Multiple states, stability and bifurcations of natural convection in a rectangular cavity with partially heated vertical walls

Journal of Fluid Mechanics

Volumn 492, Issue , 2003, Pages 63-89

  Erenburg, V ^a   Gelfgat, A Yu ^a   Kit, E ^a   Bar Yoseph, P Z ^b   Solan, A ^b  

^a TEL AVIV UNIVERSITY   (Israel)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); DAMPING; HEATING; NUMERICAL ANALYSIS; PRANDTL NUMBER;

RECTANGULAR CAVITY;

NATURAL CONVECTION;

BIFURCATION; FLUID FLOW; FLUID MECHANICS; HEATING; MATHEMATICAL MODELING; NATURAL CONVECTION; PRANDTL NUMBER;

EID: 0142246988     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112003005469     Document Type: Article

References (40)

1. BAR-YOSEPH, P. 1994 On multiple flow patterns and vortex breakdown phenomena in confined rotating flows. Comput. Fluid Dyn. J. 3, 273-292.
2. BERGHOLZ, R. F. 1978 Instability of steady natural convection in a vertical fluid layer. J. Fluid Mech. 84, 743-768.
3. BUSSE, F. H. 1967 The stability of finite amplitude cellular convection and its relation to an extremum principle. J. Fluid Mech. 30, 625-649.
4. CHADWICK, M. L., WEBB, B. W. & HEATON, H. S. 1991 Natural convection from two-dimensional discrete heat sources in a rectangular enclosure. Intl J. Heat Mass Transfer 34, 1679-1693.
5. CLIFFE, K. A. & MULLIN, T. 1985 A numerical and experimental study of anomalous modes in the Taylor experiment. J. Fluid Mech. 153, 243-258.
6. COLES, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385-425.
7. CROSS, M. C., DANIELS, P. G., HOHENBERG, P. C. & SIGGIA, E. D. 1983 Phase-winding solutions in a finite container above the convective threshold. J. Fluid Mech. 127, 155-183.
8. DRUMMOND, J. E. & KORPELA, S. A. 1987 Natural convection in a shallow cavity. J. Fluid Mech. 182, 543-564.
9. FREDERICK, R. L. & QUIROZ, F. 2001 On the transition from conduction to convection regime in a cubical enclosure with a partially heated wall. Intl J. Heat Mass Transfer 44, 1699-1709.
10. Fu, W.-S., TSENG, C.-C. & CHEN, Y.-C. 1994 Natural convection in an enclosure with non-uniform wall temperature. Intl J. Heat Mass Transfer 21, 819-828.
11. GELFGAT, A. Yu. 1999 Different modes of Rayleigh-Bénard instability in two- and three-dimensional rectangular enclosures. J. Comput. Phys. 156, 300-324.
12. GELFGAT, A. Yu. 2001 Two- and three-dimensional instabilities of confined flows: numerical study by a global Galerkin method. Comput. Fluid Dyn. J. 9, 437-448.
13. GELFGAT, A., BAR-YOSEPH, P. Z. & SOLAN, A. 1996 Stability of confined swirling flow with and without vortex breakdown. J. Fluid Mech. 311, 1-36.
14. GELFGAT, A. Yu., BAR-YOSEPH, P. Z. & SOLAN, A. 2000 Axisymmetry breaking instabilities of natural convection in a vertical Bridgman growth configurations. J. Cryst. Growth 220, 316-325.
15. GELFGAT, A. Yu., BAR-YOSEPH, P. Z., SOLAN, A. & KOWALFWSKI, T. 1999b An axisymmetry-breaking instability in axially symmetric natural convection. Intl J. Transport Phenomena 1, 173-190.
16. GELFGAT, A. Yu., BAR-YOSEPH, P. Z. & YARIN, A. L. 1997 On oscillatory instability of convective flows at low Prandtl number. J. Fluids Engng 119, 823-830.
17. GELFGAT, A. Yu., BAR-YOSEPH, P. Z. & YARIN, A. L. 1999a Stability of multiple steady states of convection in laterally heated cavities. J. Fluid Mech. 388, 315 334.
18. GELFGAT, A. Yu. & TANASAWA, I. 1994 Numerical analysis of oscillatory instability of buoyancy convection with the Galerkin spectral method. Numer. Heat Transfer A 25, 627 648.
