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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 and of . 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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Additional Information

**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