Constructal optimization of complex fin with convective heat transfer based on entransy dissipation rate minimization

Abstract

Based on the constructal theory, the constructal optimization of a complex fin is carried out by taking the minimum equivalent thermal resistance, which is defined according to entransy dissipation rate, as the optimization objective. Optimal constructal of the complex fin is obtained by tsking into consideration the entransy dissipation performance caused by heat conduction and heat convection. Comparisons between the optimal constructal with different shapes and optimization objectives of the fins are performed. Results show that there exist the optimal ratios of the height to the length of the elemental fin, central cavity and fin tip which lead to the triple minimum equivalent thermal resistance of the complex fin. By comparing the optimal constructal of the complex fin with that of the T-Y shaped fin, the structure of the complex fin will greatly improve its global heat transfer performance. When the heat transfer of the fin is two-dimensional and the root of the fin is broader, the more non-uniform the temperature at the fin root, the bigger difference of the optimal constructs the complex fin obtains, based on the minimizations of the equivalent thermal resistance and maximum thermal resistance. For the optimal design of the fin in pracuice, when the thermal safety of the fin is ensured, the constructal design scheme of the fin with minimum equivalent thermal resistance can be adopted to reduce temperature difference in the average heat transfer and improves the global heat transfer performance. This paper provides some guidelines for the optimal design of the complex fin from the point of view of heat transfer optimization.