# Analysis of Thermomechanical Stresses of a Photovoltaic Panel Using a Passive System of Cooling
## 3 Results  
The field of temperature and the maximum principal stress field when the peak heat flux is acting on the panel surface with a maximum environment temperature is shown in Figure 7. With respect to Figure 7a vs. Figure 7b, it can be seen that the temperature field was almost uniform on the whole panel body, except on the identified zone; a considerable decline in temperature operating of almost 3 \({}^{\circ}\)C resulted in decreasing the thickness of the EVA by 0.2 mm. It is important to keep in mind that this is such a thin film that it could lead to direct contact with the other materials (silicon and glass/Tedlar layers) but with advance preparation to enhance the properties of the materials this problem could be resolved [23]. Figure 7c shows schematically the field temperature distribution using rectangular fins (0.30 cm \(\times\) 0.1 cm \(\times\) 0.005 cm), having a maximum and a minimum temperature of 44.095 \({}^{\circ}\)C and 33.27 \({}^{\circ}\)C, respectively. Comparing Figure 7c with Figure 7d, it can been seen that there is a considerable drop in the maximum temperature and the back side keeps the temperature constant, while in Figure 7c a slight increase of 2 \({}^{\circ}\)C is shown. In Figure 7d, we can appreciate the response of the aluminium triangle fins (5 cm \(\times\) 5 cm \(\times\) 30 cm, 1 mm of width) as a heatsink when a heat flux is acting directly on the whole front of the panel, as it shows a decrease of 2.316 \({}^{\circ}\)C in the operational temperature compared with Figure 7c. The temperature gradient on the back panel shows a slight improvement and a major uniform gradient due to it having more area for heat transfer. Thus, the panel obtains a better power output. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \multirow{2}{*}{\begin{tabular}{c} **Thickness** \\ **(mm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Thermal** \\ **Conductivity** \\ **(W/mK)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Coefficient** \\ **of Thermal** \\ **kg/m\({}^{3}\)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Specific Heat** \\ **Expansion** \\ **1/\({}^{\circ}\)C** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Module of** \\ **Young GPa** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Ratio of** \\ **Poisson** \\ **GPa** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Tensile** \\ **Yield** \\ **Strength** \\ **GPa** \\ \end{tabular} } \\ \hline Glass & 3 & 1.8 & 2500 & \(9\times 10^{-6}\) & 795 & 0.7 & 0.2 & - \\ \hline Silicon & 0.35 & 148 & 2330 & - & 677 & 168 & 0.3 & - \\ \hline EVA & 0.5 & 0.35 & 960 & \(0.73\times 10^{-6}\) & 2090 & 2.1 & 0.4 & 0.00435 \\ \hline Tedlar & 0.1 & 0.2 & 2700 & \(0.73\times 10^{-6}\) & 1000 & 2.1 & 0.4 & 0.11 \\ \hline Aluminium & 35 & 209.3 & 2698.4 & \(0.24\times 10^{-6}\) & 900 & 70 & 0.33 & 2330 \\ \hline Air & & 0.025 & - & - & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties. Figure 7: Cont. Regarding Figure 7e, a representative decline of 5.08 \({}^{\circ}\)C in the maximum operating temperature can be seen using fins with the following dimensions: 5 cm base \(\times\) 7 cm high, 30 cm deep and a fin thickness of 1 mm. Meanwhile, its back temperature remains almost stable at 34 \({}^{\circ}\)C. This could be a good option for the fin's design; however, while the fin is higher, the temperature tends to go into a thermal equilibrium with the environment and stops cooling the panel. For that reason, this type of design is not a recommended option since the gradient rises. In order to perform the stress analysis, the following considerations were taken into account: the aluminium frame was restricted to move freely and the earth's gravity was considered at the center of the panel. Figure 8a shows the distribution of the equivalent stress of von Mises. The module experiences tensile stresses with the interconnection at the edges experiencing the highest tensile stress of 119.57 MPa.