Effect of Thermal Creep on Heat Transfer for a Two-Dimensional Microchannel Flow: An Analytical Approach

Abstract

In this paper, velocity profile, temperature profile, and the corresponding Poiseuille and Nusselt numbers for a flow in a microtube and in a slit-channel are derived analytically with an isoflux thermal boundary condition. The flow is assumed to be hydrodynamically and thermally fully developed. The effects of rarefaction, viscous dissipation, axial conduction are included in the analysis. For the implementation of the rarefaction effect, two different second-order slip models (Karniadakis and Deissler model) are used for the slip-flow and temperature-jump boundary conditions together with the thermal creep at the wall. The effect of the thermal creep on the Poiseuille and Nusselt numbers are discussed. The results of the present study are important (i) to gain the fundamental understanding of the effect of thermal creep on convective heat transfer characteristics of a microchannel fluid flow and (ii) for the optimum design of thermal systems which includes convective heat transfer in a microchannel especially operating at low Reynolds numbers.