hrgsTg Ta, 2where Sg (=agI ) is the fraction of solar insolation (I ) absorbed by the element glass and Tm isthe mean of air stream inlet and outlet temperatures, (Ti+To)/2.For air stream:

hpTp TmW dx hgTm TgW dx _mcpTo Ti: 3However, the rate of useful heat Qu extracted by the air stream can be expressed in terms ofspecific mass rate G (=m

./WL ) and Tm rather than m

.and T0 (=2 TmTi). Thus, Eq. (3)

becomes:

hpTp Tm hgTm Tg 2GcpTm TiL=dx: 4For absorber plate:

Sp hpTp Tm hrpgTp Tg UbTp Ta, 5where Sp is the total solar energy reaching the element plate minus the energy converted intoelectrical energy

Sp tgtpoIap1 F acF1 Zc: 6The first term in Eq. (6) represents the solar radiation absorbed directly by the plate, while thesecond term is the part of insolation which is not converted into electrical energy but istransmitted to and absorbed by the plate. The conversion eciency of the PV module Zc is afunction of its temperature Tc [=Tp according to assumption (g)] and is calculated by therelation, Ref. [7]:

Zc 0:1251 0:004Tc 293: 7


Regarding the bottom and sides heat loss coecient Ub, it is given by

Ub 1 2tin tc D tg=W =tin=kin 1=hw: 8

3.2. Model II PV/T collector

For glass cover:

Sg hpg hrpgTp Tg hw hrgsTg Ta, 9where hpg is the free convection HTC of the air gap of height s= 25 mm between the PVmodule and glass cover. It is computed by, Ref. [8]:

hpg k=sf1 1:441 R1 Rsin 1:8b1:6 0:66416R1=3 1g, 10where R= 1708/Ras cos b, Ras is the air gap Rayleigh number, b is the collector tilt angle(=288N, the latitude of Minia city). The notation [ ] means that only the positive value isconsidered, with zero used if this term is negative. All properties are evaluated at the air gapmean temperature, (Tp+Tg)/2.For absorber plate:

Sp hpg hrpgTp Tg hpTp Tm hrpbTp Tb: 11For air stream between absorber and bottom plates:

hpTp Tm hbTm Tb 2GcpTm TiL=dx: 12For bottom plate:

hbTm Tb hrpbTp Tb UbTb Ta, 13where Ub is given by

Ub 1 2tin D tc s tg=W =tin=kin 1=hw: 14

3.3. Model III PV/T collector

For this model, the air specific mass rate G is considered to be equally divided between thetwo identical channels on both sides of the absorber. Hence, G1=G2=G/2 since the depths ofboth channels are equal (D1=D2=D ), as they are determined according to the criterion givenby Eq. (1). The element energy balance equations areFor glass cover:

Sg hgTm1 Tg hrpgTp Tg hw hrgsTg Ta: 15For air stream 1 in upper channel:

hp1Tp Tm1 hgTm1 Tg 2G1cpTm1 Ti1L=dx: 16


For absorber plate:

Sp hp1Tp Tm1 hrpgTp Tg hp2Tp Tm2 hrpbTp Tb: 17For air stream 2 in lower channel:

hp2Tp Tm2 hbTm2 Tb 2G2cpTm2 Ti2L=dx: 18For bottom plate:

hbTm2 Tb hrpbTp Tb UbTb Ta 19where Ub is given by

Ub 1 2tin D2 tc D1 tg=W =tin=kin 1=hw: 20

3.4. Model IV PV/T collector

The energy balance equations for the jth element of the Model IV collector are similar toEqs. (15)(20) of Model III, but it should be noticed that in Model IV, the air flows first in theupper channel before turning and then passing through the lower channel. Hence, the specificmass rate G should be substituted in Eqs. (16) and (18) instead of G1 and G2. In addition, thedepth of the upper or lower channel is twice the channel depth of the other models in order tosatisfy the optimization criterion, Eq. (1), since the flow path length L is twice the absorberlength L, i.e. D1=D2=2D. Further, the temperature of the air out of the upper channel atx=L is essentially the temperature of the air entering the lower channel, i.e.

