## 3 Numerical Results and Discussions  
### Comparison between TSC and DSTSC  
The aim of this part it is to analyze the influence of a back-pass inside a Transpired Solar Collector. Thus, we compare a usual Transpired Solar Collector with our prototype of a Double Skin Transpired Solar Collector in Figure 2.  
A comprehensive numerical study was conducted, based on the two geometries previously presented in Figure 2. For each geometry we analyzed the airflow characteristics and thermal behaviour for 5 airflow rate, 100 m\({}^{3}\)/h, 200 m\({}^{3}\)/h, 300 m\({}^{3}\)/h, 400 m\({}^{3}\)/h and 500 m\({}^{3}\)/h. The solar radiation was set as 800 W/m\({}^{2}\), with 650 W/m\({}^{2}\) of direct solar radiation and 150 W/m\({}^{2}\) of diffuse solar radiation. This section summarises the findings and contributions made. The first difference between the two solar collectors that we observed was regarding the heat exchanger efficiency. In Figure 5 we can notice a higher heat exchanger efficiency for the DSTSC at every airflow rate. Figure 6 comes with additional information to better understand the causes of these differences regarding the heat exchanger efficiency, indeed, we observe that the efficiency of the perforated absorber plate of the TSC is much higher than for the DSTSC. The heat exchanger efficiency is based on the temperature difference between the exchanger (in this case, the absorber plate), the ambient air, and the outlet air (Equation (1)), where the higher the exchanger temperature, the lower the exchanger efficiency. This is the reason why the heat exchanger efficiency of the TSC is lower than for the DSTSC. The heat exchanger efficiency of the TSC varies from 40% to 64% for airflow going 100 m\({}^{3}\)/h to 500 m\({}^{3}\)/h, while for the DSTSC, the heat exchanger efficiency varies from 45% to 78%. This corresponds to a difference of the benefit of the DSTSC from 5% to 14%. \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Values** \\ \hline Air flow & 450 m\({}^{3}\)/h \\ Ambient temperature & 27.8 \({}^{\circ}\)C \\ Solar radiation & 454.5 W/m\({}^{2}\) \\ Direct & 354.5 W/m\({}^{2}\) \\ Diffuse & 100 W/m\({}^{2}\) \\ Wind speed & 0.3 m/s \\ Wind direction & 220\({}^{\circ}\) \\ Absorptivity perforated absorber plate & 0.96–0.98 \\ \hline \end{tabular}
\end{table} 
Table 2: Details of the case used for validation. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & \(\mathbf{T_{outlet}}\) & \(\mathbf{T_{P1}}\) & \(\mathbf{T_{P2}}\) & \(\mathbf{T_{P3}}\) & \(\mathbf{T_{\text{DSI}}}\) & \(\mathbf{T_{\text{DSS}}}\) & \(\mathbf{T_{\text{back}}}\) \\ \cline{2-8}  & \({}^{\circ}\)C & \({}^{\circ}\)C & \({}^{\circ}\)C & \({}^{\circ}\)C & \({}^{\circ}\)C & \({}^{\circ}\)C & \({}^{\circ}\)C \\ \hline Exp & 34.1 & 39 & 39.9 & 39.6 & 36.6 & 35.9 & 34.2 \\ Num & 33.12 & 37.89 & 37.59 & 37.18 & 35.26 & 36.2 & 33.89 \\ Temperature difference & 0.98 & 1.11 & 2.31 & 2.42 & 1.34 & 0.3 & 0.31 \\ Error & 2.87\% & 2.85\% & 5.79\% & 6.11\% & 3.66\% & 0.84\% & 0.91\% \\ \hline \end{tabular}
\end{table} 
Table 3: Comparison between CFD and experimental data. In Figure 7 it can be noticed that for airflow higher than 400 m\({}^{3}\)/h, the TSC becomes more efficient than the DSTSC from the viewpoint of the solar collector efficiency. At this stage of understanding, we explain this evolution by the fact that for higher airflow, an air by-pass appears in the upper part the DSTSC. Nevertheless, the DSTSC still gives the best performance regarding the solar collector efficiency between 100 m\({}^{3}\)/h and 400 m\({}^{3}\)/h. The solar collector efficiency of the TSC varies from 60.9% to 86.9% for airflow going from 100 m\({}^{3}\)/h to 500 m\({}^{3}\)/h, while for the DSTSC, the solar collector efficiency varies from 66.5% to 85.7%. Figures 8 and 9 show the temperature and velocity distribution for the TSC and DSTSC at an air flow of 100 m\({}^{3}\)/h. The TSC overheats a bit in the bottom part in the wooden back plate, while the DSTSC overheats in the upper part of the aluminum separation plate.