Continuum Analysis of Rarefaction Effects on a Thermally Induced Gas Flow

Mohamed Hssikou,Mohammed Alaoui,Jamal Baliti

doi:10.1155/2019/5084098

Abstract

A Maxwell gas confined within a micro cavity with nonisothermal 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 T0, while the upper and bottom ones are linearly heated in opposite directions from the cold value T0 to the hot one TH. 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-moment 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 rates T0/TH. The micro cavity aspect ratio effect is also evaluated on the flow fields in this study.

Highlights

The frequent use of small-size devices in several applications needs types of equipment that dissipate maximum amount of heat per unit area
We compare the direct simulation Monte Carlo (DSMC) and regularized 13-moment equations (R13) results by considering the test case treated by Vargas et al [18]
To stay in the considerations of macroscopic approaches, a small temperature gradient and moderate Knudsen number values are considered in this test case, T0/TH = 0.9, Kn = 0.01 and 0.1

Summary

Introduction

The frequent use of small-size devices in several applications needs types of equipment that dissipate maximum amount of heat per unit area. Regarding the dimensions of these devices, the continuum assumptions of the gas flow break down and some deviations are observed in respect of the macro scale case. The use of velocity slip and temperature jump boundary conditions proves that the rarefaction degree has a significant effect on the gas micro flows or lowpressure gas problems (Karniadakis and Beskok 2005, [4]). 0.1 ≤ Kn < 10, i.e., transition regime, the nonequilibrium effects become more important even in the bulk of flow and, the continuum theory breaks down [6, 7] In this case, the gas flow must be described from a kinetic point of view by following the governing equation of Boltzmann (3). The DSMC method is very expensive both in computational time

Objectives

Results

Conclusion