Design and analysis of multi-scale annular fins attached to a pin fin

The design of efficient fins for reducing cost, space, materials and the energy consumption for heat removal and refrigeration applications is a great challenge. In this paper, consideration is given to the constructal (optimal) design of multi-scale annular fins that are attached to a pin fin. The geometrical scales of the assembly are relaxed to reach the maximal heat transfer removed by the assembly of the fins, subject to the space and materials constraints. Based on a one-dimensional model, analytical solution is performed to deliver the amount of heat transfer density. The direct search method and the Genetic Algorithm (GA) are used to optimize the geometric configuration of the assembly. The optimization results indicate that the increment in the number of geometrical variables of the assembly remarkably enhances the thermal performance of the assembly, however, it imposes excess complexity in the optimization process. The design guidelines for the design of multi-scale fins provided after optimizations, can be useful in the design of variant cooling devices in practical engineering applications.