A comprehensive non-kinetic approach for rarefied gas flow between parallel plates

Abstract

The non-kinetic models typically offer a more straightforward approach than the complex kinetic models for microchannel gas flow problems. However, their applicability has traditionally been limited to a certain range of rarefaction. Hence, various modifications, including the slip boundary condition, non-linear viscosity, and diffusion phenomena, have been proposed. Although less explored, the wall-to-wall collision effect is also suggested for modifying the description of rarefied flow in confined areas. This paper presents a comprehensive non-kinetic approach for rarefied gas flow between parallel plates, covering a wide range of Knudsen numbers. This work integrates existing modifications and introduces new insights, specifically how gas particles specularly reflected from the walls impact the non-linear scaling functions for modifying the viscosity and diffusivity, and how to incorporate the wall-to-wall collision effect into the slip boundary condition. The uniform and cosine-law diffuse reflection models for gas–surface interaction are also compared and discussed. The proposed model is suitable for partially specular reflected gas–surface interactions and moving wall conditions, validated against classical Poiseuille and Couette flow problems. Overall, our findings expand the applicability of the non-kinetic model and enhance its accuracy in describing gas flow in confined spaces for more general conditions.