Kinetic theory of a dilute gas system under steady heat conduction

Journal of the Physical Society of Japan

Volumn 72, Issue 8, 2003, Pages 1904-1916

  Kim, Hyeon Deuk ^a   Hayakama, Hisao ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

BGK equation; Boltzmann equation; Hard core molecules; Heat conduction; Maxwell molecules; Nonequilibrium steady state; Nonequilibrium thermodynamics

Indexed keywords

ARTICLE; CALCULATION; CHEMICAL REACTION KINETICS; DENSITY; GAS; MATHEMATICAL ANALYSIS; QUALITATIVE ANALYSIS; STEADY STATE; TEMPERATURE DEPENDENCE; THERMAL CONDUCTIVITY; THERMODYNAMICS;

EID: 0242568634     PISSN: 00319015     EISSN: None     Source Type: Journal    
DOI: 10.1143/JPSJ.72.1904     Document Type: Article

References (49)

1. S. Chapman and T. G. Cowling: The Mathematical Theory of Non-uniform Gases (Cambridge University Press, London, 1970) 3rd ed.
2. P. Résibois and M. De Leener: Classical Kinetic Theory of Fluids (Wiley-Interscience, New York, 1977).
3. M. N. Kogan: Rarefied Gas Dynamics (Plenum Press, New York, 1969).
4. J. A. Mclennan: Introduction to Nonequilibrium Statistical Mechanics (Prentice Hall, Englewood Cliffs, New Jersey, 1990). This book can be obtained from http://uw.lehigh.edu/~ljm3/ljm3.html
5. C. Cercignani: Mathematical Methods in Kinetic Theory (Plenum Press, New York, 1990).
6. S. Flügge: Thermodynamics of Gases (Springer-Verlag, Berlin, 1958).
7. J. L. Lebowitz and E. W. Montroll: The Boltzmann equation (Elsevier Science, New York, 1983).
8. E. G. D. Cohen and W. Thirring: The Boltzmann equation: theory and applications (Springer-Verlag, Berlin, 1973).
9. C. Cercignani: The Boltzmann equation and its applications (Springer-Verlag, Berlin, 1988).
10. C. Cercignani: Theory and application of the Bollzmann equation (Chatto and Windus, London, 1975).
11. V. V. Aristov: Direct Method for Solving the Boltzmann equation and Study of Nonequilibrium Flows (Kluwer Academic, Dordrecht, 2001).
12. J. C. Maxwell: Collect. Pap. 2 (1890) 42.
13. J. C. Maxwell: Philos. Trans. R. Soc. 157 (1867) 49.
14. E. Ikenberry and C. Truesdell: J. Ration. Mech. Anal. 5 (1956) 1.
15. D. Burnett: Proc. London Math. Soc. 40 (1935) 382.
16. R. Schamberg: Ph. D thesis, California Institute of Technology, 1947.
17. M. Sh. Shavaliev: J. Appl. Math. Mech. 42 (1978) 698.
18. S. Reinecke and G. M. Kremer: Continuum Mech. Thermodyn. 3 (1991) 155.
19. S. Reinecke and G. M. Kremer: Continuum Mech. Thermodyn. 8 (1996) 121.
20. I. V. Karlin and A. N. Gorban: Ann. Phys. (Leipzig) 11 (2002) 783.
21. C. Cercignani: Univ. California Rep., 1964, No. AS-64-19.
22. P. L. Bhatnagar, E. P. Gross and M. Krook: Phys. Rev. 94 (1954) 511.
23. J. L. Lebowitz: Phys. Rev. 114 (1959) 1192.
24. Y. J. Park and C. S. Kim: J. Kor. Phys. Soc. 29 (1996) 466.
25. F. Bouchut and B. Perthame: J. Stat. Phys.71 (1993) 191.
26. A. Santos, J. J. Brey, C. S. Kim and J. W. Dufty: Phys. Rev. A 39 (1989) 320.
27. C. S. Kim, J. W. Dufty, A. Santos and J. J. Brey: Phys. Rev. A 39 (1989) 328.
28. C. S. Kim, J. W. Dufty, A. Santos and J. J. Brey: Phys. Rev. A 40 (1989) 7165.
29. A. Santos and J. J. Brey: Physica A 174 (1991) 355.
30. J. J. Brey, A. Santos and J. W. Dufty: Phys. Rev. A 36 (1987) 2842.
31. M. Tij and A. Santos: Phys. Fluids 7 (1995) 2858.
32. J. M. Montanero and A. Santos: Physica A 225 (1996) 7.
33. A. Santos: Phys. Rev. E 62 (2000) 6597.
34. J. D. Foch Jr.: Acta Phys. Aust. (1973) Suppl. X, p. 123.
35. K. A. Fiscko and D. R. Chapman: Rarefied Gas Dynamics Mechanics of Nonequilibrium Processes, ed. E. P. Muntz, D. P. Weaver and D. H. Campbell (American Institute of Aeronautics and Astronautics, Washington, D.C., 1989) p. 374.
36. F. E. Lumpkin III and D. R. Chapman: J. Thermophys. Heat Transf. 6 (1992) 419.
37. V. S. Galkin and V. I. Nosik: Izv. Ross. Akad. Nauk. MZhG 3 (1999) 126.
38. J. Popielawski: J. Chem. Phys. 83 (1985) 790.
39. C. S. Wang-Chang and G. E. Uhlenbeck: Studies in Statistical Mechanics, ed. J. de Boer and G. E. Uhlenbeck (North-Holland, Amsterdam, 1970) Vol. V, p. 1.
40. J. Fort and A. S. Cukrowski: Chem. Phys. 222 (1997) 59.
41. Kim H.-D. and H. Hayakawa: Chem. Phys. Lett. 372 (2003) 314.
42. http://ace.phys.h.kyoto-u. ac.jp/~kim/supplement.html
43. S. Chapman: Mem. Proc. Manchester Lit. Philos. Soc. 66 (1922).
44. D. Alonso, R. Artuso, G. Casati and I. Guarneri: Phys. Rev. Lett. 82 (1999) 1859.
45. Y. Oono and M. Paniconi: Prog. Theor. Phys. Suppl. No. 130 (1998) 29.
46. S. Sasa and H. Tasaki: cond-mat/0108365.
47. R. D. Present: Kinetic Theory of Gases (McGraw-Hill, New York, 1958).
48. Kim H.-D. and H. Hayakawa: cond-mat/0203036.
49. Please contact Kim H.-D. by e-mail. We have provided a technical note about our calculation. See also ref. 42.