To1 at xL Ti2 at xL: 21

3.5. Forced convective and radiative HTCs

Depending on the PV/T collector model, the forced convective HTCs between the turbulentairflow and both the absorber plate (hp) and the glass cover (hg) or the bottom plate (hb) arecalculated by the following correlation, Refs. [9,10]:

h k=Dhf0:0158 Re0:8 0:00181 Re 2:92 exp0:03795x=Dhg, 22where x is the distance travelled by the air from the channel entrance, and Re (=4m

./mp ) is the

Reynolds number of a certain air mass rate (m.) through a particular channel of depth D,

width W and hydraulic diameter Dh=4 flow area (WD )/wetted perimeter ( p ). All propertiesare evaluated at the air mean temperature Tm,j inside a particular channel element, so that theconvective HTCs of the upper and lower plates are equal.The radiative HTC (hrgs) between the glass cover and the sky is calculated by

hrgs sEgT 4g T 4s =Tg Ta, 23where the equivalent sky temperature (Ts) is evaluated by the simple relation, Ref. [11]:


Ts 0:0552T 1:5a : 24The radiative HTCs between the absorber plate and both glass cover (hrpg) and bottom plate(hrpb) are calculated by the formula of two infinite parallel plates (k, l ):

hrkl sTk TlT 2k T 2l =1=Ek 1=El 1: 25However, when the absorber plate is uniformly covered with PV modules, the radiative HTCbetween this combination and glass cover is estimated as:

hr pcg Fhrcg 1 F hrpg: 26

4. Performance parameters

The performance of an PV/T air collector is characterized by its air temperature rise,thermal and electrical eciencies, pumping power requirement and the net available electricalenergy. To determine these parameters for a particular model, a step-marching computationalprocedure is employed to solve the energy balance equations at dierent elements along thecollector length following the path of the airflow. In the present work, the collector isdiscretized into 20 elements (n= 20), each 0.45 m in length (=dx ) to accommodate only asingle PV module. Also, it is found that this element length satisfies assumption (f) and yieldsaccurate results as well.

4.1. Temperature rise and collector eciencies

For certain ambient and operating conditions, the temperature of the glass cover, absorberplate (=PV module), moving air etc. are initially guessed for all the elements. However, thetemperature of the air inlet to the collector and first element at x= 0 is taken equal to theambient (Ti,1=Ta), i.e. no air recycling. With these temperatures, the various HTCs and PVmodule conversion eciency (Zc) are estimated for the first element, and the balance equationsare then solved to obtain new temperatures which are compared with the old ones. Theiteration process is continued with the most updated variables until all the temperature valuesconverge. Hence, the temperature(s) of the air stream(s) leaving the first element can bedetermined, along with the element useful heat gain Qu,1 and generated PV energy EPV, 1tgtpoIacZc, 1FW dx:Using the temperature(s) of the air leaving the first element as the inlet one(s) for the next

element, the exit temperature(s) for the second element can similarly be computed. Continuingthis way from one element to the next, the temperature of the air (To) at the exit (x=L ) fromcollectors IIII is determined and, thus, the air temperature rise (ToTi). Note that thetemperature of the air leaving the Model III collector is calculated as To=(To1+To2)/2 on thebasis of equal mass rates in channels 1 and 2. For the Model IV collector, the procedure iscontinued along the path of airflow in the second channel under the absorber from x=L to thecollector exit at x= 0. However, all of the computed temperatures for Model IV are treated as


new guess values, and the whole procedure is repeated again until converged values are finallyobtained, and in turn, the airflow outlet temperature is obtained.The instantaneous useful heat gained by the airflow through PV/T Models I and II is

computed as

Qu Xnj1

Qu, j: 27

For Models III and IV with two air streams 1 and 2 above and under the absorber,respectively, the instantaneous thermal energy is evaluated by

