IJECA-ISSN: 2543-3717. June 2021 Page 43 International Journal of Energetica (IJECA) https://www.ijeca.info ISSN: 2543-3717 Volume 6. Issue 1. 2021 Page 43-54 Numerical study of a hybrid photovoltaic/thermal PVT solar collector using three different fluids A. Ghellab *1,2 , T.E. Boukelia *2,3 , S. Djimli 1,2 , A. Kaabi 4 1 Laboratory of Applied Energies and Materials, Faculty of Sciences and the Technology, Ouled Aissa BP 98, University of Jijel, ALGERIA 2 Mechanical Engineering Department, Faculty of Sciences and the Technology, Ouled Aissa BP 98, University of Jijel, ALGERIA 3 Laboratory of Mechanical and Advanced Materials, Polytechnic School of Constantine, Constantine, ALGERIA 4 Climatic Engineering Department, Faculty of Science and Technologies, Route Ain El Bey, University of Constantine1, ALGERIA .Email *:ghellab_amel@yahoo.fr and taqy25000@hotmail.com Abs tract – Hybrid photovoltaic and thermal (PV/T) systems have been widely used for the combination of PV modules and solar thermal collectors to generate both electrical energy and heat at the same time. In the present work , a numerical model has been developed to simulate the performances o f a hybrid photovoltaic/thermal (PV/T) solar collector. Furthermore, a comparative study has been performed between the hybrid PV/T work ing with three conventional working fluids; air, water, and specified nanofluid (AL2O3+ water). The obtained results show that the use of the Alumina nanofluid is the best choice to increase the heat removal, and to improve the performances of the collector with the values of 73.28%, 10.37% and 99.21% for the thermal, electrical and global efficiency respectively. On the other hand, the P VT collector working with air as the primary fluid is the worst in terms of electrical, thermal, and global performances with the lowest values of 9.506 %, 41.55%, and 65.315% respectively. Keywords: Hybrid solar collector, Nanofluid, Numerical study, Performance, Nanofluid. Received: 30/03/2021 – Accepted: 29/06/2021 I. Introduction Many academics fro m a ll over the world are attempting to meet the rising need for energy, by developing diffe rent types of solar collectors to provide a clean energy in sufficient quantities and at low costs. For many decades, the hybrid photovoltaic and therma l (PV/T ) systems have been widely used for the combination of PV and solar therma l e ffects to generate both electrical and thermal energies, as it is we ll-known that the cell effic iency is decreasing with high temperatures. Theoretical and also e xperimental research on hybrid PV/ T systems using air and/or water as working fluids were documented. For e xa mple , Previous research [1-2] found that the flat plate photovoltaic therma l (PV/T) solar co llector is a good option for low - energy applications in homes, commerc ial buildings, and industrial. Prakash [3] has presented a dynamic model o f a hybrid PV/T solar system using two fluids; air and water as working fluids. It was reported that the therma l efficiency varies fro m 50% to 67% for water heating, and fro m 17% to 51% for a ir heating. In the case of air heating, the lowe r therma l effic iency is attributable to the poor conductivity and specific heat of a ir co mpared to water. A study has developed an analytical mode to compare and contrast the performance of a PV/T collector with two layouts; single and double pass. They concluded that the double pass PV/T co llector outperformed the single pass PV/T collector [4]. However, another study has showed a PV/T a ir heater with four designs for single and double pass. He developed the therma l mode l of every system, then e xa mined the effect of air specific flow rate on the performance of each one [5]. Nine distinct designs of a combination PV/T water/a ir solar collector were evaluated by a research group, they revealed that the best design is the sheet-and-tube collector with single cover http://www.ijeca.info/ http://www.ijeca.info/ mailto:ghellab_amel@yahoo.fr mailto:taqy25000@hotmail.com A. Ghellab et al IJECA-ISSN: 2543-3717. Page 44 [6]. An e xp lic it dynamic model has been performed a PV/T co llector with a single gla zed flat plate for water heating. The model captured the instantaneous energy outputs and allowed for a detailed investigation of transient behavior across multip le collector co mponents [7]. A theoretical mode l was developed to study the effect of the channel d imension, as well as the mass flo w rate on the perfo rmance of such system. The results we re validated with those issued by their e xperience [8]. The paper looked at hybrid PV/T systems that ext ract heat fro m PV modules using air or water. He a lso e xperimented with three d ifferent ways to place the water heat exchanger inside the air channel; the