Improvement of Extracted Power of Pole Mounted Solar Panels by E ﬀ ective Cooling Using Aluminum Heat Sink under Hot Weather and Variable Wind Speed Conditions

: The increase in operating temperature of PV generators leads to degradation of their performance. These adverse e ﬀ ects of high temperatures are considered as one of the most important problems that solar panel operation faces in hot weather areas. A lot of research has been undertaken to study this aspect and ﬁnd ways of limiting the harm caused by such high temperatures. To overcome this harm and to maintain the operating temperature of the PV cells within the optimum range speciﬁed by manufacturers, cooling the solar panels often becomes indispensable. This paper discusses the heat transfer through the solar panel layers and studies the e ﬀ ect of high temperature on the solar panel performance in a hot desert environment. It also presents the development of a new solar panel structure viz. by installing an aluminum heat sink to reduce the e ﬀ ect of temperature rise and thus improve the solar panel performance. The study focuses on a pole-mounted solar panel for a street lighting apparatus in extremely hot desert conditions with ﬂuctuating wind speeds. It will be shown that adding an aluminum heat sink to the solar panel bottom mitigates the e ﬀ ect of increased temperature and hence modiﬁes the solar panel operating point by increasing both the e ﬃ ciency and the lifetime. The solar cell temperature is decreased by 16.4% as a result of the aluminum heat sink installation on the solar panel back sheet and consequently, the accumulated energy produced by the the solar panel is increased by 13.23% per day.


Introduction
Saudi Arabia is a leader in the field of fossil oil production in the Middle Eastern Gulf region. Nevertheless, in the recent years the country has made strides in harnessing new renewable energy sources to meet its energy requirements, mostly owing to the environmental sustainability of these energy sources [1]. Several investigations about solar radiation have been carried in Jeddah City Figure 1 shows the structure of solar panel considered in this study. It contains solar cells that consist of a p-n junction-based silicon layer encapsulated within a very thin film of protective sheets. These sheets are attached to both back and front sides, and are fabricated with ethyl vinyl acetate (EVA). Polyethylene terephthalate (PET) was used to fabricate the back sheet because if its high strength. This results in protection of the solar cells in addition to the junction box where the electrical output power connection terminals are located [22,23].
Energies 2020, 13, x FOR PEER REVIEW 3 of 30 Figure 1 shows the structure of solar panel considered in this study. It contains solar cells that consist of a p-n junction-based silicon layer encapsulated within a very thin film of protective sheets. These sheets are attached to both back and front sides, and are fabricated with ethyl vinyl acetate (EVA). Polyethylene terephthalate (PET) was used to fabricate the back sheet because if its high strength. This results in protection of the solar cells in addition to the junction box where the electrical output power connection terminals are located [22,23].

Solar Cell Principle of Operation
A solar cell is a p-n junction which is fabricated from silicon with few impurities. When the solar radiation strikes its surface, it forces the electrons to acquire enough energy so that electrons become free and an abundance of electron-hole pairs is created and a potential difference appears at the terminals. Then, an electric current flows if the circuit is connected to a load [24,25] as shown in Figure 2.

Solar Cell Energy Transmitted Mathematical Model
As sunlight falls on the surface of any solar cell, an amount of energy QC is trasmitted through the glass surface [21], [26][27][28][29][30] given by the following Equation (1): (1) Figure 1. The material structure layers of a solar panel [22].

Solar Cell Principle of Operation
A solar cell is a p-n junction which is fabricated from silicon with few impurities. When the solar radiation strikes its surface, it forces the electrons to acquire enough energy so that electrons become free and an abundance of electron-hole pairs is created and a potential difference appears at the terminals. Then, an electric current flows if the circuit is connected to a load [24,25] as shown in Figure 2.
Energies 2020, 13, x FOR PEER REVIEW 3 of 30 Figure 1 shows the structure of solar panel considered in this study. It contains solar cells that consist of a p-n junction-based silicon layer encapsulated within a very thin film of protective sheets. These sheets are attached to both back and front sides, and are fabricated with ethyl vinyl acetate (EVA). Polyethylene terephthalate (PET) was used to fabricate the back sheet because if its high strength. This results in protection of the solar cells in addition to the junction box where the electrical output power connection terminals are located [22,23].

