Flows Between Parallel Plates: Analytical Solutions of Regularized 13-Moment Equations for Inverse-Power-Law Models

TL;DR

This paper derives analytical solutions for stationary channel flows using regularized 13-moment equations tailored for gases with inverse power law molecules, demonstrating improved accuracy over Maxwell molecule models.

Contribution

It extends the analytical solutions of R13 equations to inverse power law gases and introduces boundary conditions for Couette, Fourier, and Poiseuille flows.

Findings

Excellent agreement with reference solutions in slip-flow regime

R13 equations for inverse power law gases outperform Maxwell molecule models

Analytical solutions for various flow types are successfully derived

Abstract

We study the structure of stationary channel flows predicted by the regularized 13-moment equations. Compared with the previous work [P. Taheri et al., Phys. Fluids, 21 (2009), 017102], we focus on gases whose molecules satisfy the general inverse power law. The analytical solutions are obtained for the semi-linear equations, and the structures of Couette, Fourier, and Poiseuille flows are solved by coupling the general solutions with newly derived boundary conditions. The results show excellent agreement with the reference solution in the slip-flow regime. Our results also show that the R13 equations derived from inverse power law models can have better accuracy than the R13 equations of Maxwell molecules with altered viscosity.