modified twin PV/T collectors were co mb ined with booster diffuse reflectors to improve the PV/T systems' e lectrica l and therma l output. By integrating low-cost e xtra system ele ments, the recommended comb ination of diffuse reflectors improved the effective operation on horizontal building roof installation [9]. Sc ientific work has focused on an experimental study by adding the propylene glycol (PG) in water as a working fluid in a PV/T solar collector. Their obtained results indicated that the using of PG-water at 25% PG concentration, reduced the effic iency of the flat plate solar collector by 15.68% , compared with pure water [10]. A hybrid PV/T collector with water as working fluid produced in a copolyme r materia l was also described and simu lated in another study. They pointed out that using the copolymer reduces the weight and cost of such systems, as well as ma king them easier to manufacture [11]. Investigation has studied the performances of a PV/T air heater with a double pass layout, and vertical fins in the bottoming channel of the absorber surface. Such enhancement improves the heat transfer area to air, and increases the efficiencies of this form of co llector, according to the researchers [12]. The literature showed the enormous efforts which have been made to enhance the heat ext raction fro m the cells in a solar PV/T co llector, in order to imp rove t he electrica l conversion efficiency by using cooling fluids which have higher thermo-physical proprieties. This condition can be realized by adding ultra-fine solid particles of millimeter or mic ro meter size to the working flu id. On this d irection, most of research works we re ma inly based on nanofluids, which are co mposed of particles dispersed in water with various concentrations ranging. Based on previous research’s review papers [13 - 15], In solar therma l systems, nanofluids can be used to improve the therma l e ffic iency and performance o f the solar collector. They found that producing a nanofluid - based solar collector e mits roughly 170 kg/year less CO2 on average than a traditional solar collector, implying that nanofluid causes less environmental da mage. However, the revie ws [16-18] summa rized the recent correlations developed to analyze the free and fo rced heat transfer convection phenomena in flow with nanoflu ids. A group of scientists has proposed a new correlation for the convective heat transfer of a Cu-water nanoflu id for both laminar and turbulent flow conditions. They determined that this correlation takes into consideration the major e le ments impacting nanofluid heat transfer and that the presence of nanoparticles improves heat transfer performance [19]. On the other hand, another group has performed a co mprehensive analysis in order to evaluate the effects of variations in volu me fraction and temperature of nanofluid on its density, specific heat, therma l conductivity and viscosity [20]. The effect of cooper nanoparticles in the presence of a magnetic fie ld on unsteady non-Darcy flo w and heat transfer over a porous wedge due to solar rad iation has been studied theoretically [21]. Another research has studied numerically the heat transfer and pressure drop of three diffe rent nanofluids which were : copper o xide (CuO), alu mina (Al2O3), o xide titaniu m (TiO2), and water as based fluid. The results illustrated that by increasing the volume of concentration of nanoparticles, the heat transfer coeffic ient increased. Furthermore, for a constant volume of concentration, the effect of CuO nanoparticles to enhance the Nusselt number was better than the two other nanoparticles; Al2O3 and TiO2 [22]. Study have reported the results of an experiment analysis, and have studied the effect of Al2O3-H2O nanofluid as an absorbing mediu m on the efficiency of flat plate solar collector. The results of the experiment showed that the use of a concentration of 0.2 % Al2O3 nanofluid increased the efficiency of the solar collector in comparison with water as wo rking fluid by 28.3%, and by using surfactant the ma ximu m enhanced efficiency is about 15.63% [23]. Scientific analysis has analyzed the effect of nanofluid on the performances of an absorber of a direct solar collector. They showed that the particle size has minimal influence on the optical propriet ies of nanofluid, and the e xtinction coefficient is linearly proportionate to volume fraction [24]. Another scientific analysis has studied experimentally the forced convectio n flow o f alu minu m o xide nanoparticles dispersed in water through a circula r p ipe. The results showed that the presence of nanoparticles in the working flu id caused a re markable increase in the heat transfer comparing to the working fluid itself [25]. Furthermo re, scientific