# Thermal Characteristics and Parametric Analysis of an Improved Solar Wall
## 4 Thermal Performance Optimization of Solar Walls  
It is found that the thermal efficiency of the current solar wall is not high by the experimental analysis. Therefore, based on the numerical simulation, the structure of this solar wall is optimized in this section. The thermal efficiency of solar walls in winter is affected by the structural dimension (aspect ratio, vent size, air channel thickness, etc. ), absorber materials and curtain angle, etc. Therefore, parametric analysis was performed based on the theoretical model. A cover, air gap, absorber plate and insulation plate formed the solar wall system. Figure 12a shows the heat transfer process of the solar wall. In the daytime, the air in the air gap is heated up by the hot absorber plate, then the indoor cold air flows into the air gap from the bottom inlet and rises to the top outlet after heating, thus completing a cycle of the heat exchange process. From the perspective of heat transfer, the heat transfer process in the solar wall is complex, involving thermal conduction, convection and radiation. The schematic diagram of the physical model is shown in Figure 12a. A thermal network for the physical model considered is shown in Figure 12b. Through the above simplifications, combined with the thermal network model and assumption conditions [28], heat balance equations of each component of the collector can be built. The heat balance equations from the thermal network at the points:  
\[\text{cover plate}\ \text{tg}:\ q_{\text{gi}}=h_{\text{go}}(t_{\text{g}}-t_{ \text{a}})+h_{\text{gi}}(t_{\text{g}}-\overline{t_{t}})+hr_{\text{cg}}(t_{ \text{g}}-t_{\text{s}}) \tag{12}\] \[\text{absorber plate}\ \text{ts}:\ q_{\text{s}}=h_{\text{su}}(t_{\text{s}}-t_{ \text{f}})+h_{\text{sd}}(t_{\text{s}}-\overline{t_{t}})+hr_{\text{cg}}(t_{ \text{s}}-t_{\text{g}})+hr_{\text{sg}}(t_{\text{s}}-t_{\text{so}}) \tag{13}\]  
\[\text{air gap}\ \overline{t_{f}}:\ h_{\text{su}}A_{\text{s}}(t_{\text{s}}- \overline{t_{t}})+h_{\text{sd}}A_{\text{s}}(t_{\text{s}}-\overline{t_{t}})+h_ {\text{gi}}A_{\text{g}}(t_{\text{g}}-\overline{t_{t}})+h_{\text{so}}A_{\text {so}}(t_{\text{so}}-\overline{t_{t}})= m_{\text{cp}}(\overline{t_{t}}-t_{\text{r1}}) \tag{14}\]  
Figure 11: The heat gain comparison of different dampers. Figure 12: Heat transfer process (**a**) and thermal network model (**b**) of the solar wall. \[\text{insulation plate }t_{\text{so}}:\ hr_{\text{sg}}(t_{\text{s}}-t_{\text{so}})+h_{ \text{so}}(\overline{t_{\text{f}}}-t_{\text{so}})=\sum_{j=0}^{N}X(j)t_{\text{so}} (N-j)-\sum_{j=0}^{N}Y(j)t_{\text{si}}(N-j) \tag{15}\]  
The values of the parameters were obtained by simulation using the MATLAB software package. According to the formulae, values of the parameters were obtained by simulation using the MATLAB software package. Experiment data on any given day were selected to verify the accuracy of the model. The values of several temperature points were obtained by simulation, and the comparison results are shown in Figure 13.  
It can be seen from Figure 13 that there was a very good agreement between experimental findings and simulation results. Average deviation indices were adopted to determine errors. (1) algebraic average deviation:  
\[\sigma_{avg}=\frac{1}{n}\sum_{n}\frac{\alpha_{c}-\alpha_{m}}{\alpha_{m}} \tag{16}\]  
(2) average absolute deviation:  
\[\sigma_{abs}=\frac{1}{n}\sum_{n}\left|\frac{\alpha_{c}-\alpha_{m}}{\alpha_{m}}\right| \tag{17}\]  
where \(\alpha_{c}\) and \(\alpha_{m}\) represent simulation and experimental values, respectively. Deviation analysis results are summarized in Table 6. \begin{table}
\begin{tabular}{c c c c} \hline \hline \
\begin{tabular}{c} **The Average Deviation** \\ \end{tabular} &
\begin{tabular}{c} **Interface Temperature of** \\ **South Wall** \\ \end{tabular} & **Outlet Temperature** & **Indoor Air Temperature** \\ \hline \(\sigma_{avg}\) & 10.5\% & 11.7\% & 5.4\% \\ \(\sigma_{abs}\) & 12.7\% & 14.3\% & 6.4\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Difference between the measured value and simulated value.