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A Stefan problem in a Bridgman crystal grower

Published online by Cambridge University Press:  26 September 2008

P. den Decker ,
R. van der Hout ,
C. J. Van Duijn  and
L. A. Peletier
P. den Decker
Affiliation:
Akzo Research Laboratories Arnhem, Applied Mathematics Department, PB 9300, 6800 SB Arnhem, The Netherlands
R. van der Hout
Affiliation:
Akzo Research Laboratories Arnhem, Applied Mathematics Department, PB 9300, 6800 SB Arnhem, The Netherlands
C. J. Van Duijn
Affiliation:
Department of Mathematics, Delft University of Technology, PB 5031, 2600 GA Delft, The Netherlands and Mathematical Institute, Leiden University, PB 9512, 2300 RA Leiden, The Netherlands
L. A. Peletier
Affiliation:
Mathematical Institute, Leiden University, PB 9512, 2300 RA Leiden, The Netherlands
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Abstract

We discuss a one-dimensional model for a Bridgman crystal grower, where the removal of heat is described by an internal heat sink. A consequence is the apparent existence of mushy regions for relatively large velocities of the cooling machine; these mushy regions are an artefact of the one-dimensional approximation. We show that for some types of cooling profiles there exists a critical speed for the existence of mushy regions, whereas for different cooling profiles no such critical speed exists. The presence of a mushy region may indicate a strong curvature of the liquid/solid interface in the real situation.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 6 , Issue 3 , June 1995 , pp. 191 - 199
Copyright
Copyright © Cambridge University Press 1995

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References

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