tea m have investigated experimentally the e ffect of density, therma l conductivity and viscosity of water and Ethylene glycol water mixture (60:40 by mass) based alumina nanofluids, on the pressure drop and pumping power for A. Ghellab et al IJECA-ISSN: 2543-3717. ( Page 45 a flat p late solar collector. It was observed that the viscosity of the Al2O3-water nanofluids e xponentially decreased with increasing in working temperature, and they have indicated the non-linear relat ion between viscosity and concentration. They showed that the pressure drops and consumed power for fluid pu mp ing of nanofluid flows are a lmost similar to that of the base liquid with low concentration [26]. Another tea m have performed a nu merical simu lation of the heat transfer enhancement and behaviors of water-γ Al2O3, and Ethylene Glycol- γ Al2O3 nanoflu ids in two different confined flow situations. Their findings revealed that the use of nanoparticles resulted in a significant increase in heat transmission. However, and according to our knowledge concluded fro m literature, no co mparative study has been presented to compare the performances of these systems using different working fluids, thus, the objective of the present study is to use nanoparticles within the working flu id for a hybrid PV/ T solar collector, and to ma ke a co mparison in terms of efficiencies between this solar collector with three diffe rent flu ids (air, water, and Alu mina nanofluid (Al2O3+water)) [27]. This study takes Constantine (North-east of Algeria) as a case study, and a nu merical model is developed by presenting energy balances for different nodes: glazing, PV ce ll, absorber, fluid and back plate, and considering the transient effects. II. Description of the studied PV/T collector Figure 1 shows a cross -sectional view of the proposed photovoltaic/thermal (PV/ T) collector. The investigated system is made up of transparent glazing located at the top of the collector, wh ich transmitted the incident solar radiation to the solar cell, and the absorber at the bottom of PV/T collector. The stagnant air in the air gap is assumed circulate under free convection. A fraction of the incident radiation is converted into electricity by the solar cell, and into heat by the absorber, which transfer the heat to the fluid flowing into a rectangular duct formed by the top absorber, and the back metallic plate supposed painted black. The cooling flu id is flowing under forced circulat ion mode. The conduct bottom is insulated in order to minimize heat losses with the amb ient. The inclination angle of the studied hybrid V/T solar collector is taken equal to the latitude of Constantine east town in Algeria. Figure 1. A cross sect ional view of t he st udied hybrid P V/T solar collect or III. Mathematical modelling To e xa mine the PV/T performances, a transient mathe matica l model under forced convection was constructed. In order to write the energy balance between the components, it would be convenient to use the analogy between electricity and heat transfer. Fig.1 shows the diffe rent heat transfer coeffic ients along various elements of the collector. It is necessary to make some assumptions to model the system considered, as:  The sky can be co mpared to a b lack body with equivalent calculated temperature.  The temperature of the soil is taken equal to the ambient temperature.  The physical proprieties of materials are assumed to be constant.  The wind is supposed blowing parallel to the faces of the system.  The fluid entering the duct is at room temperature, and the ducts flu id te mperature is a combination of the input and exit temperatures. The following are the energy balance equations for different surfaces of the PV/T collector:  Glazing: 𝑚g𝑐g 𝑑𝑇g⁄ 𝑑𝑡) = 𝑃g𝐴g + ℎ𝑣g(𝑇𝑎 − 𝑇g)𝐴g + ℎ𝑟g(𝑇𝑠 −𝑇g)𝐴g + (ℎ𝑣𝑐 + ℎ𝑟𝑐)(𝑇𝑐−𝑇g)𝐴g (1) Where mg, cg and 𝐴g denote the mass, specific heat and area of glass respectively, wh ile 𝑃g represents the rate of the energy absorbed by the glass, ℎ𝑣gand ℎ𝑟g are the heat transfer coeffic ients based on convection and radiation between the glazing and ambiance/sky respectively. On the other hand, ℎ𝑣𝑐is the convection heat transfer coeffic ient for air cavity between the solar cell and glazing, ℎ𝑟𝑐 is the heat transfer coeffic ient based on radiation between solar ce ll and gla zing. 𝑇g,𝑇𝑎 𝑇𝑠 and 𝑇𝑐 represent respectively temperatures of: glass, ambient, sky and PV cell and t represents the time. The A. Ghellab et al IJECA-ISSN: 2543-3717. 5830 1 Page 46 quantity of the energy absorbed by the glass is calculated by the following expression [28]: 𝑃g = 𝑃𝑑i𝑟 . 𝛼g−𝑑i𝑟 + 𝑃𝑑if . 