Shear work, viscous dissipation and axial conduction effects on microchannel heat transfer with a constant wall temperature

Abstract

Convective heat transfer in a microchannel rarefied gas flow with a constant wall temperature boundary condition is investigated numerically. The boundary shear work, viscous dissipation and axial conduction are all included in the study. An analytical solution is also derived for the fully developed flow condition including the boundary shear work. The proper thermal boundary condition considering the sliding friction at the wall is implemented. A comparative study is performed to quantify the effect of the shear work on heat transfer in the entrance – and the fully developed – regions of the microchannel for both gas cooling and heating. The results demonstrate that the effect of shear work on heat transfer is significant and it increases with increasing both the Knudsen number and Brinkman number. Neglecting the shear work in a microchannel slip flow leads to over- or under estimation of the Nusselt number considerably. For a fully developed flow in a microchannel with constant wall temperature boundary condition, the contribution of the shear work to heat transfer can be around 55% in the vicinity of the upper limit of the slip flow regime, regardless of how small the non-zero Brinkman number can be. Including the shear work is therefore crucial in the analysis of microchannel heat transfer and should not be neglected.