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Thermocapillary free boundaries in crystal growth

Published online by Cambridge University Press:  21 April 2006

C. Cuvelier  and
J. M. Driessen
C. Cuvelier
Affiliation:
Delft University of Technology, Department of Mathematics and Informatics, Delft, The Netherlands
J. M. Driessen
Affiliation:
Delft University of Technology, Department of Mathematics and Informatics, Delft, The Netherlands Present address: Koninklijke/Shell-Laboratorium, Amsterdam, Shell Research bv, Amsterdam, The Netherlands
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Abstract

In this paper a two-dimensional free boundary arising from the steady thermo-capillary flow in a viscous incompressible fluid is studied numerically. The problem is considered in the context of the open-boat crystal-growth technique. The motion of the fluid is governed by the Navier-Stokes equations coupled with the heat equation. The problem is solved numerically by a finite-element-method discretization. Three iterative methods are introduced for the computation of the free boundary. The non-dimensional form of the problem gives rise to the following characteristic parameters: Reynolds, Grashof, Prandtl, Marangoni, Bond, Ohnesorge, Biot numbers. The influence of these parameters on the flow field, the temperature distribution and the shape of the free boundary is studied.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 169 , August 1986 , pp. 1 - 26
Copyright
© 1986 Cambridge University Press

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