Two–dimensional solidification in a corner

Analytical and numerical techniques are used to study the solidification of 1/2 and 3/2 wedges of liquid which are initially at their fusion temperature. An enthalpy method is used to obtain numerical solutions to these problems and the results are compared with asymptotic solutions for large and sm...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 1999-09, Vol.455 (1989), p.3449-3470
Main Authors: King, J. R., Riley, D. S., Wallman, A. M.
Format: Article
Language:English
Subjects:
Aspect ratio
Asymptotic Solution
Boundary conditions
Boundary layers
Corner Solidification
Enthalpy
Geometry
Heat transfer
Integers
Liquids
Mathematics
Research Article
Solidification
Stefan Problem
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Summary:Analytical and numerical techniques are used to study the solidification of 1/2 and 3/2 wedges of liquid which are initially at their fusion temperature. An enthalpy method is used to obtain numerical solutions to these problems and the results are compared with asymptotic solutions for large and small Stefan numbers (the Stefan number being defined as the ratio of latent to sensible heats). The new solutions for small Stefan number are shown to provide surprisingly good approximations, especially for the 3/2 wedge. New results for heat transfer in a wedge (in the absence of a change of phase) are derived and applied in the asymptotic analysis, as are new conservation laws for the Stefan problem.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.1999.0460