Research ArticleTheoretical Study and Experimental Validation of EnergeticPerformances of Photovoltaic/Thermal Air Collector

Khaled Touafek ,1 Abdelkrim Khelifa,1 Lyes Boutina,1 Ismail Tabet,2 and Salim Haddad2

1Unité de Recherche Appliquée en Energies Renouvelables (URAER), Centre de Développement des Energies Renouvelables (CDER),47133 Ghardaïa, Algeria2Université de Skikda, Algeria

Correspondence should be addressed to Khaled Touafek; khaledtouafek@yahoo.fr

Received 12 June 2018; Revised 13 September 2018; Accepted 8 October 2018; Published 19 December 2018

Academic Editor: Giulia Grancini

Copyright © 2018 Khaled Touafek et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This work undertakes both simulation and experimental studies of a new design of a photovoltaic thermal solar air collector(PV/T). In order to improve the thermal and electrical performances for a specific application, the analytical expressions forthermal parameters and efficiency are derived by developing an energy balance equation for each component of the PV/T aircollector. This type of hybrid collector can be applied in the facades of buildings. The electricity and heat produced will satisfythe energy needs of the buildings, while ensuring an aesthetic view of its facades. A typical prototype was designed, constructed,and implemented in the applied research unit on renewable energies in Ghardaia, situated in the south of Algeria. This regionhas semiarid characteristics. Results obtained by an experimental test are presented and compared to those predicted throughsimulation. Results include the temperature of each component of the PV/T collector and air temperature at the inlet and outletof the channel. It has been found that the theoretical results predicted by the developed mathematical model, for instance, outlettemperature, agree with those found through experimental work.

1. Introduction

Hybrid photovoltaic thermal (PV/T) collectors convert solarenergy both into electrical and thermal energy. This conver-sion allows firstly the cooling of the solar cells and secondlythe exploitation of the resulting heat energy to heat wateror space. Applications of hybrid collectors in habitationsare beneficial from a space-saving perspective. In fact, insteadof separately using photovoltaic modules for electricity andsolar thermal energy for heat, hybrid collectors are used forthe same surface. In the literature, there are several studieson hybrid sensors applied in the habitat [1–5]. The mostimportant thing in air hybrid sensors is to have the highestair outlet temperature compared to the input air tempera-ture. To have that, several techniques are possible. They canbe classified globally in two techniques. The first concernsthe use of new coolant materials or the use of phase changematerials [6–8]. The second technique is the design of theabsorber [9–11]. In this article we are interested in the secondtechnique of optimization of the absorber.

Work on hybrid collectors has been carried out in recentyears [12–15].

Farshchimonfared et al. [16] studied a hybrid PV/T aircollector related to an air distribution system. The aim wasto optimize the channel depth. He found that increases inoptimum depth were related to an increase of the collectorarea. The integration of photovoltaic thermal solar collectorsin a building is increasingly becoming an option of firstchoice. A photovoltaic/thermal integrated collector in abuilding is able to generate higher energy output per collectorunit area compared to conventional solar panels. A hybridPV/T offers the same advantages as a photovoltaic PV collec-tor, but in addition, it offers a look that is more aestheticthan side-by-side photovoltaic modules and solar thermalcollectors and generally produces more energy for the samesurface area [17]. A PV/T air collector integrated to build-ings can be an outer layer that creates a building envelopewhich is double layered. Due to the heat source-generatedsound, their thermal characteristic is different from that ofthe usual wall [18].

HindawiInternational Journal of PhotoenergyVolume 2018, Article ID 2794068, 10 pageshttps://doi.org/10.1155/2018/2794068

In this paper, numerical simulation and experimentalvalidation of a photovoltaic thermal PV/T solar air collectorare conducted. The application of this sensor is conductedin a semiarid climate in the south of Algeria where the veryhigh temperature negatively affects the efficiency of solarcells. The evacuation of the solar cells’ heat causes their cool-ing which allows the photovoltaic sensor to perform well.The modeling of the heat transfer in the PV/T air collectoris performed to 1D for a transitional regime according to anode approach. A numerical code was developed and usedto analyze the thermal behavior as well as the thermal, electri-cal, and global electrical efficiency. Then, an experimentalprototype of the PV/T air collector was set up. The PV/Tair collector temperatures, as well as air inlet and outlet tem-peratures, were measured over a period of a day during themonth of June and November and were compared withPV/T air collector model predictions.

