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Physics of Fluids / Volume 24 / Issue 1 / ARTICLES / Micro- and Nanofluid Mechanics

Phys. Fluids 24, 012003 (2012); http://dx.doi.org/10.1063/1.3678308 (10 pages)

Numerical demonstration of the reciprocity among elemental relaxation and driven-flow problems for a rarefied gas in a channel

Shigeru Takata and Masashi Oishi

Department of Mechanical Engineering and Science, Kyoto University, Kyoto 606-8501, Japan

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(Received 8 November 2011; accepted 3 January 2012; published online 26 January 2012; corrected 2 February 2012)

Relaxations from a uniform mass/heat flow and flows driven by an external force/temperature-gradient for a rarefied gas between two parallel plates are studied on the basis of the kinetic theory of gases. By numerical computations of the linearized Bhatnagar–Gross–Krook model of the Boltzmann equation, it is demonstrated that the reciprocity among these elemental flows derived from a general reciprocity theory for time-dependent problems [S. Takata, J. Stat. Phys. 140, 985 (2010)] holds at any time and any Knudsen numbers. Moreover, a propagation of the discontinuity of the velocity distribution function (VDF) in the relaxation problems and that of the derivative discontinuity of the VDF in the driven-flow problems are demonstrated. Their relation is also clarified.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. PROBLEM
  3. RECIPROCITY OF FLUXES
  4. NUMERICAL RESULTS AND DISCUSSIONS
    1. Flux reciprocity
    2. Velocity distribution function
  5. CONCLUSION

EDITORIALLY RELATED

  1. Publisher's Note: “Numerical demonstration of the reciprocity among elemental relaxation and driven-flow problems for a rarefied gas in a channel” [Phys. Fluids 24, 012003 (2012)]
    Shigeru Takata et al.
    Phys. Fluids 24, 029901 (2012)PHFLE6000024000002029901000001

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KEYWORDS, PACS, and IPC

Keywords

Boltzmann equation, channel flow, heat transfer, kinetic theory, Knudsen flow, mass transfer, numerical analysis

PACS

  • 47.45.Ab

    Kinetic theory of gases

  • 51.10.+y

    Kinetic and transport theory of gases

  • 47.60.Dx

    Flows in ducts and channels

  • 02.60.-x

    Numerical approximation and analysis

International Patent Classification (IPC)

  • F28

    Heat exchange in general

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3678308

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    S. K. Loyalka, “Kinetic theory of thermal transpiration and mechanocaloric effect. I,” J. Chem. Phys. 55, 4497 (1971)JCPSA6000055000009004497000001.

    H. Lang, “Second-order slip effects in Poiseuille flow,” Phys. Fluids 19, 366 (1976)PFLDAS000019000003000366000001.


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