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Upscaling of a diffusion problem with interfacial flux jump leading to a modified Barenblatt model
Author(s) -
Bunoiu Renata,
Timofte Claudia
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800018
Subject(s) - homogenization (climate) , jump , flux (metallurgy) , imperfect , statistical physics , diffusion , mechanics , heat flux , physics , materials science , thermodynamics , heat transfer , ecology , biodiversity , linguistics , philosophy , quantum mechanics , metallurgy , biology
In this paper, we study the homogenization of a diffusion problem in a highly heterogeneous composite medium formed by two constituents separated by an imperfect interface, where both the temperature and the flux exhibit jumps. The presence of the flux jump leads to a modified stationary Barenblatt model. Besides, we discuss two different geometrical settings, providing a mathematical justification for a physical phenomenon which is explained by the connectivity properties of the constituents.