𝛼g−𝑑if (2) 𝑁𝑢 = 1 + 1.446 *1 − 1708⁄ 𝑎 𝖥 𝑐𝑜𝑠 𝜃+ 1 I [ 1 Such as Pdir and Pdif rep resents respect ive ly the intensity of the direct and diffuse incident radiation. The a b s o rp t i o n c o effi ci e n t s o f g l a zi n g 𝛼𝑉1−𝑑i𝑟 et 𝛼𝑉1−𝑑if are calculated from [28]. The coefficient of radiat ion heat transfer fro m the glazing to the sky is given by [29]: 1708[𝑠i𝑛( 1.8)] 1.6 𝑅𝑎 𝑐𝑜𝑠 𝜃 I ] + [( 𝑅𝑎 𝑐𝑜𝑠 𝜃⁄ ) 0.333 − 1] (8) Where 𝑅𝑎represents the Rayleigh number and 𝜃 is the h = 𝜎sg(𝑇4 − 𝑇4) (3) collector inclination angle, which can be calculated by 𝑟g g 𝑠 ⁄ (𝑇g − 𝑇𝑎) the following expression: 𝜌2 𝑐𝑝𝑔𝛽(𝑇𝑐 − 𝑇g)𝑏3 Where 𝜎 is the stephan-Boltzmann constant, sg is the 𝑅𝑎 = 𝑐⁄ 𝑎i𝑟𝜇 (9) emissivity of thermal rad iation of the glass cover, 𝑇g characterize the sky te mperature which is evaluated by Swinbank (1963) as follows [29]: 𝑇𝑠 = 0.0552(𝑇𝑎)1.5 (4) The coefficient of convective heat transfer between the glazing and ambiance is formulated by Mc Adams Where ρ, cp, β and μ are respectively the density, specific heat, therma l e xpansion coeffic ient and the dynamic viscosity of air, and g is the gravitational constant.  Solar cell: 𝑚 𝑐 ( 𝑑𝑇𝑐⁄ ) = 𝑃 . 𝐴 + (ℎ ℎ )(𝑇 − 𝑇 )𝐴 (1954) [29]: 𝑐 𝑐 𝑑𝑡 𝑐 𝑐 𝑣𝑐+ 𝑟𝑐 g 𝑐 g h𝑣g = 5.7 + 3.8. 𝑣 (5) Where v represents the wind velocity. The coeffic ient of radiation heat transfer between solar cell and glazing can be calculated fro m the following equation: + ℎ𝑐𝑐(𝑇𝑝 − 𝑇𝑐)𝐴𝑐 − 𝑄𝑒𝑙𝑒 . 𝐴𝑐 (10) Where mc, cc and 𝐴𝑐 represents respectively the mass, specific heat and area of the solar cell, 𝑃𝑐 represents the rate of the energy absorbed by the PV h = 𝜎(𝑇𝑐 + 𝑇g)(𝑇2 + 𝑇2) (6) cell, ℎ𝑐𝑐 is the heat transfer coefficient conduction 𝑟𝑐 𝑐 g ⁄ ( ⁄s𝑐 + 1⁄sg − 1) between the PV cell and the absorber plate and 𝑄𝑒𝑙𝑒is the electrical power produced by the PV module. 𝑇𝑐 Note that the symbol s𝑐 represents the emissivity of the solar cell. The coefficient of convection heat transfer for air cavity between the solar cell and glazing, is given by : Represents the PV cell te mpe rature and 𝑇𝑝 represents the absorbing plate te mperature. The rate of solar energy received by solar cell a fter transmission is calculated by the following expression [30]: h𝑣𝑐 = 𝑁𝑢. 𝑘𝑎i𝑟⁄𝐷 (7) 𝑃𝑐 = 𝑟g × 𝛼𝑐 × 𝛽𝑐 × 𝑃g (11) W h er e N u r ep r es en t s t h e Nu s s el t n u m b e r, Ka ir i s t h e air conductivity and Dh represents the hydraulic dia mete r of the air flowing in the channel. The Nusselt number can be calculated by the convection between inclined parallel flat plates [29]: Where 𝛼𝑐 is the absorption coefficient of the cell and 𝛽𝑐 is the Pac king factor which represent the ratio of cell a rea to aperture area. While the rate o f e lectrica l energy generated by the PV cell can be calculated by [30]: 𝑄𝑒𝑙𝑒 = 5𝑒𝑙𝑒 × 𝑃g × 𝛽𝑐 × 𝑟g (12) Where 5𝑒𝑙𝑒 design the electrical efficiency generated by the cell, which is estimated by the relation (3 8 ) and 𝑟g is the transmission coefficient of the glass. The heat transfer coefficient conduction between the PV cell and the absorber is calculated by: 𝑅 ⁄ 𝑘 ℎ − A. Ghellab et al IJECA-ISSN: 2543-3717. 1 ( Page 47 h𝑐𝑐 = 𝑘𝑐⁄𝑒 + 𝑘𝑝 ⁄𝑒 (13) 𝑚𝑏𝑝𝑐𝑏𝑝 ( 𝑑𝑇𝑏𝑝⁄ 𝑑𝑡) k , k and 𝑒 , e are respectively the thermal = h𝑣𝑏𝑝(𝑇f − 𝑇𝑏𝑝)𝐴𝑏𝑝 + (ℎ𝑐i + ℎ𝑣𝑎)(𝑇𝑎 − 𝑇𝑏𝑝)𝐴𝑏𝑝 c p 𝑐 p + h (𝑇 − 𝑇 )𝐴 conductivity and the thickness of PV cell and absorbing 𝑟𝑝 𝑝 𝑏𝑝 𝑏𝑝 plate.  Absorbing plate: 𝑚𝑝 𝑐𝑝 𝑑𝑇𝑝⁄ 𝑑𝑡) = ℎ𝑐𝑐(𝑇𝑐 − 𝑇𝑝)𝐴𝑐 + ℎ𝑣𝑝(𝑇f − 𝑇𝑝)𝐴𝑝 + 𝐴𝑏𝑝ℎ𝑟𝑎(𝑇𝑠𝑜i𝑙 − 𝑇𝑏𝑝) (18) Where mbp, cbp and 𝐴𝑏𝑝 represents respectively the mass, specific heat and area of the back plate, ℎ𝑐i is the + ℎ𝑟𝑝(𝑇𝑏𝑝 − 𝑇𝑝)𝐴𝑝 + 𝐴𝑝𝑃𝑝 (14) Where mp, cp and 𝐴𝑝 represents respectively the mass, specific heat and area of the absorber plate, 𝑃𝑝 represents the rate of the energy absorbed by the absorbing plate, ℎ𝑣𝑝 is the heat transfer coefficient heat transfer conduction coefficient in the insulation, ℎ𝑟𝑎 is the radiation heat transfer coefficient fro m the back plate and soil, ℎ𝑣𝑎 is the convective heat transfer coefficient for air cavity between the back plate and soil. 𝑇𝑠𝑜i𝑙 represents the temperature of the soil. The heat transfer coefficient by conduction in the insulation can be obtained by: convection between the absorber plate and the fluid, h𝑐i = 𝑘i⁄𝑒 + 𝑘𝑏𝑝⁄𝑒 (19) ℎ𝑟𝑝is the heat transfer coefficient by radiation between t h e ab s o r b er a n d b a c k p l at e. 𝑇f an d 𝑇𝑏𝑝 rep resent the temperatures of flu id and back p late respectively. 𝑃𝑝 is the rate of solar energy absorbed by the absorbing plate, which is calculated by: 𝑃𝑝 = 𝑟g × (1 − 𝛽𝑐) × 𝛼𝑐 × 𝑃g (15) i 𝑏𝑝 With k i, k bp and ei, ebp are respectively the insulating and back plate thermal conductivity and thickness. The radiation heat coefficient between back plate and soil is calculated by: h𝑟𝑎 = 𝜎s𝑏𝑝(𝑇𝑠𝑜i𝑙 + 𝑇𝑏𝑝)(𝑇2 + 𝑇2 ) (20) The heat transfer coefficient by radiation between the 𝑠𝑜i𝑙 𝑏𝑝 absorber and back plate can be given as [29]: h𝑟𝑝 = 𝜎(𝑇𝑝 + 𝑇𝑏𝑝)(𝑇2 + 𝑇2 ) The convective heat coefficient between back plate and soil 𝐻𝑣𝑎 can be taken the same as 𝐻𝑣g. 