Qu Xnj1Qu1, j Qu2, j : 28

In contrast, the instantaneous PV energy generated by any collector is determined as

EPV Xnj1

EPV, j: 29

Three kinds of average eciencies are defined for a PV/T collector. The first one is the dailythermal eciency:

ZT, d ts

tr

Qu dt

!=

tstr

ApI dt

!, 30

while the second one is the daily PV eciency:

ZPV, d ts

tr

EPV dt

!=

tstr

FApI dt

!, 31

and finally the daily combined eciency of the PV/T collector is calculated by:

ZPVT, d ts

tr

Qu dttstr

EPV dt

!=

tstr

ApI dt

!: 32

All computations are performed over the same period of time between sunrise, tr, and sunset, ts.

4.2. Fan power

Electrical energy is needed to drive the motor of the fan which forces the air through thecollector, and thus, part of the energy generated by the PV modules would be utilized for thispurpose. The amount of this energy depends on the fan system eciency and flow pumpingpower of a particular collector model. The latter could be estimated by

Pflow ApSGDP=richannel, 33


where DP is the total pressure drop experienced by the air stream in passing through a certainchannel at a mass rate G due to flow friction and losses at the channel entrance, exit andvarious fittings. The pressure drop due to friction is given by

DPfriction Xnj1rfV 2L=n=D, 34

where V (=GL/rD ) is the mean velocity of the air at the mean temperature Tm,j inside thechannel element j, and f is the friction factor for turbulent flow calculated by, Ref. [12]:

f 0:079 Re0:25 6 103 < Re < 5 105: 35Other pressure drop values due to the eects of channel entrance, exit, elbows, bends, joints,valves etc. are determined by the formula

DPother SKrV 2=2, 36where the coecient K is assigned the values of 0.5, 1.0 and 10 for the losses of entrance, exitand various fittings, respectively. For the 1808 close return bend inside the Model IV collector,its K value is taken as 2.2, Ref. [13], and the air properties are evaluated at the meantemperature of the flow at the particular location in the channel.Now, if the fan eciency is assumed to be 74%, while that of the electrical motor is taken as

90%, then the instantaneous power required for circulating a certain amount of air becomes

Pfan Pflow=ZfanZmotor 1:5Pflow: 37Hence, the daily fan power is given by

Pfan, d tstr

Pfan dt, 38

which should be supplied from a constant source (storage batteries) for steady operation.

4.3. Net available electrical energy

The daily electrical energy generated by the PV modules (EPV,d) is determined by integratingthe instantaneous values calculated by Eq. (29) over the period of sunshine. Because of thisvariability in electrical energy generation rate, the PV output is first stored in the batteriesbefore it is used for running the collector fan and/or other utilities either during the day ornight time. If 30% allowance is assumed for the energy losses in the batteries (10%), chargeregulator (5%), inverter (15%) and cabling (2.5%), then about 70% of the PV energy is storedin the batteries. However, about 80% of this stored energy becomes available when the collectorfan or other appliance consumes energy from the batteries. Thus, only 56% of the daily PV poweris useful (Euseful=0.56EPV), and in turn, the net available electrical energy can be determined as

Enet, d 0:56EPV, d Pfan, d: 39


5. Results and discussion

Performance comparisons have been performed employing the hourly data of solar intensityand ambient temperature shown in Fig. 2. These climate data are recorded at Minia Universityfor the summer day 24 June 1998, during which the prevailing wind speeds (Vw) variedbetween 0.5 and 1.5 m/s. Wind HTCs are estimated by Sharples and Charlesworth correlations[14], but an average value of hw=10 W/m

2 K is assigned for the whole day, since the Vw rangeis very limited. Values of absorptivity, transmissivity and emissivity for the various surfaces ofthe collectors are taken as: ag=0.04, tg=tpo=0.9, Eg=0.86, ap=0.94, Ep=0.95, ac=0.9, Ec=0.7and Eb=0.95. For each collector model, the performance characteristics are determined foreight specific mass rates of air, spanning the range of G= 0.0050.04 kg/s m2.The comparisons between the various performance parameters for the considered PV/T

