exergetic optimization of a solar photovoltaic thermal (pv/t) air collector

INTERNATIONAL JOURNAL OF ENERGY RESEARCH

Int. J. Energy Res. 2011; 35:813–827

Published online 16 June 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/er.1727

SHORT COMMUNICATION

Exergetic optimization of a solar photovoltaic thermal(PV/T) air collector

F. Sarhaddi�,y, S. Farahat, H. Ajam and A. Behzadmehr

Department of Mechanical Engineering, Shahid Nikbakht Faculty of Engineering, University of Sistan & Baluchestan, Zahedan

98164-161, Iran

SUMMARY

In this paper, an exergetic optimization has been developed to determine the optimal performance and designparameters of a solar photovoltaic thermal (PV/T) air collector. A detailed energy and exergy analysis has beencarried out to calculate the thermal and electrical parameters, exergy components, and exergy efficiency of a typicalPV/T air collector. The thermal and electrical parameters of a PV/T air collector include solar cell temperature,back surface temperature, outlet air temperature, open-circuit voltage, short-circuit current, maximum power pointvoltage, maximum power point current, etc. An improved electrical model has been used to estimate the electricalparameters of a PV/T air collector. Furthermore, a new equation for the exergy efficiency of a PV/T air collectorhas been derived in terms of design and climatic parameters. A computer simulation program has been alsodeveloped to calculate the thermal and electrical parameters of a PV/T air collector. The results of numericalsimulation are in good agreement with the experimental measurements noted in the previous literature. Moreover,the simulation results obtained in this paper are more precise than the one given by the previous literature, and thenew exergy efficiency obtained in this paper is in good agreement with the one given by the previous literature.Finally, exergetic optimization has been carried out under given climatic, operating, and design parameters. Theoptimized values of inlet air velocity, duct length, and the maximum exergy efficiency have been found. Parametricstudies have been also carried out. Copyright r 2010 John Wiley & Sons, Ltd.

KEY WORDS

exergy efficiency; exergetic optimization; solar photovoltaic thermal (PV/T) air collector

Correspondence

*F. Sarhaddi, Department of Mechanical Engineering, Shahid Nikbakht Faculty of Engineering, University of Sistan & Baluchestan,

Zahedan 98164-161, Iran.yE-mail: [email protected]

Received 30 September 2009; Revised 21 April 2010; Accepted 22 April 2010

1. INTRODUCTION

A solar photovoltaic thermal (PV/T) collector is a non-

adiabatic radiative heat exchanger. It receives solar

radiation energy and produces thermal and electrical

energy simultaneously. PV/T air collector systems can

be used for various applications, such as solar PV/T

dryers, PV/T greenhouses, building integrated photo-

voltaic thermal (BIPVT) systems, PV/T hybrid active

solar stills, PV/T solar water-heating systems, etc.

The energy payback time (EPBT) of a PV/T air

collector lies between 10 and 15 years depending on the

insulation and the performance of it. If the perfor-

mance of a PV/T air collector can be increased, the

energy payback time can be reduced. Therefore, the

optimized performance evaluation of a PV/T air

collector is important. The performance of a PV/T air

collector can be evaluated in terms of energy analysis

or exergy analysis.

Some deficiencies of energy analysis are mentioned

in References [1,2]. Exergy data are more practical

and realistic in comparison with the respective

energy values [1,2]. Thus, exergy analysis usually pro-

vides a more realistic view of process than energy

analysis.

A significant amount of theoretical as well as

experimental studies on the energy or exergy perfor-

mance evaluation of PV/T collector systems has been

carried out in the last 35 years.

Wolf [3] as early as in the 1970s has presented the

main concept of PV/T collector with the use of either

water or air as the coolant.

Copyright r 2010 John Wiley & Sons, Ltd.

Fujisawa and Tani [4] have compared the annual

performance of a flat-plate solar water-heating col-

lector, a PV module, a single-glazed PV/T collector

with mono-crystalline silicon solar cells, and an

unglazed one. The energetic evaluation of the

measured data showed that the single-glazed PV/T

collector is the best. In terms of exergy analysis,

unglazed PV/T collector gives the best performance.

The relations between energy and exergy, energy and

sustainable development, energy policy making, exergy

and the environment and exergy in detail have been

reported by Dincer [5].

Saitoh et al. [6] have compared the energy and

exergy efficiency of a brine-cooled PV/T collector with

a PV panel and a solar collector in Hokkaido (in

northern Japan) and given similar equations as taken

from Fujisawa and Tani [4].

Sahin et al. [7] have carried out the exergy analysis of

a PV array based on chemical potential components.

They have also obtained exergy components and PV

array exergy efficiency. Finally, they have compared

energy, electrical, exergy efficiencies under given cli-

matic and operating conditions.

Joshi and Tiwari [8] have carried out the energy and

exergy analysis of a PV/T parallel-plate air collector

for the cold climate region of India (in Srinagar). They

have reported that the instantaneous energy and

exergy efficiency of a PV/T air collector varies between

55–65% and 12–15%, respectively.

Badescu [9] has proposed an optimal operation

strategy for exergy gain maximization in open loop

thermal solar energy collection systems and

investigated the exergetic performance of an open loop

flat-plate solar collector. He has reported that the

maximum exergetic efficiency of the system is low

(usually less than 3%).

