## 4 Results and Discussion
### Validation of CPC
#### 4.3.2 CPC Validation Approach  
The CPC is modeled using the actual tilt angle of 25\({}^{\circ}\) for the experimental date of 21 May. Table 10 shows the results obtained, whereas Figure 11 shows the flow chart for the CPC validation approach.  
The above model is based on the experimental tilt angle of 25\({}^{\circ}\) towards the south. The possible heat output obtained is 10.81 kW with a fluid outlet temperature of 91.96 \({}^{\circ}\)C. From Table 11, it can be seen that for the concentration ratio of 3.1, the aperture area and useful heat are 16.71 m\({}^{2}\) and 5.99 kW, respectively. Table 12 shows the performance results obtained for the CPC utilizing the EES and experiment as shown in Section 4.3.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Output** \\ \hline \(\delta\) & 20.34 \({}^{\circ}\)C \\ \(\eta_{\text{CPC}}\) & 0.39 \\ \(G_{t}\) & 933.5 W/m\({}^{2}\) \\ h & 17.67\({}^{\circ}\) \\ \(s_{t}\) & 567.9 W/m\({}^{2}\) \\ \(T_{out}\) & 91.96 \({}^{\circ}\)C \\ \(Q_{useful}\) & 10.81 kW \\ \(\Delta\)T & 46.76 \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table}
Table 10: Results of CPC for experimental values for May 21.  
Figure 11: Flow chart for CPC validation using EES.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Time** &
\begin{tabular}{c} **Value** \\ **Position** \\ \end{tabular} & **Ta** & **Tin** & **Tout** & **\(\Delta\)P** & **I\({}_{\text{T}}\)** & **V** & **Q** & **M** & \(\eta\) & **Qin** \\ \hline \multicolumn{10}{c}{**CPC performance data on May 22**} \\
11:30 & 1 & 43 & 44.5 & 57.8 & 63 & 942.9 & 6.33 & 0.25 & 0.30 & 0.45 & 4832.95 \\
12:00 & 1 & 44.7 & 46 & 59.2 & 83 & 945.25 & 7.41 & 0.30 & 0.34 & 0.52 & 4850.98 \\
12:40 & 1 & 41.6 & 45.2 & 60.8 & 77 & 971.57 & 7.14 & 0.29 & 0.36 & 0.58 & 4894.65 \\
13:30 & 1 & 37 & 38.5 & 50 & 80 & 942.9 & 7.27 & 0.29 & 0.35 & 0.45 & 4913.90 \\ \hline \end{tabular}
\end{table}
Table 9: _Cont._The parametric analysis as shown in Table 13 demonstrates that with every 1 m\({}^{2}\) decrease in the aperture area, the heat output decreases by 3.5%. The experimental aperture area is 9.6 m\({}^{2}\), which is almost 6.8 m\({}^{2}\) (23.94%) less than 16.4 m\({}^{2}\) obtained through the EES model for the same concentration ratio as shown in Table 11, and consequently, the calculated EES heat output is 4.56 kW. Table 14 shows the experimental and theoretical values of the heat output and efficiency for 21 May.  
\begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Theoretical Value** & **Experimental Value** \\ \hline Heat output (kW) & 5.99 & 4.7 \\ Efficiency & 0.39 & 0.40 \\ Aperture area (m\({}^{2}\)) & 16.4 & 9.6 \\ Fluid outlet temperature (\({}^{\circ}\)C) & 71.11 & 63 \\ Concentration ratio & 3.1 & 3 \\ \hline \end{tabular}
\end{table}
Table 12: Comparison of EES and experimental results.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Tilt Angle** & **Eta\_cpc** & **Q\_useful** & **S\_flux** & **G\_t\_t** & **Cr** & **T\_fout** & **Width** & **Aperture** \\ \hline
25 & 0.3903 & 8.31 & 573.9 & 933.5 & 4.57 & 81.15 & 2.286 & 24.41 \\
25 & 0.3909 & 7.72 & 575.4 & 933.5 & 4.24 & 78.61 & 2.121 & 22.65 \\
25 & 0.3915 & 7.21 & 576.8 & 933.5 & 3.95 & 76.42 & 1.979 & 21.13 \\
25 & 0.3922 & 6.77 & 578.2 & 933.5 & 3.71 & 74.52 & 1.855 & 19.81 \\
25 & 0.3928 & 6.39 & 579.5 & 933.5 & 3.49 & 72.84 & 1.746 & 18.65 \\
25 & 0.3934 & 6.04 & 580.9 & 933.5 & 3.301 & 71.36 & 1.65 & 17.63 \\
25 & 0.394 & 5.99 & 582.3 & 933.5 & 3.12 & 70.04 & 1.565 & 16.41 \\ \hline \end{tabular}
\end{table}
Table 11: Parametric analysis of CPC using EES for 21 May.  
\begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Theoretical Value** & **Experimental Value** \\ \hline Heat output (kW) & 5.99 & 4.7 \\ Efficiency & 0.39 & 0.40 \\ Aperture area (m\({}^{2}\)) & 16.4 & 9.6 \\ Fluid outlet temperature (\({}^{\circ}\)C) & 71.11 & 63 \\ Concentration ratio & 3.1 & 3 \\ \hline \end{tabular}
\end{table}
Table 13: Effect of aperture area on the useful heat gained from the CPC for 21 May.