Solar Cell Principle of Operation
A solar cell is a p-n junction which is fabricated from silicon with few impurities. When the solar radiation strikes its surface, it forces the electrons to acquire enough energy so that electrons become free and an abundance of electron-hole pairs is created and a potential difference appears at the terminals. Then, an electric current flows if the circuit is connected to a load [24,25] as shown in Figure 2.

Solar Cell Energy Transmitted Mathematical Model
As sunlight falls on the surface of any solar cell, an amount of energy QC is trasmitted through the glass surface [21], [26][27][28][29][30] given by the following Equation (1): (1) Figure 2. Principle of operation of a solar cell [24].

Solar Cell Energy Transmitted Mathematical Model
As sunlight falls on the surface of any solar cell, an amount of energy Q C is trasmitted through the glass surface [21,[26][27][28][29][30] given by the following Equation (1): (1) Figure 3 shows a cross-section of the solar panel as well as its thermal resistance network. The solar energy irradiating the solar panel Q C is divided into two parts [21,31]; the useful energy and the thermal losses. The first part, i.e., the useful extracted energy, generates electrical energy Q el according to the following expression: where η el is the electrical efficiency given by: β is the temperature coefficient that relies on the material type (β = 0.004 K −1 for a monocrystalline solar cell fabricated from silicon [12,21]) and is given by Equation (4): The nominal electrical efficiency η o under the Standard Test Conditions (STC) is given by the Equation (5): As mentioned in [17,21], the P mpp is the output power (W), that is tracked at the maximum power point (MPP), and given by Equation (6): The second part is transformed into thermal energy losses Q th that can be expressed as follows: where η th is the thermal efficiency, given by: where U L is the overall heat transfer coefficient, given by Equation (9): where U t , U b and U e are the heat transfer coefficients of top, bottom and edges, respectively, given in Equations (10)- (12):  Figure 3. Solar panel (a) Cross-section (b) Thermal resistance network [21]. The properties of the layers are listed in Table 1, where the reflection coefficient of the glass ζ = 0.1, indicating the solar radiation reflected from the surface of the glass [23]. The thermal resistance of any layer is given by Equation (13) for conduction and by Equation (14) for convection or radiation [21,[32][33][34]: The heat transfer coefficient of back or front surfaces due to radiation effect hr, f-a or b-a and the surrounding air heat transfer coefficient due to convection effect hc,G-a,or,b-a are given by Equations (15)-(17):  The properties of the layers are listed in Table 1, where the reflection coefficient of the glass ζ= 0.1, indicating the solar radiation reflected from the surface of the glass [23]. The thermal resistance of any layer is given by Equation (13) for conduction and by Equation (14) for convection or radiation [21,[32][33][34]: The heat transfer coefficient of back or front surfaces due to radiation effect h r,f−a,or,b−a and the surrounding air heat transfer coefficient due to convection effect h c,G−a,or,b−a are given by Equations (15)- (17): h cv,G−a,or,b−a = Nu k a L ch (17) where L ch is the surface characteristic length [35] as given in Equation (18), T s is the sky temperature that is calculated by the empirical Equation (19), h w is the convective heat transfer coefficient due to wind speed as defined in [36], (ω r = 4-15 m/s) is the resultant wind speed due to the natural air wind speed (ω s = 4 m/s) and the turbulence air (ω t = 0-11 m/s) that is induced by movement of vehicles on the road as per Equations (20) and (21) as described in [21,[37][38][39][40]: As per Equations (20) and (21), the turbulence due to vehicles motion on the road accelerates the wind speed, which contributes to solar panel temperature reduction. As mentioned in [31,35], Nu is a Nusselt number that is calculated by Equation (22): where Re is the Reynold number that is calculated using Equation (23) and Pr is the Prandtl number that is calculated using Equation (24): As shown in Figure 4, the heat transfer losses will be distributed in the top, bottom and edges directions [21,31,41] according to Equations (25)- (27) respectively: As mentioned in [29,41,42], the solar cell operating temperature ( • C) is given by Equation (28): where NOCT indicates the normal operating cell temperature as per the manufacturer's datasheet. Tthe solar cell temperature T C relies on the value of the solar radiation and the measured wind speed [43] as given by the empirical Equation (29): To incorporate the effect of the wind speed on the convective heat transfer coefficient, a correlation shall be done in the cell temperature [31,[43][44][45][46] for both Equations (28) and (29). Then, the solar cell temperature T C is given, respectively, in the following approximate and accurate expressions: where τα = 0.9, T a,NOCT = 20 • C or 293 K, S r,NOCT = 800 W/m 2 , U L,NOCT is the overall heat transfer coefficient at NOCT, wind speed is 1 m/s at NOCT. The analysis of the absorbed solar energy by the solar panel shall follow the energy balance [21,31], as per Equation (32), where the sum of the electrical and thermal efficiencies is equal to unity: where τα = 0.9, Ta,NOCT = 20 °C or 293 K, Sr,NOCT = 800 W/m 2 , UL,NOCT is the overall heat transfer coefficient at NOCT, wind speed is 1 m/s at NOCT. The analysis of the absorbed solar energy by the solar panel shall follow the energy balance [21,31], as per Equation (32), where the sum of the electrical and thermal efficiencies is equal to unity:

