A numerical optimization of a rectangular micro-channel has been performed. Navier-Stokes and energy equations for laminar flow and conjugate heat transfer are solved using a finite volume solver. Solutions are first carefully validated with available analytical and experimental results; the shape of the micro-channel is then optimized using surrogate method. Ratios of the micro-channel width to depth and the width of the fin to the depth are selected as design variables. Design points are selected through a four-level full factorial design. A single objective function thermal resistance, formulated using pumping power as a constraint, is optimized. Mass flow rate is adjusted by the constant pumping power constraint. Kriging method is applied to construct surrogate and the optimum point is searched by sequential quadratic programming.
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