2. Theoretical Study

The designed photovoltaic/thermal air collector studied inthis work is shown in Figure 1. The PV/T air collector is com-posed of a photovoltaic module which consists of arrays ofmonocrystalline circular silicon cells covered with highlytransmitting glass. These cell arrays are interposed on anadhesive layer made of Tedlar having good thermal conduc-tivity and poor electrical conductivity. The photovoltaicmodule is to be mounted on a metal plate painted in blackto increase the absorption of the incident solar radiation fall-ing upon an absorbing plate equipped with rectangular finswhich serve as channels for air circulation. The circulationof the air in the fins collects the generated heat, and a usefulamount of thermal energy is extracted by removing hot airfrom one end of the duct leaving the cold fluid to enter at

the other end. The bottom of the sheath is covered with goodinsulation to minimize heat loss to the ambient temperature.

The thermal energy balance equations for the differentnodes of the system is shown in Figure 1.

The heat balance which describes the thermal behavior ofthe PV/T air collector can be written in the form of first orderordinary differential equations and are given for the follow-ing essential elements of the hybrid PV/T air collector:

(1) For glass

MgcgdTg

dt= qg t − hrgsAg Tg − Ts

− hcgaAg Tg − Ta

− U1 + hrgc Ag Tg − Tc ,

1

where

qg t = αgIg t Ag,

U1 =1hcdg

+1hcdc

−1 2

(2) For solar cells

MccpcdTc

dt= qc t − hcdted + hrct Ac Tc − T ted

+ U1 + hrgc Ac Tg − Tc ,3

Tg

Tc

TTed

Tp

Tb

Tin

r1/hgs

g1/hcd

c1/hcd

cd1/hted

p1/hcd

c1/hpf

c1/hbf

b1/hcd

cd1/hin

r1/hina

c1/hga

r1/hgc

1/hct

r1/htp

r1/hpb

r1/hbin

c1/hina

Tf

r

Figure 1: Photovoltaic thermal air collector.

2 International Journal of Photoenergy

where

qc t = τgαc 1 − ηpv Ig t Ac 4

The solar cell efficiency depends on the cell tempera-ture and is given by [19]

ηpv = ηref 1 − 0 0045 Tc − 25 , 5

where ηref is the reference efficiency of a solar cellat a solar irradiance of 1000Wm−2 and temperatureT ref =25

°C.

In this work, ηref = 10%.

(3) For Tedlar layer

MtedcpteddT teddt

= hcdted + hrct At Tc − T ted

− hrtp + hcdp RtpAt T ted − Tp ,6

where

Rtp =Atp

Ac7

(4) For upper plate with fins

MpcppdTp

dt= − hcdp + hrrtp ApRtp Tp − T ted

− hcpf Apηp Tp − T f − hrpbApRbp Tp − Tb ,8

where ηp is the total efficiency of the absorbing upperplate end and ηf is the fin efficiency [1, 20].

ηf =tanh mhf

λf δf,

m =2hfλf δf

1/2

,

ηp =Ac + Af inηf

Abp,

Rbp =Abp

Ac

9

(5) For fluid in the fins

Mf cpfdT fdt

= −cpf mdT f

wdx− hcpf Af Rbpηp T f − Tp

− hcbf Af T f − Tb

10

(6) For lower plate

MbcpbdTb

dt= hcbf Ab T f − Tb − hrpbAbRbp Tb − Tp

− hrbin +U2 Ab Tb − T in ,11

where

U2 =1hcdin

+1hcdb

−1

12

(7) For insulation

MincpindT indt

= −hrinaAin T in − Ts − hcinaAin T in − Ta

− hrbin +U4 Ain T in − Tb

+ Ain Tb − T in

13

The temporal variation of the components of the collec-tor of heat is low, thus mcpdT /dt can be ignored. We cansafely assume a quasistationary operation of the collector.This simplification of the equation suggests that only solarradiation has a significant effect.

