Inappropriateness of the heat‐conduction equation for description of a temperature field of a stationary gas in the continuum limit: Examination by asymptotic analysis and numerical computation of the Boltzmann equation
作者:
Yoshio Sone,
Kazuo Aoki,
Shigeru Takata,
Hiroshi Sugimoto,
A. V. Bobylev,
期刊:
Physics of Fluids
(AIP Available online 1996)
卷期:
Volume 8,
issue 2
页码: 628-638
ISSN:1070-6631
年代: 1996
DOI:10.1063/1.868846
出版商: AIP
数据来源: AIP
摘要:
It is shown analytically and numerically on the basis of the kinetic theory that the heat‐conduction equation is not suitable for describing the temperature field of a gas in the continuum limit around bodies at rest in a closed domain or in an infinite domain without flow at infinity, where the flow vanishes in this limit. The behavior of the temperature field is first discussed by asymptotic analysis of the time‐independent boundary‐value problem of the Boltzmann equation for small Knudsen numbers. Then, simple examples are studied numerically: as the Knudsen number of the system approaches zero, the temperature field obtained by the kinetic equation approaches that obtained by the asymptotic theory and not that of the heat‐conduction equation, although the velocity of the gas vanishes. ©1996 American Institute of Physics.
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