Geometric optimization of a highly conductive insert intruding an annular fin

Abstract

Annular fins are abundantly applied in industry, especially for cooling curved surfaces such as the tube wall. However, it is well-known that the fin conductive resistance reduces the total cooling performance. Therefore, in this paper, geometric optimization is carried out to reach the maximum cooling performance of an annular fin intruded by a pathway of highly conductive materials (‘insert’). The optimization objective is to reach the minimum peak temperature of the annular fin that extracts heat with constant heat flux at the fin base. The fixed total volume of the fin, as well as the fixed total volume of insert, are considered as a constraint. The optimization process is in conjunction with a numerical solution to obtain the temperature field in the fin. The results show that the optimized insert results in considerable elevation of the fin performance by reducing the peak temperature (thermal resistance) of the fin. Finally, the effects of several parameters such as the conductance ratio and the Biot number on the optimal results are reported. It has been proved that increasing the conductance ratio and Biot number reduces the peak temperature.