# Thermal Analysis of Radiation Heat Transfer of Improved Fractal Solar Collectors
## 4 Conclusions  
In this study, the thermal and hydrodynamic behaviors of 3-row, 4-row, and 5-row toroidal fractal solar collectors integrated with a parabolic dish are comprehensively investigated. This study makes significant contributions to the development of innovative solar energy systems by combining theoretical modeling, experimental verification, and numerical simulation methods. The main findings and contributions of this study can be concluded as follows:  
1. Hydrodynamic performance: The airflow velocity around the system varies between 0 m/s and 0.73 m/s. The complex geometry of the fractal structure increases heat transfer by creating turbulence and vortices, contributing to the overall efficiency of the system. 2. Radiation distribution analysis: The parabolic dish-integrated fractal solar collector exhibits a radiation intensity spectrum varying between 1000 and 2800 W/m\({}^{2}\). The maximum radiation intensity is determined at the focal point of the parabolic dish. The 3-row toroidal fractal collector effectively collects the rays reflected from the dish, forming medium-high radiation density on the collector surface. 3. Experimental and numerical comparison: The numerical analysis results converge to the experimental results by 96.84% for the 3-row toroidal structure. The slightly higher numerical results compared to experimental results are attributed to the neglect of wind speed, radiative, and other thermal losses in the numerical simulations. 4. Performance comparison of different row configurations: The 5-row toroidal fractal structure exhibits the best thermal and hydrodynamic performance among the 3-row, 4-row, and 5-row configurations. 5. Environmental factors: Cold weather conditions in March, seasonal infrared radiation amount, and wind speed affect the system performance, contributing to the resistance to temperature increase after the 45 th minute. 6. Geometric design evaluation: The proposed fractal collector geometry optimizes fluid movement and heat transfer. Each toroidal provides additional thermal energy to the toroidal above it. The heat collection capacity of the system increases with the increase in the number of toroidal rows, with the 5-row structure providing the highest temperature increase and the fastest heating rate. This study demonstrates that the fractal solar collector design integrated with a parabolic dish can provide high efficiency in solar water heating applications in terms of system integration and applicability. The novel geometry of the fractal structure enhances heat transfer and hydrodynamic performance by creating turbulence and vortices. We believe that more studies should be carried out on fractal solar collectors, which allow for more energy collection surfaces to be created in limited areas by scaling in the vertical plane. For example, studies can be conducted on increasing the system performance by using different dish geometries and reflective materials, and studies can be conducted  
Figure 13: Time-dependent temperature distribution for 3-row, 4-row, and 5-row toroidal structures. on different fractal geometries and flow directors to further optimize the flow dynamics. In addition, more comprehensive numerical models that include the effects of wind speed, humidity, and other environmental factors can be developed. It is recommended that long-term field tests be conducted to evaluate the performance of the system in different climatic conditions and throughout the year. Conceptualization, A.K. and N.R. ; methodology, A.K., N.R. and N.G. ; software, G.A.K. ; validation, A.K. and N.R. ; formal analysis, N.G. ; investigation, G.A.K. ; resources, G.A.K. and A.K. ; data curation, A.K. ; writing--original draft, N.G. and G.A.K. ; writing--review & editing, G.A.K. and N.G. ; visualization, G.A.K. and N.G. ; supervision, A.K. and N.G. ; project administration, A.K. and N.R. All authors have read and agreed to the published version of the manuscript.