Finite Element Analysis Method Design and Simulation of Fins for Cooling a Monocrystalline Photovoltaic Panel

Abstract

This research focuses on the development and simulation analysis of heat-dissipating fins made of copper, integrated into photovoltaic panels, with the aim of mitigating temperature increases during operation. This initiative arises from evidence that solar panels experience a reduction in energy efficiency when operating at temperatures higher than standard test conditions. The photovoltaic panel was simulated both without fins and with fins under standard test conditions and extreme conditions. The simulation consists of the following steps: design, meshing, selection of physical models and materials, assignment of boundary conditions, validation of the simulation, and interpretation of the results. During validation, results obtained via simulation were compared experimentally, yielding a mean absolute percentage error of 0.28%. It was concluded that the fins with the greatest heat dissipation relative to their area are those of 40 mm height; with this height, the temperature of the photovoltaic panel is reduced by 2.64 K, which represents an efficiency increase of 1.32%. Furthermore, it was concluded from the analyzed data that the efficiency of the fins increases at high temperatures.

1. Introduction

The world requires more energy every day, and this, coupled with efforts to reduce greenhouse gas emissions, has led to the adoption of renewable energy as a solution [1]. Photovoltaic solar energy has been established as a leader in sustainable energy technologies through the conversion of sunlight into electricity [2]. This technology promotes a reduction in dependence on fossil fuels and plays a vital role in mitigating climate change. Compared with those of other technologies, the use of monocrystalline photovoltaic panels for the conversion of solar energy into electricity is increasingly common. However, during their operation, these panels can reach high temperatures, which can reduce their performance [3]. Photovoltaic panels have a low conversion efficiency ranging from 4% to 23% depending on the type of solar cell [4,5], and it is estimated that an increase in temperature of 1 K above standard test conditions (STC) in monocrystalline silicon cells leads to a reduction of 0.45% in electrical efficiency [6]. In addition, photovoltaic semiconductors can degrade up to 43% more due to an increase in temperature [7]. Due to these conditions, there is a need to develop effective cooling techniques. In this context, a simple fin design for cooling a monocrystalline photovoltaic panel is proposed, which strengthens the structure and improves the electrical efficiency, allowing for greater energy per unit area. For this purpose, simulation through analysis via the finite element method is used.

Finite element method analysis in heat transfer is a powerful computational method for simulating the temperature distribution in materials and structures under various environmental conditions. This method breaks down the study domain into a mesh of small, manageable elements, upon which heat transfer equations are applied, allowing for the resolution of complex problems that include conduction, convection, and radiation. One of the advantages of the FEM in this context is its ability to model complex geometries and varied boundary conditions. However, the method requires a precise definition of the material properties and initial conditions, and the results are sensitive to the quality of the mesh used, which can increase the computational cost and require specialized expertise to ensure accurate results.

Several studies have been conducted to understand the thermal behavior of photovoltaic panels. Using FEM computational simulation tools, ref. [8] used a finite element analysis program to predict the temperature distribution within photovoltaic modules. Simulations were conducted to predict changes in the internal temperature of the modules due to the constituent materials and ambient temperature. Additionally, the results of the simulations were compared with actual measurements of internal module temperatures installed outdoors to validate the effectiveness of the simulations. The utility of the proposed simulation technique in predicting temperature changes in modules under various conditions was demonstrated, which can contribute to optimizing the manufacturing conditions of photovoltaic modules to improve their efficiency and durability.

Moreno et al. compared closed-form solutions and finite element methods for heat transfer in an almost horizontal flat plate PVT (photovoltaic thermal) water collector without glass. The performance of domestic hot water heating and the energy supply from a PVT system installed on a roof with an 8° gradient in a solar house in Madrid were evaluated. A finite element heat flow simulation was carried out and contrasted with a theoretical mathematical model to establish a correlation between the energy absorbed by the water in the PVT panel tubes and the inlet temperature, which depends on the tank temperature [9].

Pavlovic et al. conducted research on the thermal behavior of encapsulation materials for monocrystalline silicon solar cells. Finite element thermal models were established to analyze the heat distribution in solar cells. Transient thermal analyses of different solar cell stratifications, validated experimentally, were performed. The importance of selecting materials and thicknesses to maximize thermal dissipation and improve performance was identified. The possibility of optimizing the design to reduce the temperature in the cells was demonstrated, and an efficient numerical model was developed to investigate the behavior of alternative solar panels, thereby contributing to the improvement of the efficiency and design of solar cells in solar energy applications [10].

