Upscaling of a diffusion problem with interfacial flux jump leading to a modified Barenblatt model. Issue 2 (18th October 2018)

• Record Type: Journal Article
• Authors: Bunoiu, Renata; Timofte, Claudia
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 99:Issue 2(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-10-18
• Subjects: Barenblatt model -- flux jump -- homogenization -- imperfect interfaces -- 35B27 -- 80M35 -- 80M40; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201800018
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: 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. Abstract : 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.