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Semidiscrete and asymptotic approximations for the nonstationary radiative-conductive heat transfer problem in a periodic system of grey heat shields. (English. Russian original) Zbl 1290.35016

J. Math. Sci., New York 176, No. 3, 361-408 (2011); translation from Probl. Mat. Anal. 57, 69-110 (2011).
Summary: We consider semidiscrete and asymptotic approximations to a solution to the nonstationary nonlinear initial-boundary-value problem governing the radiative-conductive heat transfer in a periodic system consisting of n grey parallel plate heat shields of width \(\epsilon =1/n\), separated by vacuum interlayers. We study properties of special semidiscrete and homogenized problems whose solutions approximate the solution to the problem under consideration. We establish the unique solvability of the problem and deduce a priori estimates for the solutions. We obtain error estimates of order \(O(\sqrt{\varepsilon})\) and \(O(\epsilon)\) for semidiscrete approximations and error estimates of order \(O(\sqrt{\varepsilon})\) and \(O(\epsilon^{3/4})\) for asymptotic approximations.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure

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References:

[1] N. S. Bakhvalov, ”Averaging of the heat-transfer process in periodic media with radiation” [in Russian], Differ. Uravn. 17, No. 10, 1765–1773 (1981); English transl.: Differ. Equations 17, 1094–1100 (1982).
[2] N. S. Bakhvalov and G. P. Panasenko, Averaging processes in periodic media [in Russian], Nauka, Moscow (1984); English transl.:. Kluwer, Dordrecht etc. (1989). · Zbl 0607.73009
[3] G. Allaire and K. El Ganaoui. ”Homogenization of conductive and radiative heat transfer problem, Simulation with CAST3M,” In Proceedings of HT2005, ASME Summer Heat Transfer Conference, July 17–22, 2005, San Francisco, California, USA.
[4] K. El Ganaoui. Homogénéisation de modèles de transfers thermiques et radiatifs dans le coeur des réacteur à coloporteur gaz, PhD Thesis, Ecole Polytechnique (2006).
[5] G. Allaire and K. El Ganaoui, ”Homogenization of a conductive and radiative heat transfer problem,” Multiscale Model. Simul. 7, No. 3, 1148–1170 (2009). · Zbl 1180.35062 · doi:10.1137/080714737
[6] 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). · Zbl 1223.35298 · doi:10.1007/s10958-010-0037-4
[7] 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).
[8] 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).
[9] A. A. Amosov and A. A. Zlotnik, ”Quasi-averaged equations of the one-dimensional motion of a viscous barotropic medium with rapidly oscillating data” [in Russian], Zh. Vych. Mat. Mat. Fiz. 36, No. 2, 87–110 (1996); English transl.: Comp. Math. Math. Phys. 36, No. 2, 203–220 (1996). · Zbl 1027.35504
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