Generalized heat-transport equations: parabolic and hyperbolic models

Patrizia Rogolino, Robert Kovács, P. Ván, Vito Antonio Cimmelli

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some generalizations of the classical Liu and Coleman–Noll procedures. In both cases, constitutive equations for the entropy and for the entropy flux are obtained. For the second model, we consider a heat-transport equation which includes nonlocal terms and study the resulting set of balance laws, proving that the corresponding thermal perturbations propagate with finite speed.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalContinuum Mechanics and Thermodynamics
DOIs
Publication statusAccepted/In press - Mar 17 2018

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entropy
heat
thermodynamics
constitutive equations
conductive heat transfer
compatibility
Entropy
perturbation
Constitutive equations
Heat conduction
Thermodynamics
Fluxes
Hot Temperature

Keywords

  • Generalized heat-transport equation
  • Hyperbolic heat conduction
  • Thermal perturbations

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Physics and Astronomy(all)

Cite this

Generalized heat-transport equations : parabolic and hyperbolic models. / Rogolino, Patrizia; Kovács, Robert; Ván, P.; Cimmelli, Vito Antonio.

In: Continuum Mechanics and Thermodynamics, 17.03.2018, p. 1-14.

Research output: Contribution to journalArticle

Rogolino, Patrizia ; Kovács, Robert ; Ván, P. ; Cimmelli, Vito Antonio. / Generalized heat-transport equations : parabolic and hyperbolic models. In: Continuum Mechanics and Thermodynamics. 2018 ; pp. 1-14.
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