On competition between modes at the onset of Bénard-marangoni convection in a layer of fluid

ANZIAM Journal

Volumn 43, Issue 3, 2002, Pages 387-395

  Hashim, Ishak ^a  

^a UNIVERSITI KEBANGSAAN MALAYSIA   (Malaysia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0142168625     PISSN: 14461811     EISSN: None     Source Type: Journal    
DOI: 10.1017/s144618110001258x     Document Type: Article

References (18)

1. R. D. Benguria and M. C. Depassier, "On the linear stability theory of Bénard-Marangoni convection", Phys. Fluids A 1 (7) (1989) 1123-1127.
2. S. H. Davis and G. M. Homsy, "Energy stability theory for free surface problems: Buoyancy-thermocapillary layers", J. Fluid Mech. 98 (3) (1980) 527-553.
3. A. A. Golovin, A. A. Nepomnyashchy and L. M. Pismen, "Nonlinear evolution and secondary instabilities of Marangoni convection in a liquid-gas system with deformable interface", J. Fluid Mech. 341 (1997) 317-341.
4. I. Hashim, "Theoretical analysis of the onset of Bénard-Marangoni convection", Ph. D. Thesis, University of Strathclyde, UK, 1998.
5. I. Hashim and S. K. Wilson, "The onset of Bénard-Marangoni convection in a horizontal layer of fluid". Int. J. Engng Sci. 37 (5) (1999) 643-662.
6. D. T. J. Hurle, "Surface aspects of crystal growth from the melt", Adv. in Colloid Interface Sci. 15 (1981) 101-130.
7. D. Johnson and R. Narayanan, "Experimental observation of dynamic mode switching in interfacial-tension-driven convection near a codimension-two point", Phys. Rev. E 54 (4) (1996) 3102-3104.
8. K. C. Mills and B. J. Keene, "Factors affecting variable weld penetration", Int. Materials Rev. 35 (4) (1990) 185-216.
9. D. A. Nield, "Surface tension and buoyancy effects in cellular convection", J. Fluid Mech. 19 (1964) 341-352.
10. S. Ostrach, "Fluid mechanics in crystal growth-The 1982 Freeman Scholar Lecture", J. Fluids Engng 105 (1983) 5-20.
11. J. R. A. Pearson, "On convection cells induced by surface tension", J. Fluid Mech. 4 (1958) 489-500.
12. C. Pérez-García and G. Carneiro, "Linear stability analysis of Bénard-Marangoni convection in fluids with a deformable free surface", Phys. Fluids A 3 (2) (1991) 292-298.
13. M. J. D. Powell, "A hybrid method for nonlinear equations", in Numerical methods for nonlinear algebraic equations (ed. P. Rabinowitz), (Gordon and Breach, London, 1970) 87-114.
14. Lord Rayleigh, "On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side", Phil. Mag. 32 (6) (1916) 529-546.
15. D. Schwabe, "Surface-tension-driven flow in crystal growth melts", Crystals 11 (1988) 75-112.
16. M. Takashima, "Nature of the neutral state in convective instability induced by surface tension and buoyancy", J. Phys. Soc. Japan 28 (4) (1970) 810.
17. S. J. VanHook, M. F. Schatz, W. D. McCormick, J. B. Swift and H. L. Swinney, "Long-wavelength instability in surface-tension-driven Bénard convection", Phys. Rev. Lett. 75 (24) (1995) 4397-4400.
18. J. Zierep and H. Oertel Jr., Convective transport and instability phenomena (G. Braun, Karlsruhe, 1982).