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Entropy and temperature gradients thermomechanics: Dissipation, heat conduction inequality and heat equation

Maitournam, Mahaman-Habibou (2012) Entropy and temperature gradients thermomechanics: Dissipation, heat conduction inequality and heat equation. Comptes Rendus Mecanique, 340 (6). pp. 434-443. ISSN 1631-0721. doi:10.1016/j.crme.2012.04.001. https://resolver.caltech.edu/CaltechAUTHORS:20120806-140709103

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Abstract

An alternative and consistent approach, not appealing to the principle of virtual power and to Coleman–Noll procedure, is used to derive constitutive and governing equations involving temperature or entropy gradients, in thermomechanics of materials. Using the balance of energy, an analysis of the dissipation naturally leads to the definition of the temperature and the entropy as variational derivatives. The approach preserves the classical forms of the equations and yields to consistent form of the second law and heat conduction inequality. The framework of generalized standard materials is then suitable for deriving admissible constitutive laws. The methodology is applied, first using entropy and its gradient as state variables (with internal energy as thermodynamic potential), and second using temperature and its gradient (starting from the free energy).


Item Type:Article
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URLURL TypeDescription
http://dx.doi.org/10.1016/j.crme.2012.04.001DOIUNSPECIFIED
http://www.sciencedirect.com/science/article/pii/S1631072112000733PublisherUNSPECIFIED
Additional Information:© 2012 Académie des sciences. Published by Elsevier Masson SAS. Received 5 March 2012. Accepted 11 April 2012. Available online 26 April 2012. The author would like to thank Quoc Son Nguyen for helpful comments and suggestions, Chaire PSA André Citroën and The Division of Engineering and Applied Science of Caltech for their supports.
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Funding AgencyGrant Number
Caltech Division of Engineering and Applied ScienceUNSPECIFIED
Subject Keywords:Continuum mechanics; Continuum thermodynamics; Entropy gradient; Dissipation; Second law; Heat conduction inequality; Heat equation
Issue or Number:6
DOI:10.1016/j.crme.2012.04.001
Record Number:CaltechAUTHORS:20120806-140709103
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20120806-140709103
Official Citation:Mahaman-Habibou Maitournam, Entropy and temperature gradients thermomechanics: Dissipation, heat conduction inequality and heat equation, Comptes Rendus Mécanique, Volume 340, Issue 6, June 2012, Pages 434-443, ISSN 1631-0721, 10.1016/j.crme.2012.04.001.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32951
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:06 Aug 2012 22:52
Last Modified:09 Nov 2021 21:31

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