Models IIV are presented in Figs. 36 as a function of the air specific mass flow rate G. Ingeneral, each data point in a particular figure represents the parameter integrated value overthe day time. Smooth curves are passed through the various data sets to provide continuity. Itis evident from Fig. 3 that under the same ambient conditions, the Model I collector exhibitsthe lowest daily thermal performance irrespective of the mass rate G value. In contrast is theModel II collector which has the highest ZT,d values. Further, the daily thermal eciencies forModels III and IV are quite close to the ZT,d values of Model II in the range of G< 0.02 kg/sm2, but the deviation becomes more pronounced for Gr0.02 kg/s m2.Fig. 4 shows the maximum rise in air temperature (ToTi)max which occurs at 13:00 (local

time) when the incident solar radiation is maximum too. Clearly, the rise in the temperature of

Fig. 2. Hourly values of solar radiation intensity and ambient temperature used in the computations.


the air flowing through PV/T Models II, III and IV is nearly the same and is higher than therise experienced by air through Model I especially for G< 0.02 kg/s m2. Generally, the airtemperature rise is seen to drop, as expected, with increasing specific mass rate G regardless ofthe collector model.

Fig. 3. Variation of daily thermal eciency with air specific mass rate for PV/T collectors IIV.

Fig. 4. Variation of maximum air temperature rise with air specific mass rate for PV/T collectors IIV.


The daily electrical eciencies of the four PV/T models are shown in Fig. 5. In connectionwith Fig. 4, it is obvious that as the air temperature rise of a particular model gets less and lesswith increasing specific mass rate G, the collector ZPV,d gets correspondingly higher and higherdue to the decrease in the average temperatures of the PV modules. However, the enhancementin the value of ZPV,d is remarkably very small as compared to the increase in the value of the G

Fig. 5. Variation of daily electrical eciency with air specific mass rate for PV/T collectors IIV.

Fig. 6. Daily fan power and average PV and useful energies as a function of air specific mass rate.


rate. Further, the maximum dierence between the ZPV,d values of the various models at aparticular G rate is negligible, Fig. 5; typically less than 0.3% at G= 0.005 kg/s m2 down to0.1% at G= 0.04 kg/s m2. Accordingly, this permits us to arithmetically average the PVenergies (EPV,d) generated daily by the four models, so that it becomes possible to compare thedaily fan power Pfan,d required by each model with the daily useful energy (Euseful,d=0.56EPV,d)as shown in Fig. 6.Examination of Fig. 6 reveals that collectors I and II demand almost identical fan powers,

since each of them has only a single flow channel of depth D either above (Model I) or under(Model II) the absorber. On the other hand, the Model III collector consumes the least fanpower, while Model IV comes in the second rank. Also indicated in Fig. 6 is that these typesof PV/T collectors could aord the electrical energy necessary for pumping the hot air with amaximum rate G= 0.02 kg/s m2 for both Models I and II, G= 0.025 kg/s m2 for Model IVand G< 0.035 kg/s m2 for the Model III collector. These characteristics can, however, bequantified by defining a collector daily electro-hydraulic eciency ZPV,net as

ZPV, net Enet, d= ts

tr

FApI dt

!: 40

The various ZPV,net values for PV/T Models IIV are graphed in Fig. 7 as a function of massflow rate G. Clearly, the net available electrical energy Enet,d from the four models are almostthe same for G R 0.01 kg/s m2. With increasing G rate, however, the fan power requirementincreases too, so that Enet,d continuously decreases, with a relatively steep gradient for ModelsI and II. Also obvious in Fig. 7 is that the Enet,d available from Model III is generally morethan that of Model IV.

Fig. 7. Daily electro-hydraulic eciency for PV/T collectors IIV as a function of air specific mass rate.