Aste et al. [10] have presented the experimental and

theoretical results of a research and development

(R&D) program on the design, development, and

performance monitoring of a PV/T air collector. They

have introduced an innovative technological system for

building integration of hybrid PVT air collectors and

reported the successful commercial application of their

system as a case study.

Nayak and Tiwari [11] have presented the perfor-

mance of a PV-integrated greenhouse system for

New Delhi climatic condition and reported that the

exergy efficiency of the system is 4%.

Raman and Tiwari [12] have compared the energy

and exergy performance of a hybrid photovoltaic

double-pass and single-pass air collector. They have

shown that electrical, thermal, and exergy efficiencies

of double-pass PV/T air collector are higher than sin-

gle-pass PV/T air collector.

Joshi et al. [13] have compared the thermal perfor-

mance of a glass-to-tedlar PV/T air collector and a

glass-to-glass PV/T air collector. Their results have

been shown; a glass-to-glass PV/T air collector has a

better thermal performance than a glass-to-tedlar

PV/T air collector.

Joshi et al. [14] have carried out the performance

analysis of both PV and PV/T system in terms of

exergy efficiency and reported that the thermal energy

due to solar radiation is actually a heat loss to the PV

system where as it is a useful heat for a PV/T system.

They have also shown that the electrical (exergy) effi-

ciency of a PV system can be improved if the heat can

be removed from the PV surface.

Dubey et al. [15] have evaluated the energetic and

exergetic performance of a PV/T air collector with air

duct above the absorber plate and the one with air duct

below the absorber plate. They have investigated the

effect of design and operating parameters and four

weather conditions on the performance of above-

mentioned PV/T air collectors for five different cities of

India and found that the latter one gives better results

in terms of thermal energy, electrical energy, and

exergy gain.

Tiwari et al. [16] have carried out the energy and

exergy analysis of an integrated photovoltaic thermal

solar (IPVTS) water heater. They have reported that

the overall exergy and thermal efficiency of an IPVTS

system are maximum at the hot water withdrawal flow

rate of 0.006 kg s�1.

Sarhaddi et al. [17] have optimized a PV array based

on exergy analysis and given useful results.

Sarhaddi et al. [18] have investigated the thermal

and electrical performance of a PV/T air collector

using an improved thermal and electrical model.

In the previous studies [3–18], the exergetic optimi-

zation of solar PV/T collector systems has not been

carried out.

In this paper, an exergetic optimization of a PV/T

air collector will be developed. A detailed energy and

exergy analysis will be carried out to calculate the

thermal and electrical parameters, exergy components,

and exergy efficiency of a typical PV/T air collector.

The thermal and electrical parameters of a PV/T air

collector include solar cell temperature, back surface

temperature, outlet air temperature, open-circuit vol-

tage, short-circuit current, maximum power point

voltage, maximum power point current, etc. Some

corrections will be carried out on heat loss coefficients.

An improved electrical model will be used to estimate

the electrical parameters of a PV/T air collector, such

as open-circuit voltage, short-circuit current, max-

imum power point voltage, maximum power point

current, etc. Furthermore, a new equation for the

exergy efficiency of a PV/T air collector will be derived

in terms of design and climatic parameters. A com-

puter simulation program will be developed to predict

the thermal and electrical parameters of a PV/T air

collector. Finally, the exergetic optimization of a PV/T

air collector will be carried out; also, the effect of cli-

matic, design, and operating parameters on exergy

efficiency will be studied.

Exergetic optimization of a solar PV/T air collectorF. Sarhaddi et al.

Int. J. Energy Res. 2011; 35:813–827 r 2010 John Wiley & Sons, Ltd.

DOI: 10.1002/er

814

The exergy efficiency of a PV/T air collector is

parametrically dependent on its energy analysis.

Hence, first, the energy analysis of a PV/T air collector

will be carried out. Then, the exergy components and

exergy efficiency of a PV/T air collector will be com-

puted and optimized.

2. ENERGY ANALYSIS

2.1. Thermal analysis

The proof of governing equations on PV/T air

collector thermal analysis is not included in order to

have a brief note. More details of governing equations

derivation are found in References [8,11–13,15,16,18].

Figure 1 shows the equivalent thermal resistant cir-

cuit of a PV/T air collector [18].

Writing the energy balance equation for each com-

ponent of a PV/T air collector gives the thermal

parameters and thermal efficiency of a PV/T air col-

lector as follows:

Tcell ¼ ½ðatÞeffG1UtTamb1UTTbs�=ðUt1UTÞ; ð1Þ

Tbs ¼ ½hp1ðatÞeffG1UtTTamb1hfTf ��ðUtT1hf Þ; ð2Þ

Tf ;out ¼ ðTamb þ hp1hp2ðatÞeffG=ULÞ

� ½1� expð�WULL= _mCpÞÞ�

1Tf ;in expð�WULL=ð _mCpÞÞ; ð3Þ

�Tf ¼1

L

Z L

x¼0Tf ðxÞdx

¼ ½Tamb1hp1hp2ðatÞeffG=UL�

� ½1�½1�expð�WULL=ð _mCpÞÞ�=ðWULL=ð _mCpÞÞ�

1Tf ;in½1�expð�WULL=ð _mCpÞÞ�=ðWULL=ð _mCpÞÞ;