19. HENRY, D. & DIJKSTRA, H. (ed.) 2000 Continuation methods in fluid dynamics. Contributions to the ERCOFTAC/EUROMECH Colloquium 383, Aussois, France, 6-9 September 1998. Notes on Numerical Fluid Mechanics. Vieweg.
20. Ho, C. J & CHANG, J. Y. 1994 A study of natural convection heat tranfer in a vertical rectangular enclosure with two-dimensional discrete heating: effect of aspect ratio. Intl J. Heat Mass Transfer 37, 917 925.
21. KAMOTANI, Y., WENG, F.-B., OSTRACH, S. & PLATT, J. 1994 Oscillatory natural convection of a liquid metal in circular cylinders. J. Heat Transfer 116, 627 632.
22. KELLER, H. B. 1977 Numerical solution of bifurcation and nonlinear eigenvalue problems. In Applications of Bifurcation Theory (ed. P. H. Rabinowitz), pp. 359-384. Academic.
23. KEYHANI, M., PRASAD, V. & COX, R. 1988 An experimental study of natural convection in a vertical cavity with discrete heat sources. J. Heat Transfer 110, 616 624.
24. KHALILOLLAHI, A. & SAMMAKIA, B. 1986 Unsteady natural convection generated by a heated surface within an enclosure. Numer. Heat Transfer 9, 715 730.
25. KITAMURA, K., KOMIYAMA, K. & SAITO, T. 1984 Oscillatory motion of natural convection in rectangular cavity. Bull. JSME 27, 2463 2469.
26. KUHN, D. & OOSTHUIZEN, P. H. 1987 Unsteady natural convection in a partially heated rectangular cavity. J. Heat Transfer 109, 798-801.
27. LAKHAL, E. K., HASNAOUI, M. & VASSEUR, P. 1999 Numerical study of transient natural convection in a cavity heated periodically with different types of excitations. Intl J. Heat Mass Transfer 42, 3927 3941.
28. LAKHAL, E. K., HASNAOUI, M., VASSEUR, P. & BILGEN, E. 1994 Natural convection in a square enclosure heated periodically from part of the bottom wall. Numer. Heat Transfer A 27, 319-333.
29. LARTIGUE, B., LORENTE, S. & BOURRET, B. 2000 Multicellular natural convection in a high aspect ratio cavity: experimental and numerical results. Intl J. Heat Mass Transfer 43, 3157-3170.
30. LEE, Y. & KORPELA, S. A. 1983 Multicellular natural convection in a vertical slot. J. Fluid Mech. 126, 91 121.
31. LOPEZ, J. M., MARQUES, F. & SANCHEZ, J. 2001 Oscillatory modes in an enclosed swirling flow. J. Fluid Mech. 439, 109-129.
32. MÜLLER, G. & OSTROGORSKY, A. 1994. Convection in melt growth. In Handbook of Crystal Growth (ed. D. T. J. Hurle), vol. 2, pp. 711-781. North-Holland.
33. NOVEMBER, M. & NANSTEEL, M. W. 1987 Natural convection in rectangular enclosure heated from below and cooled along one side. Intl J. Heat Mass Transfer 30, 2433 2440.
34. PALLARES, J., GRAU, F. X. & GIRALT, F. 1999 Flow transitions in laminar Rayleigh Bénard convection in a cubical cavity at moderate Rayleigh numbers. Intl J. Heat Mass Transfer 42, 753-769.
35. POULIKAKOS, D. 1985 Natural convection in a confined fluid-filled space driven by a single vertical wall with warm and cold regions. J. Heat Transfer 107, 867 876.
36. SCHÖPF, W. & STILLER, O. 1997 Three-dimensional patters in a transient, stratified intrusion flow. Phys. Rev. Lett. 79, 4373-4376.
37. SCHRAUF, G. 1986. The first instability in spherical Couette Taylor flow. J. Fluid Mech. 166, 287-303.
38. SELVER, R., KAMOTANI, Y. & OSTRACH, S. 1998 Natural convection of a liquid metal in vertical cylinders heated locally from the side. J. Heat Transfer 120, 108-114.
39. SEZAI, I. & MOHAMAD, A. A. 2000 Natural convection from a discrete heat source on the bottom of a horizontal enclosure. Intl J. Heat Mass Transfer 43, 2257 2266.
40. TSITVERBLIT, N. & KIT, E. 1993 The multiplicity of steady flows in confined double-diffusive convection with lateral heating. Phys. Fluids A 5, 1062-1064.