𝑝 𝑏𝑝 ⁄ ( ⁄s𝑏𝑝 + 1⁄s𝑝 − 1) (16) III. 1 . Expression of convective heat transfer coefficients Where s𝑏𝑝 And s𝑝 are respectively the back plate and the absorber coefficients of emissivity. For convective e xchange between two meta llic plates and the fluid inside the duct, the heat transfer coeffic ient can be calculated by:  Fluid flowing in the duct: 𝑚f 𝑐f ( 𝑑𝑇f⁄ 𝑑𝑡) = ℎ𝑣𝑝(𝑇𝑝 − 𝑇f )𝐴f h𝑣𝑝 = h𝑣i = 𝑁𝑢 𝑘f⁄ 𝐷 (21) + ℎ𝑣𝑏𝑝(𝑇𝑏𝑝 − 𝑇f ) 𝐴f − 𝑚 𝑐f (𝑇𝑜𝑢𝑡 − 𝑇i𝑛 )𝐴f (17) W h e r e mf , cf an d 𝐴f re p r es e n t s t h e m a s s , s p e ci fi c h e at and area of the fluid respectively, ℎ𝑣𝑏𝑝 is the heat transfer coefficient convection between the fluid and the back plate, 𝑇i𝑛 and 𝑇𝑜𝑢𝑡 represent respectively the inlet and the outlet temperatures of the fluid in the duct, 𝑚 is the mass flow rate of the primary cooling fluid. Where kf is the flu id therma l conductivity, Nu is the Nusselt number for forced convection in the duct formed by the absorbed plate and the back plate. According to the literature analysis, this number can be e xpressed for different fluid examined in this work as:  For air: According to [29] and [31], the corre lation of Tan and Charters (1970) is reco mmended for pa rallel flat plate and Nusselt number can be expressed by: 𝑁𝑢𝑎i𝑟 = 0.018 𝑅𝑒0.8 𝑃𝑟0.4 (22)  Back plate: 𝑎i𝑟 𝑎i𝑟 𝑐 𝑝 ℎ A. Ghellab et al IJECA-ISSN: 2543-3717. f Page 48 Where Prair is the Prandtl number of air, Reair is the Reynolds number of air defined as:  Viscosity 𝜇w𝑎𝑡𝑒𝑟 = 2.1897 exp(−1 1) 𝑇f 4 − 3.055 exp(−8) 𝑇f 3 + 𝑅𝑒𝑎i𝑟 = 𝜌 𝑣 . 𝐷ℎ⁄𝜇 (23) 1.6028 exp (−5) 𝑇f 2 ) − 0.00375 24 𝑇f + 0.33158 (30)  Density In which ρ and μ represent the density and the dynamic viscosity of air, v is the mean velocity of air in the duct.  For water: Refe rring to [32], the Nus selt number of pure water for turbulent flow in two para lle l plates, can be calculated by the following corre lation over the we ll - known equation of Dittus -Boelter: 𝑁𝑢 w𝑎𝑡𝑒𝑟 = 0.023 𝑅𝑒0.8 𝑃𝑟0.33 (24) 𝜌w𝑎𝑡𝑒𝑟 = −1.5629 exp(−5) 𝑇f 3 + 0.01177 8 𝑇f 2 − 3.0726 𝑇f + 1227.8 (31)  Thermal conductivity 𝑘w𝑎𝑡𝑒𝑟 = 1.5362 exp(−8) 𝑇f 3 − 2.261 exp(−5) 𝑇f 2 + 0.010879 𝑇f − 1.0294 (32)  Specific heat 𝑐𝑝,w𝑎𝑡𝑒𝑟 = 1.1105 exp( −5) 𝑇f 3 − 0.0031 0 𝑇f 2 w 𝑎𝑡𝑒𝑟 w 𝑎𝑡𝑒𝑟 − 1.478 𝑇f Where Prwater is the Prandtl number of water, Rewater is the Reynolds number of water.  For nanofluid: According to [27, 33], the following correlat ion has been created to determine the Nusselt number in terms of Reynolds and Prandtl nu mbers [16], of turbulent flo w in tube using Al2O3 – water mixture under a uniform heat flux boundary condition on its wall. 𝑁𝑢𝑛f = 0.085 𝑅𝑒 0.71 𝑃𝑟0.35 (25) + 4631.9 (33)  For nanofluid: Fro m literature, the physical proprieties of nanofluids depend on parameters including the therma l propriet ies of the water as base fluid and the volume fraction of alu minu m o xides (Al2 O3) nanoparticles dispersed in water. Based on the report [27], the Eqs (34) and (35) are general relationships used to compute specific heat and the density for a classical two-phase mixture. The 𝑛f 𝑛f specific heat of the Al2O3-water nanofluid can be For 6.6 ≤ Prnf ≤13.9, 10 4 ≤ Renf ≤ 5.10 5 and 0< φ <10 % Where Prnf , Renf represent the Prandtl and the Reynolds number of the nanofluid and φ represents the volu m e fracti o n of Al2 O3 nan o p a rt i cl es . III. 2 . Expression of thermo-physical properties  For air: According to [29], the physical properties of air are assumed varying with temperature, as follows:  Viscosity 𝜇𝑎i𝑟 = [1.983 + 0.00184(𝑇f − 27)]10−5 (26)  Density 𝜌𝑎i𝑟 = 1.1774 − 0.00359(𝑇f − 27) (27)  Thermal conductivity 𝑘𝑎i𝑟 = 0.02624 + 0.0000758(𝑇f − 27) (28)  Specific heat 𝑐𝑝,𝑎i𝑟 = 1.0057 + 0.000066(𝑇f − 27) (29)  For water: The equations of the physical propriet ies of water are obtained from the equations provided in the study by Jayakumar et al [34], as: calculated by [27]: 𝑐𝑝,𝑛f = (1 − 𝜑)𝑐𝑝,w 𝑎𝑡𝑒𝑟 + 𝜑𝑐𝑝,𝑛𝑝 (34) Where Cp,nf, Cp,water and Cp,np represent respectively the specific heat of nanofluid, base fluid and nanoparticle. The nanoflu id density is calcu lated by the following relation [27]: 𝜌𝑛f = (1 − 𝜑)𝜌w𝑎𝑡𝑒𝑟 + 𝜑𝜌𝑛𝑝 (35) Where ρnf, ρwater and ρnp represent respectively the density of nanofluid, base fluid and nanoparticle. They e xist several semi-e mpirica l corre lations for calculating therma l conductivity and the dynamic viscosity. Recent models have shown that numerica l simu lations for v iscosity and thermal conductivity require more robust models that account for temperature dependency and nanoparticle size. These correlations include te mperature and volu me fraction [26, 35] in the eq (36) which represents the modified statement of Nguen: 𝜇𝑛𝑝 = 𝑒𝑥𝑝(3.00 3 − 0.0420 3𝑇f − 0.5445𝜑 + 0.0002553𝑇2 − 0.0534𝜑2 − 1.622𝜑−1 (36) A. Ghellab et al IJECA-ISSN: 2543-3717. ⁄ 𝐴 𝑃 𝑑𝑡 Page 