Three-objective shape optimization and parametric study of a micro-channel heat sink with discrete non-uniform heat flux boundary conditions

A water-cooled multi-die heat sink with parallel rectangular micro-channels was designed to satisfy the operational requirements of a multi-die processor. A shape optimization strategy based on the RSM (response surface method) was used to minimize pressure drop and die maximum case temperatures. The effects of the thermal interface materials and heat spreader between the dies and heat sink were captured by the numerical simulation. The optimization was performed for constant values of coolant flow rate and inlet temperature, as well as the power, location, and surface area of the dies. The influence of channel hydraulic diameter, Reynolds number, thermal entrance length, and total heat transfer surface area on the hydraulic and thermal performance of the heat sink was determined using CFD (computational fluid dynamics) simulations at RSM design points. A sensitivity analysis was performed to evaluate the effect of the design parameters on the response parameters. The optimum designs were achieved by minimizing a weighted objective function defined based on response parameters using JAYA algorithm. The results of weighted sum method were compared with Pareto based three-objective optimization with a NSGA-II (non-dominated sorting GENETIC algorithm). Finally, a parametric study was performed to see the effect of the design parameters on the response parameters.