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Modele przepływu ciepła w ciałach stałych

Poński M., Paluszyński J., Dubała K.

Zeszyty Naukowe Politechniki Częstochowskiej. Budownictwo

2013

Z. 19 (169)

129--134

W pracy przedstawiono modele przepływu ciepła w ciałach stałych w zależności od prędkości propagacji fal ciepła, kładąc nacisk na praktyczne wykorzystanie równań opisujących przedstawione zagadnienie. Praca ma charakter przeglądowy.

The paper presents a model of heat transfer in solids, depending on the propagation speed of thermal waves, with an emphasis on the practical use of the equations governing the presented issue. Work is a review.

Asymptotic analysis of heat propagation models

Moszyński K., Palczewski A.

Archives of Mechanics

2000

Vol. 52, nr 2

225-246

The subject of this paper is the analysis of different models of heat propagation. As is well known, one of essential disadvantages of the classical model proposed by Fourier is the infinite velocity at which heat propagates. To avoid that unphysical phenomenon, Cattaneo has proposed a hyperbolic model. An essential feature of that model is the introduction of a relaxation time for thermal processes. In recent years several new models have been proposed which retain the relaxation time phenomenon but are parabolic in their character. When the relaxation time is small, all these models lead to singularly perturbed equations. We analyze some of these models and prove that the solution of the classical heat equation (Fourier model) is a bulk approximation to exact solutions of these models. We show also that the behaviour of the Fourier model depends on the way in which it is applied. Finally, we present numerical comparison of exact solutions with the bulk solution for the test problem of heat propagation in thin metal films heated by a laser beam.