49 Regarding the nanoflu id therma l conductivity, and according to Maiga[27], this para meter can be calcu lated using the eq (37), this model has been used in this study because of his simplicity: coeffic ients which related with the input physical parameters. This equation system is solved by the iterative Guass -Siedel method, which allowed evaluating the unknowns for each time and for each component. For 𝑘𝑛f⁄ w 𝑎𝑡𝑒𝑟 k , k = 4.97𝜑2 + 2072𝜑 (37) represents respectively the thermal numerical ca lculat ion, a computer progra m was prepared in Matlab language. First, init ial guessed temperatures are used equal to ambient te mperature in order to calculate the heat transfer coefficient, which can be used nf water conductivity of nanofluid, base fluid. III. 3 . Expression of efficiencies The e xpression of the electrical effic iency generated by the cell is: 5𝑒𝑙𝑒 = 5𝑟𝑒f [1 − 𝛽𝑟 (𝑇𝑐 − 𝑇𝑟 )] (38) W h e r e 5𝑟𝑒f i s t h e r ef er en c e c el l effi cien cy at operat ing te mp eratu re Tr o f 25 °C, and 𝛽𝑟 is the coeffic ient o f t e mp erature and th ese pa ra mete rs are given by manufacturer [30]. The instantaneous PV/T collector therma l e ffic iency of can be e xp ressed by the heat ratio quantity e xtracted by the fluid used to the amount of solar radiation incident on the glazing [28]: to estimate (Tg, Tc, Tp, Tf and Tbp), then the values obtained are reinserted to calculate new temperatures of various elements. If all new values are larger than 0.01% fro m their guessed temperature, the process is repeated until the solution converges. V. Results and discussion V. 1 . Validation results  Air as working fluid The values of the thermo-physical para meters for various surfaces of the system wh ich have been used to validate the model a re found fro m literature [5], [11], and [36]. The re levant parameters used for numerica l calculations are listed in Table 1. The electrical efficiency is calculated by eq. (38), and the following η 𝑡ℎ = ∫ 𝑚 𝑐f (𝑇𝑜𝑢𝑡 − 𝑇i𝑛 )𝑑𝑡 ∫ g ( 39) values were e xperimentally validated according to [5]: βr=0.004 K -1 , ηref=12.5% . Both the absorber plate and the back plate are in cooper and the values of emissivity And the overall effic iency of the P V/T solar collector is computed by adding the therma l effic iency equivalent of electrical efficiency and the thermal efficiency [30]: and thickness of the back plate are taken as: εbp=0.9 and ebp= 3mm [5]. 5 = (5𝑒𝑙𝑒⁄ ) + 5 (4 0) T able 1. Main parameters used in simulat ion [5, 11 and 36]. 𝑜𝑣𝑒𝑟𝑎𝑙𝑙 𝑐f 𝑡ℎ Wh e re 𝑐f is the con v e rs i o n fact o r of the therm a l power plant, its value can be taken as 0.4 [30]. IV. Method of resolution Based on the finite diffe rence formulat ion, the temperature d istribution can be determined by a system of linear a lgebraic equations, these systems can be written as a matrix equation as follows [31]: 𝐴 (5, 5) × 𝑇 (5) = 𝐵 (5) (41) Where A (d imension: 5) represents a square mat rix, such its ele ments jo in the known therma l capacities of materia ls with the different heat e xchange coeffic ients between PV/T collector e le ments, T (5) is a vector containing system of the unknown’s te mperatures at the nodes and the vector B (5) which jo in the constants, thermal capacities of materials with the heat exchange First, the program was operated on a panel with a rea of 9 m 2 the input data collected of the PV/T air collector Model II fro m the co mparative study [5], in his study this model represented the highest thermal efficiency values. 𝑘 Parameters Gl azing PV ce l ls Absorbi ng pl ate In su lation Absorption coe fficient (-) αg=0.04 αc=0.9 αp=0.94 - Tran smission coe fficient (-) τg=0.9 - - - Emi ssivi ty (-) εg=0.86 εc=0.7 εp=0.95 - Th i ck ness (mm) eg= 3 ec= 0.22 ep= 3 ei=50 Th e rmal con du ctivity (w.m -1 .K -1 ) kg= 1.8 kc= 130 kp= 386 ki= 0.045 De n sity(kg.m -3 ) ρg= 2700 ρc= 2330 ρp= 8954 - S pe cifi c h e at capaci ty (J.kg - 1.K-1) cg=750 cc=836 cp=0.383 - A. Ghellab et al IJECA-ISSN: 2543-3717. Page 50 Figure 2 illustrates the comparison of the thermal efficiency of the present numerica l code with the thermal efficiency available in the study [5], the figure represents the variation of performances as a function of the air mass flow rate wh ich spanning the range of 0.005-0.04 kg/s.m 2 . The results obtained are in good agreement with those reported by [5]. The results of the present study predict the therma l effic iency within a re lative error of ±2% which may co me fro m ma king hypotheses and uncertainties in the correlations used in the mathematical analysis. Figure 2. Comparison bet ween t he present work and t hose of Hegazy V. 2 . Evolution of solar radiation intensity and ambient temperature The follo wing performance evaluation have been carried out for meteorologica l