EXACT AND APPROXIMATE SOLUTIONS TO THE STEFAN PROBLEM IN ELLIPSOIDAL COORDINATES

S. A. Kassabek; S. N. Kharin; D. Suragan

doi:10.32523/2077-9879-2022-13-3-51-66

EXACT AND APPROXIMATE SOLUTIONS TO THE STEFAN PROBLEM IN ELLIPSOIDAL COORDINATES

S. A. Kassabek
, S. N. Kharin
, D. Suragan

Nazarbayev University

Department of Mathematics
Nazarbayev University
International School of Economics
Kazakh-British Technical University

Результат исследований › рецензирование

2 Цитирования (Scopus)

Аннотация

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.

Язык оригинала	English
Страницы (с-по)	51-66
Число страниц	16
Журнал	Eurasian Mathematical Journal
Том	13
Номер выпуска	3
DOI	https://doi.org/10.32523/2077-9879-2022-13-3-51-66
Состояние	Published - 2022

ASJC Scopus subject areas

General Mathematics

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title = "EXACT AND APPROXIMATE SOLUTIONS TO THE STEFAN PROBLEM IN ELLIPSOIDAL COORDINATES",

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.",

keywords = "Electrical contact heating, Heat balance integral method, Joule heating, Softening stage, Stefan problems",

author = "Kassabek, \{S. A.\} and Kharin, \{S. N.\} and D. Suragan",

note = "Funding Information: 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{"}). Funding Information: Supported by the ISAAC (International Society for Analysis, its Applications and Computation) and by the Kazakhstan Mathematical Society Publisher Copyright: {\textcopyright} 2022, Eurasian Mathematical Journal.All Rights Reserved.",

year = "2022",

doi = "10.32523/2077-9879-2022-13-3-51-66",

language = "English",

volume = "13",

pages = "51--66",

journal = "Eurasian Mathematical Journal",

issn = "2077-9879",

publisher = "L. N. Gumilyov Eurasian National University",

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T1 - EXACT AND APPROXIMATE SOLUTIONS TO THE STEFAN PROBLEM IN ELLIPSOIDAL COORDINATES

AU - Kassabek, S. A.

AU - Kharin, S. N.

AU - Suragan, D.

N1 - Funding Information: 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"). Funding Information: Supported by the ISAAC (International Society for Analysis, its Applications and Computation) and by the Kazakhstan Mathematical Society Publisher Copyright: © 2022, Eurasian Mathematical Journal.All Rights Reserved.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - Electrical contact heating

KW - Heat balance integral method

KW - Joule heating

KW - Softening stage

KW - Stefan problems

UR - https://www.scopus.com/pages/publications/85141248188

UR - https://www.scopus.com/pages/publications/85141248188#tab=citedBy

U2 - 10.32523/2077-9879-2022-13-3-51-66

DO - 10.32523/2077-9879-2022-13-3-51-66

M3 - Article

AN - SCOPUS:85141248188

SN - 2077-9879

VL - 13

SP - 51

EP - 66

JO - Eurasian Mathematical Journal

JF - Eurasian Mathematical Journal

IS - 3

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