Numerical study of the influence of gravity on the heat conductivity on the basis of kinetic theory

Physics of Fluids

Volumn 11, Issue 11, 1999, Pages 3553-3559

  Doi, Toshiyuki ^a   Santos, Andrés ^b   Tij, Mohamed ^c  

^a TOTTORI UNIVERSITY   (Japan)

^b UNIVERSITY OF EXTREMADURA   (Spain)

^c MOULAY ISMAIL UNIVERSITY   (Morocco)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000669818     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.870212     Document Type: Article

References (39)

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14. This discovery is a consequence of the extension of the following works: Y. Sone and M. Wakabayashi, "Flow induced by nonlinear thermal stress in a rarefied gas," in Proceedings of Symposium on Mechanics of Space Flight (Institute of Space Sciences, Tokyo, 1988), p. 14 (in Japanese), quoted in Ref. 11; A. V. Bobylev, "Quasistationary hydrodynamics for the Boltzmann equation," J. Stat. Phys. 80, 1063 (1995).
15. This discovery is a consequence of the extension of the following works: Y. Sone and M. Wakabayashi, "Flow induced by nonlinear thermal stress in a rarefied gas," in Proceedings of Symposium on Mechanics of Space Flight (Institute of Space Sciences, Tokyo, 1988), p. 14 (in Japanese), quoted in Ref. 11; A. V. Bobylev, "Quasistationary hydrodynamics for the Boltzmann equation," J. Stat. Phys. 80, 1063 (1995).
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23. M. Tij, V. Garzó, and A. Santos, "On the influence of gravity on the thermal conductivity," in Rarefied Gas Dynamics, edited by R. Gatignol (Cépaduès, Toulouse, 1999) (to be published).
24. See, for instance, P. Biscari and C. Cercignani, "Stress and heat flux in non-inertial reference frames," Continuum Mech. Thermodyn. 9, 1 (1997); F. M. Sharipov and G. M. Kremer, "Heat conduction through a rarefied gas between two rotating cylinders at small temperature difference," Z. Angew. Math. Phys. 46, 680 (1995), and references therein.
25. See, for instance, P. Biscari and C. Cercignani, "Stress and heat flux in non-inertial reference frames," Continuum Mech. Thermodyn. 9, 1 (1997); F. M. Sharipov and G. M. Kremer, "Heat conduction through a rarefied gas between two rotating cylinders at small temperature difference," Z. Angew. Math. Phys. 46, 680 (1995), and references therein.
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27. P. L. Bhatnagar, E. P. Gross, and M. Krook, "A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems," Phys. Rev. 94, 511 (1954); P. Welander, "On the temperature jump in a rarefied gas," Ark. Fys. 7, 507 (1954).
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29. Y. Sone and K. Yamamoto, "Flow of rarefied gas over plane wall," J. Phys. Soc. Jpn. 29, 495 (1970); Y. Sone and Y. Onishi, "Flow of rarefied gas over plane wall," ibid. 47, 672 (1979).
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31. To be precise, mean free path in the equilibrium state at rest with density ρ and temperature T.
32. C. K. Chu, "Kinetic-theoretic description of the formation of a shock wave," Phys. Fluids 8, 12 (1965).
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34. Y. Sone, K. Aoki, H. Sugimoto, and H. Motohashi, "The Bénard problem of rarefied gas dynamics," in Ref. 17, p. 135.
35. Y. Sone, K. Aoki, and H. Sugimoto, "The Bénard problem for a rarefied gas: Formation of steady flow patterns and stability of array of rolls," Phys. Fluids 9, 3898 (1997).
36. C. S. Kim, J. W. Dufty, A. Santos, and J. J. Brey, "Hilbert-class or 'normal' solutions for stationary heat flow," Phys. Rev. A 39, 328 (1989).
37. The success of this exact analysis is essentially due to the fact that it refers to a spatially one-dimensional situation. Incidentally, some of the results (constant pressure and linear profile of temperature in x, etc.) have been obtained by an asymptotic analysis for small Knudsen numbers in Ref. 23.
38. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978), Chap. 8.
39. [0,2] for g̃>0, while the opposite happens for g̃<0. From all of this, the choice (31) seems to be a proper one.