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.
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Cuvelier et al. (1986) studied this question.
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