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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 3, Pages 510–535 (Mi zvmmf10540)  

This article is cited in 3 scientific papers (total in 3 papers)

Stationary problem of complex heat transfer in a system of semitransparent bodies with boundary conditions of diffuse reflection and refraction of radiation

A. A. Amosov

Moscow Power Engineering Institute, Moscow, Russia

Abstract: A boundary value problem describing complex (radiation-conductive) heat transfer in a system of semitransparent bodies is considered. Complex heat transfer is described by a system consisting of a stationary heat equation and an equation of radiative transfer with the boundary conditions of diffuse reflection and diffuse refraction of radiation. The dependence of the radiation intensity and optical properties of bodies on the frequency of radiation is taken into account. The unique existence of the weak solution to this problem is established. The comparison theorem is proven. Estimates of the weak solution are derived, and its regularity is established.

Key words: complex heat transfer, radiative transfer equation, diffuse reflection and diffuse refraction boundary conditions, weak solution, comparison theorem.

Funding Agency Grant Number
Russian Science Foundation 14-11-00306


DOI: https://doi.org/10.7868/S0044466917030024

Full text: PDF file (599 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:3, 515–540

Bibliographic databases:

UDC: 519.633
Received: 26.07.2016

Citation: A. A. Amosov, “Stationary problem of complex heat transfer in a system of semitransparent bodies with boundary conditions of diffuse reflection and refraction of radiation”, Zh. Vychisl. Mat. Mat. Fiz., 57:3 (2017), 510–535; Comput. Math. Math. Phys., 57:3 (2017), 515–540

Citation in format AMSBIB
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\paper Stationary problem of complex heat transfer in a system of semitransparent bodies with boundary conditions of diffuse reflection and refraction of radiation
\jour Zh. Vychisl. Mat. Mat. Fiz.
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\issue 3
\pages 510--535
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\crossref{https://doi.org/10.7868/S0044466917030024}
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\pages 515--540
\crossref{https://doi.org/10.1134/S0965542517030022}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. V. Grenkin, “Svoistva reshenii nestatsionarnoi modeli slozhnogo teploobmena”, Dalnevost. matem. zhurn., 18:1 (2018), 23–33  mathnet
    2. G. V. Grenkin, A. Yu. Chebotarev, “Stability of stationary solutions of the radiative heat transfer equations”, Comput. Math. Math. Phys., 58:9 (2018), 1420–1425  mathnet  crossref  crossref  isi  elib
    3. Chebotarev A.Yu., Koytanyuk A.E., Botkin N.D., “Problem of Radiation Heat Exchange With Boundary Conditions of the Cauchy Type”, Commun. Nonlinear Sci. Numer. Simul., 75 (2019), 262–269  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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