Solar Energy Electrical Model
A single diode model of the solar cell is considered as the common electrical model, shown in Figure  5 for a solar panel that consists of nc solar cells. The mathematical model of a single diode solar cell is shown in Appendix A. The output power Pmpp at the MPP is as given in Equation (6). Both the voltage and current at the MPP are calculated as mentioned in Appendix A by simultaneously and numerically solving Equations (A11)-(A12) or Equations (A13)-(A14) as in [21,24,[30][31][47][48][49][50].

The Methodology of Temperature Mitigation
The solar panel structure in this work is modified by installating an aluminum heat sink on its back sheet. First its shape will be selected and then its design will be performed. Finally, to obtain the experimental results, it will be assembled onto the solar panel back sheet.

Solar Energy Electrical Model
A single diode model of the solar cell is considered as the common electrical model, shown in Figure 5 for a solar panel that consists of n c solar cells. The mathematical model of a single diode solar cell is shown in Appendix A. The output power P mpp at the MPP is as given in Equation (6). Both the voltage and current at the MPP are calculated as mentioned in Appendix A by simultaneously and numerically solving Equations (A11) and (A12) or Equations (A13) and (A14) as in [21,24,30,31,[47][48][49][50].
where τα = 0.9, Ta,NOCT = 20 °C or 293 K, Sr,NOCT = 800 W/m 2 , UL,NOCT is the overall heat transfer coefficient at NOCT, wind speed is 1 m/s at NOCT. The analysis of the absorbed solar energy by the solar panel shall follow the energy balance [21,31], as per Equation (32), where the sum of the electrical and thermal efficiencies is equal to unity:

Solar Energy Electrical Model
A single diode model of the solar cell is considered as the common electrical model, shown in Figure  5 for a solar panel that consists of nc solar cells. The mathematical model of a single diode solar cell is shown in Appendix A. The output power Pmpp at the MPP is as given in Equation (6). Both the voltage and current at the MPP are calculated as mentioned in Appendix A by simultaneously and numerically solving Equations (A11)-(A12) or Equations (A13)-(A14) as in [21,24,[30][31][47][48][49][50].

