Optimization of heat transfer rate in the rectangular microchannel of different aspect ratios with constant cross sectional area

The increased power dissipation and reduced dimensions of microelectronics devices have emphasized the need for highly efficient compact cooling technologies. Microchannel heat sinks are of particular interest due to the very high rates of heat transfer they enable in conjunction with greatly reduced heat sink length scales and coolant mass flow rate. Therefore, in the present work, optimization of laminar convective heat transfer in the microchannel heat sinks is investigated for uniform heat flux and different cross sectional areas of different aspect ratios. Three-dimensional numerical simulations of general form of energy equation were performed to predict Nusselt number in the laminar flow regime. Using these results, an optimum forced convective heat transfer coefficient was computed for several cross sectional areas and Reynolds numbers, utilizing the univariable search method. Different aspect ratios have different influences on Nusselt number in thermally developing and fully developed regions for different cross sectional areas and Reynolds numbers. There exists an optimum Nusselt number for each Reynolds number and cross sectional area by varying aspect ratio. Thus, optimized state is computed and related graphs are presented.