PCM-based hybrid thermal management system for photovoltaic modules: A comparative analysis

1 Temperature regulation of photovoltaic (PV) modules increases their performance. Among 2 various cooling techniques, phase change materials (PCMs) represent an effective thermal 3 management route, thanks to their large latent heat at constant temperatures. Radiative cooling 4 (RC) is also recently explored as a passive option for PV temperature regulation. In this paper, 5 a heat sink (HS), phase change materials, and radiative cooling are integrated with photovoltaic 6 modules to get low and uniform temperature distribution along the PV module and its improved 7 performance. Eight different combinations are considered for the proposed system, including 8 HS, PCM, and RC and their various combinations. The PCM is selected according to the 9 environmental conditions of a specific location. A comprehensive 2-D model is developed and 10 analyzed in COMSOL-Multiphysics software by solving the governing equations using the 11 finite element method. The performance analysis is carried out for the climatic conditions of 12 the Atacama Desert, having high solar radiation and ambient temperature. The effects of PCM 13 height, ambient temperature, wind velocity, and solar radiation on the performance of the 14 proposed system are studied. The performance of eight different configurations is also 15 compared. The maximum reduction in PV temperature, maximum PV power and a minimum 16 drop in PV conversion efficiency are observed to be 22 K, 152 W and 14% using a combined 17 heat sink and radiative cooling systems, among all other configurations. The findings of this 18 study can be used to select the best PV cooling method among different configurations.

electricity. The PV technology is more attractive and economically viable due to its robustness 31 and less maintenance than its thermal counterpart. A photovoltaic cell consists of p-and n-type 32 semiconducting materials. The performance of a PV cell relies on incoming solar energy on the 33 PV surface, ambient temperature, dust, and wind speed. More interestingly, the ambient 34 temperature is more than 45 o C in desert areas during harsh summer conditions that may raise 35 the PV temperature to 80-100 o C. These high ambient temperatures and intense solar radiation 36 raise the PV temperature significantly.

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The efficiency of a PV cell is approximately 10-20% only, and most input energy is transformed 38 into thermal energy that raises its temperature (Chandel et al. 2015). The temperature rise in the 39 PV module reduces its efficiency and life span. The efficiency of a crystalline silicon PV cell 40 reduces by 0.4 % with a unity rise in its temperature (Du et at. 2013) and thus degrading its 41 performance. This performance degradation of the PV module resulting from the excess 42 temperature can be avoided by maintaining the PV temperature nearly at ambient temperature. 43 Concentrated PV (CPV) systems are widely adopted due to their improved power output and 44 lower land requirements. Although, the CPV system temperature is even more significant than 45 the PV module temperature due to the incidence of concentrated solar radiation on its surface. 46 This causes more performance degradation in CPV systems than in a PV system. This very high temperature of the CPV system may cause potential structural damage, which is challenging 48 for the wider adaptability and reliability of CPV systems.  performance has also been studied. It was observed that using a heat sink outside the PCM boost 164 the heat transfer from the PCM container. A comparative analysis of the eight cases of the 165 proposed system has also been carried out. This analysis's results may help select the best 166 cooling method for PV systems, especially for desert locations.  Table 1.  A few assumptions have been considered to simplify the analysis, which are as follows:

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• There is direct contact between all the components. The energy conservation and Fourier´s heat conduction laws for the PV module are written as 190 follows: Where cp, ρ, T and q are the constant pressure-specific heat capacity, fluid density, fluid 194 temperature, and heat flux, respectively.

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Conductive and unsteady state heat transfer is assumed through different solid layers of the PV 196 module, which is given by the diffusion equation of heat transfer as: Where ki, cp, i, ρi, qi, and Ti(x, y) represent the thermal conductivity, specific heat capacity, 199 density, the internal local heat generation per unit volume, and temperature of the i-th layer of 200 the PV module, respectively.

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Depending on their absorptivity, each PV layer absorbs solar irradiation, which is converted Where G(t) is incoming solar radiation, τi is the transmissivity of the layer above the i-th layer, 206 αi is the absorptivity, and Ai & Vi are the area and volume of the layer i-th layer, respectively.

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Ƞe is the electrical efficiency of the silicon layer of the PV module, and it deviates linearly from 208 its reference value at STC and is written as: Where ηref, βref, Tref and TPV are the efficiency of the PV module at standard test conditions, i.e., 211 reference efficiency (at 25 °C), temperature coefficient of efficiency, reference temperature 212 (i.e., 25 °C) and operating temperature of the PV module respectively.

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The electrical efficiency for other layers of the PV module is taken as zero. The PV power 214 generated during the simulation period is determined using the measured PV temperature, and 215 it is given as: The solar radiation, Esun incident of the PV surface is written as: Where Tamb is the ambient temperature. The surface area of the PV module, APV, is taken as 220 0.02436 m 2 , and the reference efficiency of the PV module, ηref, is taken as 15%.
where hc is the convective heat transfer coefficient, and Pr and Re are the Prandtl and Reynold where V is the velocity vector of the melted PCM, and u and v are its component velocities.

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Momentum equations: where P is the pressure of the PCM. B F is the buoyancy term vector, and S is the source term   The thermal conductivity of PCM, kpcm, depending on the phase change process, can be defined  Table 2.