The Methodology of Temperature Mitigation
The solar panel structure in this work is modified by installating an aluminum heat sink on its back sheet. First its shape will be selected and then its design will be performed. Finally, to obtain the experimental results, it will be assembled onto the solar panel back sheet.

The Methodology of Temperature Mitigation
The solar panel structure in this work is modified by installating an aluminum heat sink on its back sheet. First its shape will be selected and then its design will be performed. Finally, to obtain the experimental results, it will be assembled onto the solar panel back sheet.

Design and Selection of Aluminum Heat Sink
For this study, the heat sink is manufactured using aluminum and its shape is rectangular with length L (m), width W (m). It is connected by casting with N number of fins as shown in Figure 6a. The heat transfer from the source that has a temperature T b to the heat sink surface via interface like a thermal grease used to fill any partial space between the heat source and sink to improve the thermal conductivity. The thermal network for heat exchange includes conduction, convection and radiation with ambient air as shown in Figure 6b [51,52]. The lumped heat sink thermal resistance R Hs is presented by Equation (33): Energies 2020, 13, 3159 8 of 28 used to fill any partial space between the heat source and sink to improve the thermal conductivity. The thermal network for heat exchange includes conduction, convection and radiation with ambient air as shown in Figure 6b [51,52]. The lumped heat sink thermal resistance RHs is presented by Equation (33): The interface thermal resistance Rinr is given by Equation (13). It depends on the interface material conductivity kr (W/m. K) and the surface area A (m 2 ) and it is inversely proportional to its thickness tr (mm) [52]. Also, the contact resistance Rc between the heat source and the interface is given by Equation (13). It depends on the material properties and assembly method [51,[53][54][55][56]. The spreading resistance is determined by the Equation (34): where ѱav is the dimensionless spreading resistance that is calculated as described in [54]. The adiabatic thermal resistance per each fin is given by Equation (35): where m is the fin parameter that is defined as a heat transfer ratio between the heat transfer of a finite length fin and an infinite length fin at identical medium conditions and it is given by Equation (36). To minimize the error due to the dimensional fins when considering the thermal energy analysis [32], it is necessary to achieve (hT.tf/k ˂ 0.2): The lumped thermal resistance of total number of fins (Nf) can be calculated as a parallel circuit by Equation (37): where Rbpb is the thermal resistance of the back heat sink base plate, given by Equation (13). The thermal resistance Rfa from the heat sink fins to ambient air is calculated by Equation (14) as a parallel convection The interface thermal resistance R inr is given by Equation (13). It depends on the interface material conductivity k r (W/m. K) and the surface area A (m 2 ) and it is inversely proportional to its thickness t r (mm) [52]. Also, the contact resistance R c between the heat source and the interface is given by Equation (13). It depends on the material properties and assembly method [51,[53][54][55][56]. The spreading resistance is determined by the Equation (34): where ψ av is the dimensionless spreading resistance that is calculated as described in [54]. The adiabatic thermal resistance per each fin is given by Equation (35): where m is the fin parameter that is defined as a heat transfer ratio between the heat transfer of a finite length fin and an infinite length fin at identical medium conditions and it is given by Equation (36).
To minimize the error due to the dimensional fins when considering the thermal energy analysis [32], it is necessary to achieve (h T .t f /k < 0.2): The lumped thermal resistance of total number of fins (N f ) can be calculated as a parallel circuit by Equation (37): where R bpb is the thermal resistance of the back heat sink base plate, given by Equation (13). The thermal resistance R fa from the heat sink fins to ambient air is calculated by Equation (14) as a parallel convection and radiation thermal resistances. The total heat transfer rate Q fT from the heat sink fins surface is calculated by Equation (38): For rectangular shape fins, the efficiency η fins is given by Equation (39): Energies 2020, 13, 3159 9 of 28 As mentioned in [51,56], the optimum spacing d f between the fins is given by Equation (40): where Ra is Rayleigh number that is equal to the multiplication of Prandtl number Pr and Grashoff number Gr as in Equation (41): where T m is the mean absorbed cell temperature as given in Equation (42), ∆T is the temperature difference between solar panel layers (K) as in Equation (43): The optimum total number of fins N f is given by Equation (44): The aluminum heat sink selection depends on Equations (13), (14) and (33)- (44), using the data of Table 1 and the solar module dimensions as listed in Table 2. Properties of the thermal grease that was used as an interface between the solar panel and the aluminum heat sink has been specified in Table 3. A computational MATLAB software program was used to calculate the required heat sink parameters that matched Figure 6a, the obtained results as recorded in Table 4, where the aluminum thermal conductivity is equal to 239 W/m.K [57,58].

