Topology optimization for a water-cooled heat sink in micro-electronics based on Pareto frontier

Abstract

• An efficient Pareto frontier based design strategy for heat sinks is proposed. • A fitting formula of the Pareto frontiers is introduced to accelerate the design. • The 2D topology design results are validated by 3D CFD simulations. • Effects of temperature dependent properties on the results are significant. Topology optimization has been increasingly adopted as a non-intuitive methodology for heat sink design in the thermal management of microelectronics. In this work, a bi-objective topology optimization method for heat sink design in micro-electronics is suggested by considering the trade-off between two contradicting objectives, i.e., the heat transfer and hydraulic performances. The method in this work focused on the laminar water flow with Reynolds number less than 100 based on the channel width for a wide temperature range that covers different types of micro-electric devices. A series of Pareto frontiers were acquired for heat sink designs with different topologies, which can be used to decide the optimum design in respect of heat transfer and pressure drop. Particularly, an analytical formula in terms of inlet Reynolds numbers was obtained for the fast generation of the Pareto frontiers under different working conditions which help to determine the weight parameters of two contradicting objectives readily. The new strategy for weight parameter determination significantly reduces the workload of trial-and-error during the weight parameter determination in the traditional bi-objective topology optimization and thus accelerates the design process. Besides, the temperature-dependent physical properties (viscosity and thermal conductivity) in the design model were considered and were found to affect the design results significantly. Finally, the 3D heat sink model was reconstructed from the 2D topology optimization, and the thermal-fluid analyses were conducted. The results indicate that the 3D reconstructed model can well satisfy the design objective specified in the topology optimization, thereby confirming the validity and robustness of our design method.