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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2023. Vol 45

Finite Element Modeling of Nonstationary Problems of Heat Conduction under Complex Heat Transfer

Author(s)
Akhmat M. Ikramov1, Askhad M. Polatov1

1National University of Uzbekistan, Tashkent, Republic of Uzbekistan

Abstract
The article presents a numerical simulation of nonstationary heat conduction problems under complex heat transfer, which includes such heat transfer mechanisms as heat conduction, convection, and radiation. The Stefan-Boltzmann law describes the resulting heat transfer by radiation between two bodies, where the heat transfer coefficient is a function of the body surface temperature. An algorithm and software for solving the heat conduction problem using the finite element method were developed, and the influence of external impacts on the temperature field distribution in the vicinity of an insulated circular hole in the center of the body was studied. The temperature fields were investigated for various boundary conditions in the hole of the plate and the corresponding isotherms were given.
About the Authors

Akhmat M. Ikramov, Cand. Sci. (Phys.Math.), Assoc. Prof., National University of Uzbekistan, Tashkent, 100174, Rebublic of Uzbekistan, axmat3@yandex.ru

Askhad M. Polatov, Dr. Sci. (Phys.Math.), Prof., National University of Uzbekistan, Tashkent, 100174, Rebublic of Uzbekistan, asad3@yandex.ru

For citation
Ikramov A. M. Polatov A. M. Finite Element Modeling of Nonstationary Problems of Heat Conduction under Complex Heat Transfer. The Bulletin of Irkutsk State University. Series Mathematics, 2023, vol. 45, pp. 104–120. https://doi.org/10.26516/1997-7670.2023.45.104
Keywords
heat transfer, nonstationary process, thermal conductivity, convection, radiation, isotherms, hole, algorithm, FEM
UDC
519.63:681.51
MSC
65N30, 35Q79
DOI
https://doi.org/10.26516/1997-7670.2023.45.104
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