Assembly the Aluminum Heat Sink to the Solar Panel Back Sheet
The aluminum heat sink is installed to the back sheet of the solar panel using a silicon thermal grease to fill any cavities. The objective of the aluminum heat sink is to reduce the adverse effects of any rise in temperature. The mechanical assembly is carried out by using screw bolts to ensure a tight contact between surfaces. Heat is dissipated by heat transfer and conduction from the solar panel back sheet to the surrounding air by convection and radiation as shown in Figure 7a and the thermal resistance diagram is shown in Figure 7b. As mentioned in [11], the thermal energy rating Q r that results from the air touching the surfaces of the solar panel because of the resultant wind speed is given by Equation (45): The procedure is described by the flowchart depicted in Figure 7c.

Simulation Model
The developed mathematical model is used to estimate the solar energy absorbed by the solar panel and perform the calculations of the temperatures of the solar cell, glass, and back sheet. Using this approach both the useful extracted electrical energy beside the thermal energy can also be calculated. The simulation model can be generated, for constant average ambient temperature and varying wind speeds when the average solar radiation is constant. The solar panel properties are given as in Table 2. The location coordinates of King Abdulaziz University (KAU) situated in Jeddah, Saudi Arabia, are detailed in Table 3. The parameters of the solar radiation Sr and the wind speed ωs [59][60][61] were provided by the meteorological weather station as shown in Figure 8.

Simulation Model
The developed mathematical model is used to estimate the solar energy absorbed by the solar panel and perform the calculations of the temperatures of the solar cell, glass, and back sheet. Using this approach both the useful extracted electrical energy beside the thermal energy can also be calculated. The simulation model can be generated, for constant average ambient temperature and varying wind speeds when the average solar radiation is constant. The solar panel properties are given as in Table 2. The location coordinates of King Abdulaziz University (KAU) situated in Jeddah, Saudi Arabia, are detailed in Table 3. The parameters of the solar radiation S r and the wind speed ω s [59][60][61] were provided by the meteorological weather station as shown in Figure 8.    Simulation model is developed using computational program of MATLAB software, and simulation results are derived as follows:

Simulation of Solar Panel without a Heat Sink
This model describes the analysis of solar energy absorbed by the solar panel as shown in Figure 3. A computational MATLAB software program is run to calculate the temperatures of solar cells, glass, and back sheet as well as for calculating both the extracted electrical energy and the thermal energy including top, bottom and edge losses. The results are depicted in Tables 5-7 for various wind speeds (ωr = 1-15 m/s). Simulation model is developed using computational program of MATLAB software, and simulation results are derived as follows:

Simulation of Solar Panel without a Heat Sink
This model describes the analysis of solar energy absorbed by the solar panel as shown in Figure 3. A computational MATLAB software program is run to calculate the temperatures of solar cells, glass, and back sheet as well as for calculating both the extracted electrical energy and the thermal energy including top, bottom and edge losses. The results are depicted in Tables 5-7 for various wind speeds (ω r = 1-15 m/s).
Simulation results for the electrical characteristics without heat sink are presented in Table 8.

