### 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 language | English |
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Pages (from-to) | 1-14 |

Number of pages | 14 |

Journal | Continuum Mechanics and Thermodynamics |

DOIs | |

Publication status | Accepted/In press - Mar 17 2018 |

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### 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

*Continuum Mechanics and Thermodynamics*, 1-14. https://doi.org/10.1007/s00161-018-0643-9

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

Research output: Contribution to journal › Article

*Continuum Mechanics and Thermodynamics*, pp. 1-14. https://doi.org/10.1007/s00161-018-0643-9

}

TY - JOUR

T1 - Generalized heat-transport equations

T2 - parabolic and hyperbolic models

AU - Rogolino, Patrizia

AU - Kovács, Robert

AU - Ván, P.

AU - Cimmelli, Vito Antonio

PY - 2018/3/17

Y1 - 2018/3/17

N2 - 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.

AB - 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.

KW - Generalized heat-transport equation

KW - Hyperbolic heat conduction

KW - Thermal perturbations

UR - http://www.scopus.com/inward/record.url?scp=85044086937&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044086937&partnerID=8YFLogxK

U2 - 10.1007/s00161-018-0643-9

DO - 10.1007/s00161-018-0643-9

M3 - Article

AN - SCOPUS:85044086937

SP - 1

EP - 14

JO - Continuum Mechanics and Thermodynamics

JF - Continuum Mechanics and Thermodynamics

SN - 0935-1175

ER -