A numerical investigation of a photovoltaic thermal (PV/T) collector

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Renewable Energy 77 (2015) 43e50

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Renewable Energy

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A numerical investigation of a photovoltaic thermal (PV/T) collector

Oussama Rejeb*, Houcine Dhaou, Abdelmajid JemniLaboratoire d'Etudes des Syst�emes Thermiques et Energ�etiques, Rue Ibn Eljazzar, Ecole Nationale d'Ing�enieurs de Monastir, Universit�e de Monastir,Monastir 5019, Tunisia

a r t i c l e i n f o

Article history:Received 11 July 2014Accepted 4 December 2014Available online

Keywords:Photovoltaic thermalElectrical-performanceThermal-performance

* Corresponding author. Tel.: þ216 53918682; fax:E-mail addresses: [email protected]

(O. Rejeb).

http://dx.doi.org/10.1016/j.renene.2014.12.0120960-1481/© 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

The photovoltaic thermal collector can provide thermal and heat power at the same time.In this paper, a photovoltaic/thermal sheet and tube collector has been numerically investigated. The

paper focuses on the development of a hybrid solar collector PV/T. This model will be applied to optimizethe operation of the PVT collector in the semi-arid climate. A mathematical model has been developed todetermine the dynamic behavior of the collector, based on the energy balance of six main componentsnamely a transparent cover, a PV module, a plate absorber, a tube, water in the tube and insulation. It hasbeen validated by comparing the obtained simulation results with experimental results available inliterature, where good agreement has been noted. Using our developed model, the heat and electricalpower of sheet and tube collector has been analyzed for four typical days of year with the meteorologicalparameters of Monastir, Tunisia. Furthermore, the effect of solar radiation, the inlet water temperature,the number of glazing covers and the conductive heat transfer coefficient between plate absorber and PVmodule have been involved to identify their influence on the thermal and electrical efficiencies. Themonthly thermal and electrical energies is also evaluated.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The photovoltaic/thermal collector (PV/T) has been elaboratedto provide both heat and electrical energies at the same time. Theheat extracted from the PV modules by (cooling fluid) causes thecooling of the photovoltaic panels to stabilize its performances. Itprovides too useful heat that can be used for water heating.Raghuraman el al [1]. proposed a numerical model for liquid andair (PV/T) collector. A thermal efficiency of about 42% is obtainedwhen air is used as a working fluid. Bergene [2] proposed adetailed model of the solar flat-plate with integrated Solar cells.The total efficiency of the system (electricþ thermal) was found inthe range of 60e80%. Chow [3] developed an explicit dynamicmodel. The modeling gives a detailed analysis of the instanta-neous thermal and electrical efficiencies. The performance of thecollector is evaluated in terms of conduction heat transfer co-efficients between the plate absorber and tubes and between theabsorber and the PV module. A yield of 70% was obtained in the

þ216 73501579., [email protected]

event where the contacts are ideals. He el al [4]. carried out anexperimental study of hybrid (PV/T) of an area of 1.34 m2.Theyused silicon polycrystalline PV cells, with a conversion effective-ness of 13%. The daily thermal efficiency obtained was approxi-mately about 40%. Shan el al [5]. developed a numerical model topredict the transient performance of photovoltaicethermal col-lector with water heating in buildings for the environmentalconditions of Jiangsu, China. They analyzed the effects of watermass flow rate and series-connected PVT module number on theperformance of PV/T collector. They observed that when the massflow of water increases and the PV modules connected in seriesdecreases the performance of the collector PV/T improved.Dupeyrat el al. [6] made a numerical and experimental compari-son between a thermal photovoltaic system, a conventional solarsystem and a conventional PV system. They pointed out that the(PVT) is the most advantageous system, in terms of energy andprimary energy saving. Touafek el al. [7] designed and developed amathematical model of a photovoltaic thermal collector for do-mestic air heating and electricity production. The maximumuseful thermal power and thermal efficiency, for a sunny daystudied, obtained were respectively 290 W and 48%.