Kumar Laha et al. conducted a comparative study on the thermal performance of a photovoltaic solar panel based on a 3D model through finite element analysis. The authors focused on analyzing the operating temperature of the solar panel, which is a crucial characteristic for its efficiency and lifespan. This study explored how overheating affects panel efficiency and durability and proposed a novel approach using the finite element method to measure the relationship between temperature and efficiency. Additionally, the mesh size was adjusted to obtain accurate results, and a fin-based cooling system was introduced to reduce the panel’s temperature and improve its efficiency [11].

Work has also been conducted to understand the behavior of panels using computational fluid dynamics (CFD). Maadi et al. developed a coupled thermal–optical 3D numerical model to assess the performance of a PVT module with a glass coating. This research addresses the optical and thermophysical properties of all layers of the system, uses computational fluid dynamics to simulate heat and fluid flow, and implements a two-band radiation model to consider wavelength-dependent optical characteristics. The results were validated with experimental data [12].

Marwaha et al. developed a thermal model to accurately predict the temperature of silicon photovoltaic modules. The main focus of the model involved extracting the average convective heat transfer coefficient through CFD analysis and using it alongside the material properties of the constituent layers, such as thermal conductivity, absorptivity, and emissivity, in a one-dimensional thermal model to accurately predict the average temperature of the solar cell and other constituent layers of the photovoltaic module. Furthermore, the theoretical results were compared with the experimental values, achieving an average error of only 0.53%. This model can help researchers understand performance losses and degradation due to thermal conditions and predict solar cell temperatures under different mounting configurations [13].

Prasetyo et al. conducted research focused on optimizing photovoltaic thermal (PVT) systems by integrating fins designed to enhance thermal management and the overall efficiency of the system. The study explored different fin configurations and collector designs and evaluated their impact on the thermal and electrical performance of PVT systems. It utilized computational models and simulations to assess and refine the designs and aimed to improve heat dissipation through careful consideration of fin layout, material selection, and geometric configurations. The goal was to develop more efficient PVT systems, enhance the system’s passive cooling capabilities, and maximize the energy conversion process [14].

Previous studies on FEM and CFD simulations in the field of PV provide a solid methodological basis for this research, as these methodologies have been widely validated. In previous works, PVT technology, encapsulation techniques, and the analysis of the thermal behavior of PV panels have been explored. These studies have focused on reducing the operating temperature of the panels to increase their energy efficiency. There is a trend aimed at mitigating the operating temperature in photovoltaic modules through the implementation of cooling systems predominantly based on forced convection using water and air flows. These technological solutions integrate components such as hydraulic pumps and ventilation systems, thereby increasing the initial and operational costs of photovoltaic thermal systems, as well as their maintenance demand and the energy consumption inherent to their operation. In this context, the current research proposes an innovative PV module design, incorporating heat-dissipating fins to facilitate passive thermal evacuation and, consequently, reduce the operating temperature of the photovoltaic cells without requiring additional electrical energy consumption to increase their efficiency. To address this challenge, simulations via the finite element method are used to test the thermal behavior of the proposed copper fins with heights of 20, 40, 60, 80, and 100 mm, and for the validation of these simulations, thermal data from the PV, taken experimentally, are used. This approach seeks not only to increase the energy efficiency of the panel but also to reinforce its structural integrity. The incorporation of copper fins not only optimizes the energy conversion of photovoltaic panels through the dissipation of excessive heat but also plays a crucial role in extending the durability of these systems. This is because the accumulation of undissipated heat within the panel components can induce accelerated aging processes, prematurely deteriorating their performance and reliability.

2. Materials and Methods

The photovoltaic solar panels used in this research are located at the National University of Chimborazo, Ecuador. Figure 1 shows the panels. These panels are composed of 144 cells, each with an area of 0.0162 m². The analyzed PV has a length of 2.274 m, a width of 1.134 m, and a thickness of 0.035 m.

For the validation of the simulation, it is necessary to obtain data on the atmospheric conditions and the temperature of the photovoltaic solar panels. To this end, an Ambient Weather WS-5000 weather station (Ambient Weather in Chandler, Chandler, AZ, USA) was used to monitor atmospheric conditions, as shown in Figure 2, the manufacturer of this equipment is Ambient Weather in Chandler, United States. Additionally, the temperature of the photovoltaic solar panel was measured using a FLIR C5 thermal camera (FLIR, Wilsonville, OR, USA) and a FLUKE 62 MAX pyrometer (FLUKE, Everett, WA, USA), as illustrated in Figure 3.

