Study on topology optimization of heat sinks with axially uniform cross-sections in forced convection

Abstract

In this thesis, the computationally efficient methods for optimizing the topologies of heat sinks in forced convection is suggested. In the first technical chapter, radial plate-fin heat sinks under an L-shaped flow are optimized. To conduct optimization, the total thermal resistances need to be calculated for the given design parameters, i.e., the number of fins and the fin thickness. For this, the correlations of the pressure drop, the average Nusselt number, and the heat sink efficiency are suggested. The correlations of the pressure drop and the average Nusselt number are suggested based on the data obtained from numerical simulations, and the correlation of the heat sink efficiency is suggested by introducing corrections factor obtained from numerical simulations to the analytically derived equation for the heat sink efficiency. By using the suggested correlations, the geometries of the radial plate-fin heat sinks are optimized for various domain sizes and pumping powers. Finally, the correlations of the optimum number of fins and fin thickness are suggested. In the second technical chapter, heat sinks under a parallel flow without given shape, and array type of fins are optimized. To conduct optimization without given shape and array type of fins, the topology optimization method is used. To conduct topology optimization of heat sinks, the total thermal resistance, which is inversely proportional to the thermal performance and consists of the convective resistance and the capacity resistance, is suggested as an objective function. To reduce the computation time required for the sensitivity analysis, an alternative expression for the total thermal resistance and a local window method, which is a sensitivity analysis method with reduced computation time, are suggested. To suggest the alternative expression, the relation between the convective resistance and the thermal compliance is mathematically derived. When the alternative expression is used, the sensitivity of the total thermal resistance, which explicitly depends on the sensitivities of both the velocity and temperature fields, could be calculated with only the sensitivity of the velocity field. By using the characteristics of the velocity field, the local window method, which is a faster method for analyzing the sensitivity of the velocity field, is suggested. With the suggested topology optimization method, the computation time for optimization is reduced by 73%, and the topology-optimized heat sink with a 29% lower total thermal resistance even with a 15% reduced weight compared to the commercial heat sink is suggested.