By eliminating Tp and Tb, (11) becomes

dT f

dx+ C1T f x = C2 14

If C1 and C2 are constants obtained from the performedalgebraic calculations, the solution of the equation is

T f x =C2A1

+ T f i −C2C1

e−C1x, 15

and the outlet temperature of the air is

T f out =C2C1

+ T f i −C2C1

e−C1l 16

In the above equations, radiation and convective heattransfer coefficients are calculated using the relationships asreported in [21–23].

The wind convection heat-transfer coefficient hci−a for theair flowing over the outside surface depends primarily on thewind velocity v and is defined as

hci−a = 5 7 + 3 8v 17

The radiation heat transfer coefficient between the glasscover and the sky is given by the following relationship:

hrg−a = εgσ T2g + T2

s Tg + Ts 18

3International Journal of Photoenergy

The equivalent sky temperature is calculated by thefollowing simple correlation equation:

Ts = Ta − 6 19

The radiation heat transfer coefficient between the glasscover and the PV panel is given by the following relationship:

hrg−c = σ T2g + T2

c Tg + Tc1εg

+1εc

− 1 20

The radiation heat transfer coefficient between thePV panel and the Tedlar layer is given by the followingrelationship:

hrc−ted = σ T2c + T2

ted Tc + T ted1εc

+1εted

− 1

21

The radiation heat transfer coefficient between theupper plate and the Tedlar layer is given by the followingrelationship:

hrted−p = σ T2ted + T2

p T ted + Tp1εp

+1εted

− 1

22

The radiation heat transfer coefficient between theupper plate and the lower plate is given by the followingrelationship:

hrb−p = σ T2b + T2

p Tb + Tp1εp

+1εb

− 1 23

The radiation heat transfer coefficient between thelower plate and the insulation is given by the followingrelationship:

hrb−in = σ T2b + T2

in Tb + T in1εin

+1εb

− 1 24

The conduction heat transfer coefficient is given by thefollowing relationship:

hcd =λ

e25

The convection heat transfer coefficient of the fluid isgiven by the following relationship:

hc =λ

Dh0 0158 Re0 8

+ 0 00181 Re + 2 92 exp −0 0379x

Dh,

26

where Re is the Reynolds number

Re =ρDhvμ

, 27

where Dh is the hydraulic diameter.For the rectangular channel

Dh =2 × h ×wh +w

28

The thermal efficiency of photovoltaic solar collector iscalculated by the following relationship [24, 25]:

ηth =Qu

AcIt=mcpf To − Ti dt

Ac Itdt29

The global efficiency of the photovoltaic thermal col-lector is defined as the sum of all thermal efficiency andelectrical efficiency:

ηt = ηth + ηpv 30

3. Numerical Simulation

It is obvious from the theoretical model given above that anumerical solution can be calculated for the temperaturesTg, Tc, Tp, Tb, T in, and T f as most of the heat transfer coef-ficients are functions of these temperatures. Therefore, aniterative numerical method based on Runge-Kutta methodis used. Indeed, a program was written in Fortran 90 inorder to find the values of the temperatures of the PV/Tair collector, as well as the values of the thermal and electricalefficiency. This program is summarized by the flowchart pre-sented in Figure 2.

Furthermore, the solar PV/T air collector dimensionsand properties of working fluids, as well as the operatingconditions, are also needed. System properties and operatingconditions which are employed in this study are tabulated inTable 1. The following physical properties of air are assumedto vary linearly with temperature owing to the low tempera-ture range that can be encountered [20, 23]:

(1) Dynamic viscosity

μair = 0 0146T + 1 8343 10−5 31

(2) Density

ρair = 1 1774 − 0 00359 × T − 27 32

(3) Thermal conductivity

λair = 0 02624 + 0 0000758 × T − 27 33

4 International Journal of Photoenergy

(4) Specific heat

cpair = 1 0057 + 0 00066 × T − 27 × 1009 34

Figure 3 presents the hourly temperature variation ofessential elements of the hybrid PV/T air collector (glasscover, solar cell, layer in Tedlar, upper absorber plate, lowerabsorber plate, and insulation). It can be seen from this fig-ure that all temperatures take maximum values in an intervalof time ranging between 10 and 14 hours when the solarintensity is also maximal.