ð4Þ

_Qu ¼ _mCpðTf ;out � Tf ;inÞ

¼ ð _mCp=ULÞ½hp1hp2ðatÞeffG�ULðTf ;in � TambÞ�

� ½1� expð�WULL=ð _mCpÞÞ�; ð5Þ

Zth ¼ _Qu=ðWLGÞ

¼ ð _mCp=WLULÞ½hp1hp2ðatÞeff �ULðTf ;in � TambÞ=G�

� ½1� expð�WULL=ð _mCpÞÞ�; ð6Þ

where Tcell, Tbs, Tamb, Tf,out, �Tf , _Qu, G, _m, Cp, L, W,

and Zth are solar cell temperature, back surface tem-

perature, ambient temperature, outlet air temperature,

average air temperature in flow duct, the rate of useful

thermal energy, solar radiation intensity, the mass flow

rate of flowing air, the heat capacity of flowing air, the

length of air duct, the width of air duct, and PV/T air

collector thermal efficiency, respectively. In the above

equations, the related heat transfer coefficients are

defined as follows [18]:

ðatÞeff ¼ tg½acbc1aTð1� bcÞ � bcZel�; ð7Þ

hp1 ¼ UT=ðUT1UtÞ; ð8Þ

hp2 ¼ hf=ðUtT1hf Þ; ð9Þ

UtT ¼ ½1=Ut11=UT��1 ¼ UtUT=ðUT1UtÞ: ð10Þ

Utf ¼ ½1=hf11=UtT��1 ¼ UtThf=ðUtT1hf Þ; ð11Þ

To increase the calculations precision of PV/T air

collector thermal parameters, some corrections have

been carried out on heat loss coefficients in a same

manner of Reference [18]. These corrections are not

mentioned to have a brief note [18].

2.2. Electrical analysis

As the presence of the electrical efficiency of PV

module Zel in Equation (7), the thermal parameters of

PV/T air collector and its electrical parameters are

dependent. The calculation precision of thermal

parameters of a PV/T air collector will be improved

if the electrical efficiency of PV module is calculated in

a precise way.

In the previous studies [3–17], the electrical efficiency

of a PV module has been calculated from the following

equation:

Zel ¼ Zel;ref ½1� 0:0045ðTcell � Tamb;ref Þ�: ð12ÞFigure 1. The equivalent thermal resistant circuit of a PV/T

air collector [18].

Exergetic optimization of a solar PV/T air collector F. Sarhaddi et al.

815Int. J. Energy Res. 2011; 35:813–827 r 2010 John Wiley & Sons, Ltd.

DOI: 10.1002/er

The subscript ‘ref’ indicates the value of parameters

at the reference conditions. Equation (12) has some

deficiencies. The deficiencies of Equation (12) are

mentioned in Reference [18].

In this research, the electrical efficiency of a PV

module and its electrical parameters are calculated

from the electrical simulation of a PV module. The

proof of governing equations on PV module electrical

analysis is not included to have a brief note. A PV

module is nonlinear device and can be represented by

its current–voltage (I–V) characteristic curve. Five-

parameter photovoltaic model for I–V characteristic

curve is defined as follows [19]:

I ¼ IL � Io½expððV1IRsÞ=aÞ � 1� � ðV1IRsÞ=Rsh;

ð13Þ

where I and V represent current and voltage at load, a,

IL, Io, Rs, and Rsh are ideality factor, light current,

diode reverse saturation current, series resistance, and

shunt resistance, respectively.

The calculation relations of five parameters a, IL, Io,

Rs, and Rsh at reference conditions (Tcell,ref 5 251C,

Gref 5 1000Wm�2 [20]) or at other climatic and oper-

ating conditions (Gnew, Tcell,new) have been mentioned

in Reference [18]. These relations are not included to

have a brief note.

The electrical efficiency of a PV module can be de-

fined as the ratio of actual electrical output power to

input the rate of solar energy incident on the PV sur-

face as follows [7,8,11–18]:

Zel ¼ VmpImp=S ¼ ðVocIscÞFF=S ¼ Eel=S; ð14Þ

where Voc, Vmp, Isc, Imp, FF, and Eel are open-circuit

voltage, maximum power point voltage, short-circuit

current, maximum power point current, fill factor, and

outlet electrical power, respectively. Furthermore, the

rate of solar energy incident on the PV surface (S) is

given by

S ¼ GNsNmAmod; ð15Þ

where Ns and Nm are the number of strings and the

number of modules in series per string, respectively.

PV module area (Amod) is given by

Amod ¼ L1L2; ð16Þ

where L1 and L2 are the length of PV module and the

width of PV module, respectively.

The overall energy efficiency of a PV/T air collector

can be calculated by adding the thermal efficiency

(Equation (6)) and thermal efficiency equivalent of

electrical efficiency as follows [13,18]:

Zen;ov ¼ Zth1Zel;th ¼ Zth1ðZel=0:36Þ: ð17Þ

In Equation (17), the coefficient 0.36 is the conver-

sion factor of the thermal power plant [13,18].

3. EXERGY ANALYSIS

Exergy analysis is a technique that uses the conserva-

tion of mass and conservation of energy principles

together with the second law of thermodynamics for

the analysis, design, and improvement of energy and

other systems. Exergy is defined as the maximum

amount of work that can be produced by a system or a

flow of mass or energy as it comes to equilibrium with

a reference environment [21].

