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Discrete and asymptotic approximations for one stationary radiative–conductive heat transfer problem

  • Andrey A. Amosov EMAIL logo and Nikita E. Krymov

Abstract

Special discrete and asymptotic approximations are proposed for the boundary value problem describing a stationary radiative–conductive heat transfer in a system of absolutely black heat-conducting rods of circular cross-section. Results of numerical experiments are presented to confirm the efficiency of proposed approximations.

MSC 2010: 35Q79; 65N99
  1. Funding: The first author was supported by the Russian Science Foundation (project No. 19–11–00033). The results of the second author were obtained in the framework of the state assignments of the Russian Ministry of Education and Science (project FSWF-2020-0022).

References

[1] A. A. Amosov, Solvability of the problem of radiation heat transfer according to the Stefan–Boltzmann law. Vestn. Mosk. Univ., Vychisl. Matem. Kibern. (1980), No. 3, 18–26 (in Russian).Search in Google Scholar

[2] A. A. Amosov, Semidiscrete and asymptotic approximations to a solution to the heat transfer problem in a system of heat shields under radiation. In: Modern Problems of Mathematical Simulation, Rostov-on-Don, 2007, pp. 21–36 (in Russian).Search in Google Scholar

[3] A. A. Amosov, Stationary nonlinear nonlocal problem of radiative–conductive heat transfer in a system of opaque bodies with properties depending on radiation frequency. J. Math. Sci. 164 (2010), No. 3, 309–344.10.1007/s10958-009-9750-2Search in Google Scholar

[4] A. A. Amosov, Semidiscrete and asymptotic approximations for the nonstationary radiative–conductive heat transfer problem in a periodic system of gray heat shields. J. Math. Sci. 176 (2011), No. 3, 361–408.10.1007/s10958-011-0399-2Search in Google Scholar

[5] A. A. Amosov, Asymptotic approximations for the stationary radiative–conductive heat transfer problem in a two-dimensional system of plates. Russ. J. Numer. Anal. Math. Modelling32 (2017), No. 3, 1–14.10.1515/rnam-2017-0015Search in Google Scholar

[6] A. A. Amosov and V. V. Gulin, Semidiscrete and asymptotic approximations in the heat transfer problem in a system of heat shields under radiation. Vestnik MEI (2008), No. 6, 5–15 (in Russian).Search in Google Scholar

[7] A. A. Amosov and A. A. Kremkova. An estimate of the error of semi-discrete approximate method for solving the radiative–conductive heat transfer problem in the two-dimensional periodic structure. Vestnik MEI (2013), No. 6, 22–36 (in Russian).Search in Google Scholar

[8] A. A. Amosov and N. E. Krymov, Approximations for the stationary problem of radiative–conductive heat exchange in a system of rods of circular cross section. Vestnik MEI (2017), No. 5, 94–100 (in Russian).10.24160/1993-6982-2017-5-94-100Search in Google Scholar

[9] A. A. Amosov and N. E. Krymov, On a nonstandard boundary value problem arising in homogenization of complex heat transfer problems. J. Math. Sci. 244 (2020), No. 3, 357–377.10.1007/s10958-019-04623-0Search in Google Scholar

[10] A. A. Amosov and D. A. Maslov, Two stationary radiative–conductive heat transfer problems in a system of two-dimensional plates. J. Math. Sci. 210 (2015), No. 5, 3–14.10.1007/s10958-015-2578-zSearch in Google Scholar

[11] A. A. Amosov and D. A. Maslov. Semidiscrete approximations for the stationary radiative–conductive heat transfer problem in the two-dimensional system of plates. Russ. J. Numer. Anal. Math. Modelling31 (2016), No. 1, 1–17.10.1515/rnam-2016-0001Search in Google Scholar

[12] A. A. Kremkova, Semidiscrete and asymptotic approximations for the radiative–conductive heat transfer problem in the two-dimensional periodic structure. Vestnik MEI (2012), No. 6, 151–161 (in Russian).Search in Google Scholar

Received: 2020-02-25
Accepted: 2020-03-26
Published Online: 2020-06-04
Published in Print: 2020-06-25

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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