Size dependences of hydraulic resistance and heat transfer of fluid flow in elliptical microchannel heat sinks with boundary slip

As a well-accepted interfacial property, boundary slip condition is believed to affect hydraulic and thermal performances of various micro/nanofluidic applications. By considering the boundary slip for water flow through a microchannel heat sink, size dependences of hydraulic resistance and heat transfer of the water flow in a group of elliptical microchannel heat sinks with the same channel cross-sectional area but different length ratios of semi-major and minor axes are re-examined. The present work finds that hydraulic resistance and heat transfer of water flow in a microchannel are strongly dependent on the geometric parameters of the channel and the boundary slip condition. Both the hydraulic resistance and the convective heat transfer coefficient of the water flow in the elliptical shaped microchannel decrease with the increasing hydraulic diameter of the channel. An elliptical shaped microchannel having the largest hydraulic diameter, namely a microtube with the minimum length ratio of semi-major and minor axes being equal to one, has the smallest hydraulic resistance and the smallest heat transfer coefficient. Boundary slip at the solid-liquid interface can attenuate the hydraulic resistance and enhance the heat transfer capacity of the water flow in a microchannel, and these effects of slip on the mass and heat transfer are size-dependent. For the microchannel with a smaller hydraulic diameter, slip has a more significant attenuation effect on the hydraulic resistance and a more significant enhancement effect on the heat transfer. Geometric size optimization combined with the effective regulation of boundary slip can be a potential method to improve the mass and heat transfer of fluid flow over the micro/nanoscale.