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Title: Steady flows of a highly rarefied gas induced by nonuniform wall temperature
Authors: Kosuge, Shingo  kyouindb  KAKEN_id  orcid (unconfirmed)
Aoki, Kazuo  KAKEN_id
Takata, Shigeru  kyouindb  KAKEN_id  orcid (unconfirmed)
Hattori, Ryosuke
Sakai, Daisuke
Author's alias: 小菅, 真吾
Keywords: Boltzmann equation
confined flow
flow simulation
integral equations
molecular collisions
Monte Carlo methods
rarefied fluid dynamics
temperature distribution
Issue Date: Mar-2011
Publisher: American Institute of Physics
Journal title: Physics of Fluids
Volume: 23
Issue: 3
Thesis number: 030603
Abstract: Steady behavior of a rarefied gas between parallel plates with sinusoidal temperature distribution is investigated on the basis of the Boltzmann equation. The Cercignani–Lampis (CL) model or the Lord model for diffuse scattering with incomplete energy accommodation is adopted as the boundary condition on the plates. Most of the analysis is carried out numerically with special interest in the free-molecular limit. In the case of the CL model, the nonuniform temperature distribution of the plates may induce a steady free-molecular flow, which is in contrast with the earlier results for the Maxwell-type model [ Y. Sone, J. Méc. Théor. Appl. 3, 315 (1984) ; J. Méc. Théor. Appl. 4, 1 (1985) ]. This fact is confirmed through an accurate deterministic computation based on an integral equation. In addition, computations for a wide range of parameters by means of the direct simulation Monte Carlo method reveal that the flow field changes according to the accommodation coefficients and is classified into four types. The effect of intermolecular collisions on the flow is also examined. In the case of the Lord model, no steady flow of the free-molecular gas is induced as in the case of the Maxwell-type model. This result is extended to the case of a more general boundary condition that gives the cosine law (Lambert’s law) for the reflected molecular flux.
Rights: © 2011 American Institute of Physics
DOI(Published Version): 10.1063/1.3558872
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