The general form of exergy balance equation for a

control volume is written as [21,22]:XExinput;net �

XExoutput;net ¼

XExdestroyed; ð18Þ

whereP

Exoutput;net,P

Exinput;net, andP

Exdestroyed are

the net (desired) output exergy from control volume,

the net input exergy to control volume, and exergy

destructions in control volume, respectively.

The exergy efficiency of a PV/T air collector is de-

fined as the ratio of net output exergy to net input

exergy [21,22]:

Zex ¼P

Exoutput;netPExinput;net

¼ 1�P

ExdestroyedPExinput;net

: ð19Þ

According to Equation (19), the exergy efficiency of a

PV/T system can be calculated in terms of the net output

exergy of the system or exergy destructions in the system.

In this research, the exergy efficiency of PV/T system is

evaluated in terms of the net output exergy of the system.

3.1. The exergy destructions in controlvolume

According to the Gouy–Stodola theorem, the exergy

destructions in control volume are equal to the product

of reference environmental temperature to the entropy

generation in control volume [21,22]XExdestroyed ¼ T0

_Sgen; ð20Þ

where T0 and _Sgen are the reference environmental

temperature and the entropy generation in control

volume, respectively. Some relations for exergy

destruction components in solar collectors and PV

systems are reported in References [9,17,21,22]. These

relations are not mentioned to have a brief note.

3.2. The net input exergy of PV/T aircollector

The net input exergy of PV/T air collector includes

solar radiation intensity exergy (ExQ,sun). According to

the Petela theorem, it is given by [1,2]XExinput;net ¼ ExQ;sun

¼ S½1� 4ðTamb=TsunÞ=31ðTamb=TsunÞ4=3�;

ð21Þ

where Tsun is the sun’s temperature in Kelvin.



DOI: 10.1002/er

816

3.3. The net output exergy of PV/T aircollector

It includes thermal exergy and electrical exergy

[8,11,12,14–16]XExoutput;net ¼

XExthermal1

XExelectrical: ð22Þ

The thermal exergy includes the thermal exergy of

PV/T system and the thermal exergy of PV systemXExthermal ¼ Exthermal;PV=T1Exthermal;PV: ð23Þ

The thermal exergy of PV/T system includes the ex-

ergy changes of flowing air in air duct [21,22]

Exthermal;PV=T ¼ _mCp½Tf ;out � Tf ;in � Tamb

� lnðTf ;out=Tf ;inÞ�1 _mRTamb

� lnðPf ;out=Pf ;inÞ; ð24Þ

where R, Pamb, Pf,in, and Pf,out are gas constant,

ambient pressure, agent fluid pressure at entrance and

exit from PV/T air collector, respectively.

The thermal exergy of PV system includes the exergy

changes of initial and final mass in control volume. As

the inlet and outlet mass flow rate to control volume

are equal, there is no accumulation of mass in control

volume; therefore, initial and final mass in control

volume is constant and equal to PV module mass. The

exergy changes of the mass in control volume is defined

as [7,14,17,21,22]

Exthermal;PV ¼ ðmcellCp;cell=DtÞ

½Tcell � Tamb � Tamb lnðTcell=TambÞ�

� ðVocIsc � VmpImpÞTcell=Tsun:

ð25Þ

The first terms on the right hand side of the Equa-

tion (25) indicate physical exergy changes and the

second terms show exergy changes due to the varia-

tions of chemical potential in PV module [7,14], where

mcell and Dt are PV module mass and time interval,

respectively.

The electrical exergy includes only the outlet elec-

trical power of PV module [7,14,17]:XExelectrical ¼ VmpImp ¼ Eel: ð26Þ

3.4. The exergy efficiency of PV/T aircollector

Substituting Equations (21)–(26) into Equation (18)

and considering exergy efficiency definition (Equation

(19)), the exergy efficiency of a PV/T air collector is

obtained:

Zex ¼_mCp½Tf ;out � Tf ;in � Tamb lnðTf ;out=Tf ;inÞ�1 _mRTamb lnðPf ;out=Pf ;inÞ

S½1� 4ðTamb=TsunÞ=31ðTamb=TsunÞ4=3�

1ðmcellCp;cell=DtÞ½Tcell � Tamb � Tamb lnðTcell=TambÞ� � ðVocIsc � VmpImpÞTcell=Tsun1VmpImp

S½1� 4ðTamb=TsunÞ=31Tamb=TsunÞ4=3�

:

Equation (27) is a new equation for the exergy effi-

ciency of a PV/T air collector in terms of thermal, elec-

trical, design parameters, and climatic conditions.

It includes all of the exergy components of a PV/T air

collector. On the other hand, the electrical parameters

appear in this equation directly. In the previous studies

[4,6,8,11,12,15,16], the exergy efficiency of a PV/T air

collector has been calculated from the following equation:

Zex ¼ Zth½1� ðTamb=Tf ;outÞ�1Zel¼ _Qu½1� ðTamb=Tf ;outÞ�=ðWLGÞ

þ Zel;ref ½1� 0:0045ðTcell � Tamb;ref Þ�: ð28Þ

Equation (28) has some deficiencies; first, Equation (28)

does not include the pressure exergy terms of airflow and

the exergy components of chemical potential in PV

module. Second, Equation (28) has a significant error at

low solar radiation intensity. At low solar radiation in-

tensity, it gives PV/T exergy efficiency equal to the elec-

trical efficiency of the reference conditions (ZexEZel,ref50.12). The equivalence of the solar cell and ambient

temperature and the negligible amount of _Qu are the

reasons of this fact.