data wh ich concern Constantine town in east Algeria (36°70’, 6°37’), for the typical summe r day 30 July 2015, and during which the prevailing ma xima l and min ima l te mperatures are respectively equal to 43°C and 22°C, according to [37]. The calculat ion of the d ifferent para meters is during the sunshine and the collector represents an area of 1m long by 1 m wide and the wind speed was taken equal to 0.5m/s. Figure 3 represents the variation of solar radiation and ambient temperature of the typical day on hourly basis. It can be seen that the radiation varies fro m a min imu m value of 290.206 W/ m 2 at 8:00h and 17:00h to a maximu m value of 920.88 W/m 2 at 13:00h. Figure 3. Hourly variation of solar intensity and ambient temperature of t he t ypical day V. 3 . Comparative results The proprieties of the conventional working fluid, a re evaluated as a function of temperature by using equations: Eqs (26)-(29) for a ir and Eqs (30) -(33) for water. However, the proprieties of the Alu mina nanofluid are simulated by using Eqs (34)-(37) at different temperatures using 2% as a volu me fract ion of Al2O3 nanoparticles in the base fluid that is water. Figure 4 shows the effect of mass flo w rate on the therma l e ffic iency of the PV/T system. It is observed that the therma l effic iency increases with the increase of the mass flow rate and the results illustrates that the therma l efficiency of nanofluid is the highest comparing with those of water and a ir, since the increase in the mass flo w rate, enhance the convection heat transfer fro m the absorbing plate to the flowing flu id and leads to reduce the thermal losses fro m the absorbing plate to ambiance. These results are agrees well with [5], [15] and [23]. Figure 4. Variat ion of t hermal efficiency wit h mass flow rat e for: air, wat er and Alumina nanofluid A. Ghellab et al IJECA-ISSN: 2543-3717. Page 51 Figure 5 shows the hourly variation of the outlet temperature of three different working flu ids, wh ich were : a ir, water and A lu mina nanofluid. The outlet temperature o f d ifferent flu ids increases with local time as radiation increases and present their ma ximu m at 13:00h, because the solar radiat ion is collected on the absorbing plate then transferred to the working fluid and it can be seen that the outlet temperature of the Alumina nanofluid presents the highest temperature with a significant diffe rence co mpared with those of water and air. Whereas, the ma ximu m outlet te mperature of nanofluid is 3.72°C higher than water and 11.77°C more than air. Figure 5. Comparison between the simulated outlet temperatures of different working fluids: air, wat er and Alumina nanofluid Figure 6 represents the variation with time of the rate of heat extracted by the fluid when the mass flow rate is taken equal to 0.04kg/s. The results of this figure indicate that the quantity of heat extracted by the nanofluid is higher than the other two fluids, because the presence of Al2 O3 nanoparticles in the nanofluid enhances its therma l conductivity and density than water and air, which imp roves the heat transfer coefficient fro m the absorber plate to the flowing fluid. These results are in good agreement with that reported in literature. Values of the heat extracted by working fluid is substituted in Eq (3 9 ) to calculate the therma l effic iency which is function of the specific heat and mass flow rates of the three working fluids, because of the highest values of the outlet temperature of nanofluid, it ’s re ma rkab le in Figure 7 that the therma l effic iency of the nanofluid beco mes higher compared to other two fluids. The ma ximu m values of therma l effic iency are found to be: 73.28%, 67.67% and 41.55%, of nanofluid, water and a ir, respectively. It’s re markable in Figure 8 that the temperature of the cell when the nanofluid is flowing is relatively lower than those of other fluids, this has a direct impact on the electrical efficiency, so it is clear in Figure 6. Hourly variation of heat gain of t hree fluids: air, wat er and Alumina nanofluid Figure 7. Hourly variation of thermal efficiency for t he t hree working fluids Figure 8. Hourly variation of PV cell t emperature for the t hree cooling fluids A. Ghellab et al IJECA-ISSN: 2543-3717. Page 52 Figure 9 that this fluid represents the best electrical efficiency compa ring to those of water and air because the increase in te mperature of the ce ll causes the decrease in electrical effic iency. It is noted from results of Figure 7 and Figure 9 that the therma l efficiency rises when operating temperature increases but in the same time the electrica l efficiency decreases, this conflict impose to calculate the overall effic iency using Eq (40) in order to determine which flu ids represents the