Optimal design of geometric parameters of double-layered microchannel heat sinks

Abstract This work uses an optimization procedure consisting of a simplified conjugate-gradient method and a three-dimensional fluid flow and heat transfer model to investigate the optimal geometric parameters of a double-layered microchannel heat sink (DL-MCHS). The overall thermal resistance R T is the objective function to be minimized, and the number of channels N , channel width ratio β , lower channel aspect ratio α l , and upper channel aspect ratio α u are the search variables. For a given bottom area (10 × 10 mm) and heat flux (100 W/cm 2 ), the optimal (minimum) thermal resistance of the double-layered microchannel heat sink is about R T  = 0.12 °C/m 2 W. The corresponding optimal geometric parameters are N  = 73, β  = 0.50, α l  = 3.52, and, α u  = 7.21 under a total pumping power of 0.1 W. These parameters reduce the overall thermal resistance by 52.8% compared to that yielded by an initial guess ( N  = 112, β  = 0.37, α l  = 10.32, and α u  = 10.93). Furthermore, the optimal thermal resistance decreases rapidly with the pumping power and then tends to approach an constant value. As the pumping power increases, the optimal values of N , α l , and α u increase, whereas the optimal β value decreases. However, increasing the pumping power further is not always cost-effective for practical heat sink designs.