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Thermocapillary convection in a cylinder with a strong non-uniform axisymmetric magnetic field

Published online by Cambridge University Press:  26 April 2006

Yu Yu Khine  and
John S. Walker
Yu Yu Khine
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, IL 61801, USA
John S. Walker
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, IL 61801, USA
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Abstract

This paper treats a surface-tension-driven liquid-metal flow in a cylinder with a steady externally applied non-uniform axisymmetric magnetic field. The top boundary consists of an annular free surface around a solid disk, modelling the Czochralski growth of silicon crystals. A radial temperature gradient produces a decrease of the surface tension from the disk edge to the vertical cylinder wall. The magnetic flux density is sufficiently large that inertial effects and convective heat transfer are negligible. First we present large-Hartmann-number asymptotic solutions for magnetic fields with either a non-zero or a zero axial component at the free surface. The asymptotic solutions indicate that a purely radial magnetic field at the free surface represents a singular limit of more general magnetic fields. Secondly we present numerical solutions for arbitrary values of the Hartmann number, and we treat the evolution of the thermocapillary convection as the axial magnetic field at the free surface is changed continuously from the full field strength to zero.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 276 , 10 October 1994 , pp. 369 - 388
Copyright
© 1994 Cambridge University Press

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