Impact of cross-section geometry on microchannel heat sink performance in the presence of slip and temperature jump boundary conditions

The geometry of microchannels plays a crucial role in determining the heat transfer efficiency and pressure drop in microchannel heat sinks. The choice of channel shape is often guided by practical factors, such as manufacturability, system integration, and cost-effectiveness. This study aims to evaluate the thermohydraulic performance of laminar flow in microchannels with various cross-sectional geometries, including rectangular, trapezoidal, double-trapezoidal, elliptical and rhombic shapes. This analysis considers the effects of slip velocity and temperature jump at the channel walls, as to date, research on the thermal characterization of microchannels operating in the slip flow regime – particularly those with hydrophobic or superhydrophobic surfaces – remains limited. The heat transfer problem is addressed by assuming a constant heat transfer rate along the axial direction of the channel walls with a uniform temperature distribution around the perimeter of the cross-section. This condition is particularly relevant for microchannels subjected to an imposed heat flux, especially when the channel walls are constructed from materials with high thermal conductivity. The numerical results reveal that rectangular and double-trapezoidal (hexagonal) cross-sections demonstrate the highest thermohydraulic performance, whereas the rhombic cross-section performs the worst. Moreover, the outcomes presented here highlight that the rhombic geometry is the most sensitive to slip effects, while the double-trapezoidal geometry is the least sensitive.