## 4 Results and Discussion
The average temperatures of the PV section and the acrylic plate are estimated as follows [36]:  
\[T_{\text{PV}}=\frac{(T_{\text{PVb}}+T_{\text{PVu}})}{2}, \tag{23}\]  
\[T_{\text{AP}}=\frac{(T_{\text{APb}}+T_{\text{APu}})}{2}, \tag{24}\]  
respectively; where  
\[T_{\text{PVb}}=T_{\text{PVu}}-\frac{q_{\text{E,S}}}{1000}\Delta T=41.99\ ^{ \circ}\text{C} \tag{25}\]  
is the temperature of the bottom surface of the PV section; \(T_{\text{PVu}}=44.99\ ^{\circ}\text{C}\) is the temperature of the upper surface of the PV section; \(\Delta T=3\text{ K}\) is the temperature difference between the two surfaces of the PV section for the considered mounting method of the PV modules and the assumption that the temperature of the upper surface of the PV section \(T_{\text{PVu}}\) is equal to the PV cell temperature; \(q_{\text{E,S}}=1000\) W/m\({}^{2}\) is the solar irradiance corresponding to the temperature difference \(\Delta T=3\text{ K}\); \(T_{\text{APb}}=27.38\ ^{\circ}\text{C}\) is the temperature of the bottom surface of the acrylic plate; and \(T_{\text{APu}}=27.12\ ^{\circ}\text{C}\) is the temperature of the upper surface of the acrylic plate. In this regard, the temperature \(T_{\text{PVu}}\) is obtained from the following equation:  
\[q_{\text{r,PV}}=\epsilon_{\text{PV}}\sigma_{\text{SB}}F\Big{(}T_{\text{PVu}}^ {4}-T_{\text{a}}^{4}\Big{)}, \tag{26}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Unit**} & \multicolumn{2}{c}{**Simulation**} \\ \cline{3-4}  & & **First** & **Second** \\ \hline \(\theta\) & Degrees & 37 & 90 \\ \(T_{\text{o}}\) & \({}^{\circ}\text{C}\) & 44.03 & 34.3 \\ \(T_{\text{a,av}}\) & \({}^{\circ}\text{C}\) & 33.01 & 28.15 \\ \(v_{\text{i}}\) & m/s & 0.498 & 0.524 \\ \(v_{\text{o}}\) & m/s & 0.535 & 0.545 \\ \(v_{\text{air}}\) & m/s & 0.517 & 0.534 \\ \(\alpha_{\text{PV}}\sigma_{\text{PV}}q_{\text{E,S}}\) & W & 226.98 & 136.6 1 \\ \(\alpha_{\text{A}}\tau_{\text{AP}}S_{\text{AP}}q_{\text{E,S}}\) & W & 191.65 & 115.34 2 \\ \(Q_{\text{air}}\) & W & 342.8 & 201.05 \\ \(q_{\text{t,AP}}S_{\text{AP}}\) & W & 3.803 & 2.031 \\ \(q_{\text{c,PV}}S_{\text{PV}}\) & W & 17.069 & 12.23 \\ \(q_{\text{r,PV}}S_{\text{PV}}\) & W & 32.067 & 25.42 \\ \(Q_{\text{cl}}\) & W & 31.777 & 19.124 \\ \(h_{\text{assuming that the appropriate view factor \(F\) is equal to 1. Comparisons of the temperatures obtained in this simulation and the corresponding measured values from [39] are shown in Figure 2.  
The second simulation is performed with the following parameters: an inclination angle of \(\theta=90^{\circ}\) to the horizontal plane; \(L_{\rm TS}+L_{\rm AP}=0.52\) m; and other parameters as in the first simulation. The results of the second simulation are listed in Table 1. Based on Table 1, the Rayleigh number is \(\mathrm{Ra}=7.9744\times 10^{7}\). Accordingly, the free convection heat transfer from the upper surfaces of the PV section and the acrylic plate is again laminar. The results of this exercise are also generated after the ninth iteration. By comparing the results of the first simulation from Table 1 with the experimental and simulated results from Figure 2 and reference [39], one can see that almost identical values are obtained for the velocity of the air at the outlet of the solar chimney \(v_{\rm o}\), the temperature of the bottom surface of the PV section \(T_{\rm PVb}\), and the temperature of the upper surface of the PV section \(T_{\rm PVu}\). When the inclination with respect to the horizontal plane increases from \(\theta=37^{\circ}\) to \(\theta=90^{\circ}\), the solar irradiance decreases from \(q_{\rm E,S}=1000\) W/m\({}^{2}\) to \(q_{\rm E,S}\)sin\((37^{\circ})=601.815\) W/m\({}^{2}\). This means that the temperatures of the PV section, the acrylic plate, and the air at the outlet of the solar chimney should be significantly reduced.