Heat transfer study of poly-c PV system integrated with phase change material under semi-arid area (Errachidia- Drâa Tafilalet)

. The high operating temperature of the photovoltaic (PV) modules decreases significantly its efficiency. The integration of phase change material (PCM) is one of the feasible techniques for reducing the operating temperature of the PV module. A numerical simulation of the PV module with PCM and without PCM has been realized. The thermal behavior of the PV module was evaluated at the melting and solidification processes of PCM. The results show that the integration of RT35HC PCM with a thickness of 4 cm reduces the temperature of the PV module by 8 °C compared to the reference module. Compared the RT35 and RT35HC, we found that the latent heat has a significant effect on the PCM thermal comportment. Furthermore, it has been found that the thermal resistance of the layers plays an important role to dissipate the heat from the PV cells to the PCM layer, consequently improving the heat transfer inside the PV/PCM system.


Introduction
The photovoltaic (PV) module can absorb up to 80% of incident solar radiation. A very small amount is transformed into electricity, while the rest is converted into heat, which increases the operating temperature of the PV module. The temperature remains one of the important parameters that can affect the PV cell performance.
1 °C increases in the PV panel temperature above 25 ° C leads to reduce the output power and conversion efficiency by 0.65% and 0.08% respectively [1] , for a crystalline silicon PV operating above 25 °C typically, shows a temperature-dependent power decrease with a coefficient of 0.4%/K [2]. Many studies have been interested to enhance the PV module performances by decreasing the PV module temperature. Zhou et al [3] studied the thermal behavior of the polycrystalline PV module, the authors showed that the performance of the PV modules can be improved by optimizing the back sheet, and the aluminum alloy sheet performed best on heat dissipation and the highest module temperature scarcely changed within proper scope of thickness, Moreover, several works focused on the different cooling technologies to decrease the PV module temperature operating and consequently increasing its performances. Elbreki et al [4] focused on passive and active heat dissipation approaches to define the range of temperature reduction that is possible. H.G. Teo et al [5] introduce the active cooling of the photovoltaic module, they concluded that without active cooling, the temperature of the module was high and the solar cells cannot reach an efficiency up to 9 %. However, when the module operated in an active cooling state, the temperature dropped significantly, which resulted in an increase of efficiency until 14%. Likewise, Shukla et al [6] discussed various cooling techniques such as forced and natural air cooling, hydraulic, heat pipe cooling, cooling with phase change materials and thermoelectric cooling of photovoltaic panels. They claimed that the the integration of phase change material (PCM) as a cooling medium presents an alternative to the energy performance of the PV module. The heat being absorbed or returned during the transition from one state to another. In other research works [7], [8] the investigation and analysis of the available thermal energy storage systems incorporating PCMs for use in different applications; extensive efforts have been made to apply the latent heat storage method to solar energy systems [7]. In this sense, the authors agreed on the advantage of coupling the PCM to the PV modules. Four different PV/PCM systems were tested under three insolation intensities to determine the performance of each PCM. Changing the mass of PCM and thermal conductivities of PCM and PV/PCM system has an effect on thermal regulation of the PV. A maximum temperature reduction of 18 °C was achieved for 30 min while 10 °C temperature reduction was maintained for 5 h at 1000 W/m 2 insolation [2]. Browne et al [9] explained that the regulation of the PV systems temperature comprised of crystalline silicon cells appears to be the most economically viable for the use of PV/PCM systems, as increases in temperature have the most detrimental effect on the efficiency of silicon Similarly Ahmad et al [10] developed a PV/PCM system to reduce the PV panel temperature, the system has been evaluated outdoors with two PCMs in two different climates, they concluded that the PCMs attained higher temperature drop in warm and stable weather conditions of Vehari region than the cooler and variant weather conditions of Dublin. Kibria et al [11] developed an a transient one-dimensional energy balance model to examine the thermal performance of a PV module integrated with PCM storage system, the result indicates that the PCM are shown to be an effective means of limiting the temperature rise in the PV devices thus increasing the thermal performance up to 5%. Further, research works has focused on numerical methods dealing with phenomena related to PCM. Voller [12]- [14] discussed the numerical method which can be used to simulate with PCM problems, an enthalpy method is developed for analysis of one-dimensional phase change problems under heat conduction [13]. He also develops a rapid implicit solution technique for the enthalpy formulation of conduction controlled phase change problems, and he provides an overview of the numerical methods that can be used to deal with non-linear phenomena associated with the solidification phase change processes. In the first case, he focused on the fixed and distorting grid solutions from Stefan problems, the discussion is extended to include fixed grid methods directed to more general phase change systems [14], a survey of phase change formulation reveals that the most common approach applied in the solution of phase change problems is the formulation using the enthalpy method [15]. In the present study, a two dimensional thermal model for polycrystalline silicon PV modules coupled with PCM was developed by finite volume method. Temperature evolution and its distribution throughout the layers of the PV module without and with PCM was discussed, effect of thickness and latent heat of the PCM was analysed.

