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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...

Identification of basic thermal technical characteristics of building materials

Stanislav Šťastník, Jiří Vala, Hana Kmínová (2007)

Kybernetika

Modelling of building heat transfer needs two basic material characteristics: heat conduction factor and thermal capacity. Under some simplifications these two factors can be determined from a rather simple equipment, generating heat from one of two aluminium plates into the material sample and recording temperature on the contacts between the sample and the plates. However, the numerical evaluation of both characteristics leads to a non-trivial optimization problem. This article suggests an efficient...

Initial traces of solutions to a one-phase Stefan problem in an infinite strip.

Daniele Andreucci, Marianne K. Korten (1993)

Revista Matemática Iberoamericana

The main result of this paper is an integral estimate valid for non-negative solutions (with no reference to initial data) u ∈ L1loc (Rn x (0,T)) to(0.1)   ut - Δ(u - 1)+ = 0,  in D'(Rn x (0,T)),for T > 0, n ≥ 1. Equation (0.1) is a formulation of a one-phase Stefan problem: in this connection u is the enthalpy, (u - 1)+ the temperature, and u = 1 the critical temperature of change of phase. Our estimate may be written in the form(0.2)  ∫Rn u(x,t) e-|x|2 / (2 (T - t)) dx ≤ C,   0 <...

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