As a summary to the preceding paragraphs, the following can be concluded. First, theModel II collector shows a comparable thermal performance with those of Models III and IVup to G< 0.02 kg/s m2, but it has a better thermal performance for higher G rates. Second,the PV energy generated from Model II is relatively higher than those of other models, but itsamount is close to that of Model III in the range of Gr0.02 kg/s m2. Third, the Model IIcollector consumes a large amount of fan power relative to that required by Model III orModel IV for pumping the same G rate under similar ambient conditions. Of course, this has adirect impact on the net PV energy available for domestic purposes.In light of the above summary, it is evident that better judgment on the performances of

these four PV/T models could be critically assessed by comparing their overall performances(including thermal, electrical and fan power parameters) under similar operational conditions.Therefore, it becomes convenient to define a collector daily overall eciency as:

Zoverall Qu, d Enet, d=tstr

ApI dt: 41

The computed Zoverall values for PV/T Models IIV are plotted in Fig. 8 over the range of0.005 R G R 0.04 kg/s m2. Generally, the overall eciency of a particular PV/T modelincreases with an increase in air mass rate G, attains a maximum value and then decreases witha further increase in G. This is attributed to the sharp increase in fan power with increasing G,while the accompanying enhancements in the generated PV energy (Fig. 6) and the collectedheat (Fig. 3) are, respectively, slight and moderate. Also obvious in Fig. 8 is that the Model Icollector has the lowest overall performance among the other models for all mass rates G. Inthe range of G< 0.02 kg/s m2, Models IIIV has almost identical overall performances. For

Fig. 8. Daily collector overall eciency for models IIV as a function of air specific mass rate.


Table 1Comparison between daily performance parameters for collector IIV with Ep=0.9 and Ec=0.7

a,b

G (kg/s m2) Qu (Wh/day) DTmax (K) EPV (Wh/day) ZPVT (%) Pfan (Wh/day) Enet (Wh/day) Zoverall (%)

Model I0.005 17,510 48.0 3018 29.0 28.6 1662 27.1

(21,607) (59.4) (2741) (34.4) (28.8) (1506) (32.7)

0.010 25,358 35.4 3237 40.4 212 1601 38.1(28,404) (39.6) (3118) (44.6) (212) (1534) (42.3)

0.015 29,686 27.8 3359 46.7 687 1194 43.7

(31,947) (29.9) (3293) (49.8) (688) (1156) (46.8)0.020 32,445 22.9 3437 50.7 1586 339 46.4

(34,189) (24.1) (3395) (53.1) (1586) (315) (48.9)0.030 35,783 16.9 3532 55.6 5168 3190 46.1

(36,923) (17.4) (3510) (57.2) (5169) (3204) (47.7)0.040 37,736 13.4 3588 58.4 11,975 9966 39.3

(38,554) (13.6) (3574) (59.6) (11,976) (9975) (40.4)

Model II0.005 20,971 56.3 3133 34.1 28.8 1726 32.1

(24,926) (66.7) (2901) (39.5) (28.9) (1596) (37.5)0.010 29,128 39.4 3311 45.9 212 1642 43.5

(33,121) (44.6) (3179) (51.3) (213) (1567) (49.0)

0.015 33,390 30.2 3411 52.0 688 1222 49.0(37,086) (33.4) (3324) (57.1) (689) (1172) (54.1)

0.020 36,030 24.5 3476 55.9 1587 359 51.5(39,428) (26.6) (3413) (60.6) (1588) (323) (56.2)

0.030 39,163 17.8 3556 60.4 5171 3180 50.9(42,071) (19.0) (3518) (64.5) (5174) (3204) (55.0)

0.040 40,983 13.9 3604 63.0 11,979 9961 43.9(43,541) (14.7) (3578) (66.6) (11,984) (9980) (47.5)

Model III

0.005 21,197 57.2 3053 34.3 7.8 1702 32.4(27,783) (74.9) (2700) (43.1) (7.8) (1504) (41.4)

