Three-dimensional bifurcations of a two-phase Rayleigh-Benard problem in a cylinder

International Journal of Heat and Mass Transfer

Volumn 44, Issue 10, 2001, Pages 1823-1836

  Lan, C W ^a   Wang, C H ^a  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

BUOYANCY; COMPUTATIONAL METHODS; INTERFACES (MATERIALS); PRANDTL NUMBER; TWO PHASE FLOW;

BUOYANCY FLOW; RAYLEIGH-BENARD THEORY;

HEAT CONVECTION;

BIFURCATION; BUOYANCY; CONVECTION; CYLINDER; HEAT TRANSFER; MASS TRANSFER; PRANDTL NUMBER;

EID: 0034744594     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0017-9310(00)00248-9     Document Type: Article

References (27)

1. J. Pannu, G. Joglekar, P.A. Rice, Natural convection to cylinders of phase change material used for thermal storage, AIChE Symposium Series (1980) 47-55.
2. H.W. Hale, R. Viskanta, Solid-liquid phase change heat transfer and interface motion in materials cooled from above and below, Int. J. Heat Mass Transfer 23 (1980) 283-292.
3. G. Muller, A. Ostrogorsky, Convection in melt growth, in: D.T.J. Hurle (Ed.), Handbook of Crystal Growth, North-Holland, Amsterdam, 1993, pp. 709-819.
4. D.T.J. Hurle, E. Jakeman, Introduction to the techniques of crystal growth, PhysicoChem. Hydrodyn. 2 (1981) 237-244.
5. D.T.J. Hurle, E. Jakeman, A.A. Wheeler, Hydrodynamic stability of the melt during solidification of a binary alloy, Phys. Fluids 23 (1983) 624-627.
6. S.F. Liang, A. Vidal, A. Acrivos, Buoyancy-driven convection in cylinder geometries, J. Fluid Mech. 86 (1969) 239-256.
7. G.S. Charlson, R.L. Sani, Thermoconvective instability in a bounded cylindrical fluid layer, Int. J. Heat Mass Transfer 13 (1970) 1479-1496.
8. G.S. Charlson, R.L. Sani, Finite amplitude axisymmetric thermoconvective flow in a bounded cylindrical layer of fluid, Int. J. Heat Mass Transfer 14 (1971) 2157-2160.
9. Y. Yamaguchi, C.J. Chang, R.A. Rrown, Multiple buoyancy-driven flows in vertical cylinder heated from below, Philos. Trans. R. Soc. Lond. A 312 (1984) 519-552.
10. G. Muller, G. Neumann, W. Weber, Natural convection in vertical Bridgman configurations, J. Crystal Growth 70 (1984) 78-93.
11. G. Neumann, Three-dimensional numerical simulation of buoyancy-driven convection in vertical cylinders heated from below, J. Fluid Mech. 214 (1990) 559-678.
12. G.R. Hardin, R.L. Sani, Buoyancy-driven instability in a vertical cylinder: binary fluids with Soret effect. Part II: weakly non-linear solutions, Int. J. Numer. Methods Fluids 17 (1993) 755-786.
13. C. Wagner, R.C. Friedrich, R. Narayanan, Comments on the numerical investigation of Rayleigh and Marangoni convection in a cylinder, Phys. Fluids 6 (1994) 1425-1433.
14. M. Wanschura, H.C. Kuhlmann, H.J. Rath, Three-dimensional instability of axisymmetric buoyant convection in cylinders heated from below, J. Fluid Mech. 326 (1996) 399-415.
15. C.W. Lan, M.C. Liang, M.K. Chen, Stability and bifurcation analyses of a two-phase Rayleigh Benard problem in a cavity, Phys. Fluids 10 (1998) 1329-1343.
16. C.J. Chang, R.A. Brown, Natural convection in steady solidification: finite element analysis of a two-phase Rayleigh-Benard problem, J. Comput. Phys. 53 (1984) 1-26.
17. M.C. Liang, C.W. Lan, A finite-volume/Newton method for a two-phase flow problem using primitive variables and collocated grids, J. Comput. Phys. 127 (1996) 330-345.
18. S.H. Davis, U. Muller, C. Dietsche, Pattern selection in single-component systems coupling Benard convection and solidification, J. Fluid Mech. 144 (1984) 133-151.
19. L.D. Landau, E.M. Lifshitz, Fluid Mechanics, second ed., vol. 6, Pergamon Press, Elmsford, 1987, p. 217.
20. C.W. Lan, M.C. Liang, Multigrid methods for incompressible heat flow problems with an unknown interface, J. Comput. Phys. 152 (1999) 55-77.
21. H.B. Keller, Numerical solution of bifurcation and nonlinear eigenvalue problems, in: P.H. Rabinowi (Ed.), Applications of Bifurcation Theory, Academic Press, New York, 1977, pp. 359-384.
22. Y. Saad, M.H. Schultz, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput. 7 (1986) 856-869.
23. R. Seydel, Numerical computation of branch points in nonlinear equations, Numer. Math. 33 (1979) 339-352.
24. Fluent UNS 5.0 User Manual, Fluent Inc., 1999.
25. C.W. Lan, M.C. Liang, Three-dimensional simulation of vertical zone-melting crystal growth: from symmetry breaking to multiple states, J. Crystal Growth 208 (2000) 327-340.
26. G.B. McFadden, S.R. Coriell, Solutal convection during directional solidification, in: Proceedings of the First National Fluid Dynamics Congress, Cincinnati, OH, 25-28 July 1988.
27. M.D. Impey, D.S. Riley, A.A. Wheeler, K.H. Winters, Bifurcation analysis of solutal convection during directional solidification, Phys. Fluids A 3 (1991) 535-550.