Non-Newtonian Couette-Poiseuille flow of a dilute gas

Mohamed Tij; Andrés Santos

doi:10.3934/krm.2011.4.361

Article Contents

2011, Volume 4, Issue 1: 361-384. Doi: 10.3934/krm.2011.4.361

This issue Previous Article Coordinates in the relativistic Boltzmann theory Next Article Heisenberg picture of quantum kinetic evolution in mean-field limit

Non-Newtonian Couette-Poiseuille flow of a dilute gas

Mohamed Tij^1, and
Andrés Santos^2,

1.
Département de Physique, Université Moulay Ismaïl, Meknès
2.
Departamento de Física, Universidad de Extremadura, E-06071 Badajoz

Received: September 2010

Revised: October 2010

Published: March 2011

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Abstract

The steady state of a dilute gas enclosed between two infinite parallel plates in relative motion and under the action of a uniform body force parallel to the plates is considered. The Bhatnagar-Gross-Krook model kinetic equation is analytically solved for this Couette-Poiseuille flow to first order in the force and for arbitrary values of the Knudsen number associated with the shear rate. This allows us to investigate the influence of the external force on the non-Newtonian properties of the Couette flow. Moreover, the Couette-Poiseuille flow is analyzed when the shear-rate Knudsen number and the scaled force are of the same order and terms up to second order are retained. In this way, the transition from the bimodal temperature profile characteristic of the pure force-driven Poiseuille flow to the parabolic profile characteristic of the pure Couette flow through several intermediate stages in the Couette-Poiseuille flow are described. A critical comparison with the Navier-Stokes solution of the problem is carried out.

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Mathematics Subject Classification: Primary: 76P05, 82B40; Secondary: 82C40, 82C05.

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