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Propagation of melting front in structurally heterogeneous media having phase transitions of inhomogeneities
Author(s) -
Savatorova V.L.,
Talonov A.V.,
Shirochin D.L.
Publication year - 2010
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.200900370
Subject(s) - homogenization (climate) , heat transfer , materials science , simple (philosophy) , front (military) , phase (matter) , mechanics , thermodynamics , physics , biodiversity , ecology , philosophy , epistemology , quantum mechanics , meteorology , biology
Problems of propagation of melting (solidification) front in close to periodical heterogeneous media are studied using a structure homogenization technique. Our method describes not only the averaged behavior of the material of a cell as the classic homogenization techniques do, but also the local behavior of the material within a cell. The generalized formulation of the problems allows us to model more complicated than the commonly studied problems, e.g. problems when the inhomogeneities (e.g.frozen liquid layers) may perturb phase transformation (melting) and change their properties during the propagation of heat front. It is shown that for materials of relatively simple geometry, an analytical solution can be obtained to the heat conductivity problem in the heterogeneous media with phase transformations of the layers. Although the analytical solution to the generalized problem is not as simple as the classic self‐similar solution to the one‐dimensional problem, it keeps some main features of the classic solution. In particular, it is shown that in the case of a fixed heat input, the coordinate of melting front in the direction of the heat transfer is directly proportional to the square root of time. Applications of the new techniques to specific heterogeneous media are presented.