Several investigations on the effect of the thermal and electricalefficiencies of PV/T collector were carried out. Chow el al. [8]

Nomenclature

A surface area (m2)C specific heat (JKg�1K�1)k thermal conductivity (Wm�1K�1)Pac packing factorG solar irradiation (Wm�2)h heat transfer coefficient (Wm�2K�1)Nu Nusselt numberRa Rayleigh numberPr Prandtl numberPe perimeter (m)t time (s)m:

RMS mass flow rate (kgs�1) root mean squarepercentage deviation

Greekb solar cell temperature coefficient (K�1)d thickness (m)r density (Kgm�3)

h efficiencyt transmittanceε emissivity

Subscriptsamb ambientenv environnementg glazingPV photovoltaic modulePab absorber platet tubew wateri insulationcond conductionconv convectionelec electricalout outletin inletth thermalWi wind

O. Rejeb et al. / Renewable Energy 77 (2015) 43e5044

evaluated the performance of glazed PV/T and unglazed one. Theyshowed that the exergetic efficiency of the unglazed collector isbetter than the glazed collector. Fujisawa el al. [9] evaluatedexperimentally the performance of PV/T single cover, uncover PV/T,PV module and flat plate collector. Their results showed that theelectrical energy of the unglazed PV/T collector is better than theglazed PV/T collector. However, the thermal energy gain of coverPV/T is better than the PV/T uncover.

Efficiency of (PV/T) collector is affected by the meteorologicalcondition climatic (Solar radiation, ambient temperature and windspeed). Several studies were carried out in Hong Kongwith a humidsubtropical climate and in Europe. To the best knowledge of theauthors, no attempt has been made in the previous works for thesemi-arid climatic with hot summer and mild winter. The paper

Fig. 1. PV/T colle

focuses on the development of a hybrid solar collector PVT. Thismodel will be applied to optimize the operation of the PVTcollectorin the semi-arid climate.

The main objective of the present study is to state the evolutionof heat and electrical gain under Monastir (Tunisia) climatic con-ditions. Furthermore, a parametric study has been conducted inorder to analyze the electrical and thermal performances of PV/Tcollector. The monthly thermal and electrical energies is alsoevaluated.

2. Mathematical model

The PV/T sheet and tube considered, in the current study, isshown in Fig. 1. It consists of glazing, PV module which has as a

ctor water.

O. Rejeb et al. / Renewable Energy 77 (2015) 43e50 45

role of converting sunlight into electrical energy, a copper platewhich has a role of absorbing sunlight, six tubes were attached tothe absorber plate, in these tubes circulate coolant (water) whichhas a role of evacuating the heat stored by the absorber plate.Glass wool is used to minimize heat loss from the absorber plateand tubes.

Various assumptions have been made to facilitate the theoret-ical analysis:

� The physical properties of the collector components areconstant.

� The water flow rate in the tubes is presumably uniform.� The temperature of the tube and the working fluid vary alongwith the y direction.

� The sky is assimilated as a blackbody.

Considering these assumptions, the equations governing theheat transfer in various components of PV/T collector are given asfollows:

For glass cover

rgdgCgdTgdt

¼ avGþ hray;g/env

�Tsky � Tg

�þ hwi

�Tamb � Tg

�þ �hray;pv/g þ hconv;pv/g

��Tpv � Tg

�þ kgdg

v2Tgðx; yÞ

vx2þ v2Tgðx; yÞ

vy2

!(1)

For PV module

rpvdpvCpvdTpvdt

¼ apvGtg þ�hray;pv/g þ hconv;pv/g

��Tg � Tpv

�� Eelec þ hcond;pv/pab

�Tpab � Tpv

�

þ kpvdpv

v2Tpvðx; yÞ

vx2þ v2Tpvðx; yÞ

vy2

!

(2)

Table 1Parameters used in simulations.

Components Parameters Value Unit

PV/T collector Area, Ac 1.5 m2

Slope 35� e

Glazing Thickness, dg 0.004 mSpecific heat, Cg 670 ðJ=kgKÞDensity, rg 2200 ðkg=m3ÞThermal conductivity, kg 0.9 ðW=mKÞEmissivity, εg 0.88 ————

PV module Specific heat, Cpv 900 ðJ=kgKÞThermal conductivity, kpv 140 ðW=mKÞEmissivity, εpv 0.93Reference cell efficiency, h0 17.8 %Packing factor, Pac 0.8Solar cell temperature coefficient, b 0.405 K�1

Absorber Plate Density, rpab 2702 ðkg=m3ÞThermal conductivity, kpab 310 ðW=mKÞ

Tube Density, rt 2702 ðkg=m3ÞThermal conductivity, kt 310 ðW=mKÞTube number 6 e

Diameter of tube, D 0.008 mThickness, dt 0.0012 m

Insulation Thickness, di 0.05 mDensity, ri 20 ðkg=m3ÞThermal conductivity, kpv 0.030 ðW=mKÞ

For Plate absorber � �

dTpabdt

¼ hcond;pv/pab Tpv � Tpab

þ Apab;t

Apabhcond;pab/t

�Tt � Tpab

�

þ hcond;pab/i

�Ti � Tpab

�

þ kpabdpab

v2Tpabðx; yÞ

vx2þ v2Tpabðx; yÞ

vy2

!