Equation (17) was used to calculate the outlet tempera-ture of the hybrid PV/T air collector. The adopted mass flowrate values are equal to 0.01 kg/s, 0.02 kg/s, and 0.04 kg/s.Figure 4 displays the hourly variation of the fluid temper-ature at the outlet for different mass flow rates. It can beobserved from this figure that maximal temperaturesoccurred at 43°C, 38.5°C, and 34°C for the respectivemass flow rates of 0.01 kg/s, 0.02 kg/s, and 0.04 kg/s. Itcan be inferred that these temperatures vary with solarradiation intensity.

Figure 5 displays the influence of the channel length onthe outlet air temperature at constant channel width andmass flow rate being equal to 0.04 kg/s. It is observed thatthe outlet air temperature increases with an increase in thechannel length. The increased outlet air temperature is dueto the increase in the heat exchange area which results in adecrease in air velocity; hence, a low heat transfer coefficientis favorable.

The effect of channel length on thermal, electrical, andglobal efficiency in the case of a fluid with a mass flow rateequal to 0.04 kg/s and a channel depth equal to 0.1m isgraphed in Figure 6.

It is observed that the thermal efficiency increases withan increase in channel length, while the electrical outputdecreases with an increase in channel length. The decreasein electrical efficiency is due to the increased PV temperature.

4. Experimental Validation

In Figure 7, a prototype of the hybrid photovoltaic thermalair collector is shown. It has a south orientation and is tiltedat an angle equal to that of the site where it is installed, in thiscase 32.49° in the south of Algeria (Ghardaia) to maximizethe intensity of the solar radiation that falls on it. The PV/Tair collector was made with a monocrystalline PV moduleof 40W, with a 0.5m surface area and an air layer of 0.1mfor collecting hot air. Instrumentation devices are installedto measure the data relating to the thermal and electrical per-formances of the PV/T air collector.

A type k thermoelectric device for measuring tempera-ture is used to measure the temperature of each componentof the PV/T air collector. Each thermocouple is placed onthe surface of each element of the PV/T collector and pho-tovoltaic module. A current and voltage sensor has beeninstalled for measuring the electrical performance. A data-

Table 1: Input parameters for numerical calculations.

Parameter Values Parameter Values

Ai 0. 5× 1 cpc 700

h 0.1 cpted 560

δf × hf × l f 0.001× 0.05× 1 cpp 465

τg 0.90 cpin 880

αg 0.05 ρc 2700

αc 0.95 ρc 2330

λg 1 ρp 7833

λc 148 ρin 15

λted 0.033 ρted 1200

λin 0.041 εg 0.88

λp 54 εc 0.35

σ 5.675e−8 εted 0.35

vw 2 εp 0.95

cpg 840 εin 0.05

Reading parameters andconstants:(i) Geometry of the collector.

(ii) Physical properties of the collector

Initialization temperatures Tgi, Tci Tted, Tpi, Tin, Tfi

Data depending temperatures:(i) Solar radiation.

(ii) Fluid properties.(iii) Heat transfer coefficients.

Calculation of temperature:Tf, Tc, Tted, Tin,Tp, Tb

(i) Definitions/evaluations:(ii) Thermal efficiency

(iii) Electrical efficiency(iv) Global efficiency

Yes

Program

Time loop: t = 1. n

(i) Evaluation of the main elements of matrix

No

i < n

End

Yes, i = i + ΔT

∣Tk+1 − Tk ∣ ≤ 𝜀

Figure 2: Flowchart for the computer program.

5International Journal of Photoenergy

acquisition instrument was also connected to record alldata on the performance of the PV/T collector.

Test standards such as that of ASHRE are used mainly forthe determination of instantaneous thermal efficiency.

Figure 8 displays the hourly variation of the inlet andoutlet air temperatures for the day 15 June 2014. Figure 9displays the variation of temperature elements of the PV/Tair collector.