0.010 29,140 40.0 3277 45.8 56.8 1778 43.7(33,798) (46.3) (3118) (52.2) (57.0) (1689) (50.2)

0.015 33,115 30.5 3396 51.6 183 1719 49.3(36,487) (33.5) (3303) (56.3) (183) (1667) (54.0)

0.020 35,507 24.6 3470 55.1 421 1522 52.4

(38,081) (26.3) (3408) (58.7) (421) (1487) (56.0)0.030 38,274 17.8 3558 59.2 1366 626 55.0

(39,952) (18.5) (3524) (61.5) (1367) (606) (57.3)

0.040 39,844 13.9 3609 61.4 3156 1135 54.7(41,056) (14.3) (3587) (63.1) (3157) (1148) (56.4)

Model IV0.005 20,726 55.8 3005 33.6 14.7 1668 31.7

(27,551) (74.3) (2588) (42.6) (14.9) (1434) (41.0)(continued on next page)


higher mass rates Gr0.02 kg/s m2, it is seen that the Model III overall performance exceedsthose of Models IV and II, as they rank in the second and third places, respectively. This bestoverall performance can be explained by the fact that under similar operational conditions, theModel III collector demands the least fan power with respect to the other models, while thecollected thermal and PV energies are very comparable to those of Models II and IV.The numeric values of some selected performance parameters for PV/T Models IIV are

listed in Table 1. Also reported between parentheses are the countervalues for these parameterswhen both the absorber and PV cells have selective properties, i.e. Ep=0.1 and Ec=0.2.Inspection of the non-selective data in Table 1 reveals, that the Model II collector is rathermore eective than Model IV in converting solar energy into thermal (Qu,d) and electrical(EPV,d) energies; therefore, it has a slightly better combined eciency, ZPV/T,d. Although thisfinding appears to contradict the conclusion made by Sopian et al. [1] that Model IV has asuperior performance to that of Model II, it should be pointed out that in Ref. [1], the flowchannel depth-to-length ratio was arbitrarily chosen. It fact, Sopian et al. [1] indirectly studiedthe eect of (D/L ) ratio on the performances of Models II and IV by varying the absorberlength L (=1 or 2 m) with respect to a single channel depth D= 10 cm. In the present study,the channel (D/L) ratio is determined according to the optimization criterion given by Eq. (1)which, as examined by Hegazy [5,15], eectively maximizes the thermal performance of flatplate solar air collectors. The eect of channel (D/L) ratio on the performance of the Model IIPV/T collector was also demonstrated by Bhargava et al. [3] (D= 5, 10 and 15 cm whileL=L= 2 or 5 m), as well as by Prakash [2], D= 1, 2, and 3 cm for a fixed length L=L.Hence, it can be concluded that the output gains from such PV/T air collectors could bemaximized too by selecting the ratio (D/L) optimally as prescribed by Eq. (1).Further inspection of Table 1 shows that enhancing the selectivity of the absorber plate

(Ep=0.1) and PV cells (Ec=0.2) improves the collection of useful heat (Qu,d) and, in turn, thecombined eciency (ZPVT,d), but at the expense of the generated PV energy, especially at lowflow rates G< 0.02 kg/s m2. Keeping in mind that the main objective of using PV/T collectors

Table 1 (continued )

G (kg/s m2) Qu (Wh/day) DTmax (K) EPV (Wh/day) ZPVT (%) Pfan (Wh/day) Enet (Wh/day) Zoverall (%)

0.010 28,652 39.3 3225 45.1 109 1697 42.9(34,025) (46.6) (3031) (52.4) (109) (1588) (50.4)

0.015 32,839 30.3 3348 51.2 352 1523 48.6(36,933) (33.9) (3236) (56.8) (353) (1459) (54.3)

0.020 35,415 24.6 3428 54.9 813 1107 51.7

(38,498) (26.7) (3355) (59.2) (814) (1065) (55.9)0.030 38,409 17.8 3525 59.3 2649 675 53.4