4. FORMULATION OFOPTIMIZATION PROBLEM

The energy and exergy models presented in the previous

sections have been inserted into a MATLAB computa-

tional program. In this program, most of the climatic,

operating, and design parameters of PV/T air collector

can be variables. The formulation of optimization

problem, considering the quantities Tamb, Tamb,ref, Tcell,ref,

Tf,inETamb, Tsun, G, Gref, Dt, Zel,ref, L1, L2, Amod, W,

Voc,ref, Vmp,ref, Isc,ref, Imp,ref, ac, bc, aT, tg, R, Pf,inEPamb,

Vw, and Nm as constant parameters is given by

Maximize Zex ¼ Equation ð27Þ;

subject to

Equations ð1Þ�ð11Þ; Equations ð13Þ�ð16Þ

and

0:001inp15ms�1;

L1pLp13L1m;

Tcell;Tf ;out;Tbs; �Tf ;Pf ;out; _m;mcell;Cp;Cp;cell; Io;

IL;Rs;Rsh; a; Isc;Voc; Imp;Vmp;S;UL;Ut;

ðatÞeff ; hp1; hp2; hfX0;

Ns;NcX1 and are integer: :

8>>>>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>>>>:

(27)



DOI: 10.1002/er

where Vin and L are independent parameters and Tcell,

Tf,out, Tbs, �Tf , Pf,out, _m, mcell, Cp, Cp,cell, Io, IL, Rs, Rsh,

a, Isc, Voc, Imp, Vmp, S, UL, Ut, Ns, Nc, (at)eff, hp1, hp2,and hf are dependent parameters in optimization

procedure. The number of constraint equations,

independent optimization parameters, and dependent

optimization parameters are 16, 2, and 26, respectively.

The objective function and its constraint equations are

nonlinear. Therefore, a real-coded genetic algorithm

program has been developed to optimize the objective

function [23].

5. RESULTS AND DISCUSSION

5.1. Experimental validation

The experimental results of Joshi et al. [13] for a PV/T

air collector make it possible to verify the results

obtained by our computer simulation. The measured

data in Reference [13] include the solar radiation

intensity, ambient temperature, inlet and outlet air

temperature, solar cell temperature, back surface

temperature, inlet air velocity, open-circuit voltage,

short-circuit current, and outlet electrical power.

Additional information about the experiment method

and its conditions are found in Reference [13]. The

simulated values of outlet air temperature, solar cell

temperature, back surface temperature, open-circuit

voltage, short-circuit current, outlet electrical power,

thermal efficiency, electrical efficiency, and overall

energy efficiency in this work have been validated by

their corresponding experimental values in Reference

[13]. Further, a comparison between the simulated

values of outlet air temperature, solar cell temperature,

back surface temperature, outlet electrical power,

thermal efficiency, electrical efficiency, and overall

energy efficiency in this work and their corresponding

calculated values in Reference [13] have been carried

out. The experimental and calculated values of the

parameters described above have been obtained from

the figures and tables of Reference [13].

The climatic, operating, and design parameters of

the PV/T air collector during validation process are

described in Table I.

They correspond to the experimental system

described by Joshi et al. [13], except that they did not

report the wind speed observed over the course of their

tests. This affects the convective heat transfer coeffi-

cient between the PV/T air collector surface and the

ambient air.

In Table I, a wind speed of 1m s�1 is assumed to

have a comparison with the experimental data. On the

other hand, additionally performed calculations for

different wind speeds are also reported in the next

section.

To compare the simulated results with the experi-

mental measurements, a root mean square percentage

deviation (RMS) has been evaluated by following

equation [13,19]:

RMS ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX½100� ðXsim;i � Xexp;iÞ=Xsim;i�2=n;

qð29Þ

where n is the number of the experiments carried

out.

The variations of solar radiation intensity, ambient

temperature, inlet air temperature, and inlet air velo-

city during the test day are shown in Figure 2.

The simulated values of outlet air temperature, solar

cell temperature, back surface temperature and the

corresponding experimentally measured data during

the test day are shown in Figure 3.

The calculated values of these parameters presented

by Joshi et al. [13] are also shown in the same figure for

comparison. In this figure, the subscript ‘sim’ indicates

Table I. The values of climatic, operating, and design para-

meters during validation process, optimization procedure, and

parametric studies of PV/T air collector [13,18,20].

