# Numerical Investigation of Thermal Efficiency of a Solar Cell
## 3 Results and Discussion  
### Experimental Results  
Table 1 shows the variation in the outlet temperature of the water and thermal efficiency with different values of heat input. As clearly observed from Table 1, the thermal efficiency increases with the increase in heat input, which was clear to be an obvious phenomenon. Later parts of the manuscript will clearly justify the reason for the aforementioned statement. Tables 2-4 show the heat lost from various components and surfaces of the PV cell. Table 5 shows heat transfer because of convection and radiation from the bottom surface of the PV cell. Tables 6-8 show the heat lost from the pipe surface. Uncertainty (unpredictable) in heat transfer is also being tabulated. Figure 7 shows the irradiation measured using the digital solar meter for one day with bright sunlight. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(Q_{input}\) **(W)** & \(T_{atm}\) (°C) & \(T_{water, in}\) (°C) & \(T_{water, out}\) (°C) & \(\eta_{thermal}\) \\ \hline
230.04 & 35.1 & 31.8 & 32.5 & 15.92 \\
258.61 & 40.1 & 32.5 & 33.6 & 38.18 \\
209.94 & 39.9 & 32.9 & 33.9 & 44.52 \\
257.83 & 37.2 & 32.4 & 33.7 & 53.17 \\
146.40 & 40.1 & 32.5 & 33.1 & 57.46 \\
110.33 & 39.5 & 32.8 & 33.2 & 49.85 \\
68.16 & 37.6 & 33.1 & 33.3 & 52.77 \\
23.64 & 38.9 & 33.3 & 33.35 & 42.89 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Variation of thermal efficiency with heat input. Figure 6: Validation of various models. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(Q_{net\ input}\) **(W)** & \(Q_{\textit{connection}}\) **(W)** & \(Q_{\textit{radiation}}\) **(W)** & \(Q_{\textit{total},\textit{\ cross section}}\) **(W)** \\ \hline
197.16 & 6.75 & 1.67 & 8.42 \\
208.54 & 4.87 & 1.23 & 6.1 \\
167.44 & 3.52 & 0.87 & 4.39 \\
212.21 & 3.65 & 0.88 & 4.53 \\
118.44 & 1.98 & 0.48 & 2.46 \\
90.86 & 1.51 & 0.36 & 1.87 \\
59.95 & 1.79 & 0.42 & 2.21 \\
21.06 & 0.66 & 0.16 & 0.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Total heat transfer due to convection and radiation from a cross section of PV cell. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(Q_{net\ input}\) & \(Q_{\textit{glass}}\) & \(Q_{\textit{adhesive}}\) & \(Q_{\textit{pv cell}}\) & \(Q_{\textit{solder}}\) & \(Q_{\textit{substrate}}\) & \(Q_{\textit{total correction}}\) \\
**(W)** & **(W)** & **(W)** & **(W)** & **(W)** & **(W)** & **(W)** \\ \hline
197.16 & 3.78 & 0.13 & 0.15 & 0.13 & 2.57 & 6.75 \\
208.54 & 2.73 & 0.09 & 0.11 & 0.09 & 1.85 & 4.87 \\
167.44 & 1.98 & 0.07 & 0.08 & 0.07 & 1.33 & 3.52 \\
212.21 & 2.05 & 0.07 & 0.08 & 0.07 & 1.38 & 3.65 \\
118.44 & 1.13 & 0.04 & 0.04 & 0.04 & 0.73 & 1.98 \\
90.86 & 0.87 & 0.03 & 0.03 & 0.03 & 0.55 & 1.51 \\
59.95 & 1.02 & 0.03 & 0.04 & 0.03 & 0.66 & 1.79 \\
21.06 & 0.40 & 0.01 & 0.02 & 0.01 & 0.23 & 0.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Heat transfer through convection from a different cross section of PV cell. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(Q_{\textit{net\ input}}\) & \(Q_{\textit{glass}}\) & \(Q_{\textit{adhesive}}\) & \(Q_{\textit{pv cell}}\) & \(Q_{\textit{solder}}\) & \(Q_{\textit{substrate}}\) & \(Q_{\textit{total radiation}}\) **(W)** \\ \hline
197.16 & 1.04531 & 0.00735 & 0.00881 & 0.00231 & 0.60657 & 1.67 \\
208.54 & 0.76988 & 0.00541 & 0.00648 & 0.00170 & 0.44347 & 1.23 \\
167.44 & 0.54640 & 0.00384 & 0.00460 & 0.00121 & 0.31155 & 0.87 \\
212.21 & 0.55241 & 0.00388 & 0.00465 & 0.00122 & 0.31537 & 0.88 \\
118.44 & 0.30449 & 0.00214 & 0.00255 & 0.00067 & 0.16872 & 0.48 \\
90.86 & 0.23100 & 0.00162 & 0.00193 & 0.00051 & 0.12540 & 0.36 \\
59.95 & 0.26901 & 0.00189 & 0.00225 & 0.00059 & 0.14804 & 0.42 \\
21.06 & 0.10377 & 0.00072 & 0.00086 & 0.00022 & 0.05036 & 0.16 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Heat transfer through radiation from a different cross section of PV cell.