Heat transfer and convection onset in a compressible fluid: [Formula Presented] near the critical point

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 63, Issue 5, 2001, Pages

  Kogan, Andrei B ^a   Meyer, Horst ^a  

^a DUKE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85035247349     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.63.056310     Document Type: Article

References (54)

1. D. J. Tritton, Physical Fluid Dynamics (Oxford Science, Oxford, 1988), Section 14.6 and Appendix.
2. A. Schlueter, D. Lortz, and F. Busse, J. Fluid Mech. 23, 129 (1965).
3. G. Ahlers, M. Cross, P. Hohenberg, and S. Safran, J. Fluid Mech. 110, 297 (1982).
4. S. Gauthier, T. Desmarais, and G. Iooss, Europhys. Lett. 10, 543 (1989).
5. E. A. Spiegel, Annu. Rev. Astron. Astrophys. 9, 323 (1971).
6. X. Chavanne, Proceedings LT21, Czech. J. Phys. 46 (Suppl S1), 91 (1996).
7. Sh. Ashkenazi and V. Steinberg, Phys. Rev. Lett. 83, 3641 (1999).
8. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics: Vol. 6 Fluid Mechanics (Pergamon, Oxford, 1959).
9. M. Gitterman and V. Steinberg, Vys. Temp. 8, 799 (1970) [High Temp. USSR 8, 754 (1970)].
10. M. Gitterman and V. Steinberg, Prikl Mat. Mekh. 34, 325 (1970) [J. Appl. Math. Mech. USSR 34, 305 (1971)].
11. M. Gitterman, Rev. Mod. Phys. 50, 85 (1978).
12. P. Carlès and B. Ugurtas, Physica D 126, 69 (1999).
13. A. B. Kogan and H. Meyer, J. Low Temp. Phys. 112, 419 (1998). Here the listing of (Formula presented) was accidentally omitted, but has been presented in the Ph.D. thesis by A. B. Kogan.
14. A. B. Kogan, Ph.D. thesis, Duke University, 2000 (unpublished), available as a pdf document.
15. F. Zhong and H. Meyer, Phys. Rev. E 51, 3223 (1995).
16. M. Assenheimer and V. Steinberg, Phys. Rev. Lett. 70, 3888 (1993).
17. Sh. Ashkenazi, Ph.D. thesis, Weizmann Institute of Science, Rehovot, Israel, 1997 (unpublished).
18. X. Chavanne, Phys. Rev. Lett. 79, 3648 (1997).
19. X. Chavanne, Ph.D. thesis, Université Joseph Fourier, Grenoble, Oct. 1997 (unpublished).
20. J. J. Niemela, L. Skrbek, K. R. Sreenivasan, and R. J. Donnelly, Nature (London) 404, 837 (2000).
21. X. Xu, K. M. S. Bajaj, and G. Ahlers, Phys. Rev. Lett. 84, 4357 (2000).
22. S. Grossmann and D. Lohse, J. Fluid Mech. 407, 27 (2000).
23. A. Kogan, D. Murphy, and H. Meyer, in NASA Document D-18925, 2000, p. 197.
24. A. Kogan, D. Murphy, and H. Meyer, Phys. Rev. Lett. 82, 4635 (1999).
25. A. Kogan, D. Murphy, and H. Meyer, Physica B 284, 208 (2000).
26. S. Amiroudine, P. Bontoux, and B. Zappoli (private communication, 1999).
27. S. Amiroudine, A. B. Kogan, H. Meyer, and B. Zappoli, Proceedings of the 20th International Congress of Theoretical and Applied Mechanics, ICTAM 2000, Chicago, edited by J. W. Phillips (unpublished).
28. A. Onuki and R. A. Ferrell, Physica A 164, 245 (1990).
29. C. Pittman, L. H. Cohen, and H. Meyer, J. Low Temp. Phys. 46, 155 (1982).
30. R. P. Behringer, A. Onuki, and H. Meyer, J. Low Temp. Phys. 81, 71 (1990).
31. In the paper by Carlès and Ugurtas 12, Fig. 2 shows the predicted vertical gradient (Formula presented) for (Formula presented) as a function of (Formula presented) for various values of h, and illustrates how the shape of the convection onset curve changes with h. For (Formula presented) the Rayleigh regime is no longer observable for (Formula presented) this is for (Formula presented) These plots are very similar to those for (Formula presented) we have produced during the design stage of our experiment.
32. C. C. Agosta, S. Wang, L. H. Cohen, and H. Meyer, J. Low Temp. Phys. 67, 237 (1987).
33. S. Wang, C. Howald, and H. Meyer, J. Low Temp. Phys. 79, 151 (1990).
34. C. Pittman, T. Doiron, and H. Meyer, Phys. Rev. B 20, 3678 (1979).
35. D. Murphy, J. Low Temp. Phys. 114, 389 (1999).
36. G. Ahlers has pointed out that in convective turbulence, where the temperature profile through the fluid layer is stronly nonlinear, the assumption of parallel heat flow though the walls and the fluid is not correct. However his numerical simulations using the thermal conductivity of (Formula presented) the aspect ratio of the cell and the conductance of the stainless steel wall indicate that for our high aspect ratio, the assumption mentioned above appears to introduce only a negligible error. We are very much obliged to Ahlers for attracting our attention to this point and for his calculation.
37. J. M. Pfotenhauer and R. J. Donnelly, Adv. Heat Transfer 17, 65 (1985).
38. J. S. Olafsen and R. P. Behringer, J. Low Temp. Phys. 106, 673 (1997).
39. J. A. Lipa and Q. Li, Proceedings LT21, Czech. J. Phys. 46 (Suppl S1), 185 (1996).
40. A. Patashinski and A. Burin, NASA Document No. D-18925, 2000, p. 301.
41. D. Murphy and H. Meyer, J. Low Temp. Phys. 97, 509 (1994).
42. R. Behringer and G. Ahlers, J. Fluid Mech. 125, 219 (1982).
43. C. W. Meyer, G. Ahlers, and D. Cannell, Phys. Rev. A 44, 2514 (1991).
44. A. L. Woodcraft, P. G. J. Lucas, R. G. Matley, and W. Y. T. Wong, J. Low Temp. Phys. 114, 109 (1999).
45. V. Croquette, Contemp. Phys. 30, 153 (1989).
46. S. Grossmann and D. Lohse, Phys. Rev. Lett. 86, 3316 (2001).
47. R. P. Behringer and G. Ahlers, Phys. Lett. A 62, 329 (1977).
48. R. Behringer, Rev. Mod. Phys. 57, 657 (1985).
49. S. Amiroudine, P. Bontoux, P. Larroude, B. Gilly, and B. Zappoli, J. Fluid Mech. (to be published).
50. L. H. Cohen, M. Dingus, and H. Meyer, J. Low Temp. Phys. 61, 79 (1985).
51. F. Zhong and H. Meyer, J. Low Temp. Phys. 114, 231 (1999).
52. Y.-I. Miura, H. Meyer, and A. Ikushima, J. Low Temp. Phys. 55, 247 (1984).
53. F. Zhong, A. B. Kogan, and H. Meyer, J. Low Temp. Phys. 108, 161 (1997).
54. G. R. Brown and H. Meyer, Phys. Rev. A 6, 364 (1972).