The effect of surface tension and kinetic undercooling on a radially-symmetric melting problem

Back, Julian M., McCue, Scott W., Hsieh, Mike Hou-Ning, & Moroney, Timothy J. (2014) The effect of surface tension and kinetic undercooling on a radially-symmetric melting problem. Applied Mathematics and Computation, 229, pp. 41-52.

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Abstract

The addition of surface tension to the classical Stefan problem for melting a sphere causes the solution to blow up at a finite time before complete melting takes place. This singular behaviour is characterised by the speed of the solid-melt interface and the flux of heat at the interface both becoming unbounded in the blow-up limit. In this paper, we use numerical simulation for a particular energy-conserving one-phase version of the problem to show that kinetic undercooling regularises this blow-up, so that the model with both surface tension and kinetic undercooling has solutions that are regular right up to complete melting. By examining the regime in which the dimensionless kinetic undercooling parameter is small, our results demonstrate how physically realistic solutions to this Stefan problem are consistent with observations of abrupt melting of nanoscaled particles.

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11 citations in Scopus
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10 citations in Web of Science®

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ID Code: 63271
Item Type: Journal Article
Refereed: Yes
Keywords: Stefan problem, surface tension, kinetic undercooling, nanoparticle melting, blow-up, regularisation, Gibbs-Thomson
DOI: 10.1016/j.amc.2013.12.003
ISSN: 0096-3003
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Theoretical and Applied Mechanics (010207)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Solution of Differential and Integral Equations (010302)
Divisions: Current > Institutes > Institute for Future Environments
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2013 Elsevier
Copyright Statement: This is the author’s version of a work that was accepted for publication in Applied Mathematics and Computation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Mathematics and Computation, [Volume 229, (25 February 2014)] DOI: 10.1016/j.amc.2013.12.003
Deposited On: 11 Oct 2013 00:38
Last Modified: 29 Feb 2016 17:01

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