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Eurasian Mathematical Journal, 2022, Volume 13, Number 3, Pages 51–66
DOI: https://doi.org/10.32523/2077-9879-2022-13-3-51-66 (Mi emj446) 		 
Exact and approximate solutions to the Stefan problem in ellipsoidal coordinates

S. A. Kassabeka, S. N. Kharinb, D. Suragana

a Department of Mathematics, Nazarbayev University, 53 Kabanbay batyr St, Astana, Kazakhstan
b International School of Economics, Kazakh British Technical University, 59 Tole bi St, Almaty, Kazakhstan
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DOI: https://doi.org/10.32523/2077-9879-2022-13-3-51-66
Abstract: In this paper, we present exact and approximate solutions of the Stefan problems in ellipsoidal coordinates. We consider two models of electrical contact heating for melting process. The first problem describes the contact heating for liquid and solid zones based on the two-phase Stefan problem, where time $t$ is present as a parameter. Contact heating including softening processes are described by a mathematical model based on the three-phase Stefan problem for the ellipsoidal heat equation. Numerical results are presented and discussed.
Keywords and phrases: softening stage, electrical contact heating, Stefan problems, Joule heating, heat balance integral method.
Funding agency Grant number
Nazarbayev University 091019CRP2120
Ministry of Education and Science of the Republic of Kazakhstan AP09258948
OR11466188
The authors were supported by the Nazarbayev University Program 091019CRP2120 "Centre for Interdisciplinary Studies in Mathematics (CISM)" and the second author was supported by the grant no. AP09258948 "A free boundary problems in mathematical models of electrical contact phenomena" and by the grant no. OR11466188 ("Dynamical Analysis and Synchronization of Complex Neural Networks with Its Applications").
Received: 14.11.2021
Bibliographic databases:
Document Type: Article
MSC: 80A22, 40C10
Language: English
Citation: S. A. Kassabek, S. N. Kharin, D. Suragan, “Exact and approximate solutions to the Stefan problem in ellipsoidal coordinates”, Eurasian Math. J., 13:3 (2022), 51–66
Citation in format AMSBIB
\Bibitem{KasKhaSur22}
\by S.~A.~Kassabek, S.~N.~Kharin, D.~Suragan
\paper Exact and approximate solutions to the Stefan problem in ellipsoidal coordinates
\jour Eurasian Math. J.
\yr 2022
\vol 13
\issue 3
\pages 51--66
\mathnet{http://mi.mathnet.ru/emj446}
\crossref{https://doi.org/10.32523/2077-9879-2022-13-3-51-66}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4494212}
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