Abstract
In these notes we are concerned with heat conduction described by using the entropy balance. The main advantage of this approach consists in recovering the positivity of the absolute temperature, necessary to prove thermodynamical consistency, directly by solving the equation. We introduce the model and discuss its thermomechanical consistency. Then, we investigate from the analytical and mechanical point of view, the Stefan problem written in terms of the entropy balance and using a generalized version of the principle of virual power including the effects of microscopic forces, responsible for the phase transition process. We prove existence of a solution in a fairly general physical framework, accounting for possible thermal memory effects and local interactions between the phases. Uniqueness is proved in the case no thermal memory nor local interactions are considered.
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References
E. Bonetti, 2002, Global solution to a nonlinear phase transition model with dissipation, Adv. Math. Sci. Appl., 12, 355–376.
E. Bonetti, 2003, A new approach to phase transitions with thermal memory via the entropy balance, submitted.
E. Bonetti, P. Colli, M. Frémond, 2003, A phase field model with thermal memory governed by the entropy balance, Math. Models Methods Appl. Sci., 13, 1565–1588.
E. Bonetti, M. Frémond, 2003, A phase transition model with the entropy balance, Math. Methods Appl. Sci., 26, 539–556.
G. Bonfanti, M. Frémond, F. Luterotti, 2000, Global solution to a nonlinear system for irreversible phase changes, Adv. Math. Sci. Appl. 10, 1–24.
P. Colli, M. Frémond, O. Klein, 2001, Global existence of a solution to a phase field model for supercooling, Nonlinear Anal. Real World Appl. 2, 523–539.
P. Colli, G. Gentili, C. Giorgi, 1999, Non linear systems describing phase transition models compatible with thermodynamics, Math. Models Methods Appl. Sci. 9, 1015–1037.
M. Frémond, A. Visintin, 1985, Dissipation dans le changement de phase. Surfusion. Changement de phase irreversible, C. R. Acad. Sci. Paris Sér. I Math. 301, 1265–1268.
M. Frémond, 2001, Non-smooth Thermomechanics, Springer-Verlag, Heidelberg.
P. Germain, 1973, Mécanique des milieux continus, Masson, Paris.
M.E. Gurtin, A.C. Pikin, 1968, A general theory of heat conduction with finite wave speeds, Arch. Rational Mech. Anal., 31, 113–126.
J. J. Moreau, 1966, Fonctionnelles convexes, Séminaire sur les équations aux dérivées partielles, Collège de France, and 2003, Dipartimento di Ingegneria Civile, Tor Vergata University, Roma.
J.L. Lions, E. Magenes, 1972, Non-homogeneous boundary value problems and applications, Vol. I, Springer-Verlag, Berlin.
F. Luterotti, G. Schimperna, U. Stefanelli, 2001, Existence result for a nonlinear model related to irreversible phase changes, Math. Models Methods Appl. Sci. 11, 1–17.
A. Visintin, 1996, Models of phase transition, Birkhäuser, Basel.
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Colli, P., Bonetti, E., Frémond, M. (2005). Entropy balance versus energy balance Application to the heat equation and to phase transitions. In: Frémond, M., Maceri, F. (eds) Mechanical Modelling and Computational Issues in Civil Engineering. Lecture Notes in Applied and Computational Mechanics, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32399-6_23
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DOI: https://doi.org/10.1007/3-540-32399-6_23
Publisher Name: Springer, Berlin, Heidelberg
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