Solar PV/T air collector parameters Value

PV module type Siemens SP75,

monocrystalline silicon

The length of PV module, L1 1.2 m

The width of PV module, L2 0.527 m

The number of modules in

series per string, Nm

1

The number of strings, Ns 2

The short-circuit current at

the reference conditions, Isc,ref

Ns� 4.8 A

(for total PV array)

The open-circuit voltage at

the reference conditions, Voc,ref

Nm� 21.7 V


The maximum power point current

at the reference conditions, Imp,ref

Ns� 4.4 A


The maximum power point voltage

at the reference conditions, Vmp,ref

Nm� 17 V


The solar radiation intensity at

the reference conditions, Gref

1000 W m�2

The ambient temperature at

reference conditions, Tamb,ref

298.15 K

The solar cell temperature at

reference conditions, Tcell,ref

298.15 K

The electrical efficiency at

the reference conditions, Zel,ref

0.12

The sun temperature, Tsun 5760 K

The current temperature coefficient, a 2.06 mA 1C�1

The voltage temperature coefficient, b �0.077 V 1C�1

The transmitivity of glass cover tg 0.95

The absorptivity of solar cell, ac 0.85

The absorptivity of tedlar, aT 0.5

The length of air duct, L 1.2 m

The width of PV/T air collector, W 0.45 m

The packing factor of solar cell, bc 0.83

The wind speed, Vw 1 m s�1

The time interval, Dt 3600 s

The ambient pressure, Pamb 101 kPa



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818

Figure 2. The variations of solar radiation intensity, ambient temperature, inlet air temperature, and inlet air velocity during the test day [13].

Figure 3. The simulated and calculated values of outlet air temperature, solar cell temperature, back surface temperature, and the

corresponding experimentally measured data during the test day.



DOI: 10.1002/er

the simulated values of parameters in this work and the

subscript ‘cal’ shows the calculated values of para-

meters by Joshi et al. [13]. According to this figure, it is

observed that there is a good agreement between the

experimental and simulated values of these parameters.

Further, the RMS percentage deviation of these

parameters are 2.37, 12.58, and 8.63%, respectively.

The RMS percentage deviation of these parameters

reported by Joshi et al. [13] are 4.75, 16.38, and

14.99%, respectively. It is observed from the figure that

our simulated results are more precise than the calcu-

lated results of Reference [13].

The simulated and experimental values of open-cir-

cuit voltage and short-circuit current during the test

day are shown in Figure 4.

The values of RMS percentage deviation are 2.24

and 13.25%, respectively. It is observed from the figure

that there is a good agreement between the simulated

and experimental values of these parameters. The

electrical model used in Reference [13] (Equation (12))

cannot estimate open-circuit voltage and short-circuit

current.

Figure 5 shows the simulated values of maximum

power point voltage, maximum power point current,

and the experimental and simulated values of electrical

power during the test day.

The experimental values of maximum power point

voltage and maximum power point current are not

mentioned in Reference [13]. Furthermore, the elec-

trical model used in Reference [13] (Equation (12))

cannot estimate the electrical parameters of PV/T air

collector. However, the electrical model used in this

work is able to predicate the electrical parameters.

The experimental and simulated values of outlet

electrical power and the calculated values of outlet

electrical power presented by Joshi et al. [13] during the

test day are shown in the same figure. The respective

values of RMS percentage deviation are 5.3 and

11.05%, respectively. It is observed that there is a good

agreement between the simulated and experimental

values of outlet electrical power. Further, it is observed

that the simulated values of outlet electrical power in

this work are more precise than the calculated values of

electrical power presented by Joshi et al. [13].

Figure 6 shows the experimental and simulated

values of overall energy efficiency, thermal efficiency,

and electrical efficiency during the test day.

The calculated values of these efficiencies presented

by Joshi et al. [13] are also shown in the same figure for

comparison. According to this figure, it is observed

that there is a good agreement between the experi-

mental and simulated values of these efficiencies.

Further, the RMS percentage deviations of these effi-

ciencies are 5.51, 24.42, and 5.32%, respectively. The

RMS percentage deviations of these efficiencies

reported by Joshi et al. [13] are 9.81, 28.56, and

11.02%, respectively. It is observed that our simulated

results are more precise than the calculated results of

Reference [13].

The simulated and experimental values of exergetic

efficiency described by Equations (27) and (28) during

the test day are shown in Figure 7.

Figure 4. The simulated and experimental values of open-circuit voltage and short-circuit current during the test day.



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820

Figure 5. The simulated values of maximum power point voltage, maximum power point current, and the simulated and

experimental values of electrical power during the test day.

Figure 6. The experimental and simulated values of overall energy efficiency, thermal efficiency, and electrical efficiency during the test day.



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The respective values of RMS percentage deviation

are 5.15 and 5.57%, respectively. It is observed from

the figure that there is a good agreement between the

simulated and experimental values of the exergetic

efficiency described by Equations (27) and (28).

A comparison between the experimental values of

exergetic efficiency given in Equation (27) and the

one given by Equation (28) is also carried out in

the same figure. It is clear from the figure that there

is a good agreement between these two exergy

efficiencies with a RMS of percentage deviation

(RMS)5 2.36%.

According to Figures 6 and 7, it is observed that the

behavior of exergy efficiency with respect to the var-

iations of climatic, operating, and design parameters is

so similar to the electrical efficiency of PV/T air col-

lector. The exergy shows the quality of energy. The

quality of thermal energy (thermal exergy) in a PV/T

air collector is low (Zex,thp2%); therefore, the exergy

efficiency value of a PV/T air collector is near to its

electrical efficiency value (ZexEZelE11%).

The good agreement between experiment and

simulation that are shown in the previous figures

(Figures 3–7) indicates that the assumption of a wind

speed as 1m s�1 in the calculations is reasonable.

