This article presents a steady-state 3-D conjugate heat transfer and single-phase liquid flow simulation in the microchannel heat sink (MCHs). The 3-D governing equations with boundary conditions are solved for a constant heat flux of 200 W/cm2, applied at the bottom surface of MCHs. An array of microchannels with three different cross-sections—uniform, converging, and diverging—are investigated for a fixed chip dimension of 20-mm length, 4-mm width, and 0.15-mm substrate thickness. This article aims to present a comparative analysis of the hydraulic and thermal performance of MCHs with three different cross-sections. Simulations are performed for volume flow rate and microchannel depth range of 20–140 mL/min and 0.25–1.25 mm, respectively, with silicon microchannel using water as the working fluid. Numerical simulations are performed using COMSOL Multiphysics 5.3. Comparative analysis shows that for a wide range of volume flow rate, diverging channels MCHs shows superior thermohydraulic performance. Furthermore, it is observed that with an increase in depth or aspect ratio of the channel, there is a significant reduction in pumping power requirement with some marginal reduction in thermal performance. Furthermore, to calculate the optimized channel dimensions for minimum thermal resistance and pressure drop, a MATLAB code was written. Based on the results, the optimized channel dimensions are identified. The work presented and discussed in this article is relevant and beneficial for designing compact MCHs for electronic cooling applications.