(3)For Tube

rtdtAtdyCtdTtdt

¼ Apab;thcond;pab/t

�Tpab � Tt

�þ Pehconv;t/fdy

�Tf � Tt

�

þ Ai;thcond;t/iðTi � TtÞ þ ktdt

v2Ttv2y

!(4)

Water in the tube

rf AfdyCfdTfdt

¼ Pehconv;t/fdy�Tt � Tf

��m

:CfDTf (5)

For Insulation

ridiCidTidt

¼ hcond;t/iAi;t

AiðTt � TiÞ þ hcond;pab/i

�Tpab � Ti

�

þ hwiðTamb � TiÞ þ kidi

v2Tiðx; yÞ

vx2þ v2Tiðx; yÞ

vy2

!(6)

The heat transfer coefficients used in the different energy bal-ances equations cited above are given as follows:

2.1. Heat transfer coefficients

2.1.1. Radiative coefficientsThe radiation heat transfer coefficient between the glazing and

sky, after assuming that the sky is a black body with a temperatureof Tsky is obtained by using the following equation.

hray;g/env ¼ εgs�T2g þ T2sky

��Tg þ Tsky

�(7)

Fig. 2. Comparisons of numerical results of thermal and electrical efficiencies ac-cording to the reduced temperature ðTin � TambÞ=G with experimental results [16].

Table 2RMS values.

Thermal efficiency Electrical efficiency

RMS 0.575% 2.31224%

O. Rejeb et al. / Renewable Energy 77 (2015) 43e5046

where s is the Stefan Boltzmann constant and εg is the emissivity ofthe glazing

Swinbank [10] suggest a simple relation, between the skytemperature and the ambient temperature.

Tsky ¼ 0:0522*T1:5amb (8)

The heat transfer radiation hray;pv/g between the glazing andthe photovoltaic module is reported in Ref. [11]:

hray;pv/g ¼s�T2g þ T2pv

��Tg þ Tpv

�1εpv

þ 1εg� 1

(9)

2.1.2. Conductive coefficientsThe convection heat transfer due to wind is estimated by the

following correlation [12]:

Fig. 3. Variations of ambient temperature and the horizontal solar radiation of four topical dOctober.

hwi ¼ 2:8þ 3Vwi (10)

The convective heat transfer coefficient hconv;pv/g between glasscover and PV is reported in Ref [13]:

hconv;pv/g ¼ Nuakada

(11)

where ka; da are respectively the thermal conductivity of air gapand the distance between the glass and the PV module. Nua is theNusselt number, expressed by the following correlation [13]

Nua ¼ 1þ 1:44�1� 1708

Rada cos q

�*

"1� 1708ðsin qÞ1:66

Rada cos q

#

þ"ðRada cos qÞ0:33

5830� 1

#* (12)

This expression is valid for tilt angles ranging from 0� to 75�

The convective heat transfer coefficient,hconv;t/f , within thetube, Bejan [14] proposed a relation which is used in the currentresearch.

ays of meteorological parameters of Monastir namely 3 January, 20 April, 17 July and 8

Fig. 4. Variations of thermal and electrical power of PV/T collector.

20 40 60 80 100Photovoltaic temperature (°C)

0.00

0.20

0.40

0.60

0.80

Ther

mal

effi

cien

cy

0.12

0.13

0.14

0.15

0.16

0.17

Elec

trica

lef fi

cien

cy

Thermal efficiency

Electrical efficiency

Fig. 5. Variations of thermal and electrical efficiencies with the PV temperature.

0 10 20 30 40Inlet water temperature (°C)

0.0

0.2

0.4

0.6

0.8

The

rmal

effi

cien

cy

0.00

0.04

0.08

0.12

0.16

0.20E

lect

rical

effi

cien

cy

Fig. 6. Variations of thermal and electrical efficiencies with the inlet watertemperature.

