# Thermal Performance Analysis of a Double-Pass Solar Air Collector: A CFD Approach
## 3 Results and Discussion
### Thermal Behavior
The presented elbow inlet temperature refers to the average temperature at the outlet of the cavity (z = 2.0 m) in positions y = 0.1255 m to y = 0.1645 m, where the height of the elbow is 0.036 m. As expected, the temperatures corresponding to flow 1 (0.01 kg/s) are higher than flow 2 (0.02 kg/s). Therefore, all the air temperatures at the elbow inlet are lower than the air temperatures at the outlet of the cavity z = 2.0 m. On the other hand, the elbow outlet air temperatures and the duct inlet air temperatures are the same. Figure 11 shows the heat transfer coefficients (HTC\({}_{\text{p-cav}}\)) in the cavity for both air flow rates. As expected, the coefficients are lower when the airflow is lower and higher when the air flow rate is higher. Configurations with an inlet from below ((a) and (b)) have a high coefficient at the entry, which decreases to subsequently increase until it reaches a maximum near the outlet for configuration (a) and at the outlet (z = 2.0 m) for configuration (b). It is also noted that configuration (a) has a sharp increase and then a decrease from z = 0.2 m to z = 0.8 m, which is caused by the rise of the jet until it reaches the cover (see Figures 4a and 5a). In contrast, configurations with an inlet from the top (c and d) have an increase in the HTC\({}_{\text{p-cav}}\) in the region near the entry; then, it sharply declines to later gradually increase towards the region near the outlet where it reaches its maximum value. For example, the maximum HTC\({}_{\text{p-cav}}\) values with flow 1 are 15.0 W/(m\({}^{2}\) K), 15.8 W/(m\({}^{2}\) K), 16.0 W/(m\({}^{2}\) K), and 15.9 W/(m\({}^{2}\) K), while for flow 2 of 24.4 W/(m\({}^{2}\) K), 22.3 W/(m\({}^{2}\) K), 21.9 W/(m\({}^{2}\) K), and 25.0 W/(m\({}^{2}\) K), for configurations (a), (b), (c) and (d). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Flow 1: 0.01 kg/s**} & \multicolumn{2}{c}{**Flow 2: 0.02 kg/s**} \\ \hline  & **Configuration** & \(\mathbf{T_{elb,in}}\) **(K)** & \(\mathbf{T_{elb,out}}\) **(K)** & \(\mathbf{T_{elb,in}}\) **(K)** & \(\mathbf{T_{elb,out}}\) **(K)** \\ \hline (a) & Down–Down & 308.7 & 311.0 & 303.2 & 304.9 \\ (b) & Down–UP & 309.7 & 310.5 & 303.8 & 304.1 \\ (c) & Up–Up & 308.2 & 308.5 & 303.5 & 304.0 \\ (d) & Up–Down & 307.8 & 309.8 & 302.9 & 304.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Air temperatures in the elbow inlet and outlet of the U-shape double-pass CPC. In configurations where the air enters from the top ((c) and (d)), there is a high HTC\({}_{\text{p-cav}}\) at z = 0.1 m; nevertheless, all configurations have the maximum HTC\({}_{\text{p-cav}}\) in the region near the outlet. The above observations indicate that the HTC\({}_{\text{p-cav}}\) maximums correspond to the presence of the eddies produced by the sudden expansion at the inlet. While in the region near the outlet, there are also high HTC\({}_{\text{p-cav}}\) at z = 2.0 m in configuration (b), but in configurations (a), (c), and (d), it occurs around z = 1.8 m to z = 1.9 m. For configurations  
Figure 11: Flat-plate receiver heat transfer coefficients (HTC\({}_{\text{p-cav}}\)). (a) Down–Down; (b) Down–Up; (c) Up–Up; (d) Up–Down. (c) and (d), this occurs because the fluid becomes turbulent in the final region of the cavity as air is forced out of the manifold elbow. Table 7 shows the pressure drop in each configuration for the two mass flow rates. First, the highest pressure drop is seen in the bottom outlet configurations (a and d). Moreover, the pressure drop increases three to four times with the highest air flow rate.