# Numerical Investigation of Thermal Efficiency of a Solar Cell
## 3 Results and Discussion
### Numerical Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Net Heat Input**} & \multicolumn{2}{c}{**Theoretical**} & \multicolumn{2}{c}{**Numerical Water**} & \multicolumn{2}{c}{**Theoretical**} & \multicolumn{2}{c}{**Numerical**} \\ \cline{2-6}  & **Inlet Water** & **Outlet Water** & **Temperature** & **Thermal** & **Thermal** \\  & **Temperature in \({}^{\circ}\)C** & **Temperature in \({}^{\circ}\)C** & **Outlet in \({}^{\circ}\)C** & **Efficiency** & **Efficiency** \\ \hline
461.27 & 32.9 & 33.9 & 33.89 & 0.226547 & 0.224281 \\
584.59 & 32.4 & 33.7 & 33.69 & 0.232385 & 0.230597 \\
326.28 & 32.5 & 33.1 & 33.09 & 0.192167 & 0.188965 \\
250.30 & 32.8 & 33.2 & 33.16 & 0.167 & 0.1503 \\
165.14 & 33.1 & 33.3 & 33.25 & 0.12656 & 0.09492 \\
58.00 & 33.3 & 33.35 & 33.34 & 0.090079 & 0.072063 \\
478.09 & 28.8 & 29.1 & 29.04 & 0.131147 & 0.104918 \\
503.01 & 28.8 & 29.2 & 29.16 & 0.166199 & 0.149579 \\
494.78 & 29.8 & 30.3 & 30.29 & 0.211205 & 0.206981 \\
456.55 & 29.3 & 29.9 & 29.89 & 0.274668 & 0.27009 \\
244.25 & 29.6 & 29.8 & 29.74 & 0.171135 & 0.119794 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Different ambient conditions considered for validation. Figure 8: Theoretical versus numerical efficiency. reaches the maximum point at noon hours and again starts to decline thereafter, whereas there was no significant variation in diffuse radiation. Average daily global radiation of 776 W/m\({}^{2}\) was observed, whereas the average daily diffuse radiation was 163 W/m\({}^{2}\). As observed in Figure 9, the thermal efficiency of solar PV cells increases up to a particular limit and then remains constant. This is in accordance, considering all the irreversibilities and attending the second law efficiency. So, the thermal efficiency can be increased by varying the velocity at the inlet, density of the fluid, and characteristic length at the entry. The present work proposes a semi-empirical relation between the thermal efficiency and Reynolds number (Equation (14)), using regression analysis. \[\eta_{Thermal}=0.002\times Re^{0.89}=f(Re) \tag{14}\]  
Figure 10 shows the variation in electrical efficiency versus the ratio of heat carried away by water to heat input. From Figure 10, it was viable that the electrical efficiency varies significantly with the cooling of PV cells. When over 40% of the heat input was carried away by water, maximum electrical efficiency was achieved. The maximum electrical efficiency of the cooling cell under normal conditions was around 15% to 18%. This efficiency improved up to 20% with cooling. Thus, cooling of PV cells proved to be beneficial. The decrease in efficiency with temperature was observed in the experimental setup as observed in the existing literature [2; 3; 25; 27]. Cooling of the panel improves efficiency and the electrical output as seen in earlier findings [8; 13; 15; 19; 27]. A 9% to 20% improvement in thermal efficiency was also observed in our study, similar to [PERSON] et al. [19] and [PERSON] et al. [19]. Transformation efficiency improvement by 4% to 5% was also observed, as discovered by [PERSON] et al. [32]. Similar results were achieved through the numerical model, making it a reliable numerical model. Figure 9: Graphical representation of thermal efficiency versus Reynolds number at inlet.