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The atmospheric wavelength-dependent emissivities and PV surface emissivities are given in 330   Table 3.    Table 4.    It is clear from Fig. 3 (a)  cell was simulated as a heat flux. Fig. 4 (a) also depicts that the maximum and average ambient 373 temperatures are 301.15 K and 291.95 K, respectively. The maximum and average wind 374 velocities are 8.0 m/s and 5.9 m/s, respectively, as given in Fig. 3 (b). the reduction is also lower than the HS cooling system alone, as shown in Fig. 4 (c). It indicates 393 that the PCM cooling system can homogenize the temperature reduction in the PV system, but 394 the reduction directly depends on the PCM melting and environmental temperatures. Another PV thermal management method under the ambient conditions of the selected location is the 396 radiative cooling system coupled to the front side of the PV system. The temperature reduction 397 using the RC system can reach a maximum of around 10 K in the period with lower wind 398 velocity. However, the reduction is lower in the rest of the simulated period due to the increase 399 in the wind velocity, as shown in Fig. 4 (d). Combining an HS and RC system (HS+RC) has 400 the best results in reducing the PV operation temperature among all configurations. It is due to 401 the ambient conditions that allow each cooling system to enhance the heat transfer to the 402 ambient according to the variation in the wind velocity. As shown in Fig. 4 (e), the temperature periods.

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Nevertheless, the reduction in PV operation temperature is still lower than the HS+RC 409 configuration, reaching only a maximum reduction of around 12 K, as shown in Fig. 4 (f).  for different system configurations. Fig. 7 (a) shows that the maximum PV power is 150 W 438 when a heat sink cooling system is coupled to the back side of the PV system as compared to 439 141 W peak power in a PV-only system. Coupling a PCM cooling system to the back side of 440 the PV system modifies the PV peak power. It is observed that the increase in the PCM layer 441 thickness reduces the PV peak power. The best PCM height for maximum PV power) is at the 442 minimum PCM thickness, i.e., 1.5 mm, as observed in Fig. 7 (b). Adding a HS cooling system 443 to the PCM further allows some improvements in the PV power peak. The peak power for this configuration is reached using a 1.5 mm PCM thickness. Furthermore, it is possible to reach a 445 minimum increment in the PV power peak for the rest of the simulated period, as is observed 446 in Fig. 7 (c). Fig. 7 (d) shows the increment in the PV power peak when a radiative cooling 447 system is placed on the front side of the PV module. In this case, the PV power peak reaches 448 around 144 W. It is also observed in Fig. 7 (e) that combining HS and RC systems allows it to  Fig. 8 (c).

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The combination of a PCM and HS cooling systems can enhance the heat transfer to the 495 ambient, thus reducing the thermal resistance and reaching a PV conversion efficiency of 496 around 13.6%. When a radiative cooling system is added as a thermal management system in 497 the PV front side, it can control the PV operation temperature and conversion efficiency, thus, 498 allowing to maintain the minimum PV conversion efficiency of 13.3% during the minimum 499 wind velocity period, as shown in Fig. 8 (d). The RC system performs best during the minimum 500 wind velocity period.

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In addition, the combination of HS and RC systems shows the best cooling performance and 502 the PV conversion efficiency enhancement, presenting a minimum PV conversion efficiency of 503 around 14%, as shown in Fig. 8 (e). It is due to the complementation of the two cooling systems 504 to work under different environmental conditions, principally with the variations of wind 505 velocity, which impacts the convection heat transfer to the ambient. Fig. 8 (f) shows the 506 variation in PV conversion efficiency when a combination of PCM and RC cooling systems is 507 applied to cool the PV module, allowing it to maintain a minimum PV conversion efficiency of 508 13.4%. When a HS is coupled to the PCM+RC cooling system, the minimum PV conversion 509 system can be maintained at over 13.62% Fig. 8 (g). As mentioned, the PCM cooling system 510 has a lower effect in controlling the PV operation temperature than the HS and RC systems.

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However, the PCM cooling system can be coupled with solar energy conversion systems to 512 store the remanent heat and enlarge the electricity generation time, as studied by Montero et al.

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(2021). Fig. 9 shows the PV conversion efficiency for the analyzed cooling system    configurations is also discussed. The following conclusions have been drawn:

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• PV energy generation follows solar irradiation and is also affected by desert 541 environmental conditions.
• A heat sink can effectively control the PV operational temperature and is the best 543 cooling system for individuals. Also, combining with other passive cooling systems 544 enhances its performance and, thus, allows for further reduction in the PV operation 545 temperature.

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• Heat sink and radiative cooling systems can work as complementary systems, managing 547 and controlling the PV operational temperature and adapting its performance to the daily 548 variation of the wind velocity in the selected location.

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• The PCM cooling system shows lower performance compared with HS and RC 550 individual systems; the lower PCM thickness has the best performance to control the 551 PV operation temperature due to the increase in thermal resistance that does not allow 552 to transfer of the remanent heat to the ambient.

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• The maximum reduction in PV temperature is observed using the HS+RC system, which 554 is 22 K in high wind velocity. Similarly, the maximum PV power is 152 W which is 555 found while using the HS+ RC system as a thermal management system.

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• The HS+RC system resulted in a minimum drop in PV conversion efficiency, which is 557 found to be 14% among all other systems.

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• The wind velocity affects the performance of HS and RC systems the most; on the other 559 hand, the ambient temperature controls the PCM melting temperature.  Availability of data and materials: All data are given in the manuscript.

Cover letter 576
The Editor-in-Chief 577

Environmental Science and Pollution Research Journal, 578
Dear Prof. Philippe Garrigues, 579 We are submitting our manuscript entitled "PCM-based hybrid thermal management system for 580 photovoltaic modules: A comparative analysis" for possible publication in the Environmental Science 581 and Pollution Research Journal. 582 In this manuscript, a heat sink (HS), PCM, and radiative cooling are integrated with photovoltaic 583 modules to get low and uniform temperature distribution along the PV module and its improved 584