On the second-order temperature jump coefficient of a dilute gas

Abstract

We use LVDSMC (low-variance deviational Monte Carlo) simulations to calculate, under linearized conditions, the second-order temperature jump coefficient for a dilute gas whose temperature is governed by the Poisson equation with a constant forcing term, as in the case of homogeneous volumetric heating. Both the hard-sphere gas and the BGK model of the Boltzmann equation, for which slip/jump coefficients are not functions of temperature, are considered. The temperature jump relation and jump coefficient determined here are closely linked to the general jump relations for time-dependent problems that have yet to be systematically treated in the literature; as a result, they are different from those corresponding to the well-known linear and steady case where the temperature is governed by the homogeneous heat conduction (Laplace) equation.