Oscillatory Marangoni convection in a conducting fluid layer with a deformable free surface in the presence of a vertical magnetic field

Acta Mechanica

Volumn 164, Issue 3-4, 2003, Pages 199-215

  Hashim, I ^a   Arifin, N M ^a  

^a UNIVERSITI KEBANGSAAN MALAYSIA   (Malaysia)

Author keywords

[No Author keywords available]

Indexed keywords

CONDUCTIVE MATERIALS; DEFORMATION; ELECTRIC CONDUCTIVITY; LINEAR SYSTEMS; MAGNETIC FIELD EFFECTS; MATHEMATICAL MODELS; PRANDTL NUMBER; SURFACES; SYSTEM STABILITY;

CONDUCTING FLUID LAYER; CRITICAL WAVENUMBER; LINEAR STABILITY THEORY; OSCILLATORY MARANGONI CONVECTION;

FLUID DYNAMICS;

EID: 0142247352     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00707-003-0008-7     Document Type: Article

References (26)

1. Bénard, H.: Les tourbillons cellulaires dans une nappe liquide. Rev. Gen. Sci. Pures Appl. 11, 1261-1271 (1900).
2. Rayleigh, L.: On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side. Phil. Mag. 32, 529-546 (1916).
3. Pearson, J. R. A.: On convection cells induced by surface tension. J. Fluid Mech. 4, 489-500 (1985).
4. Schwabe, D.: Marangoni effects in crystal growth melts. PhysicoChem. Hydrodyn. 2, 263-280 (1981).
5. Scriven, L. E., Sternling, C.V.: On cellular convection driven by surface-tension gradients: effects of mean surface tension and surface viscosity. J. Fluid Mech. 19, 321-340 (1964).
6. Smith, K. A.: On convective instability induced by surface-tension gradients. J. Fluid Mech. 24, 401-414 (1966).
7. Takashima, M.: Nature of the neutral state in convective instability induced by surface tension and buoyancy. J. Phys. Soc. Japan 28, 810 (1970).
8. Vidal, A., Acrivos, A.: Nature of the neutral state in surface-tension driven convection. Phys. Fluids 9, 615-616 (1966).
9. Takashima, M.: Surface tension driven instability in a horizontal liquid layer with a deformable free surface. II. Overstability. J. Phys. Soc. Japan 50, 2751-2756 (1981).
10. Takashima, M.: Surface tension driven instability in a horizontal liquid layer with a deformable free surface. I. Stationary convection. J. Phys. Soc. Japan 50, 2745-2750 (1981).
11. Nield, D. A.: Effects of magnetic field on streamlines in Bénard convection cells induced by surface tension and buoyancy. Z. Angew. Math. Phys. 17, 340-342 (1966).
12. Maekawa, T., Tanasawa, I.: Effect of magnetic field on onset of Marangoni convection. Int. J. Heat Mass Transfer 31, 285-293 (1988).
13. Wilson, S. K.: The effect of a uniform magnetic field on the onset of Marangoni convection in a layer of conducting fluid. Q. J. Mech. Appl. Math. 46, 211-248 (1993).
14. Wilson, S. K.: The effect of a uniform magnetic field on the onset of oscillatory Marangoni convection in a layer of molten silicon. Microgravity Sci. Tech. 7, 228-233 (1994).
15. Wilson, S. K.: The effect of a uniform magnetic field on the onset of steady Marangoni convection in a layer of conducting fluid with a prescribed heat flux at its lower boundary. Phys. Fluids 6, 3591-3600 (1994).
16. Kaddame, A., Lebon, G.: Overstability in Marangoni convection of an electrically conducting fluid in presence of an external magnetic field. Microgravity Quart. 3, 1-6 (1993).
17. Hashim, I., Wilson, S. K.: The effect of a uniform vertical magnetic field on the onset of oscillatory Marangoni convection in a horizontal layer of conducting fluid. Acta Mech. 132, 129-146 (1999).
18. Chandrasekhar, S.: Hydrodynamic and hydromagnetic stability. Oxford: Oxford University Press 1961.
19. Takashima, M., Hirasawa, M., Nozaki, H.: Buoyancy driven instability in a horizontal layer of electrically conducting fluid in the presence of a vertical magnetic field. Int. J. Heat Mass Transf 42, 1689-1706 (1999).
20. Fortran Library Manual Mark 12. Oxford: The Numerical Algorithms Group 1987.
21. Palmer, H. J., Berg, J. C.: Hydrodynamic stability of surfactant solutions heated from below. J. Fluid Mech. 51, 385-402 (1972).
22. Wilson, S. K.: The effect of a uniform magnetic field on the onset of steady Bénard-Marangoni convection in a layer of conducting fluid. J. Engng. Math. 27, 161-188 (1993).
23. Pérez-Garcia, C., Carneiro, G.: Linear stability analysis of Bénard-Marangoni convection in fluids with a deformable free surface. Phys. Fluids A 3, 292-298 (1991).
24. Skarda, J. R. L., McCaughan, F. E.: Exact solution to stationary onset of convection due to surface tension variation in a multicomponent fluid layer with interfacial deformation. Int. J. Heat Mass Transf 42, 2387-2398 (1999).
25. Hashim, I.: On competition between modes at the onset of Bénard-Marangoni convection in a layer of fluid. Austral. & New Zealand Indust. Appl. Math. J. 43, 387-395 (2001).
26. Baumgart, J., Gewald, R., Rupp, R., Stierlen, J., Muller, G.: The use of magnetic fields and microgravity in melt growth of semiconductors: A comparative study. Proc. VIIth European Symp. on Materials and Fluid Sciences in Microgravity, ESA SP-295, 47-58 (1990).