(40,340) (18.7) (3486) (62.0) (2650) (698) (56.1)0.040 40,101 14.0 3582 61.8 6136 4130 50.9

(41,451) (14.4) (3557) (63.6) (6138) (4146) (52.7)a Numbers between parentheses are for Ep=0.1 and Ec=0.2.b Note:

tstrApI dt 70, 716 Wh/day.


is to provide the rural farmer with sucient electrical energy to operate his domesticappliances, it can, thus, be concluded that selective properties are inappropriate for such typeof collectors, particularly when they are used in remote tropical or subtropical regions whichalso have harsh climates.Finally, a brief comment is in order about how to maximize the dierence between the

Table 2Values of air temperature rise, useful PV energy and fan power two hours after/before sunrise/set for collector IIV

G (kg/s m2) (T0Ti) (K) Euseful (W) Pfan (W)

8 h 18 h 8 h 18 h 8 h 18 h

Model I0.005 18.2 13.0 95.4 70.7 1.94 2.01

0.010 12.8 9.1 98.8 72.6 14.4 15.00.015 9.8 6.9 101 73.5 46.8 48.60.020 8.0 5.6 102 74.1 108 112

0.025 6.7 4.7 103 74.5 207 2160.030 5.8 4.1 103 74.8 353 3670.035 5.1 3.6 103 75.0 554 576

0.040 4.5 3.2 104 75.2 819 852Model II

0.005 22.5 16.4 97.1 71.6 1.95 2.010.010 15.3 11.1 99.8 73.0 14.5 15.0

0.015 11.6 8.4 101 73.8 46.9 48.70.020 9.3 6.8 102 74.3 108 1130.025 7.8 5.7 103 74.7 208 216

0.030 6.7 4.9 103 74.9 354 3670.035 5.9 4.4 104 75.1 555 5770.040 5.3 3.9 104 75.3 820 852

Model III0.005 22.7 16.3 95.8 70.9 0.53 0.540.010 15.1 10.7 99.3 72.8 3.86 4.00.015 11.2 8.0 101 73.8 12.5 12.9

0.020 8.9 6.3 102 74.3 28.7 29.80.025 7.3 5.2 103 74.7 54.9 57.10.030 6.3 4.4 103 75.0 93.4 97.0

0.035 5.5 3.9 104 75.2 146 1520.040 4.8 3.4 104 75.4 216 224

Model IV

0.005 22.2 16.0 95.1 70.6 1.0 1.030.010 13.1 10.7 99.4 72.5 7.37 7.660.015 10.0 8.0 101 73.5 24.0 24.9

0.020 8.1 6.4 102 74.1 55.4 57.60.025 6.8 5.3 103 74.5 106 1100.030 5.9 4.5 103 74.8 181 1880.035 5.2 4.0 104 75.0 284 295

0.040 4.6 3.5 104 75.2 419 436


useful electrical energy (Euseful,d) and the fan power (Pfan,d) required for forcing the air throughthe collector, primarily to cool the PV modules and secondarily to collect solar energy as a lowtemperature heat. From a design point of view, one should employ PV modules with highconversion eciency Zc and packing factor F to improve the generation rate of PV energy. Onthe other hand, significant savings in the fan power requirements can be achieved by using acontroller (e.g. time clock, light sensitive switch, thermostat etc.) to regulate the operation ofthe fan according to a certain policy, since the ambient conditions are widely varying along theday and over the year. As shown in Table 2, it would be disadvantageous to pump high flowrates through the collector in the periods of low solar irradiation (I< 400 W/m2), particularlyduring the two hours interval after sunrise and before sunset. As a matter of fact, the earlymorning and late afternoon periods are both characterized by low ambient temperature andlow levels of incident solar radiation. Hence, power savings during these two periods couldamount to 25% of the daily fan power requirements. Also, a dierent control strategy shouldbe planned for the operation of the PV/T collector during winter, when climate conditions arenot favourable, and the demand for electrical energy is great.