Within the framework of this research, the experimental uncertainty was estimated by applying Gauss’s law of error propagation. This calculation was based on the use of Equation (1), which allows quantification of the uncertainty associated with indirect measurements from the uncertainties of the variables directly measured [15].

(1)$W_R={\left[{\left(\frac{\partial R}{{\partial x}_1}{W}_1\right)}^2+{\left(\frac{\partial R}{{\partial x}_2}{W}_2\right)}^2+...+{\left(\frac{\partial R}{{\partial x}_n}{W}_n\right)}^2\right]}^{\frac{1}{2}}$

In Table 1, the experimental accuracy of the instruments used in the experiment is presented.

In Figure 4, Figure 5 and Figure 6, the curves for solar radiation, ambient temperature, and relative humidity can be observed, which are used in this research. These data were collected at the facilities of the National University of Chimborazo from 6 March to 11 March 2024, throughout the 24 h of each day.

The fins added to the PV system as an alternative for cooling are made of copper due to its high thermal conductivity, with the aim of improving the dissipation of heat generated during the conversion of sunlight into electricity. The integration of the copper fins with the PV serves as a thermal bridge that extends the surface area in contact with the surrounding air, thereby facilitating the evacuation of heat [16,17]. This design helps maintain photovoltaic cells in an optimal temperature range, which is crucial because their energy conversion efficiency decreases significantly with increasing temperature. The fins used in this research had a thickness of 5 mm, and four fin heights of 20 mm, 40 mm, 60 mm, 80 mm, and 100 mm were tested. The design of the fins in conjunction with the PV is shown in Figure 7.

The simulation was carried out with the steady-state thermal tool of the Ansys Workbench. The simulation process begins with the design of the prototype in Ansys SpaceClaim, with the same dimensions as the original, as shown in Figure 8. The materials used in its construction and their thermal properties can be seen in Table 2.

A photovoltaic panel is composed of several layers of different materials that fulfill specific functions. The glass layer improves light transmission for greater energy efficiency, offers superior resistance to environmental and chemical degradation, and allows for lightweight and flexible designs, adapting to various applications and operating conditions [18]. The EVA layers serve as an encapsulation material for solar cells, protecting them from the environment and ensuring their electrical insulation [19]. PET provides protection against moisture and thermal variations, offers structural support to flexible or portable panels, and improves integrity and durability. CFRP provides a good strength-to-weight ratio, which significantly improves the rigidity and durability of the panel without adding much additional weight. Aluminum is used in the panel frames, and copper is used in the fins. Due to its good thermal conductivity, aluminum is a good heat sink to the environment, which allows the temperature of the PV to be reduced [11].

Once the prototype has been designed and the materials assigned, the next stage is the discretization process [20]. For the finite element analysis, a mesh composed of 138,000 elements was generated. The aspect ratio, an indicator that reflects the proportionality and geometric uniformity of the mesh elements, directly influences the precision and stability of the obtained numerical results. The resulting configuration of the solar panel after meshing is shown in Figure 9.

In this research, FEM simulation was used for heat transfer since it is an advanced computational technique used to predict and analyze the distribution of temperatures, heat flows, and thermal changes in materials and systems under various conditions. CFD was not used because there are no significant changes in the fluids involved in the photovoltaic panel [10], as exists in a PVT that works with air or water [21]. This methodology is based on the discretization of the study domain in a set of finite elements [22], where the heat transfer equations are applied individually, allowing a detailed and precise analysis of thermal phenomena. To model the photovoltaic solar panel, the conduction Equation (2), convection Equation (3), and radiation Equation (4) are used [23].

(2)$\frac{\partial }{\partial t}\left(\rho c_{p}T\right)=\nabla .\left(\mathrm{k}\nabla \mathrm{T}\right)+Q$

(3)$q=hA\left(T_s-T_{\infty }\right)$

(4)$q=ϵ\sigma A\left(T_s^4-T_{amb}^4\right)$

To model the transfer of thermal energy in a photovoltaic panel, we have Equation (5) [23].

