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

TL;DR

This paper uses LVDSMC simulations to determine the second-order temperature jump coefficient in dilute gases, revealing differences from classical models where temperature is governed by the Laplace equation.

Contribution

It provides the first calculation of the second-order temperature jump coefficient for gases with temperature governed by the Poisson equation, considering both hard sphere and BGK models.

Findings

The temperature jump coefficient differs from the classical steady-state case.

Results show the coefficient depends on the governing equation for temperature.

The study extends understanding of temperature jumps in non-homogeneous conditions.

Abstract

We use LVDSMC simulations to calculate the second-order temperature jump coefficient for a dilute gas whose temperature is governed by the Poisson equation with a constant forcing term. Both the hard sphere gas and the BGK model of the Boltzmann equation are considered. Our results show that the temperature jump coefficient is different from the well known linear and steady case where the temperature is governed by the homogeneous heat conduction (Laplace) equation.