Exact analytical results for the thermosolutal MHD Marangoni boundary layers

International Journal of Thermal Sciences

Volumn 47, Issue 7, 2008, Pages 848-857

  Magyari, E ^a   Chamkha, A J ^b  

^a ETH ZURICH   (Switzerland)

^b MANUFACTURING ENGINEERING DEPARTMENT   (Kuwait)

Author keywords

Boundary layers; Dual solutions; MHD; Similarity solutions; Thermosolutal Marangoni convection

Indexed keywords

APPROXIMATION THEORY; BOUNDARY LAYERS; FUNCTION EVALUATION; MASS TRANSFER; QUADRATIC PROGRAMMING; TEMPERATURE MEASUREMENT;

DUAL SOLUTIONS; QUADRATIC FUNCTIONS; SIMILARITY SOLUTIONS; THERMOSOLUTAL MARANGONI CONVECTION;

MAGNETOHYDRODYNAMICS;

EID: 42949112546     PISSN: 12900729     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijthermalsci.2007.07.004     Document Type: Article

References (38)

1. L.G. Napolitano, Microgravity Fluid Dynamics, in: 2nd Levitch Conference, Washington, 1978
2. L.G. Napolitano, Marangoni boundary layers, in: Proc. 3rd European Symposium on Material Science in Space, Grenoble, ESA SP-142, June 1979
3. Christopher D.M., and Wang B. Prandtl number effects for Marangoni convection over a flat surface. Int. J. Thermal Sci. 40 (2001) 564-570
4. Eyer A., Leist H., and Nitsche R. Floating zone growth of silicon under microgravity in sounding rocket. J. Crystal Growth 71 (1985) 173-182
5. Straub J. The role of surface tension for two phase heat and mass transfer in the absence of gravity. Exp. Thermal Fluid Sci. 9 (1994) 253-273
6. Napolitano L.G. Surface and buoyancy driven free convection. Acta Astronautica 9 (1982) 199-215
7. Napolitano L.G., and Golia C. Coupled Marangoni boundary layers. Acta Astronautica 8 (1981) 417-434
8. Napolitano L.G., and Russo G. Similar axially symmetric Marangoni boundary layers. Acta Astronautica 11 (1984) 189-198
9. Golia C., and Viviani A. Marangoni buoyant boundary layers. L'Aerotechnica Missili e Spazio 64 (1985) 29-35
10. Golia C., and Viviani A. Non isobaric boundary layers related to Marangoni flows. Meccanica 21 (1986) 200-204
11. Napolitano L.G., Carlomagno G.M., and Vigo P. New classes of similar solutions for laminar free convection problems. Int. J. Heat Mass Transfer 20 (1977) 215-226
12. Pop I., Postelnicu A., and Groşan T. Thermosolutal Marangoni forced convection boundary layers. Meccanica 36 (2001) 555-571
13. Arafune K., and Hirarta A. Interactive solutal and thermal Marangoni convection in a rectangular open boat. Numer. Heat Transfer Part A 34 (1998) 421-429
14. Croll A., Muller-Sebert W., and Nitsche R. The critical Marangoni number for the onset of time-dependent convection in silicon. Mater. Res. Bull. 24 (1989) 995-1004
15. Okano Y., Itoh M., and Hirata A. Natural and Marangoni convections in a two-dimensional rectangular open boat. J. Chem. Engrg. Japan 22 (1989) 275-281
16. Arafune K., Sugiura M., and Hirata A. Investigation of thermal Marangoni convection in low and high Prandtl number fluids. J. Chem. Engrg. Japan 32 (1999) 104-109
17. Arafune K., and Hirata A. Thermal and solutal Marangoni convection in In-Ga-Sb system. J. Crystal Growth 197 (1999) 811-817
18. Slavtchev S., and Miladinova S. Thermocapillary flow in a liquid layer at minimum in surface tension. Acta Mechanica 127 (1998) 209-224
19. Schwabe D., and Metzger J. Coupling and separation of buoyant and thermocapillary convection. J. Crystal Growth 97 (1989) 23-33
20. Napolitano L.G., Viviani A., and Savino R. Double-diffusive boundary layers along vertical free surfaces. Int. J. Heat Mass Transfer 35 (1992) 1003-1025
21. Al-Mudhaf A., and Chamkha A.J. Similarity solutions for MHD thermosolutal Marangoni convection over a flat surface in the presence of heat generation or absorption effects. Heat Mass Transfer 42 (2005) 112-121