O. Rejeb et al. / Renewable Energy 77 (2015) 43e50 47

200 400 600 800 1000Solar irradiance (W/m²)

0.00

0.20

0.40

0.60

0.80

Therm

al e

ffic

iency

0.00

0.04

0.08

0.12

0.16

0.20

Ele

ctrica

l effic

iency

Fig. 7. Variations of thermal and electrical efficiencies with solar radiation.

0.2 0.4 0.6 0.8 1.0Packing factor

0.00

0.20

0.40

0.60

0.80

Therm

al effic

iency

0.00

0.04

0.08

0.12

0.16

0.20

Ele

ctr

ical effic

iency

Fig. 9. Variation of the thermal and electrical efficiency with the packing factor.

O. Rejeb et al. / Renewable Energy 77 (2015) 43e5048

Re<23000Nut ¼ 4:364 (13)

Re>23000Nut ¼ 0:023Re0:8Pr0:4 (14)

2.1.3. Conduction coefficientsThe conduction heat transfer coefficient between two neigh-

boring component layers m and n can be expressed by thefollowing correlation [11]:

hcond;m/n ¼ 1dmkm

þ dnkn

(15)

2.2. Expression of energy analysis

In order to evaluate the performance of the PV/T system, thethermal and electrical efficiencies are calculated.

The thermal efficiency of the PV/T can be described as [15]

hth ¼ m:Cp;f ðTout � TinÞ

AcG(16)

210Number of glass cover

0.0

0.2

0.4

0.6

0.8

Ther

mal

effi

cien

cy

0.00

0.04

0.08

0.12

0.16

0.20

Ele

ctric

al e

ffici

ency

Fig. 8. Variations of the thermal and electrical efficiencies for different numbers ofglazing covers.

m:,Cp;f G and Ac are water flow rate, specific heat of water, solar

radiation and area of collector, respectively.The electrical efficiency of the photovoltaic thermal collector is

stated as [16]

hel ¼ h0�1� b

�Tpv � 298

�(17)

whereh0 and b respectively represent the coefficient for photovoltaic

conversion efficiency and coefficient for photovoltaic conversionefficiency at reference temperature (298 K).

3. Results and discussion

In order to investigate the dynamic thermal and electricalbehavior of PV/T collector, a finite volume method has beenadopted to solve numerically the above system of equations(1)e(6). We have programmed our simulation in FORTRAN 90. Thesimulation carried out for the parameters values is summarized inTable 1.

3.1. Verification

In order to validate the mathematical model proposed in thiswork, a comparison between our numerical results and experimental

0 100 200 300 400 500Conductive heat transfer coefficienct between module photovoltaic and plate absorber (W/m²K)

0.00

0.20

0.40

0.60

Therm

al e

ffci

ency

0.00

0.04

0.08

0.12

0.16

0.20

Ele

ctrica

l effci

ency

Fig. 10. Variations of the thermal and electrical efficiencies with the conductive heattransfer coefficient between the plate absorber and the PV module.

Fig. 11. The predicted monthly electrical and thermal energy-outputs of PV/T sheet and tube collector.

O. Rejeb et al. / Renewable Energy 77 (2015) 43e50 49

results available in literature has been conducted.We have tested thevalidity of our numerical model under the same condition given byBhattary [17]. A mean root square percentage deviation (RMS) isutilized. It is given by [18,19].

RMS ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP ½100�Xexp;i � Xnum;i�=�Xexp;i

�2nexp

vuut (18)

where Xnum;i,Xexp;i represent respectively the numerical andexperimental values, nexp is the number of the experiments car-ried out.

In Fig. 2, we have plotted the thermal and electrical efficienciesgiven by Bhattary [17] and our model. We have observed that theresult of the current research is in good agreement with experi-mental results. In detail, the (RMS) are tabulated in Table 2.

We have also noticed that our model is effective and it can beused to predict the performance of PV/T collector.

3.2. Results and discussion

To study the PV/T collector behavior under Monastir climaticconditions, the numerical calculations have been carried out onfour typical days of the year for meteorological parameters ofMonastir namely 3 January, 20 April, 17 July and 8 October.

The variations of ambient temperature and the horizontalsolar radiation of four topical days are depicted in Fig. 3. Withregard to these parameters, the variations of electrical and heatpower are presented in Fig. 4. The maximum thermal and elec-trical power occurred in summer day and the minimum thermaland electrical power is observed in winter day. It's explained bythe higher solar radiation in summer day and the lower solarradiation in winter day.

