Mathematical modeling and multi-objective optimization on the rectangular micro-channel heat sink

A microchannel heat sink (MCHS) is a compact and efficient liquid-cooling device that satisfies the heat dissipation requirements of high-power electronic equipment. This study develops a mathematical model of a rectangular MCHS based on the differential equation of energy conservation and derives the thermal resistance using structural parameters. Single phase flow and fully developed conditions are considered. The correlations of the convective heat transfer coefficient and the flow resistance are examined and comparatively studied for wide-ranging geometric parameters. Both experimental and numerical methods are employed to validate the model. The effect of the height–width ratio on the thermo-hydrodynamic performance indicates a ratio greater than ten is uneconomical. Finally, a multiobjective optimization model is established to simultaneously minimize the thermal resistance and the pumping power. The Pareto front is obtained using the non-dominated sorting genetic algorithm, and the optimal case reduces the thermal resistance by 25% compared to the experimental case under the same pumping power consumption. The mathematical model and the multiobjective optimization method are beneficial for the design of an MCHS owing to the high convenience and reliability.