System description
The PV/PCM system consists of eight layers, the first six are the polycrystalline silicon photovoltaic (PV) module layers, followed by the PCM which is covered by aluminum sheet. The system is subject to variable meteorological conditions of the Er-rachidia region taken on June 25, 2020, as shown in Figure1. To study the heat transfer in the PV/PCM system, we took into account the convection and radiation exchanges on the two front and rear sides of the system and by conduction between layers of the PV/ PCM system. Figure 2 describes the heat exchanges on boundary conditions, PV module's layers and inclination. The height of the PV/ PCM system taken for this study is 0,1 m. The PCM layer is 0.02 m thick, filled in an aluminum container 0.002 m thick.  Table 1 and Table 2 and the thermo-physical commercial PCMs used in this work are listed in Table 3. The thermodynamic study of PV module coupled with PCM has been performed using volume finite analysis approach with Ansys fluent software. The simulation was based on a two-dimensional model, using the following simplified assumptions:  Thermal properties of all materials in the module were presumed to be isotropic and temperatureindependent.  The model sides was taken to be adiabatic.  Solar radiation which was neither reflected nor converted to electricity became thermal energy.  The back and the front of the PV module were taken to view the ground and sky respectively.  There is not any agent deposited on the PV surface affecting the absorptivity of the PV module.

Energy equation for solid part
Within the layers of the PV module, the dominant transfer mode is conduction. Consequently, the applied heat transfer equation by diffusion, after simplifications, is expressed by the following equation:

Radiation Heat transfer
The incident radiation I(t), after falling on the glass which is a semi-transparent medium, a part of this radiation is absorbed through the thickness of the layer of the glass, another part is reflected, and the remaining part passes through the glass and be transmitted to adjacent layers. Figure 3 represent distribution of the radiation flux falling on the glass. The sum of the three radiations, that absorbed, transmitted and reflected would be equal to the incident radiation. Different works have focused their research on the distribution of radiation in a semi-transparent medium [16], [17], and discrete ordinate (DO) model is one of models solves radiative heat transfer problems involving semitransparent media. In this work, we implement DO model in FLUENT, which uses a conservative finitevolume approach and which will be discuss in the section below.
The term describes the gain of intensity due to blackbody emission of medium where: Integrating equation 3 over control discrete angle,

Boundary condition
For both the front and backsides of the PV module, we considered the radiation and convection losses, which can be expressed as follows: Upper side: Bottom side Soil temperature «T gr » was assumed to be equal to ambient temperature «T amb ». The temperature of the sky «T sky » could be obtained in kelvin approximately by this equation [19].
( ) = ( ) − 6 (7) The convection heat transfer coefficient of the module is related to the wind speed and could be calculated by the equation [20]:

Energy equation for PCM
To analyze the PCM module, we considered the following assumptions [11]:  The heat transfer mode in the PCM is pure conduction.  The thermo-physical properties of PCM are constant and identical in the two phases.  PCM is homogeneous and isotropic.  The PCM is initially in solid phase A material in phase transition, i.e. solid to liquid or liquid to solid, the energy conversion for constant thermo-physical properties of this material can be expressed in terms of temperature and total enthalpy as follows [12]: The enthalpy formulation for a conduction controlled phase change can be written as [12]: = . ( . ∆ ) (9) H is related to the temperature in term of the local liquid fraction f and latent heat L as = ∫ + (10) Liquid fraction, f, is calculated as:

Model Validation
We validated the present study without and with PCM by our experimentally obtained results, and by a previous experimental study by Park et al. [22]. This comparative study shows that the results obtained with our thermal model are in good agreement with our experimental results (see Figure 4), also consistent with the results of Park et al. [22] as shown in Figure 5 in the case of a PV module without PCM. The validation of the temperature variation without PCM. The temperature variation of the PV module with PCM integration is calculated from the model and is compared with the study of Park et al. (2014), as shown in Figure 6. The results of the computer simulation were consistent with the results obtained by Park et al and the comparison between them verified the accuracy of the model.  3 Result and discussion 3.1 Temperature distribution in the PV module without PCM Figure 7 shows the temperature profile in the PV module at 14:10, which is the time when the PV module reaches its maximum operating temperature. The profile describes the temperature distribution from the first layer which is the glass to the Tedlar We note that the temperature increases with respect to the thickness of the PV module until reaching a maximum of 63,7 °C inside the solar cells, due to its high absorption, and the high transmissivity of the glass. Then the temperature begins to decrease at the level of the lower EVA located after the solar cell and Tedlar, which exchange the heat with the environment. The energy, which is not used for the production of electricity, is transformed into heat, due to the temperature difference between the layer of solar cell and the borders of the module would be transferred from solar cells to the front and back layers. The heat transfer varies according to the thermal resistance values of each layer listed in Table 4. The thermal resistance of the two layers, Tedlar and EVA inferior, located at the back of the solar cells is higher than those of glass and EVA superior located at the front of the solar cells. This difference in thermal resistance allows to the heat exchange of being very easy through the upper EVA and the glass, which is why we have the temperature of the glass, is higher than that of the Tedlar.

