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Journal of Elasticity

Erschienen in:

01.02.2014

A Revised Exposition of the Green–Naghdi Theory of Heat Propagation

verfasst von: Swantje Bargmann, Antonino Favata, Paolo Podio-Guidugli

Erschienen in: Journal of Elasticity | Ausgabe 2/2014

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Abstract

We offer a revised exposition of the three types of heat-propagation theories proposed by Green and Naghdi. Those theories, which make use of the notion of thermal displacement and allow for heat waves, are at variance with the standard Fourier theory; they have attracted considerable interest, and have been applied in a number of disparate physical circumstances, where heat propagation is coupled with elasticity, viscous flows, etc. (Straughan in Heat waves. Applied mathematical sciences, vol. 177. Springer, Berlin, 2011). However, their derivation is not exempt from criticisms, that we here detail, in hopes of opening the way to reconsideration of old applications and proposition of new ones.

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Here, at variance with what we did when writing (9)–(11) to keep our notation lighter, we have carefully distinguished the heat-influx and free-energy constitutive mappings according to the type of theory they are meant for: e.g., we have written \(\widehat{\psi}_{\text{I}}\) in the case of Type I theory and \(\widehat{\psi}_{\text{II}},\widehat{\psi}_{\text{III}}\) in the other two cases.

In fact, it would be necessary to take κ≥0 (a reasonable assumption) and κ ^⋆⋆=0, an assumption that he have seen to be expedient also to obtain the ‘heat equation’ (39), and that, together with (26)₂, would yield (40).

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Titel: A Revised Exposition of the Green–Naghdi Theory of Heat Propagation
verfasst von: Swantje Bargmann
Antonino Favata
Paolo Podio-Guidugli
Publikationsdatum: 01.02.2014
Verlag: Springer Netherlands
Erschienen in: Journal of Elasticity / Ausgabe 2/2014
Print ISSN: 0374-3535
Elektronische ISSN: 1573-2681
DOI: https://doi.org/10.1007/s10659-013-9431-8

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