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Title: Parabolic temperature profile and second-order temperature jump of a slightly rarefied gas in an unsteady two-surface problem
Authors: Takata, Shigeru  kyouindb  KAKEN_id  orcid (unconfirmed)
Aoki, Kazuo  KAKEN_id
Hattori, Masanari  kyouindb  KAKEN_id  orcid (unconfirmed)
Hadjiconstantinou, Nicolas G.
Keywords: Boltzmann equation
boundary-value problems
kinetic theory
Knudsen flow
slip flow
stochastic processes
Issue Date: Mar-2012
Publisher: American Institute of Physics
Journal title: PHYSICS OF FLUIDS
Volume: 24
Issue: 3
Thesis number: 032002
Abstract: The behavior of a slightly rarefied monatomic gas between two parallel plates whose temperature grows slowly and linearly in time is investigated on the basis of the kinetic theory of gases. This problem is shown to be equivalent to a boundary-value problem of the steady linearized Boltzmann equation describing a rarefied gas subject to constant volumetric heating. The latter has been recently studied by Radtke, Hadjiconstantinou, Takata, and Aoki (RHTA) as a means of extracting the second-order temperature jump coefficient. This correspondence between the two problems gives a natural interpretation to the volumetric heating source and explains why the second-order temperature jump observed by RHTA is not covered by the general theory of slip flow for steady problems. A systematic asymptotic analysis of the time-dependent problem for small Knudsen numbers is carried out and the complete fluid-dynamic description, as well as the related half-space problems that determine the structure of the Knudsen layer and the coefficients of temperature jump, are obtained. Finally, a numerical solution is presented for both the Bhatnagar-Gross-Krook model and hard-sphere molecules. The jump coefficient is also calculated by the use of a symmetry relation; excellent agreement is found with the result of the numerical computation. The asymptotic solution and associated second-order jump coefficient obtained in the present paper agree well with the results by RHTA that are obtained by a low variance stochastic method.
Rights: Copyright 2012 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in PHYSICS OF FLUIDS 24, 032002 (2012) and may be found at
DOI(Published Version): 10.1063/1.3691262
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