## 4 Results
### The Impact of the Inner Helical Fins Pitch (P)  
In the second section, according to the obtained numerical results from the last section (Section 4.3), Model 2 (see Figure 2) is considered as the selected model here. Results from the last section showed that Model 2 has the maximum heat transfer coefficient with the highest pressure drop. Therefore, to study the impact of the inner helical fins pitch, this model is used. In this section, the impact of the inner helical fins pitch on the thermal efficiency of the system is evaluated numerically. Four various pitches of the inner helical fins including 250, 500, 750 and 1000 mm are considered, and the obtained outcomes are compared with the simple collector (without fins). The considered models here are shown in Figure 3. The variation of heat transfer coefficient versus different inlet velocity for various models is illustrated in Figure 13.  
According to Figure 13, it can be concluded that firstly, all the proposed models show higher heat transfer coefficient more than the simple collector (without fins). Secondly, it is depicted that among the studied models  
The variations of pressure drop and friction factor (f) versus various inlet velocities for various models are illustrated in Figure 15a,b, respectively. Figure 15a depicts that all models have higher pressure drop compared to the case without helical fins obviously because of the presence of swirl flows. The greatest pressure drop belongs to the case with P = 250 mm, and the case with P = 1000 mm shows the lowest pressure drop among the investigated models. Additionally, as the inlet velocities rise, the pressure drop increases due to the effect of forced convection in the channel. This trend is the same for all models. Moreover, by increasing the inlet velocities, the differences between the studied models and the model are not significant. Figure 14: Contours of temperature at outlet and a slice (X = 0) for various models at V\({}_{\text{Inlet}}\) = 0.1256 m/s. rise. This point could be important considering the pressure drop factor, as the differences between the cases with P = 500, 750 and 1000 mm are very low. Figure 15b shows that the trend of variation of fraction factor among the models is the same with pressure drop (Figure 15a). On the other hand, as same as Figure 15a, the highest and lowest friction factor belong to the cases with P = 250 mm and P = 1000 mm, respectively. However, it should be focused that the variation of friction factor with inlet velocities is not the same with pressure drop and they are exactly the opposite. By increasing the inlet velocity, the friction factor declines. According to Equation (5), the  
Figure 15: (a) Pressure drop and (b) friction factor (f) variation with the inlet velocity for various models at P = 500 mm. friction factor is directly related to pressure drop; however, the squared velocity is placed at the denominator of the equation. The streamline with the contour of temperature for various models are presented in Figure 16. The impact of changing the schematic of the collector on temperature distribution in the outlet port and also the heat transfer rate is presented clearly in this figure. Accordingly, all models show better temperature distribution than the case without fins. Figure 16: _Cont._  
The best parameter to study comprehensively the impact of efficient parameters on the performance of the proposed collector is thermal efficiency (\(\eta\)), which is calculated by Equation (6). The variation of this parameter is presented in Figure 17. Therefore, it can be concluded firstly that all the models illustrate higher thermal performance than the case without fins, which means that the values of thermal performance are higher than unity. Furthermore, the greatest and smallest thermal performance improvement (compare to the case without fins) belong to the case with P = 1000 mm by 21.53% and the case with P = 250 mm by 14.1% for the latest velocity, respectively. Figure 16: The streamline with contours of temperature for various models.