Direct cooling of an electronic chip of 25mm × 25mm in size is analyzed as a function of channel geometry for single-phase flow of water through small hydraulic diameters. Fully developed laminar flow is considered with both constant wall temperature and constant channel wall heat flux boundary conditions. The effect of channel dimensions on the pressure drop, the outlet temperature of the cooling fluid and the heat transfer rate are presented. The results indicate that a narrow and deep channel results in improved heat transfer performance for a given pressure drop constraint.