# Thermal Analysis of Radiation Heat Transfer of Improved Fractal Solar Collectors
## 3 Results and Discussions
The temperature scale between 293.15 K and 320 K allows us to understand the micro-level thermal and hydrodynamic properties of the system. This shows that there is a temperature increase of approximately 27 K around the toroid and confirms the effective heat transfer capability of the system. The velocity vectors show that complex and regular flow patterns are formed around the toroid. In particular, the vortices formed around each toroid represent the turbulent flow that increases heat transfer. In the center of both toroidal structures, low temperature is observed in blue. This shows that cold water passes through the toroidal and heats up. In addition, towards the outer surface of the toroidals, the temperature increases with green and yellow colors, and upward moving vectors are observed in the upper parts. This shows that the heated water rises with natural convection and confirms the effectiveness of the passive heat transfer mechanism in the system as hydrodynamic movement. In the vicinity of the toroidals, it is observed that the temperature gradually decreases from yellow to green and blue. This distribution shows that the heat is spread to the environment and the system is constantly transferring heat. When the flow rate and temperature relationship is evaluated, it is generally observed that the flow rate increases in high temperatures (yellow and orange areas). This shows that the heated water moves faster, and thus the heat transfer capacity of the system increases. Complex flow patterns are observed in the region between the two toroidal structures. This shows that the toroidals affect each other's flow and heat transfer properties. This interaction contributes additionally to the overall efficiency of the system. A boundary layer is observed right next to the toroidal, where the flow rate decreases and the temperature increases. This shows the region where heat transfer is most intense. As a result, the complex geometry of the toroidal optimizes fluid motion and heat transfer. The vortices and turbulence form increase heat transfer, while the natural convection currents ensure passive operation of the system. These findings reveal that the fractal collector design can provide high efficiency in solar water heating applications. The radiation distribution analysis of the parabolic dish integrated fractal solar collector was performed. The velocity vectors colored according to the incident radiation in the middle plane are given in Figure 12. The system exhibited a radiation intensity spectrum ranging from 1000 W/m\({}^{2}\) to 2800 W/m\({}^{2}\). The maximum radiation intensity was observed at the focal point of the parabolic dish, and this region was represented in red. It was observed that the fractal collector with a three-layer toroidal structure effectively collected the rays reflected from the dish, and the radiation intensity was at medium-high levels, represented by yellow and orange colors on the collector surface. The ray paths were shown with green and yellow lines, clearly showing the distribution of radiation within the system. The peripheral radiation levels were shown with colors ranging from green to yellow and were determined to be lower in intensity compared to the center. This analysis proved the effectiveness of the parabolic dish and toroidal collector combination in concentrating and collecting solar rays. It was concluded that the system was designed to optimize the incoming radiation and that the parabolic geometry of the dish effectively focused the beams onto the toroidal collector. Figure 7.0 Velocity vector colored by static temperature at the mid-plane (**a**) general view, (**b**) enlarged view on the right side of fractal region, (**c**) enlarged view on the first toroidal, and (**d**) enlarged view on the second and third toroidals.