The simulated parameters errors compared with

those obtained by the experimental measurement is

explained as follows:

� the temperature coefficients of current and voltage

have been assumed constant. In practical cases, they

have slight fluctuation due to the solar radiation

intensity and PV module temperature variations;

� the experimental and calculated results of

Reference [13] have been obtained from the

figures of Reference [13] by interpolation and

curve fitting methods. This subject decreases the

precision of measured data;

� wind speed is not constant and has a direct effect

on the overall heat loss coefficient that can

decrease the precision of calculated overall heat

loss coefficient in the computer simulation;

� the product of effective absorptivity and trans-

mittivity,(at)eff, has been assumed constant while

it is changing during the day with the change of

solar incidence angle on PV/T collector surface.

5.2. Optimization results

The type of PV/T air collector, its selected environmental,

design conditions, and constant parameters during the

optimization procedure are described in Table I. The

typical results of optimization procedure under the

sample conditions of Table I, Tf,in5Tamb5300K,

Figure 7. The simulated and experimental values of exergetic efficiency described by Equations (27) and (28) during the test day.



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822

Pf,in5Pamb5101kPa, Vw51ms�1, G5700Wm�2,

Nm51, are been given in Table II.

5.3. Parametric studies

The values of climatic, operating, and design para-

meters in the parametric studies of PV/T air collector

are described in Table I. In order to plot the following

figures, some parameters are assumed that are men-

tioned above each figure. The rest of the parameters

needed to plot the following figures are used from

Table I.

Figure 8 shows the behavior of the exergy efficiency

as a function of inlet air velocity (Vin) and duct length

(L), it is presented to a range of operational and design

conditions where the exergy efficiency takes a global

maximum value.

The incremented quantities are inlet air velocity

from 0.001 to 15m s�1 and duct length from 1.2 to

15.6m. It is observed from this figure that there is a

global maximum point and the coordinate of this point

shows the values of optimized parameters. The calcu-

lated values of global maximum point are

Vin,opt 5 4.83m s�1, Lopt 5 6m, Zex,max 5 11.12%. In

the optimized value of duct length (Lopt 5 6m), the

exergy efficiency increases from �10 to �11.12%

initially and then after attaining the inlet air velocity of

Vin 5 4.83m s�1, it decreases to�8.3%. This indicates

the optimum value of inlet air velocity for given cli-

matic and design parameters (Table I). To illustrate the

behavior of exergy efficiency with respect to duct

length, Figure 9(a) has been plotted.

According to this figure, the exergy efficiency has a

slight variation (�11%) with respect to the changes of

duct length (1.2pLp15.6m) in the optimum value of

inlet air velocity (Vin,opt 5 4.83m s�1). However, there

Figure 8. The exergy efficiency as a function of inlet air velocity and duct length.

Table II. The typical results of optimization procedure under

the sample conditions of Table I, Tf,in 5 Tamb 5 300 K, Pf,in 5

Pamb 5 101 kPa, Vw 5 1 m s�1, G 5 700 W m�2, and Nm 5 1.

Optimization parameters Value

The maximum exergy efficiency, Zex,max 11.12%

The optimum inlet air velocity, Vin,opt 4.83 m s�1

The optimum length of air duct, Lopt 6 m

The thermal efficiency, Zth 28.15%

The electrical efficiency, Zel 10.12%

The overall energy efficiency, Zen,ov 56.7%

The outlet air temperature, Tf,out 315 K

The solar cell temperature, Tcell 323.5 K

The back surface temperature, Tbs 318.72 K

The average air temperature, �Tf 308.11 K

The rate of useful thermal energy, _Qu 532.16 W

The rate of solar energy incident

on the PV/T surface, S

2213.4 W

The open-circuit voltage, Voc 19.06 V

The short-circuit current, Isc 17 A

The maximum power point voltage, Vmp 14.81 V

The maximum power point current, Imp 15.13 A

The light current, IL 16.99 A

The diode reverse saturation current, Io 0.466 A

The series resistance, Rs 0.059OThe shunt resistance, Rsh 116.422OThe ideality factor, a 1.73 eV

The overall heat transfer coefficient, UL 6.86 W m�2 K�1

The heat capacity of flowing air, Cp 1 kJ kg�1 K�1

The number of strings, Ns 5

The product of effective absorptivity

and transmittivity, (at)eff

0.67

The penalty factor due to the presence

of solar cell material, glass, and EVA, hp1

0.79

The penalty factor due to the presence of

interface between tedlar and working fluid, hp2

0.68



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Figure 9. (a) The variations of exergy efficiency with respect to duct length and (b) the variations of exergy efficiency with respect

to inlet air temperature.

Figure 10. (a) The effect of solar radiation intensity on the exergy efficiency and (b) the variations of exergy efficiency according

to the changes of wind speed.



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824

is a optimized point for duct length that is equal with

Lopt 5 6m.

It is assumed that PV/T air collectors are connected

in series. For a number of PV/T air collectors con-

nected in series, the outlet temperature of the first

collector will be the inlet for second collector, the

outlet temperature of the second will be the inlet for

the third and so on.

The variations of exergy efficiency with respect to

inlet air temperature are plotted in Figure 9(b). The

exergy efficiency has a slight change with respect to

inlet air temperature variations (�11.2%). This sub-

ject allows the designer to optimize PV/T air collector

with respect to other conditions such as design lim-

itations and thermal applications.