Simulation of Solar Panel with an Aluminum Heat Sink
This model describes the analysis of solar energy absorbed to the solar panel with the aluminum heat sink. The heat is dissipated by conduction with the solar panel back sheet via thermal grease, the properties of which are enumerated in Table 9. A computational MATLAB software program was run to calculate the temperatures of solar cell, glass, and back sheet. Also, both the salutary electrical energy and the thermal energy including top, bottom and edge losses were calculated by the same program.
The results are listed in Tables 10-12 for various wind speeds (ω r = 1-15 m/s). The results indicate that the temperature of the solar cell is decreased and the heat transfer through the solar panel bottom is increased due to the installation of the aluminum heat sink. The more wind speed increases the more temperature decreases. Table 13 presents simulation results for the solar panel electrical characteristics with the aluminum heat sink. When wind speed increases, temperature decreases and therefore the electrical efficiency improves and the extracted power increases. Table 9. Thermal grease properties.

Parameters of the Thermal Grease Values & Units
Brand GD380 Thermal Paste Colour Gray Specific gravity 2.5 G/Cc Thermal conductivity 2.2 W/m.K Operating temperature −50~200 • C Table 10. Layers temperature at various wind speed for the simulation model with an aluminum heat sink (T a = 315 K).

Comparison of Results of the Two Simulation Models
This section discusses the comparison of results of the two simulation models, without heat sink and with aluminum heat sink. The aluminum heat sink which is installed to the solar panel back sheet via thermal grease improves the thermal conductivity and appears to be effective at lowering the temperature. The aluminum heat sink causes a decrease in the thermal resistance of the bottom surface of the solar panel, which is equal to the inverse value of the heat transfer coefficient. When the aluminum heat sink is installed, the heat transfer through the bottom surface is increased, as shown in Figures 9 and 10, leading to a decrease in the solar cell temperature for similar weather conditions and wind speed where the the thermal losses are decreased and the extracted power is increased. The average ambient temperature is (T a = 315 K) for this research, and the location is Jeddah, the coordinates for which have been given in Table 3. Jeddah is situated near the Equator and has hot weather during most parts of the year. The aluminum heat sink installation reduces the solar cell temperature which enhances the solar panel electrical characteristics. Thanks to the aluminum heat sink, the temperature and the thermal losses are decreased and the resulting average voltage drop is also decreased, then the solar panel open circuit and the MPP voltages V oc and V mpp are increased as shown in Figure 11. Also, the solar panel short circuit and the MPP currents I sc and I mpp are increased as shown in Figure 12. Consequently, the maximum power point is increased and the accumulative energy per day is increased.

Comparison of Results of the Two Simulation Models
This section discusses the comparison of results of the two simulation models, without heat sink and with aluminum heat sink. The aluminum heat sink which is installed to the solar panel back sheet via thermal grease improves the thermal conductivity and appears to be effective at lowering the temperature. The aluminum heat sink causes a decrease in the thermal resistance of the bottom surface of the solar panel, which is equal to the inverse value of the heat transfer coefficient. When the aluminum heat sink is installed, the heat transfer through the bottom surface is increased, as shown in Figures 9 and 10, leading to a decrease in the solar cell temperature for similar weather conditions and wind speed where the the thermal losses are decreased and the extracted power is increased. The average ambient temperature is (Ta = 315 K) for this research, and the location is Jeddah, the coordinates for which have been given in Table 3. Jeddah is situated near the Equator and has hot weather during most parts of the year. The aluminum heat sink installation reduces the solar cell temperature which enhances the solar panel electrical characteristics. Thanks to the aluminum heat sink, the temperature and the thermal losses are decreased and the resulting average voltage drop is also decreased, then the solar panel open circuit and the MPP voltages Voc and Vmpp are increased as shown in Figure 11. Also, the solar panel short circuit and the MPP currents Isc and Impp are increased as shown in Figure 12. Consequently, the maximum power point is increased and the accumulative energy per day is increased.     It is clear that reduction in the solar cell temperature reduction has enhanced the electrical efficiency. This results are shown in Figure 13. Also, Figure 14 indicates that solar panel maximum output power is also increased.  It is clear that reduction in the solar cell temperature reduction has enhanced the electrical efficiency. This results are shown in Figure 13. Also, Figure 14 indicates that solar panel maximum output power is also increased. It is clear that reduction in the solar cell temperature reduction has enhanced the electrical efficiency. This results are shown in Figure 13. Also, Figure 14 indicates that solar panel maximum output power is also increased.