(5)$q=\rho V{c}_{p}dT$

Heat losses in the PV system are mainly produced via radiation from glass to the sky, convection to the environment, and reflection from radiation. To calculate the convection coefficient, the following relationship is used (6) [24]:

(6)$Nu=\frac{hL}{k}=0.13{Re}^{0.703}{(1+sin\beta )}^{0.38}$

To facilitate the simulation of the photovoltaic solar panel using the FEM, the following assumptions were used:

The properties of the materials used in PV are independent of temperature.

• -. Dust and partial shadows have no effect on the analysis.

• -. Thermal contact between capable materials is considered ideal.

• -. The analysis is carried out at steady state for greater ease in the analysis [25].

3. Results and Discussion

For the validation of the simulation, simulated temperature measurements under the atmospheric conditions of the National University of Chimborazo were compared with the data experimentally taken from the analyzed photovoltaic panel, and the mean absolute percentage error (MAPE) was calculated as shown in Equation (7) [25].

(7)$MAPE=\frac{1}{n}\sum _{i=1}^n\left|\frac{A_i-F_i}{A_i}\right|\times 100\%$

From the comparative evaluation between the datasets obtained through simulation and those derived from experimental measurements, an average absolute percentage error of 0.28% was calculated. This value indicates a high correlation and minimal deviation between the simulated and experimental results, highlighting the predictive accuracy of the numerical model used and its ability to reliably replicate the conditions and behaviors observed experimentally. Figure 10 shows the temperature profile of the simulated photovoltaic panel under atmospheric conditions in the city of Riobamba used for validation. Figure 11 shows the experimentally obtained temperature profile of the photovoltaic panel.

Once the methodology used was validated, the photovoltaic solar panel with copper fins used to decrease its temperature was simulated with fin heights of 20, 40, 60, and 80 mm. This work was carried out under STC conditions, that is, with a solar irradiance of 1000 W/m² and a temperature of 298.15 K. Figure 12 shows the temperature profile that the photovoltaic panel without fins reaches under STC conditions. Under these conditions, it reaches a maximum temperature of 330.26 K, a minimum temperature of 306.28 K, and an average temperature of 326.09 K. These temperatures serve as a reference for evaluating the performance of the copper fins at different heights.

Figure 13 shows the temperature profile of the photovoltaic panel with 20 mm high fins under STC conditions. Under these conditions, a maximum temperature of 328.64 K, a minimum temperature of 306.38 K, and an average temperature of 324.52 K were obtained.

Figure 14 shows the temperature profile of the photovoltaic panel with 40 mm high fins under STC conditions. Under these conditions, a maximum temperature of 327.81 K, a minimum temperature of 306.43 K, and an average temperature of 323.45 K were obtained.

Figure 15 shows the temperature profile of the photovoltaic panel with 60 mm high fins under STC conditions. Under these conditions, a maximum temperature of 327.43 K, a minimum temperature of 306.48 K, and an average temperature of 322.65 K were obtained.

Figure 16 shows the temperature profile of the photovoltaic panel with 80 mm high fins under STC conditions. Under these conditions, a maximum temperature of 327.13 K, a minimum temperature of 306.52 K, and an average temperature of 322.02 K were obtained.

In Figure 17, the temperature profile of the photovoltaic panel with 100 mm high fins under STC conditions can be observed. Under these conditions, a maximum temperature of 326.71 K, a minimum temperature of 306.30 K, and an average temperature of 321.63 K were recorded.

To understand the behavior of the PV under extreme conditions, an analysis was conducted using the maximum temperature recorded during the study period, which was 229.05 K, and solar radiation of 1556.3 W/m². In Figure 18, the temperature profiles of the panel can be observed as follows: (a) without fins, (b) with 20 mm fins, (c) with 40 mm fins, (d) with 60 mm fins, (e) with 80 mm fins, and (f) with 100 mm fins.

Figure 19 shows the variation in the photovoltaic panel temperature relative to the fin height. The relationship observed fits a second-degree polynomial model, characterized by its parabolic curvature. The fit of the model to the data was quantified using a determination coefficient of 0.9989. This value, which is close to unity, shows agreement between the proposed theoretical model and the measurements, indicating that the model is capable of accurately explaining the variability in the panel temperature as a function of fin height.

