Analytical modeling of fluid flow and heat transfer in microchannel/nanochannel heat sinks

Laminar forced convection in two-dimensional rectangular microchannels and nanochannels under hydrodynamically and thermally fully developed conditions is investigated analytically in the slip-flow regime. Closed-form solutions for fluid friction and Nusselt numbers are obtained by solving the continuum momentum and energy equations with the first-order velocity slip and temperature jump boundary conditions at the channel walls. An isoflux thermal boundary condition is applied on the heat sink base. The results of the present analysis are presented in terms of the channel aspect ratio, hydraulic diameter, momentum and thermal accommodation coefficients, Knudsen number, slip velocity, Reynolds number, and Prandtl number. It is found that fluid friction decreases and heat transfer increases compared with no-slip flow conditions, depending on the aspect ratios and Knudsen numbers that include the effects of the channel size or rarefaction and the fluid/wall interaction.