Continuum analysis of rarefaction effects on a thermally-induced gas flow

TL;DR

This study investigates rarefaction effects on thermally-induced gas flow in a micro cavity using extended continuum theories, comparing results from regularized 13-moment equations with classical Navier-Stokes-Fourier predictions across different Knudsen numbers.

Contribution

It applies the R13 moment equations to analyze rarefaction effects in thermally-driven micro flows, extending beyond classical continuum models.

Findings

R13 equations capture non-linear rarefaction effects more accurately.

Flow behavior varies significantly with Knudsen number and heating rates.

Micro cavity aspect ratio influences flow patterns and temperature distribution.

Abstract

A Maxwell gas confined within a micro cavity with non-isothermal walls is investigated in the slip and early transition regimes using the classical and extended continuum theories. The vertical sides of the cavity are kept at the uniform and environmental temperature T_0, while the upper and bottom ones are linearly heated in opposite directions from the cold value T_0 to the hot oneT_H. The gas flow is, therefore, induced only by the temperature gradient created along the longitudinal walls. The problem is treated from a macroscopic point of view by solving numerically the so-called regularized 13-moment equations (R13) recently developed as an extension of Grad 13-moments theory to the third order of the Knudsen number powers in the Chapman-Enskog expansion. The gas macroscopic properties obtained by this method are compared with the classical continuum theory results (NSF) using the first and second order of velocity slip and temperature jump boundary conditions. The gas flow behavior is studied as a function of the Knudsen number (Kn), nonlinear effects, for different heating ratesT_0/T_H . The micro cavity aspect ratio effect is also evaluated on the flow fields in this study.