A generalized slip-flow theory for a slightly rarefied gas flow induced by discontinuous wall temperature

TL;DR

This paper extends slip-flow theory to account for discontinuous wall temperature in slightly rarefied gases, providing a new framework for analyzing flow near abrupt boundary changes.

Contribution

It introduces an extended slip-flow theory that handles discontinuous boundary conditions, supported by numerical results and a new kinetic boundary layer concept.

Findings

Extended slip-flow theory for discontinuous boundary conditions

Numerical validation of the new boundary layer model

Derivation of a source-sink condition for flow velocity

Abstract

A system of fluid-dynamic-type equations and their boundary conditions derived from a system of the Boltzmann equation is of great importance in kinetic theory when we are concerned with the motion of a slightly rarefied gas. It offers an efficient alternative to solving the Boltzmann equation directly and, more importantly, provides a clear picture of the flow structure in the near-continuum regime. However, the applicability of the existing slip-flow theory is limited to the case where both the boundary shape and the kinetic boundary condition are smooth functions of the boundary coordinates, which precludes, for example, the case where the kinetic boundary condition has a jump discontinuity. In this paper, we discuss the motion of a slightly rarefied gas caused by a discontinuous wall temperature in a simple two-surface problem and illustrate how the existing theory can be extended. The discussion is based on our recent paper [Taguchi and Tsuji, J. Fluid Mech. 897, A16 (2020)] supported by some preliminary numerical results for the newly introduced kinetic boundary layer (the Knudsen zone), from which a source-sink condition for the flow velocity is derived.