The Experimental Setup Models
The experimental setup model is implemented as per the schematic diagram shown in Figure 15. This setup uses a 250-Watt solar panel to charge 200 Ah deep cycle gel battery via 30 A MPPT solar charger controller. The battery is used to energize a 84-watt street lighting fixture. As per the Saudi Arabian General Authority of Meteorology and Environmental Protection [62], as well as the data obtained from King Abdulaziz University (KAU) weather station, which is shown in Figure 8, the highest ambient temperature is observed during summer season in June, so this study was conducted under June climatic conditions to study the effect of maximum temperature on the solar panel performance. The solar panel was installed at a fixed tilt angle (θ = 25 • ), orientation south, sloped by azimuth angle (φ = 10 • ) towards the west direction. The details of the set up as well as the results are presented as follows.

The Experimental Setup Model without Heat Sink
This case elaborates the effect of temperature on the solar panel performance without using the heat sink as detailed in Figure 3. The average readings during daylight hours in June are presented in Table 14, where T a is the average ambient temperature, T SFS is the solar panel front surface temperature, and T SBS is the temperature of the solar panel back surface. Table 14. Readings without a heat sink.

The Experimental Setup Model with an Aluminum Heat Sink
This case studied the effect of temperature on the solar panel performance using the aluminum heat sink as detailed in Figure 7. The average readings during daylight hours in June are presented in Table 15, where T HSS is the heat sink outlet surface temperature.

Comparison and Comments
This section discusses the comparison of the results of the two experimental setup models, with and without the aluminum heat sink. The comparison at this stage is limited to the solar panel electrical characteristics at variable ambient temperatures during different parts of the day, as shown in Figure 16. The maximum solar panel front surface temperature without cooling is 50.8 • C and it dropped to 48.2 • C for the same time of the day (2:00 p.m.) when the aluminum heat sink was used-a drop of about 3.7%. When the maximum solar panel back surface temperature without cooling was 48.5 • C, it dropped to 42.4 • C for the same time (2:30 p.m.) when the heat sink was used-a decrease of 14.3%. Results of the experiment for the solar panel output voltage, current, and power are plotted with ambient temperature as shown in Figures 17-19, respectively. The maximum open circuit voltage V oc (V) without heat sink is recorded as 33 V at 8:30 a.m. while this value is 34.5 V (at 8:30 a.m.) when the heat sink is used-an increase of about 4.5%. Moreover, maximum power point voltage V mpp is changed from 24.5 to 26.7 V at 7:30 a.m. when a heat sink is used-an increase of 9%. The maximum power point current I mpp is recorded as 6 A without heat sink while it was 6.5 A when heat sink was used, time being constant at 1:00 p.m.-a decrease of 6.67%. From the results of this experiment, it can be concluded that the electrical characteristics of the solar panel are enhanced when aluminum heat sink is used. This is because of a decrease in the solar cell temperature leading to a rise in the open circuit voltage as well as the maximum power voltage. There is a slight decrease in output current due to the fall in temperature as shown in Figures 17 and 18, respectively. The output power is increased and the electrical energy generated by the solar panel is increased as shown in Figure 19. Values for all points are increased-for example at 9 a.m. the power increased from 63 to 79 which is a 25.4% increase at an ambient temperature of 37 • C. As a result of the increase in solar panel output power throughout the daylight hours, the output energy increased from 1587 watt/day to 1797 watt/day amounting to a 13.23% increase overall. The insertion of aluminum heat sink to the solar panel decreases the solar cell temperature and limits the hot spot phenomena, which increases the life of the unit. Figure 20 shows the thermal images of solar panel surfaces with and without aluminum heat sink.  Figure 20 shows the thermal images of solar panel surfaces with and without aluminum heat sink.

