# Thermal Analysis of Radiation Heat Transfer of Improved Fractal Solar Collectors
## 3 Results and Discussions  
In this study, the thermal behavior of an improved fractal solar collector integrated with a parabolic dish was investigated both experimentally and numerically. In experiments conducted in the Turkestan region of Kazakhstan, the fractal structure was fed with main  
Figure 5: A schematic of radiation on an opaque wall. water, and the effects of heat transfer by radiation and convection were observed. The collector used in the experiment consists of a 3-toroidal structure. While modeling the computational fluid dynamics (CFD) of the system, a fully structured computational grid was created in order to correctly define the collector geometry together with the inlet and outlet pipes. Mesh sensitivity analysis was performed to ensure the reliability and accuracy of the numerical analysis. This analysis was performed to show that the solution was independent of the mesh density and that the results did not change significantly according to the mesh quality. Analyses were performed with six different mesh densities using ANSYS Fluent. The outlet temperature parameter was examined to evaluate mesh sensitivity. As seen from Figure 6, the results become more sensitive as the number of elements of the mesh structures is increased. However, after a certain point, the effect of increasing the number of elements on the results decreases. This shows that the mesh structure is sufficient for the optimum solution between computational cost and result accuracy. During the creation of the computational grid, special attention was paid to the regions near the solid walls where the inlet-outlet and flow are located and where thermal changes are expected. The model mesh network of the 3-raws fractal collector defines (a) air and liquid flow dynamics, (b) the collector area with parabolic dish (c), and (d) specifically, the inlet and outlet pipe regions, as seen in Figure 7. The number of tetrahedral and hexagonal elements created in these grids was seen to be 7.7 million, 8.6 million, and 9.1 million elements for 3-row, 4-row, and 5-row toroidal structures, respectively. The experimental and numerical analysis results of one hourly data of the outlet water temperatures of the proposed design were compared, and the distributions of these data depending on time are given in Figure 8. In both curves, it is seen that the increase rate is quite slow at the beginning, and approximately 20 min later, the increase rate starts to rise significantly. In the third quarter, it is seen that the increase rate starts to slow down and that the increase is almost asymptotic towards the last minute. This situation shows that the heat transfer rate coming from radiation is effective alone until the first 20 min, and then the parabolic dish effect has a positive contribution. The reasons for the resistance to the temperature increase seen in the third quarter can be listed as follows: cold weather conditions in March, the fact that infrared radiation (direct IR) can be more than visible light, especially in winter months or when the sun angle is low, and the effect of wind speed on heat loss. It was calculated that there is a 3.16% difference between the outlet water temperatures. This increase seen in the numerical results is due to the neglect of wind speed, radial, and other thermal losses in the simulations. In particular, it is assumed that the parabolic dish focuses on the sun rays and that there is no loss in radiation values. In line with these assumptions, the dish surface is modeled as opaque and smooth, and the internal emissivity and diffuse fraction values are assumed to be zero. Being opaque means that the material does not allow light to pass through but either reflects or absorbs it. Figure 6: Mesh sensitivity analysis. Smoothness indicates that the surface does not contain any protrusions or indentations, even at the micro level.