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Homogenization of a Conductive-Radiative Heat Transfer Problem

Zakaria Habibi (2012)

ESAIM: Proceedings

This paper focuses on the contribution of the second order corrector in periodic homogenization applied to a conductive-radiative heat transfer problem. Especially, for a heat conduction problem in a periodically perforated domain with a non-local boundary condition modelling the radiative heat transfer, if this model contains an oscillating thermal source and a thermal exchange with the perforations, the second order corrector helps us to model the gradients which appear between the source area...

Hyperbolic heat conduction in two semi-infinite bodies in contact

J. A. López Molina, Macarena Trujillo Guillén (2005)

Applications of Mathematics

We find, under the viewpoint of the hyperbolic model of heat conduction, the exact analytical solution for the temperature distribution in all points of two semi-infinite homogeneous isotropic bodies that initially are at uniform temperatures T 0 1 and T 0 2 , respectively, suddenly placed together at time t = 0 and assuming that the contact between the bodies is perfect. We make graphics of the obtained temperature profiles of two bodies at different times and points. And finally, we compare the temperature...

Hysteresis operators in phase-field models of Penrose-fife type

Pavel Krejčí, Jürgen Sprekels (1998)

Applications of Mathematics

Phase-field systems as mathematical models for phase transitions have drawn a considerable attention in recent years. However, while they are suitable for capturing many of the experimentally observed phenomena, they are only of restricted value in modelling hysteresis effects occurring during phase transition processes. To overcome this shortcoming of existing phase-field theories, the authors have recently proposed a new approach to phase-field models which is based on the mathematical theory...

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