It is clearly noticed that the temperature of each constit-uent element of the PV/T collector reaches it maximum valueat noon of the day. This is obviously due to the considerableamount of solar radiation incident on the PV/T at this time,

which results in a high-rate absorption of solar radiation bythe PV/T collector. However, it should be noted that each ele-ment reaches its maximum value depending on its location inthe system and its physical characteristics. The temperaturesof the front part of the PV/T collector and the upper platehave higher values when compared to the other elements ofthe PV/T collector. The temperature reaches 60°C at noonof the day for the front of the collector and 50°C for the upperplate, while the temperature of the other components do notexceed 45°C in the same period.

We notice that a temperature difference in the rangeof about 9°C is achieved between the inlet and outlet duringthe time interval ranging between 10 and 14 hours. This isexplained as follows. Because of the increase in the tempera-ture of the upper plate that is bonded to the PV module,

52

48

44

40

36

32

28

24

8 10 12 14Time (hour)

Tem

pera

ture

(°C)

16 18

TgTcTted

TpTbTin

Figure 3: Hourly variation of the PV/T air collector elementtemperature.

44

42

40

38

36

34

32

30

28

26

248 10 12 14 16 18

Mf = 0.01 kg s−1

Mf = 0.02 kg s−1

Mf = 0.04 kg s−1

Time (hour)

Tem

pera

ture

(°C)

Figure 4: Hourly variation of the temperature of the fluid.

36

34

32

30

28

26

24

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2Length (m)

Tem

pera

ture

(°C)

Tf

Figure 5: Variation of the fluid temperature in the PV/T aircollector.

100

80

60

40

20

0

0.0 0.1 0.2 0.3 0.4 0.5 0.6Lenght (m)

Effici

ency

(%)

0.7 0.8 0.9 1.0 1.1 1.2

𝜂th

𝜂t

𝜂pv

Figure 6: Variation of the efficiency of the PV/T air collector.

6 International Journal of Photoenergy

the upper plate absorbs the heat generated by the PVmodule. When the air flows naturally through the channel,a convective exchange occurs between the lower and upperplates with air, and the air takes the heat generated by thetwo plates which increases their temperature at the outletof PV/T air collector.

Figure 10 shows the current-voltage characteristic curvesobtained by the experimental tests in the morning and eve-ning for the two collectors, that is, the photovoltaic moduleand the hybrid PV/T air collector. The results showed thatfor the same surface of the PV and PV/T collector, there isan increase of 7 to 30% of the current intensity of the hybridPV/T relative to the photovoltaic module.

In Figure 11, the comparison between the resultsobtained by experimental numerical modeling of the airtemperature at the outlet of the PV/T air collector is pre-sented. Polynomial interpolation is implemented to approxi-mate the experimental results. The approximation curve isexpressed by (35), in the local time (TL) between 8 hours

and 17 hours and at the temperature between 25°C and40°C. It is given by

T f out exp = −659 03457 + 195 48251TL− 20 32914TL2 + 0 94632TL3

− 0 01688TL435

The coefficient of determination (R2) is the key param-eter which serves as the basis of comparison between thesimulated and experimental results of the fluid outlet temper-atures. The correlation coefficient (R2) has been evaluated byusing the following expression [25]:

R2 = 1 −∑k

i T f out−Exp − T f out−Theo2

∑ki T f out−Exp − T f out−mav

2 36

Data acquisitionPVT air collector

PV module

Figure 7: Photo of the experimental prototype.

9 10 11 12 13 14 15 16 17 18 19

27

30

33

36

39

42

4515-06-2014

Tem

pera

ture

(°C)

Time (Hour)

Tf_outTf_inl

Figure 8: Hourly variations of the inlet and outlet air temperaturesof the PV/T collector.

9 10 11 12 13 14 15 16 17 18 1920

25

30

35

40

45

50

55

60 15-06-2014

Tem

pera

ture

(°C)

Time (Hour)

Tp_expTp_exp

Tg_expTin_exp

Figure 9: Hourly variation of the temperature elements of thePV/T.

7International Journal of Photoenergy

The correlation coefficient (R2) is an indicator for judgingthe quality of a linear regression, either single or multiple, at avalue between 0 and 1. We found that the R2 value is equal to0.7, in we find this value acceptable.