Figure 20 shows the cooling percentage as a function of fin height within the range of heights studied. At a height of 20 mm, the cooling percentage is 38.58%; at a height of 40 mm, the cooling percentage is 64.86%; and at a height of 60 mm, the cooling percentage is 85.52%. This demonstrates that as the height of the fins increases, they become less efficient, with a height of 40 mm, which is half of the range used in this research, having a cooling percentage of 64.86%. This phenomenon suggests an optimization in cooling efficiency of approximately 40 mm, where a balance is achieved between thermal dissipation and the increase in contact surface area, indicative of a nonlinear relationship between the height of the fins and cooling efficiency.

Table 3 shows the temperatures of the photovoltaic panels at different fin heights. By analyzing the PVs with fins 40 mm high, it is noted that the temperature, compared to that when no fins are used, is reduced by 2.64 K. This reduction would result in an efficiency increase of 1.32% under standard test conditions. This efficiency increase under operating conditions is greater, as under these conditions, the panel reaches an average temperature of 333.15 K, and its efficiency is reduced by 17 to 18% [10].

In Table 4, the temperature and efficiency data for the PV panels with and without fins under STC conditions and extreme conditions can be observed. Analyzing these data, it is apparent that the higher the panel temperature relative to STC conditions, the greater the efficiency increase of the panels compared to the panel without fins.

Profitability Analysis

For the profitability analysis, an average radiation of 800 W/m² and five effective peak hours per day were considered. Since this study was conducted in Ecuador, the costs of both raw materials and kWh, as they are in this country, were considered. Table 5 shows the analysis.

From the study conducted, it is found that the implementation of this technology costs 67.83 US dollars, and the investment recovery would take 11.17 years.

4. Conclusions and Recommendations

A methodology was developed and applied based on the finite element method for the simulation of a photovoltaic panel integrated with heat dissipation fins. Through computational analysis, variations in the fin height were examined, allowing the characterization of temperature profiles in the photovoltaic system under different configurations. The results indicated an optimal height of 40 mm, which allows for heat dissipation efficiency, establishing an optimal balance between temperature reduction and the increase in the surface area of the fins. From the data obtained, it can be concluded that there is an inversely proportional relationship between the temperature and the efficiency of the PV.

From this study, under extreme conditions and STC conditions, it can be observed that as the temperature increases relative to STC conditions, the efficiency also increases. Therefore, it can be said that the fins are more efficient when the temperature is higher.

The validation of the FEM simulation models was achieved through correlation with rigorous experimental data acquired using high-precision instrumentation, including the Ambient Weather WS-5000 weather station, the FLIR C5 thermal camera, and the FLUKE 62 MAX pyrometer. This empirical corroboration ensures the reliability of the simulations and confirms the effectiveness of the determined fin height as the most efficient for the thermal management of photovoltaic panels, highlighting the importance of integrating advanced computational analysis methods with experimental tests in the design of high-performance photovoltaic systems.

Future investigations could explore different materials for the fins beyond copper, such as aluminum alloys, composite materials, or nanomaterials with superior thermal properties, to assess their impact on the cooling efficiency and structural integrity of the panel. Additionally, studies could be developed on the integration of fins in PVT systems, evaluating how heat dissipation simultaneously improves electricity generation and the production of useful heat for residential or industrial applications.

In the economic analysis, it can be observed that with the economic conditions in Ecuador, the investment recovery period is 11.17 years.

Author Contributions

Conceptualization, R.C.-E. and J.C.-E.; methodology, D.V.; software, J.C.-E.; validation, F.J.; formal analysis, E.R.Z.L.; investigation, D.C.C.; resources, R.C.-E.; data curation, R.C.-E.; writing—original draft preparation, R.C.-E.; writing—review and editing, M.M.P.G.; visualization, J.C.-E.; supervision, R.C.-E.; project administration, R.C.-E.; funding acquisition, R.C.-E. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

No new data were created or analyzed in this study. Data sharing is not applicable to this article.

Conflicts of Interest

The authors declare no conflict of interest.

