{"title":"Determination of the Thermal Conductivity and Volumetric Heat Capacity of Substance from Heat Flux","authors":"A. Yu. Gorchakov, V. I. Zubov","doi":"10.1134/s0965542524700039","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Mathematics and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0965542524700039","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.
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