Figure 10(a) shows the effect of solar radiation

intensity on the exergy efficiency.

It is observed that the exergy efficiency increases

from�3 to�11.43% initially and then it decreases to

�10.8% after the solar radiation intensity reaches

about 290Wm�2. This indicates the optimum value of

solar radiation intensity for given climatic and design

parameters (Table I).

Figure 10(b) shows the variations of exergy effi-

ciency according to the changes of wind speed. The

exergy efficiency increases from �11.09 to �11.4%

while wind speed is increasing from 0 to 10m s�1.

6. CONCLUSIONS

On the basis of this study, the following conclusions

have been drawn:

� The numerical simulation results of this study are

in good agreement with the experimental mea-

surements noted in the previous literature.

Furthermore, it is observed that the simulation

results obtained in this paper are more precise

than the one given by the previous literature.

� The new exergy efficiency obtained in this paper is

in good agreement with the one given by the

previous literature (for inlet air velocity less than

5m s�1).

� Increasing inlet air velocity or solar radiation

intensity, the exergy efficiency of a PV/T air

collector increases initially and then decreases

after attaining inlet air velocity or solar radiation

intensity of about a maximum point.

� The exergy efficiency of a PV/T air collector has a

slight change with respect to duct length or inlet

air temperature. This subject allows the designer

to optimize PV/T air collector with respect to

other conditions such as design limitations and

thermal applications.

� While increasing wind speed, the exergy efficiency

of a PV/T air collector increases.

NOMENCLATURE

a 5 ideality factor (V)

A 5 area (m2)

Cp 5 specific heat capacity of air

(J kg�1K�1)

Cp;cell 5 specific heat capacity of silicon

solar cell (J g�1K�1)

dx 5 elemental length of flow duct (m)

E 5 power (W)

EVA 5 ethyl vinyl acrelate

Ex 5 exergy (W)

FF 5 fill factor (dimensionlees)

G 5 solar radiation intensity (Wm�2)

h 5heat transfer coefficient (Wm�2K�1)

hp1 5penalty factor due to the presence

of solar cell material, glass, and EVA

hp2 5 penalty factor due to the presence of

interface between tedlar and

working fluid

I 5 circuit current (A)

I–V 5 current–voltage

L 5 dimensions of solar module, duct

length, the length of PV/T air

collector, thickness (m)

mcell 5mass of PV module (g)_m 5mass flow rate of air (kg s�1)

n 5 number of experiments

Nc 5 number of cells in PV module

Nm 5 number of modules in series per

string

Ns 5 number of string

P 5 pressure (Pa)

PV 5 photovoltaic

PV/T 5 photovoltaic/thermal collector_Q 5 heat transfer rate (W)

R 5 gas constant (kJ kg�1K�1),

resistance (O)RMS 5 root mean square percentage

deviation (%)

S 5 the rate of solar energy incident on

the PV surface (W)_Sgen 5 entropy generation (WK�1)

t 5 time interval (s)

T 5 temperature (K)

T0 5 reference environmental

temperature (K)

Ub 5 an overall back loss coefficient from

flowing air to ambient (Wm�2K�1)

UL 5 an overall heat loss coefficient from

the PV/T air collector to the

environment (Wm�2K�1)

Ut 5 an overall heat transfer coefficient

from solar cell to ambient through

glass cover (Wm�2K�1)

UT 5 a conductive heat transfer coefficient

from solar cell to flowing air through

tedlar (Wm�2K�1)



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UtT 5 an overall heat transfer coefficient

from glass-to-tedlar through solar

cell (Wm�2K�1)

Utf 5 an overall heat transfer coefficient

from glass-to-air through solar cell

and tedlar (Wm�2K�1)

V 5 circuit voltage (V), wind speed

(m s�1)

W 5 the width of PV/T air collector (m)

X 5 experimental or simulated value of

parameter

Greek symbols

a 5 absorptivity, current temperature

coefficient (mA 1C�1)

(at)eff 5 the product of effective

absorptivity and transmittivity

b 5 packing factor, voltage

temperature coefficient (V 1C�1)

D 5 difference in current, temperature,

time, and voltage

Z 5 efficiency (%)

t 5 transmittivity

Subscripts

1 5 length

2 5width

amb 5 ambient

b 5 back

bs 5 back surface of tedlar

c 5 solar cell

cal 5 calculated

cell 5 cell, module

conv 5 convection

destroyed 5 destroyed

el 5 electrical

electrical 5 electrical

en 5 energy

ex 5 exergy

exp 5 experimental

f 5 fluid flow

g 5 glass

i 5 insulation, ith parameter

in 5 inlet

input 5 input

L 5 light current

max 5maximum

mod 5module

mp 5maximum power point

net 5 net

new 5 new

o 5 reverse saturation

oc 5 open-circuit

opt 5 optimum

out 5 outlet

output 5 output

Q 5 heat transfer

ov 5 overall

PV 5PV

PV/T 5PV/T

rad 5 radiative

ref 5 reference

s 5 series

sc 5 short-circuit

sh 5 shunt

sim 5 simulated

sun 5 sun

t 5 top

T 5 tedlar

th 5 thermal

thermal 5 thermal

u 5 useful

w 5wind

ACKNOWLEDGEMENTS

The authors acknowledge Prof. A. D. Sahin [7] forresponding to our inquiries.

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