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

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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.

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References

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Authors and Affiliations

  1. National Research University “Moscow Power Engineering Institute”, 14, Krasnokazarmennaya St., Moscow, 111250, Russia

    A. A. Amosov & D. A. Maslov

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  1. A. A. Amosov
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  2. D. A. Maslov
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Correspondence to A. A. Amosov.

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Translated from Problemy Matematicheskogo Analiza 82, September 2015, pp. 3-14.

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Amosov, A.A., Maslov, D.A. Two Stationary Radiative-Conductive Heat Transfer Problems for a System of Two-Dimensional Plates. J Math Sci 210, 557–570 (2015). https://doi.org/10.1007/s10958-015-2578-z

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