Optimization of a Microchannel Heat Sink with Varying Channel Heights and Widths

The optimal tapered channel design of a microchannel heat sink is obtained by a combined optimization procedure that includes a model of a three-dimensional microchannel heat sink and a simplified conjugate-gradient method. The objective function to be minimized is the overall thermal resistance with the number of channels N, channel-width ratio β, height-tapered ratio Λ _y , and width-tapered ratio Λ _z as the design parameters. It is shown that the thermal resistance in all its relationships with the individual parameters exhibits a decrease followed by an increase. The thermal resistance is sensitive to the variations in the channel number, channel-width ratio, or width-tapered ratio while less sensitive to the height-tapered ratio. Optimization results show that for a given pumping power (0.5 W), the optimal design variables are N = 78, β = 0.78, Λ _z  = 0.59, and Λ _y  = 0.81 with a corresponding minimum overall thermal resistance of 0.087 K W^?1. These optimal design variables produce a 37.6% decrement in thermal resistance compared to the initial parallel-channel design estimate (N = 71, β = 0.85, Λ _z  = 0.99, and Λ _y  = 0.99). Additionally, as the pumping power increases, the optimal thermal resistance decreases and the corresponding optimal values of N increase; whereas, β, Λ _z , and Λ _y decrease.