# Thermal Analysis of Radiation Heat Transfer of Improved Fractal Solar Collectors
## 3 Results and Discussions
The time-dependent temperature distributions of 3-row, 4-row, and 5-row toroidal fractal array solar collectors integrated with parabolic dish are comparatively presented in Figure 7.1 In the 3-row structure, it is observed that the parabolic dish starts to concentrate the sun rays in the first 20 min, and the temperature reaches approximately 314 K at the end of the 60-min period. However, due to the thermal mass of the system in the 3-row structure, heat transfer is initially slow. Between 20 and 40 min, internal emissivity and diffuse fraction values minimize heat loss and rapidly increase the temperature at the focal point. It is observed that turbulent flows and vortices begin to form between the toroidal structures after 20 min, and with the increasing heat transfer rate, the overall temperature of the system reaches thermal stability between 50 and 60 min. In each of these stages, the interaction of the parabolic dish and the fractal structure determines the overall performance of the system. The heat transfer, which is slow at the beginning, accelerates over time and eventually reaches thermal equilibrium. The fact that the 3-row structure reaches a lower maximum temperature compared to other configurations is explained by the fact that it contains less toroidal structure and therefore has less heat transfer surface. In the 4-row structure, the effect of the parabolic dish is seen to start to concentrate the rays in a similar way to the 3-row structure within the first 10 min. However, it was observed that the heat transfer started a little faster in the 4-row structure. The reason for this is that, thanks to the additional toroidal structure and the dish, more heat transfer surface is provided, and faster heating is observed in the initial phase compared to the 3-row structure. Between 35 and 60 min, the system approaches thermal equilibrium and reaches a higher temperature (around 319 K) compared to the 3-row structure. This can be explained by the increased heat transfer capacity provided by the additional toroidal structure. In the 5-row structure, the dish operates similarly to other configurations in the first 10 min, and faster heating is experienced because it provides the largest heat transfer surface. A rapid increase was observed between 10 and 30 min as the increasing turbulent flow and vortices maximized the heat transfer, and between 30 and 60 min the system approached thermal equilibrium and reached the highest temperature (around 323 K). As the number of toroidal structures increases, the heat transfer surface and convection currents become stronger, which increases turbulence and vortices and improves heat transfer. In addition, each additional toroidal structure increases the thermal mass of the system and provides a more homogeneous distribution of heat within the system. Thus, it is seen that the 5-row structure has a more stable and high-temperature profile. As a result, it is seen that the heat collection capacity of the system increases with the increase in the number of toroidal rows. The 5-row structure provides the highest temperature increase and the fastest heating rate. This analysis shows that the integration of the number of toroidal structures and the parabolic dish in the solar collector design significantly increases the overall performance of the system. Figure 7.2 Velocity vectors colored according to incident radiation in the mid-plane.