22. Magyari E., and Chamkha A.J. Exact analytical solutions for thermosolutal Marangoni convection in the presence of heat and mass generation or consumption. Heat Mass Transfer 43 (2007) 965-974
23. Christopher D., and Wang B. Marangoni convection around a bubble in microgravity, heat transfer. In: Lee J.S. (Ed). Proceedings of the 11th international Heat Transfer Conference vol. 3 (1998), Taylor & Francis, Levittown 486-494
24. M. Hainke, J. Friedrich, D. Vizman, G. Müller, MHD effects in semiconductor crystal growth and alloy solidification, in: Proceedings of the International Scientific Colloquium, Modelling for Electromagnetic Processing, 2003, pp. 73-78
25. Baumgartl J., Budweiser W., Müller G., and Neumann G. Studies of buoyancy driven convection in a vertical cylinder with parabolic temperature profile. J. Crystal Growth 97 (1989) 9-17
26. J. Baumgartl, M. Gewald, R. Rupp, J. Stierlein, G. Müller, The use of magnetic fields and microgravity in melt growth of semiconductors: A comparative study, in: Proceedings VII European Symposium on Materials and Fluid Sciences under Microgravity, ESA SP-295, pp. 47-58
27. Baumgartl J., and Müller G. Calculation of the effects of magnetic field damping on fluid flow-comparison of magnetohydrodynamic models of different complexity. Microgravity Quarterly 2 (1992) 197
28. B. Fischer, J. Friedrich, C. Kupfer, D. Vizman, G. Müller, Experimental and numerical analysis of the influence of rotating magnetic fields on heat transport in Rayleigh Benard configurations, in: Proc. 3rd Int. Conf. on Transfer Phenomena in Magnetohydro-Dynamic & Electroconducting Flows, 1997, pp. 337-342
29. Fischer B., Friedrich J., Kupfer C., Müller G., and Vizman D. Experimental and numerical analysis of the influence of a rotating magnetic field on convection in Rayleigh Benard configurations. Transfer Phenomena in Magnetohydrodynamics and Electroconducting Flows (1999), Kluwer, Dordrecht 279-294
30. Friedrich J., Lee Y., Fischer B., Kupfer C., Vizman D., and Müller G. Experimental and numerical study of Rayleigh-Benard convection affected by a rotating magnetic field. Phys. Fluids 11 (1999) 853-861
31. B. Fischer, J. Friedrich, U. Hilburger, G. Müller, Systematic study of buoyant flows in vertical melt cylinders under the influence of rotating magnetic fields, in: Proc. EPM2000, 2000, pp. 497-502
32. Witkowski L.M., and Walker J.S. Flow driven by Marangoni convection and rotating magnetic field in a floating-zone configuration. Magnetohydrodynamics 37 (2001) 112-118
33. Priede J., Gerbeth G., and Thess A. Theoretical Aspects of Thermocapillary Convection in Liquid Metals under Magnetic Fields Influence. Electromagnetic Processing of Materials vol. 94 (1994), Nagoya, Japan und als Publ. bei ISIJ Japan
34. J. Priede, G. Gerbeth, A. Thess, Thermocapillary instabilities in liquid metals: Hartmann number versus Prandtl-number, Magnetohydrodynamics, in: Proc. Energy Transfer in MHD Flows, Conference, Aussois, France, 1994, pp. 571-580
35. Rudraiah N., Venkatachalappa M., and Subbaraya C.K. Combined surface tension and buoyancy-driven convection in a rectangular open cavity in the presence of a magnetic field. Int. J. Non-Linear Mech. 30 (1995) 759-770
36. Hashim I., and Arifin N.M. Oscillatory Marangoni convection in a conducting fluid layer with a deformable free surface in the presence of a vertical magnetic field. Acta Mechanica 164 (2003) 199-215
37. Cramer K.R., and Pai S.-I. Magnetofluid Dynamics for Engineers and Applied Physicists (1973), Scripta Publishing Company, Washington, DC
38. Abramowitz M., and Stegun I.A. Handbook of Mathematical Functions (1964), Dover, New York