6. Conclusions

On the basis of the comparisons made, the following conclusions can be drawn:

1. For a particular model, the thermal eciency is enhanced with the increase of air specificmass flow rate. This is accompanied with a noticeable decrease in air temperature rise alongwith a sharp increase in fan power requirement. In contrast, the enhancement in thegenerated PV energy is slight so that the net available electrical energy decreasesdramatically with increasing air flow rate.

2. The Model I PV/T collector has the lowest overall performance, while the other modelsexhibit very comparable ones up to a specific mass rate G R 0.02 kg/s m2. For higher Gvalues, Model III has the highest overall performance followed by the Model IV collector.For each model, however, there exists a critical rate of mass flow beyond which collectoroverall performance decreases.

3. The flow channel (D/L) ratio is an important design parameter also influencing theperformance of PV/T air collectors. For variable mass flow operation, however, theoptimum ratio which eectively maximizes the thermo-electric gains from such collectors is(D/L)optimum=2.5 103.

4. Owing to the variability of ambient conditions along the day and over the year, a significantsaving in the net available electrical energy may be realized through the use of a controllerto regulate the operation of the fan according to a certain strategy.

5. The use of selective absorber plate and PV cells is totally inappropriate for such types ofPV/T collectors due to the resultant reduction in the generated PV energy, especially at lowflow rates of air.

6. Performance comparisons indicate that the Model III PV/T collector is the most suitablecandidate design for converting solar energy into low quality heat and high quality electrical


energy. On the other hand, it is simple to be built by local craftsmen in the rural areas ofdeveloping countries.

References

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[2] Prakash J. Transient analysis of a photovoltaic-thermal solar collectors for cogeneration of electricity and hotair/water. Energy Conversion and Management 1994;35(11):96772.

[3] Bhargava AM, Garg HP, Agarwal RK. Study of a hybrid solar system-solar air heater combined with solarcells. Energy Conversion and Management 1991;31(5):4719.

[4] Cox III CH, Raghuraman P. Design considerations for flat-plate photovoltaic/thermal collectors. Solar Energy

1985;35(3):22741.[5] Hegazy AA. Performance of flat plate solar air heaters with optimum channel geometry for constant/variable

flow operation. Bull of Faculty of Engineering, Minia University 1998;17(1):5970.

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[7] Bergene T, Lovvik OM. Model calculation on a flat-plate solar heat collector with integrated solar cells. SolarEnergy 1995;55(6):45362.

[8] Hollands KGT, Unny TE, Raithby GR, Konicek L. Free convective heat transfer across inclined air layers.ASME Journal of Heat Transfer 1976;98(2):18993.

[9] Biehl FA. Test results and analysis of a convective loop solar air collector. Proc. 6th National Passive SolarConf., Portland, Oregon, 1981: cited in [10].

[10] Altfeld K, Leiner W, Fiebig M. Second law optimization of flat-plate solar air heaters. Part 1: The concept of

net exergy flow and the modeling of solar air heaters. Solar Energy 1988;41(2):12732.[11] Swinbank WC. Long wave radiation from clear skies. Quarterly Journal of the Royal Meteorological Society

1963;89:339.

[12] Harnett JP, Koh JCY, McComas ST. A comparison of predicted and measured friction factors for turbulentflow through rectangular ducts. ASME Journal of Heat Transfer 1962;84(1):828.

[13] Daugher RL, Franzini JB, Finnemore EJ. Fluid Mechanics with Engineering Applications. McGraw-Hill, 1989:p. 239.

[14] Sharples S, Charlesworth PS. Full-scale measurements of wind-induced convective heat transfer from a roof-mounted flat plate solar collector. Solar Energy 1998;62(2):6977.

[15] Hegazy AA. Optimum channel geometry for solar air heaters of conventional design and constant flow oper-

ation. Energy Conversion and Management 1999;40(7):75874.


Documents

Comparative Study of the Performances of Four Photovoltaic-Thermal Solar Air Collectors