Generalized heat-transport equations: parabolic and hyperbolic models

  title={Generalized heat-transport equations: parabolic and hyperbolic models},
  author={Patrizia Rogolino and R{\'o}bert Kov{\'a}cs and P{\'e}ter V{\'a}n and Vito Antonio Cimmelli},
  journal={Continuum Mechanics and Thermodynamics},
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… 
Numerical treatment of nonlinear Fourier and Maxwell-Cattaneo-Vernotte heat transport equations
Some Exact Solutions to Non-Fourier Heat Equations with Substantial Derivative
A system of hyperbolic-type inhomogeneous differential equations (DE), describing non-Fourier heat transfer with substantial derivative thin films, is considered and exact harmonic solutions to these equations are obtained for the Cauchy and the Dirichlet conditions.
Differential consequences of balance laws in extended irreversible thermodynamics of rigid heat conductors
It is proved that, under an opportune choice of the initial conditions, a solution of the Cauchy problem for the system of differential consequences is also a solution for the originalSystem of balance laws, namely the higher-order system obtained by taking into account the time and space derivatives of the original system.
Analytical and numerical modelling of ballistic heat conduction observed in heat pulse experiments
Among the three heat conduction modes, the ballistic propagation is the most difficult to model. In the present paper, we discuss its physical interpretations and showing different alternatives to
Generalized ballistic-conductive heat transport laws in three-dimensional isotropic materials
General constitutive equations of heat transport with second sound and ballistic propagation in isotropic materials are given using non-equilibrium thermodynamics with internal variables. The
Emergence of Non-Fourier Hierarchies
It is demonstrated that the Guyer-Krumhansl equation can be the next appropriate extension of Fourier’s law for room-temperature phenomena in modeling of heterogeneous materials and it is shown that non-Fourier temperature history can be produced by mixing different solutions of Fouriers law.
Functional kinetic equations in mathematical modeling of coupled processes in solids
In this paper, we consider the role of functional kinetic equations in models of solid mechanics. It is shown that the choice of time-non-locality kernels allows both the finite speed of signal
Local versus nonlocal constitutive theories of nonequilibrium thermodynamics: the Guyer–Krumhansl equation as an example
On the example of the celebrated Grad’s 13-moment system of kinetic theory of rarefied gases and phonon hydrodynamics, it is proved that the constitutive equations of nonequilibrium thermodynamics


Weakly Nonlocal And Nonlinear Heat Transport In Rigid Solids
A weakly nonlocal and nonlinear theory of heat conduction in rigid bodies is proposed. The constitutive equations generalize these of Fourier, Maxwell-Cattaneo and Guyer-Krumhansl. The proposed model
Nonequilibrium temperatures, heat waves, and nonlinear heat transport equations
A dynamical nonequilibrium temperature has been proposed to describe relaxational equations for the heat flux. This temperature provides an alternative description to the Maxwell-Cattaneo equation.
Universal heat conduction -- the thermodynamics of some weakly nonlocal theories
A linear irreversible thermodynamic framework of heat conduction in rigid conductors is introduced. The deviation from local equilibrium is characterized by a single internal variable and a current
Universality in heat conduction theory: weakly nonlocal thermodynamics
A linear irreversible thermodynamic framework of heat conduction in rigid conductors is introduced. The deviation from local equilibrium is characterized by a single internal variable and a current
Nonlinear evolution and stability of the heat flow in nanosystems: Beyond linear phonon hydrodynamics
A heat transport equation incorporating nonlocal and nonlinear contributions of the heat flux is derived in the framework of weakly nonlocal nonequilibrium thermodynamics. The motivation for these
Generalized heat conduction in heat pulse experiments
A Unified Field Approach for Heat Conduction From Macro- to Micro-Scales
A universal constitutive equation between the heat flux vector and the temperature gradient is proposed to cover the fundamental behaviors of diffusion (macroscopic in both space and time), wave
A generalized Coleman–Noll procedure for the exploitation of the entropy principle
A generalization of the classical Coleman–Noll procedure for the exploitation of second law of thermodynamics in the presence of first-order non-local constitutive functions is proposed. The local
The effects of nonlocality on the evolution of higher order fluxes in nonequilibrium thermodynamics
The role of gradient dependent constitutive spaces is investigated on the example of Extended Thermodynamics of rigid heat conductors. Different levels of nonlocality are developed and the different
Rational Extended Thermodynamics
1 Tour d'Horizon 2 Early Version of Extended Thermodynamics 1 Paradox of Heat Conduction and Shear Diffusion 1.1 Heuristic Derivation of the Laws of Fourier and Navier-Stokes 1.2 Parabolic Laws of