Conclusions
This paper discussed steady state heat transfer through solar panel layers and studied the effect of high temperatures on the solar panel performance in a hot desert environment with varying wind speed. In our simulation it has been found that the solar cell temperature is decreased when an aluminum heat sink is installed. The total thermal resistance is decreased due to the high thermal conductivity and large surface area of the aluminum heat sink due to its fins. Subsequently, there is acceleration of heat transfer through the solar panel back surface leading to a decrease of 11 °C in the solar cell temperature. In the experimental stage, it was concluded that the installation of aluminum heat sink on the solar panel back

Conclusions
This paper discussed steady state heat transfer through solar panel layers and studied the effect of high temperatures on the solar panel performance in a hot desert environment with varying wind speed. In our simulation it has been found that the solar cell temperature is decreased when an aluminum heat sink is installed. The total thermal resistance is decreased due to the high thermal conductivity and large surface area of the aluminum heat sink due to its fins. Subsequently, there is acceleration of heat transfer through the solar panel back surface leading to a decrease of 11 • C in the solar cell temperature. In the experimental stage, it was concluded that the installation of aluminum heat sink on the solar panel back surface leads to a decrease in the solar cell temperature by 16.4%, which leads to an enhancement of the electrical characteristics in the form of increase in both the open circuit voltage and maximum power point voltage. It also produces a slight reduction in the maximum power point current. In the experimental stage, the overall extracted electrical energy from the solar panel with aluminum heat sink is increased by more than 13.23% per day when compared with the case when no such a heat sink was not used. This validates the theoretical and simulation studies that have shown that the heat sink installation effectively mitigates the temperature negative effect and enhances the solar panel electrical performance.
Therefore, this paper concludes that the installation of the aluminum heat sink on the back surface of solar panels leads to a mitigation of the solar cell temperature and limits the hot spot phenomena. It also enhances the electrical characteristics and increases both solar panel efficiency and lifetime.

Acknowledgments:
The authors would like to thank. Gulf Lighting Company helped us the manufacture of the aluminum heat sink which we used in our experiments, for which we are thankful to them.

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix A
The mathematical model of a single diode solar cell electrical model is described (as shown in Figure 5) for a solar panel that consists of n c solar cells. The open circuit voltage is denoted by V oc . The short circuit current is I sc , while V pv , and I pv are the output voltage and current. I L is the light current, I o is the reverse saturation current, while V d and I d are the diode voltage and current respectively. All these parameters rely on the thermal voltage V T that depends on the solar cell temperature [24,30,31,[47][48][49], where (1≤ a ≤ 2) is the diode ideality factor, (K BZ = 1.3807 × 10 −23 J/K) is the Boltzmann constant, (q = 1.602 × 10 −19 C) is the electron charge. The electrical performance is described as per the following equations:  where E g is the bandgap energy that relies on the material type, E go = 1.12 eV or 1.794 × 10 −19 J and the constant C g = 2.677 × 10 4 for silicon. The output power P mpp at the MPP is given in Equation (6). There are many methods to calculate the Voltage V mpp and current I mpp at the MPP, as mentioned in [31], by differentiation of the output power P = VI with respect to the voltage V that is given in Equation (A11). The current I mpp at the MPP is given by Equation (A12), then V mpp and I mpp are given by simultaneously numerical solution for Equations (A11) and (A12): where I mpp can be calculated starting from an initial guess and using numerical root-finding algortigms such as those implemented in fsolve or fzero functions of the MATLAB software. Then, the resulting value of I mpp can be substituted in Equation (A14) to get V mpp .