best performances of the PV/T system, the sa me co mment was established by [5], [8] and [30], so the Figure 10 e xh ibits the evolution of the overa ll efficiency of the panel for the three fluids and it can be seen from results that the overall effic iency of Alu mina nanofluids is h igher by about 6.15 % and 33.9 % than water and a ir, respectively, because nanoparticles give the nanofluids the highest density and lower specific heat and according to [15] less heat is required to raise the temperature of the nanofluid and thus ma king the output temperature and e fficiency becomes higher. Figure 9. Elect rical efficiency variation wit h t he t hree st udied fluids Figure 10. Hourly variation t he overall efficiency of t he t hree working fluids VI. Conclusion According to the theoretical results obtained from the numerical calcu lation of the performances of a hybrid photovoltaic/thermal (PV/T) solar collector, using three diffe rent cooling flu ids: Alu mina nanoflu id, water and air, the following conclusions have been drawn:  The model was validated and the results obtained are in good agree ment with those reported by literature.  The increase in mass flow rate e xtending over the range: 0.005-0.04 kg/s, leads to raise the efficiencies by decreasing the heat losses from absorbing plates to the ambiance.  The outlet te mperature of the system using nanofluid is higher than the two other systems using water and air.  The results show that using nanofluid as cooling flu id, the electrica l e fficiency increases due to the decrease of the temperature of the PV cell.  The hybrid (PV/T) system using Alumina nanofluid presents the highest therma l effic iency, compared to the system using water and air as working fluids, respectively (73.28%, 67.67% and 41.55%).  The overall effic iency of the system using nanofluid (99.21% ) is higher than water (93.06%) and air (65.31%), because the presence of nanop articles in water increases the thermal proprieties of this fluid. NOMENCLATURE 𝐴: t he area of t he component of the syst em, m 2 cp : t he specific heat of the component of the syst em, J/kg .K Dh : hydraulic diamet er, m e: T he t hickness of t he component , m ℎ𝑣g is t he convective heat t ransfer coefficient bet ween the glazing and ambiance, W/m 2 .K ℎ𝑟g is t he radiat ion heat t ransfer coefficient from t he glazing t o t he sky, W/m 2 .K ℎ𝑣𝑐 is t he convection heat transfer coefficient for air cavity bet ween t he solar cell and glazing, W/m 2 .K ℎ𝑟𝑐 is t he radiat ion heat t ransfer coefficient bet ween solar cell and glazing, W/m 2 .K ℎ𝑐𝑐 is t he heat t ransfer coefficient conduction bet ween t he PV cell and t he absorber plate, W/m 2 .K ℎ𝑣𝑝 is t he heat t ransfer coefficient convection bet ween t he absorber plat e and t he fluid, W/m 2 .K ℎ𝑟𝑝is t he heat t ransfer coefficient by radiat ion bet ween t he absorber and back plat e, W/m 2 .K ℎ𝑣𝑏𝑝 is t he heat t ransfer coefficient convection between t he fluid and t he back plate, W/m 2 .K ℎ𝑐i is t he heat t ransfer conduct ion coefficient in t he insulation, W/m 2 .K ℎ𝑟𝑎 is t he radiat ion heat t ransfer coefficient from t he back plate and soil, W/m 2 .K ℎ𝑣𝑎 is t he convective heat t ransfer coefficient for air cavity bet ween t he back plate and soil, W/m 2 .K A. Ghellab et al IJECA-ISSN: 2543-3717. Page 53 𝑄𝑒𝑙𝑒is t he elect rical power produced by t he P V module, W/m 2 g:t he gravit ational constant, m 2 /s. k: t hermal conduct ivity W/m.K m : t he mass of t he component of t he system, kg 𝑚 is t he mass flow rate of the fluid, kg/s Nu represents t he Nusselt number P : t he energy absorbed by t he component of the system, W/m 2 Pdir and Pdif represents respectively t he intensit y of t he direct and diffuse incident radiation, W/m 2 𝑅𝑎represents the Rayleigh number T : t emperature, K, °C t : t ime, hr v t he wind velocity, m/s INDEX a: ambient air: air bp: back plate c: P V cell f : fluid g: Glass i: insolat ing in: inlet nf: nanofluid out : out let p: absorbing plate. s: sky soil: soil wat er: wat er GREC S YMBOLS 𝛼𝑉1−𝑑i𝑟 et 𝛼𝑉1−𝑑if : t he absorption coefficients of glazing 𝜎 is t he st ephan-Boltzmann constant, σ = 5.67×10 −8 W⋅m −2 ⋅K −4 s is t he emissivity of thermal radiation of the component. 𝜃 : t he collector inclination angle, ° ρ : t he densit y, kg/ m 3 β : t hermal expansion coefficient, 1/K 𝛽𝑐 is t he P acking factor 𝛽𝑟 is t he t emperature coefficient μ : t he dynamic viscosity φ : volume fraction of Al2 O3 nanoparticules 5𝑒𝑙𝑒 design t he elect rical efficiency generated by the cell, % 5𝑟𝑒f is t he reference cell efficiency, % 5𝑡ℎT he instantaneous t hermal efficiency of t he P V/T collector, % 5𝑜𝑣𝑒𝑟𝑎𝑙𝑙 t he overall efficiency of t he P V/T solar collector, % References [1] A. 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