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In this paper, an entropy generation minimization (EGM) procedure is employed to optimize the overall performance of microchannel heat sinks. This allows the combined effects of thermal resistance and pressure drop to be assessed simultaneously as the heat sink interacts with the surrounding flow field. New general expressions for the entropy generation rate are developed by considering an appropriate control volume and applying mass, energy, and entropy balances. The effect of channel aspect ratio, fin spacing ratio, heat sink material, Knudsen numbers, and accommodation coefficients on the entropy generation rate is investigated in the slip flow region. Analytical/empirical correlations are used for heat transfer and friction coefficients, where the characteristic length is used as the hydraulic diameter of the channel. A parametric study is also performed to show the effects of different design variables on the overall performance of microchannel heat sinks.