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

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.