# Thermal Analysis of Radiation Heat Transfer of Improved Fractal Solar Collectors
## 3 Results and Discussions
The simulation results show that the low-internal emissivity value increases the heat retention capacity of the dish, and the temperature at the focal point increases up to 350 K. This finding is consistent with the high temperature increase in the experimental study and confirms the energy efficiency of the system. However, the diffuse fraction effect shows that the dish surface scatters the incident light minimally and mostly reflects specular. The intense red region (around 350 K) at the bottom of the parabolic dish confirms that the rays are effectively focused. This is consistent with the high heat transfer rate observed in the experimental study and proves the optical efficiency of the system. In the simulation, it is understood that the dish minimally absorbs and mostly reflects the incoming visible and infrared radiation. Simulation results show that these low absorptivity values prevent the dish from heating up, and a large portion of the incoming energy is directed to the fractal collector. Therefore, it is understood that it is consistent with the high energy transfer rate observed in the experimental study. However, the temperature distribution in the collector clearly shows that the gradual temperature increases from the lower fractal to the upper fractal (approximately from 293 K to 350 K) confirms the heat transfer mechanism observed in the experimental study. This supports that each fractal level provides additional thermal energy to the next level. The flow lines show the movement of water in the system. Starting from the lower fractal, the water moving upwards heats up at each fractal level. This flow model confirms the thermodynamic circulation observed in the experimental study. The blue regions around the parabolic dish show the heat exchange with the environment. However, the high temperature at the focal point (350 K) shows that the dish minimizes thermal losses. As a result, the optical properties of the parabolic dish (low internal emissivity, diffuse fraction, and absorptivity) and the thermal performance of the fractal collector are consistent with the experimental study. The velocity vectors colored according to the static temperature in the middle plane are given in Figure 11a. Figure 11b allows us to understand the thermal and hydrodynamic properties of the fluid motion and temperature distribution in the middle plane of the fractal collector system in an integrated manner. The temperature scale varies between 293.15 K and 350 K. This shows that the system can increase the water temperature by approximately 57 K. In addition, the velocity vectors clearly show the complex flow patterns in the system. The highest temperatures are observed in the red-orange areas in the regions corresponding to the focal points of the parabolic dish. This confirms that the dish effectively concentrates the sun rays. In general, it is observed that the flow velocity also increases in the red and orange high temperature regions. This shows that the heated water moves faster, and thus the heat transfer capacity of the system increases. In Figure 11c, where the velocity vectors and temperature distribution are given for the first toroidal, it is seen that there are vortices and turbulence regions around the system. Significant temperature gradients  
Figure 10: Enlarged view of path line temperature at the middle plane on the fractal collector. are observed inside and around the fractal structures. These gradients indicate that heat transfer is continuous, and there is an effective heat distribution in different regions of the system. The complex structure of the fractal geometry causes the fluid to spread in different directions and to merge again. This provides a large surface area for heat transfer and increases the overall efficiency of the system. In Figure 11d, the flow dynamics, temperature distribution, and micro-level operation of the system around the fractal collector top and middle toroids are given in detail.