Abstract
A free surface problem arising in the Czochralski (CZ) crystal growth process is considered. A mathematical model accounting for the interaction of the molten material with applied and induced magnetic fields, temperature-induced convection, rotating boundaries and a free surface is given. The model described avoids some common simplifying assumptions and allows for more general geometries, and non-axisymmetric (fully three-dimensional) and time-dependent flow fields. It accounts for the induced magnetic field and avoids non-realistic idealized boundary conditions on the magnetic field. The use and limitations of the model in optimization of crystal growth are also discussed.
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