The electrical and thermal powers are synchronized to theevolution of the solar radiation.

Fig. 5 shows the variation of the thermal and electrical effi-ciencies with the PV temperature. The increase of the PV temper-ature decrease the electrical efficiency. However, the increase of PVtemperature increase the thermal efficiency.

Fig. 6 reports the variation of the thermal and electrical effi-ciencies with the inlet water temperature. Increasing the inlettemperature of water leads to an increase in the temperature of thePV module and therefore, its electrical efficiency decreases. Simi-larly, the thermal efficiency decreases according to an increase in

water inlet temperature. This is due to an increase in the level of theabsorber temperature, consequently the thermal losses is onthe rise.

Fig. 7 shows the variation of the thermal and electrical effi-ciencies with solar radiation. The more of the solar radiationincreases the temperature of PV, rises consequently, the electricalefficiency decreases. However, increasing the solar radiationleads to an increase in solar heat gain and hence thermal effi-ciency increases. solar energy due to high reflection and lowtransmisstance. The choice of a single glazed solar collectorprovides the best compatibility between electrical and thermalefficiencies.

Fig. 8 illustrates the variations of the thermal and electrical ef-ficiencies for different numbers of glazing covers. When the num-ber of the glazing covers is increased, an increase and decrease ofthermal efficiency and electrical efficiency are respectivelyobserved. This could be explained by the fact that raising thenumber of glazing covers contributes, on one hand, to reduce heatlosses and on the other hand, to minimizing the amount of absor-bed solar energy due to high reflection and low transmisstance. Thechoice of a single glazed solar collector provides the best compat-ibility between electrical and thermal efficiencies. Fig. 9 shows thevariation of the thermal and electrical efficiencies with the packingfactor. An increase in the packing factor entails an increase inelectrical efficiency. However, an increase in the packing factorleads to a decrease in thermal efficiency. The more the surface areaof photovoltaic modules increases the more the electrical perfor-mance and hence the thermal efficiency decreases.

Fig. 10 illustrates the variations of the thermal and electricalefficiencies with the conductive heat transfer coefficient betweenthe plate absorber and the PV module. Increasing the conductiveheat transfer between the plate absorber and the PV module leadsto an increase in thermal and electrical efficiencies. Fig. 10 alsoshows that the increase of the conductive heat transfer betweenthe plate absorber and the PV module, beyond 300 W/m2K vale,does not provide a significant improvement in thermal and elec-trical efficiencies.

The monthly electrical and thermal output energies of photo-voltaic thermal sheet and tube collector (see Fig. 1) by consideringthe Monastir climatic conditions are shown in Fig. 11. It can be seenthat the maximum electrical and thermal output energy wererespectively of 8.119 kWh/m2 and 49.44 kWh/m2. These resultshave been obtained in the month of July; which is characterized bythe highest solar radiation in the year.

O. Rejeb et al. / Renewable Energy 77 (2015) 43e5050

4. Conclusion

In summary, a mathematical model for a solar photovoltaicthermal (PV/T) has been developed. The validity of this model istested by comparing simulation results to experimental ones foundin the literature [17]. A good agreement was obtained. A sensitivityanalysis of same parameters has been made. Numerical resultsshow that the increase of packing factor and heat conduction co-efficient between the photovoltaic module and the plate absorberenhances electrical efficiency while both decreases with the in-crease of the inlet water temperature and the solar radiation. Thethermal efficiency of the PV/T water collector increases with thesolar radiation and heat conduction coefficient between thephotovoltaic module and the plate absorber. However, it decreaseswith the rise of the inlet water temperature and the packing factor.The single cover glazing is a favorable choice to retain between theelectrical and thermal efficiencies. Moreover, the monthly electricaland thermal output energies of photovoltaic thermal sheet andtube collector are examined under Monastir (Tunisia) climaticconditions. It is concluded that the uncovered PV/T yields the bestelectrical performance, payback period and economic efficiency. Ithas found that the maximum electrical and thermal output energywere respectively of 8119 kWh/m2 and 49,44 kWh/m2.

Acknowledgments

The first author would thank Pr. Christophe M�en�ezo Head of theChair INSA de Lyon/EDF «Habitats and Energy Innovations» e

(CETHIL) for helpful discussions.

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