Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Thermodynamics of a non-simple heat conductor with memory

Authors: Giovambattista Amendola, Mauro Fabrizio and Murrough Golden
Journal: Quart. Appl. Math. 69 (2011), 787-806
MSC (2010): Primary 80A20, 74F05
DOI: https://doi.org/10.1090/S0033-569X-2011-01228-5
Published electronically: July 1, 2011
MathSciNet review: 2894001
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Abstract: A generalization is given of the linearized constitutive equation, proposed by Gurtin and Pipkin for the heat flux in a rigid heat conductor, which includes the effects of both the histories of the temperature gradient $ \mathbf{g}$ and of $ \nabla\mathbf{g}$. This new contribution yields a non-simple material, for which the Second Law of Thermodynamics assumes a modified form, characterized by an extra flux, depending on the material. Some standard free energy functionals are adapted to these new materials, including an explicit formula for the minimum free energy.

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Giovambattista Amendola
Affiliation: Dipartimento di Matematica Applicata “U. Dini”, via F. Buonarroti 1c, 56127-Pisa, Italy
Email: amendola@dma.unipi.it

Mauro Fabrizio
Affiliation: Dipartimento di Matematica, Piazza di Porta S. Donato 5, 40127-Bologna, Italy
Email: fabrizio@dm.unibo.it

Murrough Golden
Affiliation: School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland
Email: murrough.golden@dit.ie

DOI: https://doi.org/10.1090/S0033-569X-2011-01228-5
Keywords: Memory effects, heat conduction
Received by editor(s): May 11, 2010
Published electronically: July 1, 2011
Additional Notes: The work of the first two authors was performed with support from the Italian C.N.R. and M.I.U.R
The research of the third author was supported by the Dublin Institute of Technology
Article copyright: © Copyright 2011 Brown University

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