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Approximate solutions to one-phase Stefan-like problems with space-dependent latent heat

Part of: Parabolic equations and systems Miscellaneous topics - Partial differential equations Representations of solutions Thermodynamics and heat transfer General summability methods

Published online by Cambridge University Press:  15 June 2020

J. BOLLATI Open the ORCID record for J. BOLLATI [Opens in a new window]  and
D. A. TARZIA
J. BOLLATI
Affiliation:
Departamento Matemática - FCE, Universidad Austral-CONICET, Paraguay 1950, S2000 FZF, Rosario, Argentina, emails: [email protected]; [email protected]
D. A. TARZIA
Affiliation:
Departamento Matemática - FCE, Universidad Austral-CONICET, Paraguay 1950, S2000 FZF, Rosario, Argentina, emails: [email protected]; [email protected]
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Abstract

The work in this paper concerns the study of different approximations for one-dimensional one-phase Stefan-like problems with a space-dependent latent heat. It is considered two different problems, which differ from each other in their boundary condition imposed at the fixed face: Dirichlet and Robin conditions. The approximate solutions are obtained by applying the heat balance integral method (HBIM), the modified HBIM and the refined integral method (RIM). Taking advantage of the exact analytical solutions, we compare and test the accuracy of the approximate solutions. The analysis is carried out using the dimensionless generalised Stefan number (Ste) and Biot number (Bi). It is also studied the case when Bi goes to infinity in the problem with a convective condition, recovering the approximate solutions when a temperature condition is imposed at the fixed face. Some numerical simulations are provided in order to assert which of the approximate integral methods turns out to be optimal. Moreover, we pose an approximate technique based on minimising the least-squares error, obtaining also approximate solutions for the classical Stefan problem.

Keywords

Stefan problemvariable latent heatheat balance integral methodrefined heat balance integral methodexact solutions

MSC classification

Primary: 80A22: Stefan problems, phase changes, etc.
Secondary: 40C10: Integral methods 35R35: Free boundary problems 35K05: Heat equation 35C05: Solutions in closed form
Type
Papers
Information
European Journal of Applied Mathematics , Volume 32 , Issue 2 , April 2021 , pp. 337 - 369
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

†

The present work has been partially sponsored by the Project PIP No. 0275 from CONICET-UA, Rosario, Argentina, by the Project ANPCyT PICTO Austral 2016 No. 0090 and by the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement 823731 CONMECH.

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