Numerical shape optimization for high performance of a heat sink with pin-fins

The design optimization of a 7x7 pin-fin heat sink is performed numerically. To achieve higher thermal performance of the heat sink, the thermal resistance at the junction of the chip and the heat sink and the overall pressure drop in the heat sink have to be minimized simultaneously. The fin height (h), fin width (w), and fan-to-heat sink distance (c) are chosen as the design variables, and the pressure drop (DeltaP) and thermal resistance (theta(ja)) are adopted as the objective functions. To obtain the optimum design values, we used the finite-volume method for calculating the objective functions, the Broydon-Fletcher-Goldfarb-Shanno method for solving the unconstrained nonlinear optimization problem, and the weighting method for predicting the multiobjective problem. The results show that the optimum design variables for the weighting coefficient of 0.5 are as follows: w=4.653 mm, h=59.215 mm, and c=2.669 mm. The objective functions corresponding to the optimal design are calculated as DeltaP=6.82 Pa and theta(ja)=0.56 K/W. The Pareto solutions are also presented for various weighting coefficients, and they offer very useful data for designing a pin-fin heat sink.