{"title":"Analytical Method for Calculating Eigenvalues in the Problem of Nonstationary Heat Conduction of a Spherical Body","authors":"Yu. V. Vidin, V. S. Zlobin","doi":"10.1134/s0018151x23020190","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A method for investigating characteristic equations is proposed, and analytical formulas are obtained for determining the roots of the characteristic equation in the problem of nonstationary heat conduction of a spherical body. These formulas make it possible to determine any required number of roots with high accuracy, which is especially important when solving heat conduction problems at the initial moment of time. The proposed method can be used to study more complex characteristic equations arising in other heat transfer problems.</p>","PeriodicalId":13163,"journal":{"name":"High Temperature","volume":"164 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"High Temperature","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1134/s0018151x23020190","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
A method for investigating characteristic equations is proposed, and analytical formulas are obtained for determining the roots of the characteristic equation in the problem of nonstationary heat conduction of a spherical body. These formulas make it possible to determine any required number of roots with high accuracy, which is especially important when solving heat conduction problems at the initial moment of time. The proposed method can be used to study more complex characteristic equations arising in other heat transfer problems.
期刊介绍：
High Temperature is an international peer reviewed journal that publishes original papers and reviews written by theoretical and experimental researchers. The journal deals with properties and processes in low-temperature plasma; thermophysical properties of substances including pure materials, mixtures and alloys; the properties in the vicinity of the critical point, equations of state; phase equilibrium; heat and mass transfer phenomena, in particular, by forced and free convections; processes of boiling and condensation, radiation, and complex heat transfer; experimental methods and apparatuses; high-temperature facilities for power engineering applications, etc. The journal reflects the current trends in thermophysical research. It presents the results of present-day experimental and theoretical studies in the processes of complex heat transfer, thermal, gas dynamic processes, and processes of heat and mass transfer, as well as the latest advances in the theoretical description of the properties of high-temperature media.
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