Advertisement

Journal of Mathematical Sciences

, Volume 210, Issue 5, pp 557–570 | Cite as

Two Stationary Radiative-Conductive Heat Transfer Problems for a System of Two-Dimensional Plates

  • A. A. Amosov
  • D. A. Maslov
Article

We consider two nonlinear stationary radiative-conductive heat transfer problems in a system of two-dimensional heat-conducting plates of width \( \varepsilon \) separated by vacuum interlayers. We establish comparison theorems and obtain estimates for the weak solution, in particular, the two-sided estimate umin ≤ u ≤ umax and estimates of the form \( {\left\Vert {D}_xu\right\Vert}_{L^2\left({G}^{\varepsilon}\right)}=O\left(\sqrt{\varepsilon}\right) \) and \( {\left\Vert {D}_xu\right\Vert}_{L^2\left({G}^{\varepsilon}\right)}=O\left(\sqrt{\varepsilon /\uplambda}\right) \). Bibliography: 10 titles.

Keywords

Heat Transfer Weak Solution Asymptotic Approximation Comparison Theorem Heat Transfer Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. A. Amosov, “Semidiscrete and asymptotic approximations to a solution to the heat transfer problem in a system of heat shields under radiation” [in Russian], In: Modern Problems of Mathematical Simulating, pp. 21–36, Rostov-na-Donu (2007).Google Scholar
  2. 2.
    A. A. Amosov and V. V. Gulin, “Semidiscrete and asymptotic approximations in the heat transfer problem in a system of heat shields under radiation” [in Russian], Vestnik MEI No. 6, 5–15 (2008).Google Scholar
  3. 3.
    A. A. Amosov, “Nonstationary radiative-conductive heat transfer problem in a periodic system of grey heat shields” [in Russian], Probl. Mat. Anal. 47, 3–42 (2010); English transl.: J. Math. Sci., New York 169, No. 1, 1–45 (2010).Google Scholar
  4. 4.
    A. A. Amosov, “Semidiscrete and asymptotic approximations for the nonstationary radiative-conductive heat transfer problem in a periodic system of grey heat shields” [in Russian], Probl. Mat. Anal. 57, 69–110 (2011); English transl.: J. Math. Sci., New York 176, No. 3, 361–408 (2011).Google Scholar
  5. 5.
    A. A. Kremkova, “Semidiscrete and asymptotic approximations for the radiative-conductive heat transfer problem in a two-dimensional periodic structure” [in Russian], Vestnik MEI No. 6, 151–161 (2012).Google Scholar
  6. 6.
    A. A. Amosov and A. A. Kremkova, “Error estimate for the semidiscrete method for solving the radiative-conductive heat transfer problem in a two-dimensional periodic structure” [in Russian], Vestnik MEI No. 6, 22–36 (2013).Google Scholar
  7. 7.
    A. A. Amosov, “Solvability of the problem of radiation heat transfer according to the Stefan–Boltzmann law” [in Russian], Vestnik MGU, Ser. Vych. Mat. Kibern. No. 3, 18–26 (1980).Google Scholar
  8. 8.
    A. A. Amosov, “Stationary nonlinear nonlocal problem of radiative-conductive heat transfer in a system of opaque bodies with properties depending on radiation frequency” [in Russian], Probl. Mat. Anal. 43, 3–34 (2009); English transl.: J. Math. Sci., New York 164, No. 3, 309–344 (2010).Google Scholar
  9. 9.
    M. Krizek and L. Liu, “On a comparison principle for a quasilinear elliptic boundary value problem of a nonmonotone type,” Appl. Math. 24, No. 1, 97–107 (1996).MATHMathSciNetGoogle Scholar
  10. 10.
    A. A. Amosov, “Nonstationary nonlinear nonlocal problem of radiative-conductive heat transfer in a system of opaque bodies with properties depending on radiation frequency” [in Russian], Probl. Mat. Anal. 44, 3–38 (2010); English transl.: J. Math. Sci., New York 165, No. 1, 1–41 (2010).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.National Research University “Moscow Power Engineering Institute”MoscowRussia

Personalised recommendations