Optimal thermal design of pin-fin heat sinks with variable fin density in natural convection

Abstract

In this study, pin-fin heat sinks with variable fin density in natural convection are thermally optimized. Since a numerical simulation for pin-fin heat sinks yields high computational cost, pin-fin heat sinks are modeled as fluid-saturated porous media. A Brinkman-Forchheimer extended Darcy flow model and the one-equation model are adopted for the momentum and energy equations, respectively. A model for the effective thermal conductivity is newly proposed to calculate the heat dissipation rate at the base, which is simple but accurate. The validity of the proposed model is confirmed by comparing with the previous experimental data. With the assistant of surrogate-based optimization, the optimal distribution of the porosity is obtained which minimizes the thermal resistance of a heat sink. It is found that the optimized pin-fin heat sink with variable fin density has 7% lower thermal resistance and 24% less weight than the optimized pin-fin heat sink with uniform fin density.