Quasistationary nonlinear problem of thermal conduction with spherical symmetry in the region with a free boundary
DOI:
https://doi.org/10.70474/v7695v88Keywords:
nonlinear heat equation, spherical symmetry, boundary condition, Stefan's problem, integral equations, electrical contactsAbstract
The article discusses a boundary value single-phase problem with a free boundary for a quasistationary nonlinear inhomogeneous heat conduction equation with a spherically symmetric thermal field. The domain of the problem is degenerated at the initial moment of time. To find a free boundary, the problem is supplemented by Stefan’s condition. It is assumed that thermal conductivity and latent heat of melting depend on temperature. The study of the boundary value problem was carried out by transforming it to an equivalent system of integral equations, for which a proof of solvability and uniqueness of the solution was obtained. An iterative algorithm for the numerical solution of a system of integral equations has been developed. The results of a computational experiment on the analytical solution of a boundary value problem have been presented.
Downloads
References
Lykov, A.V. Teoriya teploprovodnosti [Theory of heat conduction], Moscow: Vysshaya shkola, 1967, 600 p.
Holm, R. Electrical Contacts, IL, Moscow, 1961, 464 p.
Kharin, S.N. Nauryz, T.A. One-phase spherical Stefan problem with temperature dependent coefficients, Eurasian Mathematical Journal, 12, 1, 2021, 49-56, https://doi.org/10.32523/2077-9879-2021-12-1-49-56 DOI: https://doi.org/10.32523/2077-9879-2021-12-1-49-56
Kassabek, S.A. Kharin, S.N. Suragan, D. Exact And Approximate Solutions To The Stefan Problem In Ellipsoidal Coordinates, Eurasian Mathematical Journal, 13, 3, 2022, 51-66, https://doi.org/10.32523/2077-9879-2022-13-3-51-66 DOI: https://doi.org/10.32523/2077-9879-2022-13-3-51-66
Kassabek, S.A. Suragan, D. Numerical approximation of the one-dimensional inverse Cauchy–Stefan problem using heat polynomials methods, https://doi.org/10.1007/s40314-022-01896-1
Tikhonov, A.N. Samarskii, A.A. Equations of Mathematical Physics, (5th edition), Nauka, Moscow, 1977
Friedman, A. Partial differential equations of parabolic type, M.: “MIR”, 1968, 428 p.
Rubinstein, L.I. Stefan’s Problem, Zvaizgne Publishing House, Riga, 1967, 461 p.
Krasnov, M.L. Integral Equations, Nauka, Moscow, 1975
Fikhtengolts, G.M. Course of Differential and Integral Calculus, Volume II, Moscow: FIZMATLIT, 2003, 864 p.
Matveev, N.M. Methods of integration of ordinary differential equations, Moscow: Vysshaya shkola, 1967, 564 p.
Kolmogorov, A.N. Fomin, S.V. Elements of the Theory of Functions and Functional Analysis, Moscow, Nauka, 1976, 542 p.
Additional Files
Published
Issue
Section
License
Copyright (c) 2025 Kazakh Mathematical Journal
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
One can find the license terms "CC Attribution-NonCommercial-NoDerivatives 4.0" here.
