# Thermal Analysis of Radiation Heat Transfer of Improved Fractal Solar Collectors
## 1 Introduction  
The importance of using solar energy has increased in order to find solutions to the increasing energy needs and to eliminate the damage caused by fossil fuels to the environment [1, 2]. Just as electricity can be produced from solar energy through solar panels, which are increasingly used in industrial applications [3], heat energy production is also possible through solar collectors. Solar collectors, which have become widespread in recent years, play a very important role in converting the sun's radiant energy into thermal energy [4, 5]. Incident rays and reflected rays are important factors that determine the efficiency of solar collector-based systems. The incident ray constitutes the original ray beam emitted from the sun and reaching the collector surface. This energy-carrying ray hits the surface at an incidence angle. The intensity of the incident ray expresses the amount of energy per unit area and varies depending on factors such as the position of the sun and the atmospheric conditions. The reflected ray is the part of the incident ray that returns after hitting the surface. Reflection can be specular or diffuse depending on the properties of the surface. In specular reflection, the ray is reflected in a single direction, while in diffuse reflection, it is scattered in different directions. According to the laws of reflection, the reflection angle is equal to the incidence angle, and the incident ray, reflected ray, and surface normal are in the same plane. Studies on new-generation solar collectors have increased in recent years to benefit more efficiently from solar energy. Improvement studies on the generally used flat plate solar collectors are ongoing [6]. However, studies on concentrator systems for higher efficiency are also gaining importance, and parabolic trough collectors stand out in this field [7; 8; 9]. Apart from the development of new approaches in the design of these collectors [10; 11], various methods are also being investigated to improve the performance of parabolic trough collectors. Improvements in absorber surface designs [12; 13], use of nanofluids [14; 15; 16], and the examination of different heat transfer fluids [17; 18] are among these methods. In addition to studies on increasing solar collector efficiency using different materials, there are also solar collector design studies with different geometric structures. Fractal-structured solar collectors, which have been increasingly used in recent years and are the leading design studies, are based on structural theory [19; 20]. Application of the basic principles of fractal geometry to the design of solar collectors [21] and the presentation of a new fractal solar collector design based on structural theory [22] are examples of theoretical studies. These studies show that fractal-structured collectors can be more efficient than flat collectors. Absorbers and their locations in the aperture region of the collectors are the main problems of the design of solar collectors. A fractal solar collector is obtained by the fractal placement of absorbers on a parabolic concentrator plane in the form of toroidal tubes. Studies have been reported that heat transfer and fluid flow properties are increased in solar collectors with fractal geometric structures compared to flat-structure collectors [23; 24; 25]. Other studies on solar collectors with fractal geometric structures have reported an increased thermal efficiency [26; 27; 28; 29]. Studies to improve thermal performance and to reduce the cost of fractal solar collectors through innovative production techniques based on advanced materials have increased in recent years [30; 31; 32]. In addition to parabolic concentrators, compound parabolic concentrators (CPCs) [33] and Fresnel lens technology [34] also play an important role in solar energy applications. Linear Fresnel reflectors are also being investigated for increased efficiency [35]. Performance analysis of parabolic trough collectors under non-uniform solar flux conditions has been conducted [36; 37].