Heat transfer analysis of cellular heat exchanger based on a fresh fractal Vicsek model by Galerkin finite element method

Abstract

The energy density is increasing in modern industry, and the lack of heat transfer efficiency is one of the fatal problems of current equipment, which seriously affects the improvement of production level. The cellular heat exchanger is a kind of heat exchanger used in different fields. It plays an irreplaceable role in energy saving, efficiency improvement and reducing pressure drop. However, when the geometric shape of the fractal heat exchanger is very complex, the heat transfer analysis is impossible or difficult to show. Therefore, the objective of this project is to solve the difficulty of analysis on complex fractal heat exchangers and have a better representation of the physics. A totally fresh tessellation method, which can be used to analyze complex fractal heat exchangers, is introduced in this essay. By the research process, surjective hole-fill maps for Vicsek fractal were established, and Vicsek fractal was represented by continuous tessellations, and the fractal Vicsek model was expressed by continuous subdivision. The transfer theory on fractals and Galerkin finite element method were used to analyze the heat transfer of fractals and tessellations. The results of two analyses, the fractal model and the tesselation model, were almost the same, and confirm the function of the tessellation method in the analysis of complex heat exchangers. Furthermore, it provides a new way to solve the difficult problem of heat transfer analysis of complex geometric heat exchangers.