Nomenclature

FEA	Finite element analysis
FEM	Finite element analysis method
PV	Photovoltaic
EVA	Ethylene-vinyl acetate
PET	Polyethylene terephthalate
CFRP	Carbon fiber reinforced polymer
STC	Standard test conditions
PVT	Photovoltaic thermal
CFD	Computational fluid dynamics
Nu	Nusselt number
MAPE	Mean absolute percentage error
Ai	Actual value for the ith observation
Fi	Forecasted value for the ith observation
n	Number of observations
L	Characteristic length [m]
t	Time [s]
V	Volume [m3]
cp	Specific heat at constant pressure [J/(kg·K)]
T	Temperature [K]
k	Thermal conductivity [W/m·k]
Q	Internal heat source [W/m3]
q	Heat transfer rate [W]
h	Convection heat transfer coefficient [W/m2·K]
A	Area through which heat transfer occurs [m2]
x	Independent variable
W	Uncertainty of the independent variable
R	Uncertainty
Greek letters
ρ	Density [kg/m3]
$\sigma$	Stefan–Boltzmann constant [W/m2K4]
$\in$	Surface emissivity
$\beta$	Angle that the panel forms with the horizontal [rad]
Subscripts
s	Surface
∞	Far from the surface
Amb	Ambient

Footnotes

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Figures and Tables

Figure 1. Photovoltaic solar panels in the field.

Figure 2. Ambient Weather WS-5000.

Figure 3. FLIR C5 thermal camera and FLUKE 62 MAX pyrometer.

Figure 4. Solar Radiation.

Figure 5. Ambient Temperature.

Figure 6. Relative Humidity.

Figure 7. Design of the fined solar panel.

Figure 8. Photovoltaic panel in Ansys SpaceClaim.

Figure 9. Mesh photovoltaic panel.

Figure 10. Temperature profile simulated under atmospheric conditions in the city of Riobamba.

Figure 11. Experimental temperature profile under atmospheric conditions in the city of Riobamba.

Figure 12. Simulated finless PV panel under STC.

Figure 13. Photovoltaic panel temperature profile with 20 mm high fins.

Figure 14. Photovoltaic panel temperature profile with 40 mm high fins.

Figure 15. Photovoltaic panel temperature profile with 60 mm high fins.

Figure 16. Photovoltaic panel temperature profile with 80 mm high fins.

Figure 17. Temperature profile of photovoltaic panel with 100 mm high fins.

Figure 18. Temperature profiles of photovoltaic panel under extreme conditions.

Figure 19. Fin temperature depending on their temperature.

Figure 20. Cooling percentage based on fin height.

Table 1

Experimental accuracy analysis of the instruments used.

Equipment	Parameter	Accuracy	Manufacturer	Uncertainty Value	Range
Weather Station WS-5000	Solar Irradiance	± 15%	Ambient Weather	0.001 W/m2	0 to 2367.798 W/m2
	Ambient temperature	± 2 °F	Ambient Weather	0.1 °F	−40 to 149 °F
	Ambient humidity	± 5%	Ambient Weather	1%	10 to 99%
Pyrometer 62 MAX	Temperature	1.0%	FLUKE	0.2 °F	−22 °F to 1202 °F
Thermographic camera C5	Temperature	±5.5 °F	FLIR	1 °F	32 to 212 °F

Table 2

Thermal properties of materials used in solar panels.

Materials	Density (kg/m3)	Thermal Conductivity (W/(m·K))	Specific Heat (J/(kg·K))
Glass	3000	1.8	5000
EVA	945	0.35	2090
PET	1350	0.275	1275
Tape	1012	0.19	2000
CFRP	1490	6.83	1130
Silicon	2330	148	700
Aluminum	2689	237.5	951
Copper	8933	400	385

Table 3

Photovoltaic panel temperatures at different fin heights.

Fin Heights (mm)	Maximum Temperature (K)	Minimum Temperature (K)	Average Temperature (K)
0	330.26	306.28	326.09
20	328.64	306.38	324.52
40	327.81	306.43	323.45
60	327.43	306.48	322.65
80	327.13	306.52	322.02

Table 4

Average temperatures and efficiencies under STC and extreme conditions.

Fin Heights (mm)	STC Conditions		High Conditions
	Average Temperature (K)	Increased Efficiency (%)	Average Temperature (K)	Increased Efficiency (%)
0	326.09	0	338.91	0
20	324.52	0.785	336.99	0.96
40	323.45	1.32	335.66	1.625
60	322.65	1.72	334.63	2.14
80	322.02	2.035	333.81	2.55
100	321.63	2.23	333.31	2.8

Table 5

Profitability analysis.

	Efficiency (%)	Annual Production (kWh)	kWh Cost (US Dollars)	Annual Production (US Dollars)	Production 10 Years (US Dollars)	Production 20 Years (US Dollars)
Photovoltaic panel	20.75	549.71	0.15	82.46	824.57	1649.13
Photovoltaic panel with fins	22.07	590.19	0.15	88.53	885.29	1770.57

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