Demonstration of a rarefied gas flow induced near the edge of a uniformly heated plate

Physics of Fluids

Volumn 9, Issue 11, 1997, Pages 3530-3534

  Sone, Yoshio ^a   Yoshimoto, Minoru ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001524624     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869461     Document Type: Article

References (33)

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7. M. Knudsen, "Eine Revision der Gleichgewichtsbedingung der Gase. Thermische Molekularströmung," Ann. Phys. (Leipzig) 31, 205 (1910).
8. M. Knudsen, "Thermischer Molekulardruck der Gase in Röhren," Ann. Phys. (Leipzig) 33, 1435 (1910).
9. Y. Sone and K. Yamamoto, "Flow of rarefied gas through a circular pipe," Phys. Fluids 111, 1672 (1969); Erratum: Phys. Fluids 12, 2301 (1970).
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12. S. K. Loyalka, "Comments on Poiseuille flow and thermal creep of a rarefied gas between parallel plates," Phys. Fluids 17, 1053 (1974).
13. Y. Sone and E. Itakura, "Analysis of Poiseuille and thermal transpiration flows for arbitrary Kudsen numbers by a modified Knudsen number expansion method and their data use," J. Vac. Soc. Jpn. 38, 92 (1990) (in Japanese).
14. T. Ohwada, Y. Sone, and K. Aoki, "Numerical analysis of the Poiseuille and thermal transpiration flows between two parallel plates on the basic of the Boltzmann equation for hard-sphere molecules," Phys. Fluids A 1, 2042 (1989); Erratum: Phys. Fluids A 2, 639 (1990).
15. Y. Sone and K. Aoki, Molecular Gas Dynamics (Asakura, Tokyo, 1994) (in Japanese).
16. Y. Sone, "Flow induced by thermal stress in rarefied gas," Phys. Fluids 15, 1418 (1973).
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18. K. Aoki, Y. Sone, and T. Yano, "Numerical analysis of flow induced in a rarefied gas between noncoaxial cylinder with different temperatures for entire range of the Knudsen number," Phys, Fluids A 1, 363 (1989).
19. M. N. Kogan, "Kinetic theory in aerothermodynamics," Prog. Aerospace Sci. 29, 271 (1992).
20. K. Aoki, Y. Sone, and N. Masukawa, "A rarefied gas flow induced by a temperature field," in Rarefied Gas Dynamics, edited by J. Harvey and G. Lord (Oxford University Press, Oxford, 1995), Vol. I, p. 35.
21. Y. Sone, K. Aoki, S. Takata, H. Sugimoto, and A. V. Bobylev, "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," Phys. Fluids A 8, 628 (1996).
22. K. Aoki, Y. Sone, and Y. Waniguchi, "A rarefied gas flow induced by a temperature field: Numerical analysis of the flow between two coaxial elliptic cylinders with different uniform temperatures," Comput. Math. Appl. (to be published).
23. G. A. Bird, Molecular Gas Dynamics (Oxford University Press, Oxford, 1976).
24. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford University Press, New York, 1994).
25. In the present computation, the quarter domain is divided into 80×80 cells, and 1,280,000 particles are put in the quarter domain (200 particles per cell on the average).
26. The flow cannot be obtained simply by reversing the direction of the flow in Ref. 22, since tne problem is nonlinear.
27. The flow vanishes in the free molecular case Kn = ∞ from the general theorem in Y. Sone, "Highly rarefied gas around a group of bodies with various temperature distributions. II. Arbitrary temperature variation," J. Méc. Théor. Appl. 4, 1 (1985).
28. Y. Sone, "Asymptotic theory of flow of rarefied gas over a smooth boundary I," in Rarefied Gas Dynamics, edited by L. Trilling and H. Y. Wachman (Academic, New York, 1969), Vol. 1, p. 243.
29. Y. Sone, "Asymptotic theory of flow of rarefied gas over a smooth boundary II," in Rarefied Gas Dynamics, edited by by D. Dini (Editrice Tecnico Scientifica, Pisa, 1971), Vol. 2, p. 737.
30. Y. Sone, "Asymptotic theory of a steady flow of a rarefied gas past bodies for small Knudsen numbers," in Advances in Kinetic Theory and Continuum Mechanics, edited by R. Gatignol and Soubbaramayer (Springer-Verlag, Berlin, 1991), p. 19.
31. Near the corners of the vessel, the gas is stagnant and at nearly uniform temperature. Thus, important singular effects are not expected there.
32. The thermal stress slip flow (Ref. 16) of the second order of the Knudsen number is a similar circulating flow, including its direction, to the nonlinear thermal stress flow.
33. m, although the temperature field of a stationary gas in the continuum limit was recently reported (Ref. 21) not correctly to be described by the heat-conduction equation.