Multi-Objective Optimization of Micro Pin-Fin Arrays for Cooling of High Heat Flux Electronics

The thermal management capability of various candidates of micro-pin fin arrays is investigated. An integrated circuit having a footprint of 4 × 3 mm with micro-pin fin array having circular, airfoil and convex cross-section is considered. The three pin fin cross-sections along with the cooling schemes are optimized to handle a uniform heat flux of 500 W/cm² applied to the top surface of the electronic chip. A fully three-dimensional, steady-state conjugate heat transfer analysis was performed on each cooling configuration and a constrained multi-objective optimization was carried out for each of the three micro-pin fin shapes to find pin fin designs configurations capable of cooling such high heat fluxes. The design variables were the geometric parameters defining each pin fin cross section, height of the chip and inlet speed of the coolant. The two simultaneous objectives were to minimize maximum temperature and pressure drop (pumping power), while keeping the maximum temperature below 85°C. A response surface was constructed for each objective function and was coupled with a genetic algorithm to arrive at a Pareto frontier of the best trade-off solutions. Stress-deformation analysis incorporating the hydrodynamic and thermal loads was performed on each of the three optimized configurations. The maximum displacement was found to be on the nano-level, and the Von-Mises stress for each configuration was found to be significantly below the yield strength of Silicon.