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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2024, Volume 64, Number 4, Pages 658–670
DOI: https://doi.org/10.31857/S0044466924040067
(Mi zvmmf11733)
 

Mathematical physics

Determination of the thermal conductivity and volumetric heat capacity of substance from heat flux

A. Yu. Gorchakov, V. I. Zubov

Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, 119333, Moscow, Russia
Abstract: The study of nonlinear problems related to heat transfer in a substance is of great practical important. Earlier, this paper’s authors proposed an effective algorithm for determining the volumetric heat capacity and thermal conductivity of a substance based on experimental observations of the dynamics of the temperature field in the object. In this paper, the problem of simultaneous identification of temperature-dependent volumetric heat capacity and thermal conductivity of the substance under study from the heat flux at the boundary of the domain is investigated. The consideration is based on the first (Dirichlet) boundary value problem for a one-dimensional unsteady heat equation. The coefficient inverse problem under consideration is reduced to a variational problem, which is solved by gradient methods based on the application of fast automatic differentiation. The uniqueness of the solution of the inverse problem is investigated.
Key words: thermal conductivity, coefficient inverse problems, gradient, heat equation, heat flow.
Received: 22.09.2023
Revised: 04.11.2023
Accepted: 20.11.2023
English version:
Computational Mathematics and Mathematical Physics, 2024, Volume 64, Issue 4, Pages 833–847
DOI: https://doi.org/10.1134/S0965542524700039
Bibliographic databases:
Document Type: Article
UDC: 519.653:519.658
Language: Russian
Citation: A. Yu. Gorchakov, V. I. Zubov, “Determination of the thermal conductivity and volumetric heat capacity of substance from heat flux”, Zh. Vychisl. Mat. Mat. Fiz., 64:4 (2024), 658–670; Comput. Math. Math. Phys., 64:4 (2024), 833–847
Citation in format AMSBIB
\Bibitem{GorZub24}
\by A.~Yu.~Gorchakov, V.~I.~Zubov
\paper Determination of the thermal conductivity and volumetric heat capacity of substance from heat flux
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2024
\vol 64
\issue 4
\pages 658--670
\mathnet{http://mi.mathnet.ru/zvmmf11733}
\crossref{https://doi.org/10.31857/S0044466924040067}
\elib{https://elibrary.ru/item.asp?id=74490707}
\transl
\jour Comput. Math. Math. Phys.
\yr 2024
\vol 64
\issue 4
\pages 833--847
\crossref{https://doi.org/10.1134/S0965542524700039}
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    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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