## On upscaling heat conductivity for a class of industrial problems

• Calculating effective heat conductivity for a class of industrial problems is discussed. The considered composite materials are glass and metal foams, fibrous materials, and the like, used in isolation or in advanced heat exchangers. These materials are characterized by a very complex internal structure, by low volume fraction of the higher conductive material (glass or metal), and by a large volume fraction of the air. The homogenization theory (when applicable), allows to calculate the effective heat conductivity of composite media by postprocessing the solution of special cell problems for representative elementary volumes (REV). Different formulations of such cell problems are considered and compared here. Furthermore, the size of the REV is studied numerically for some typical materials. Fast algorithms for solving the cell problems for this class of problems, are presented and discussed.

Author: O. Iliev, I. Rybak, J. Willems urn:nbn:de:hbz:386-kluedo-15422 Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (120) Report English 2007 2007 Fraunhofer-Institut für Techno- und Wirtschaftsmathematik 2008/05/28 Multiscale problems ; domain decomposition; effective heat conductivity ; numerical upscaling Fraunhofer (ITWM) 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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