An analytical solution of convective heat transfer in microchannel or nanochannel

Abstract The two-dimensional energy equation with a first-order velocity slip model and a temperature jump model is studied analytically and a solution consisting of an infinite series is obtained. Impacts of viscous dissipation, axial conduction and rarefied effect on the local Nusselt number, the asymptotic Nusselt number and the bulk temperature profile of fluid are investigated. Results show that the cooling effect of the fluid benefits from the higher rarefied effect and axial conduction effect, as well as the lower viscous dissipation. The asymptotic dimensionless bulk temperature of fluid converges to a constant value that is higher than the wall temperature at a given set of Brinkman number, Peclet number and Knudsen number regardless of the inlet conditions. When neglecting axial conduction and the rarefied effect, the asymptotic Nusselt number with or without viscous dissipation is 17.5 or 7.54, respectively. Effects of axial conduction on the asymptotic Nusselt number are negligible when the Peclet number is greater than 10, while its influence on the non-dimensional bulk temperature of fluid and local Nusselt number can be neglected only when Pe > 100.