Analysis of gaseous flow in a micropipe with second order velocity slip and temperature jump boundary conditions

Abstract

In this paper, second order velocity slip and temperature jump boundary conditions are used to solve the momentum and energy equations along with isoflux thermal boundary condition at the surface of the micropipe. The flow is assumed to be hydrodynamically and thermally fully developed inside the micropipe and viscous dissipation is included in the analysis. The solution yields closed form expressions for the temperature field and Nusselt number (Nu) as a function of various modeling parameters, namely, Knudsen number and Brinkman number (Br). For the given values of Br, the maximum difference of Nu between continuum flow with first order slip model and continuum and, second order slip model is found to be 35.67 and 34.62 %, respectively. Present solution exhibits good agreement with the other theoretical models. © 2014, Springer-Verlag Berlin Heidelberg.