## 3 Results and Discussion
### Numerical Results
#### 3.2.2 Effect of Fins on Thermal Performance at Different Seasons of the Year  
Figure 13a shows the predicted temperature difference \(\Delta T\) when using the FEM-CFD simulations from 6 a.m. to 6 p.m. on 1 March 2020 (late winter) with a constant inlet temperature \(T_{i}\) of 27 \({}^{\circ}\)C (corresponding to the initial \(T_{i}\) measured experimentally on that day) and a constant inlet velocity of 0.0076 m/s (0.36 L/min) for the different CPC collectors. Figure 13a also shows the power (energy per unit time) on the absorber surface obtained with the ray tracing simulations. Figure 13b shows an image of the incident angle of the solar rays impacting the CPC collector on the same day at noon (12 p.m.), for illustration purposes. It can be seen that the highest available power is obtained with the CPC absorber with continuous fins, while the lowest power available is obtained with  
Figure 12: Contour plot of the temperatures of the CPC absorber and cross section at the outlet at 12 p.m. (noon) on 1 March 2020: CPC absorber without fins (**a,b**); CPC absorber with segmented fins (**c,d**); CPC absorber with continuous fins (**e,f**). the CPC absorber without fins. This results in an increase in \(\Delta T\) with the increase in the surface area of the absorber due to the fins. Figure 13c,d show the results for early winter (15 January 2021) with a constant inlet temperature \(T_{i}\) of 23 \({}^{\circ}\)C (corresponding to the initial \(T_{i}\) measured experimentally on that day) and a constant inlet velocity of 0.0076 m/s (0.36 L/min) for the different CPC collectors. It can be seen that a similar \(\Delta T\) is obtained for both days (early and late winter) when similar CPCs are compared with each other because the average power (from 8 a.m. to 5 p.m.) on the absorber surfaces is similar on both days (Table 2). Figure 13e,f show the results for summer (9 July 2020) with a constant inlet temperature \(T_{i}\) of 34 \({}^{\circ}\)C (corresponding to the initial \(T_{i}\) measured experimentally on that day) and a constant inlet velocity of 0.0076 m/s (0.36 L/min) for the different CPC collectors. It can be seen that for summer (Figure 13e), the average power on the surfaces of the different absorbers is similar (Table 2) due to the incident angle of the solar rays impacting them (Figure 13f), which results in a similar increase in \(\Delta T\). It is noted that the average power on the finned absorbers of the non-tracking CPC is lower in summer when compared to winter (Table 2). Figure 13: Predicted temperature difference \(\Delta T\) and power on the absorber surface for the different CPC collectors (left image) and image of the incident angle of the solar rays impacting the CPC at noon for illustration purposes (right image): (**a,b**) on late winter (1 March 2020) with a constant inlet temperature of 27 \({}^{\circ}\)C and inlet velocity of 0.0076 m/s; (**c,d**) on early winter (15 January 2021) with a constant inlet temperature of 23 \({}^{\circ}\)C and an inlet velocity of 0.0076 m/s; (**e,f**) on summer (9 July 2020) with a constant inlet temperature of 34 \({}^{\circ}\)C and an inlet velocity of 0.0076 m/s. Figure 14 shows both the transverse and the longitudinal incidence angle modifier (_IAM_) for the different CPC absorbers, which was calculated using the ray tracing simulations and the following equation [35]:  
\[IAM(\theta)=\frac{\eta_{o}(\theta)}{\eta_{o}(0^{\circ})} \tag{5}\]  
where \(\eta_{o}(\theta)\) is the optical efficiency as a function of the incidence angle \(\theta\) and \(\eta_{o}(0^{\circ})\) is the optical efficiency when \(\theta=0^{\circ}\). \(\eta_{o}(\theta)\) was estimated using the maximum value given by the following equation [36]:  
\[\eta_{o}(\theta)=\frac{P_{c}(\theta)}{A_{a}I} \tag{6}\]  
where \(P_{c}(\theta)\) is the power on the absorber as a function of the incidence angle \(\theta\).