Application of Standard and Refined Heat Balance Integral Methods to One-Dimensional Stefan Problems

The work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions that enable us to test the accuracy of the approximate solu...

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Bibliographic Details
Published in:SIAM review 2010-03, Vol.52 (1), p.57-86
Main Authors: Mitchell, S. L., Myers, T. G.
Format: Article
Language:English
Subjects:
Approximation
Boundary conditions
Coefficients
Error rates
Exact sciences and technology
EXPOSITORY RESEARCH PAPERS
Heat
Heat balance
Heat equation
Integral transforms
Mathematical analysis
Mathematical integrals
Mathematical models
Mathematics
Melting
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Sequences, series, summability
Solids
Studies
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Description
Summary:The work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions that enable us to test the accuracy of the approximate solutions. We also consider situations where no analytical solution is available and compare these to numerical solutions. It is popular to use a quadratic profile as an approximation of the temperature, but we show that a cubic profile, seldom considered in the literature, is far more accurate in most circumstances. In addition, the refined integral method can give greater improvement still, and we develop a variation on this method which turns out to be optimal in some cases. We assess which integral method is better for various problems, showing that it is largely dependent on the specified boundary conditions.
ISSN:0036-1445
1095-7200
DOI:10.1137/080733036