We did not study the effect of pressure on electricaland thermal efficiencies. We consider that the temperatureis too low for there to be an influence of the pressureon the heat transfer and consequently on the efficiency ofthe collector.

5. Conclusion

In this work, a hybrid PV/T system was investigated,modeled, constructed, and tested. It was found that by com-bining a PV module with an air collector, the electrical per-formances are noticeably enhanced. The resulting thermal

energy can be exploited to achieve thermal comfort in abuilding. A mathematical model based on energy balancewas developed. Simulation results of this model obtained byusing FORTRAN 90 programming language are plotted.The temperatures in the inlet and outlet are monitored andrecorded. It was found that the temperature at outlet is higherthan the temperature at the inlet, which suggests that a heatexchange has taken place and this is the reason for theimprovement of the PV module performances.

The results found through simulation were compared tothose found experimentally. Their comparison does showgood agreement. This agreement is more pronounced in thecase of the inlet and outlet fluid temperatures.

In conclusion, the combination of the PV module withthe thermal collector would enhance the electrical perfor-mances of the PV module and the resulting thermal energycan be used for other purposes, for instance, to achievethermal comfort in a building when this combination is wallintegrated. In other applications, when water is used insteadof air, the heated water can be used for sanitary purposes.

As a future work to further improve the performances ofsuch systems, the PV module is to be replaced by a high-efficiency PV module and a reflector is used to concentratesolar radiation upon it.

Nomenclature

A: Surface (m2)Cp: Specific heat (J kg−1 k−1)Dh: Hydraulic diameter (m)e: Thickness (m)hc: Convective-exchange coefficient (Wm−2 k−1)hr : Radiative-exchange coefficient (Wm−2 k−1)h: Channel depth (m)I: Solar intensity (Wm−2)l: Length of the collector (m)m: Mass flow (kg·s−1)M: Mass (kg)n: Number of finsR: Area ratioRe: Reynolds numberq: Heat flow (W)P: Power (W)t: Time (s)Tl: Local time (hour)T : Temperature (°C)v: Speed (m s−1)w: Width of the collector (m)U : Heat transfer coefficient (Wm−2 k−1)x: Distance (m).

Greek Symbols

α: Absorbanceδ: Thickness of fin (m)ε: Emissivityη: Efficiencyλ: Thermal conductivity (Wm−1 k−1)ρ: Density (kgm−3)

0 2 4 6 8 10 12 14 16 18 200.0

0.3

0.6

0.9

1.2

1.5

1.8

2.1

2.4

Voltage (V)

Curr

ent (

A)

Hour 12

PVPV/T

Figure 10: Current-voltage characteristic curves of the PV/T aircollector and PV module.

8 9 11 12 13 14 15 16 17

21

24

27

30

33

36

39

42

45

48

Tem

pera

ture

(°C)

Time (hour)

Equation

y = intercept + B1⁎x^1 + B2⁎x^2+ B3⁎x^3 + B4⁎x

^4

Weight No weightingResidual sum of squares

547,83128

Adj. R-square 0.88076

B

Value Standard errorIntercept −659,03457 143,37995

B1 195,48251 47,99109B2 −20,32914 5,91116B3 0,94632 0,31782B4 −0,01688 0,0063

Tfout_Exp

Polynomial fitTfout_�e

Figure 11: Validation of the mathematical model.

8 International Journal of Photoenergy

μ: Dynamic viscosity (kg·m−1 s−1)σ: Stefane-Boltzmann constant (Wm−2 K−4)τ: Transmittanceζ: Convergence criterion.

Subscripts and Abbreviations

a: Ambientb: Lower platebp: Bottom surface of absorber platec: Solar cellf : Fluidinl: Inletg: Glass coverin: Insulatorp: Upper platepv: Electricout: Outlets: Skyted: TedlarExp: Experimentalt: Totalth: Thermaltp: Top surface of absorber plateTheo: Theorymav: Mean value.

Data Availability

All data used in this work is included in the paper.

Conflicts of Interest

The authors declare that there is no conflict of interestregarding the publication of this paper. This research wasperformed as part of the requirements during the employ-ment of the authors at the Unit of Applied Research inRenewable Energy (URAER)

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