The one-dimensional Stefan problem with non-Fourier heat conduction

Marc Calvo-Schwarzwälder*, Timothy G. Myers, Matthew G. Hennessy

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

14 Citations (Scopus)

Abstract

We investigate the one-dimensional growth of a solid into a liquid bath, starting from a small crystal, using the Guyer-Krumhansl and Maxwell-Cattaneo models of heat conduction. By breaking the solidification process into the relevant time regimes we are able to reduce the problem to a system of two coupled ordinary differential equations describing the evolution of the solid-liquid interface and the heat flux. The reduced formulation is in good agreement with numerical simulations. In the case of silicon, differences between classical and non-classical solidification kinetics are relatively small, but larger deviations can be observed in the evolution in time of the heat flux through the growing solid. From this study we conclude that the heat flux provides more information about the presence of non-classical modes of heat transport during phase-change processes.

Original languageEnglish
Article number106210
JournalInternational Journal of Thermal Sciences
Volume150
DOIs
Publication statusPublished - Apr 2020

Bibliographical note

Funding Information:
M.C.S. acknowledges that the research leading to these results received funding from “La Caixa” Foundation and the Ferran Sunyer i Balaguer Foundation. M.G.H and T.G.M received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 707658 . T.G.M. acknowledges the support of a Ministerio de Ciencia e Innovación grant MTM2017-82317-P. The authors have been partially funded by the CERCA programme of the Generalitat de Catalunya . The authors thank F. X. Alvarez and L. Sendra for providing the KCM data.

Funding Information:
M.C.S. acknowledges that the research leading to these results received funding from ?La Caixa? Foundation and the Ferran Sunyer i Balaguer Foundation. M.G.H and T.G.M received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk?odowska-Curie grant agreement No. 707658. T.G.M. acknowledges the support of a Ministerio de Ciencia e Innovaci?n grant MTM2017-82317-P. The authors have been partially funded by the CERCA programme of the Generalitat de Catalunya. The authors thank F. X. Alvarez and L. Sendra for providing the KCM data.

Publisher Copyright:
© 2019 Elsevier Masson SAS

Structured keywords

  • Engineering Mathematics Research Group

Keywords

  • Guyer-Krumhansl equation
  • Heat transfer
  • Maxwell-Cattaneo law
  • Non-fourier heat conduction
  • Phase change
  • Stefan problem

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