Effect of integration of different PCM in the PV module with different thickness
To reduce the temperature of the PV module, we tested two different types of PCMs, with different thermophysical properties. Figure 8 shows the temperature evolution of the PV module without PCM, and after integration of the PCM. The two PCMs start to melt once their fusion temperature is reached, and consequently the temperature of the module begins to drop. As shown in Figure 8, the RT35HC begins its fusion at 9:00 am with a drop of temperature of 5±2°C , and complete its fusion at 1:30 pm, while the RT44HC begins its fusion at 10:00 am and, complete its fusion at 13:30 am with a drop of temperature of 3±1°C. The moment when the PCM is completely melted, its liquid fraction is equal to 1, we find that the temperature of the system begins to increase and, the temperature of the PV/PCM system exceeds the maximum temperature of the reference PV module. We consider that PCM in its liquid state acts as an insulator due to its low thermal conductivity. From figure 8, 9 and 10, we see that by adding thickness, the time to store the energy as latent heat will be longer and, therefore, the temperature of the PVmodule will decrease as the thickness of the PCM layer increases. If we evaluate the maximum temperature reached by the PV module, we find that the PCM RT44HC decreases the temperature of the PV module by 3°C for a thickness of 0.03m better than the RT35HC. On the other hand, we find that the PCM RT35HC gives a lower temperature of the reference module and the module with RT44HC from 9:30 am to 3:40 pm. The PCM RT35HC remains in its fluid state a longer time than the RT44HC, which allows it to increase the module temperature, which reaches almost to the reference module temperature. We raise the thickness of the PCM again to 0.04 m; we find that the PCM RT35HC gives better results than the PCM RT44Hc, with a drop in module temperature of 8°C compared to the reference module. For the RT44HC, it is important to note that it is not completely melted which indicates that there was an unused amount of PCM.

Latent heat effect
In this section, we evaluate the effect of latent heat for a PCM RT35HC and RT35 with the same melting temperature and different latent heat. The thermophysical properties of RT35Hc are listed in Table 5. From figure 11, we see that the RT35 PCM with a thickness of 0.04cm coupled to the PV module gives an operating temperature exceeding that obtained with the RT35HC with the same thickness, which requires increasing the thickness of the PCM. As shown in Figure  11, we increased the thickness of PCM RT35 to 0.06m to have the temperature obtained by the PCM RT35HC, which implies latent heat to a non-negligible importance in a PCM. We conclude that latent heat has a significant effect on the PCM. The PCM RT35 having a latent heat is divided by 1.5 of that of RT35HC requires a thickness of 1.5 of that of RT35HC to decrease the temperature of the module to the same level as RT35HC.  Figure 11. Temperature evolution for PV module for different thickness of PCM RT35

Temperature distribution in the PV/PCM (RT35HC) system
In this section, we discuss the temperature distribution profile in the PV / PCM (RT35HC) system.
From Figure 12, we notice that the maximum temperature difference of the PV/PCM system between the eastern back side and the front side reaches a maximum of 27°C. In contrast to the PV module without PCM, we find that the difference between the maximum temperature of the front side and the back side are almost the same as shown in Figure 6 in Section 1.
Once the PCM begins its fusion we see that the temperature of rear face Begin to drop. We justify this result by: 1) the heat, which is concentrated at the level of the solar, cells when and dissipates in both directions, before it reaches the last layer; it would be absorbed by the PCM.
2) The aluminum back layer exchanges more heat with the environment because of its high conductivity.
In order to demonstrate the thermal behavior of the PCM integrated PV module, we choose the moment when the solar cells reach their maximum temperature, 3:30 pm, and we plot the temperature profile along its thickness (see Figure (13,a,b)). Figure (13,a) shows a temperature distribution profile from the glass where the sunlight enters to the first layer of aluminum, likewise Figure  (13,b) shows the temperature profile in the PCM and its aluminum boxing.

Conclusion
The PV module reaches a maximum temperature, which is equal to 63.7 °C. The PCM cooling system was investigated to examine the effects on temperature reduction and thermal behavior of PV module in the Errachidia climate. Different PCMs are tested with different thickness, the results clearly show that PCM gives an effective way of regulating the increase in the operating temperature of PV module; we found also that the thickness of the PCM is an important parameter, which influences the thermal behavior of the PCM. The results of the study are synthesized below:  The solar cell reaches the maximum temperature in the PVmodule  The temperature distribution inside the PV module depends on thermal resistance of the layers  RT35HC decrease the temperature of the PV module by 8°C better than the RT44HC for one day  Comparing RT35Hc and RT35, we find that the latent heat is a significant effect in thermal comportment of PCM, for the RT35 which have a low latent heat, it need to increase its thickness  The thermal resistance of layers affects heat dissipated by the solar cell and absorbed by the PCM.