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A three-dimensional solid–fluid conjugated model is coupled with a simplified conjugate-gradient method to optimize the flow and heat transfer in a water-cooled, silicon-based double-layer microchannel heat sink (MCHS). Six design variables: channel number, bottom channel height, vertical rib width, thicknesses of two horizontal ribs, and coolant velocity in the bottom channel are optimized simultaneously to search for a minimum of global thermal resistance. The optimal design variables are obtained at fixed pumping powers, coolant volumetric flow rates, and pressure drops through the MCHS, respectively. The dependences of design variables on the increased pumping power, volumetric flow rate, and pressure drop are discussed. Although the combined optimization is proven effective only for the double-layer MCHS with a specific dimension, it is expected that the proposed design strategy provide a valuable …