Analytical Modeling of Fluid Flow and Heat Transfer in Micro/Nano-Channel Heat Sinks

Laminar forced convection in two-dimensional rectangular micro and nano-channels under hydrodynamically and thermally fully developed conditions is investigated analytically in the slip flow regime (0.001 < Kn < 0.1). 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. Isoflux thermal boundary condition is applied on the heat sink base. Results of the present analysis are presented in terms of 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 to no-slip flow conditions, depending on aspect ratios and Knudsen numbers that include effects of the channel size or rarefaction and the fluid/wall interaction.