Thermal Transpiration Flow in Annular Microchannels

Thermal transpiration flows of rarefied gases in annular channels are considered, where the driving force for the flow is a temperature gradient applied in the channel walls. The influence of gas rarefaction, aspect ratio of the annulus, and surface accommodation coefficient on mass and heat transfer in the process are investigated. For this, the linearized Navier–Stokes–Fourier (NSF) and regularized 13-moment (R13) equations are solved analytically, and a closed-form expression for Knudsen boundary layers is obtained. The results are compared to available solutions of the Boltzmann equation to highlight the advantages of the R13 over the NSF equations in describing rarefaction effects in this particular thermally-driven flow. Through comparisons with kinetic data it is shown that R13 equations are valid for moderate Knudsen numbers, i.e., Kn < 0.5, where NSF equations fail to describe the flow fields properly.