Different thermodynamic theories and different heat conduction laws

DOI10.1515/JNETDY.2009.016zbMath1195.80001MaRDI QIDQ963643

Vito Antonio Cimmelli

Publication date: 13 April 2010

Published in: Journal of Non-Equilibrium Thermodynamics (Search for Journal in Brave)

zbMATH Keywords

nonequilibrium thermodynamicsCattaneo equationGuyer-Krumhansl equationheat conduction with finite speed

Mathematics Subject Classification ID

Related Items (36)

Nonlinear heat-transport equation beyond Fourier law: application to heat-wave propagation in isotropic thin layers ⋮ Universality in heat conduction theory: weakly nonlocal thermodynamics ⋮ Cattaneo-Vernotte equation versus Fourier thermoelastic hyperbolic heat equation ⋮ The paradox of Fourier heat equation: a theoretical refutation ⋮ An approach of a heat-flux dependent theory for micropolar porous media ⋮ Entropy principle and recent results in non-equilibrium theories ⋮ Heat-pulse propagation along nonequilibrium nanowires in thermomass theory ⋮ Theories and heat pulse experiments of non-Fourier heat conduction ⋮ Constitutive equations for heat conduction in nanosystems and nonequilibrium processes: an overview ⋮ Understanding of flux-limited behaviors of heat transport in nonlinear regime ⋮ Finite-speed heat propagation as a consequence of microstructural changes ⋮ A phenomenological study of pore-size dependent thermal conductivity of porous silicon ⋮ Size effects in non-linear heat conduction with flux-limited behaviors ⋮ Mesoscopic approach to inviscid gas dynamics with thermal lag ⋮ Heat flow influence on the Cauchy stress tensor in a thermal wave ⋮ Macroscopic heat transport equations and heat waves in nonequilibrium states ⋮ Elementary scales and the lack of Fourier paradox for Fourier fluids ⋮ Weakly nonlocal thermodynamics of anisotropic rigid heat conductors revisited ⋮ Dynamical temperature and renormalized flux variable in extended thermodynamics of rigid heat conductors ⋮ Analysis of three nonlinear effects in a continuum approach to heat transport in nanosystems ⋮ Effects of heat flux on \(\lambda\)-transition in liquid \({}^4\)He ⋮ Transition to ballistic regime for heat transport in helium II ⋮ Local versus nonlocal constitutive theories of nonequilibrium thermodynamics: the Guyer-Krumhansl equation as an example ⋮ Differential consequences of balance laws in extended irreversible thermodynamics of rigid heat conductors ⋮ Fitting thermal conductivity and optimizing thermoelectric efficiency in \(S i_c G e_{1 - c}\) nanowires ⋮ Representations of acting processes and memory effects: general fractional derivative and its application to theory of heat conduction with finite wave speeds ⋮ Entropy analyses for hyperbolic heat conduction based on the thermomass model ⋮ Thermodynamic approach to vortex production and diffusion in inhomogeneous superfluid turbulence ⋮ A nonlinear model of thermoelectricity with two temperatures: Application to quasicrystalline nanowires ⋮ Nonlinear propagation of coupled first- and second-sound waves in thermoelastic solids ⋮ On the evaluation of non-Fourier effects in heat pulse experiments ⋮ Modelling of elastic heat conductors via objective rate equations ⋮ Generalized heat-transport equations: parabolic and hyperbolic models ⋮ Non-Fourier heat removal from hot nanosystems through graphene layer ⋮ Mesoscopic description of boundary effects in nanoscale heat transport ⋮ Exploitation of the entropy principle: Proof of Liu theorem if the gradients of the governing equations are considered as constraints

Cites Work

• Comments ``On the relationship between extended thermodynamics and the wave approach to thermodynamics
• A phenomenological scaling approach for heat transport in nano-systems
• Survey of some branches of thermodynamics
• Systematic remarks on objectivity and frame-indifference, liquid crystal theory as an example
• On the thermomechanics of interstitial working
• Second sound and internal energy in solids
• The thermodynamics of elastic materials with heat conduction and viscosity
• Avere una memoria tenace crea gravi problemi
• On the thermodynamics of second sound in dielectric crystals
• A mathematical foundation for thermodynamics
• On the wave approach of thermodynamics and some problems of nonlinear theories
• On the constitutive relations for second sound in elastic solids
• Weakly nonlocal and nonlinear heat transport in rigid solids
• Thermoelasticity without energy dissipation
• Thermodynamics with internal variables. I: General concepts. II: Applications
• Determination of material functions through second sound measurements in a hyperbolic heat conduction theory
• Numerical reconstruction of heat pulse experiments
• Boundary conditions in the presence of internal variables.
• Extended irreversible thermodynamics and the Jeffreys type constitutive equations
• Extended thermodynamics -- consistent in order of magnitude
• Thermodynamics of anisotropic solids near absolute zero.
• A historical note on the entropy principle of Müller and Liu
• A diffusive-hyperbolic model for heat conduction
• A gradient theory of internal variables
• Application of diffusive internal variables in complex fluids
• A sketch of continuum thermodynamics
• On the causality requirement for diffusive-hyperbolic systems in non-equilibrium thermodynamics
• Generalization of the evolution criterion in extended irreversible thermodynamics
• On the evolution of higher order fluxes in non-equilibrium thermodynamics
• A generalized dynamical theory of thermoelasticity
• On the entropy inequality
• A general theory of heat conduction with finite wave speeds
• Reciprocal Relations in Irreversible Processes. I.
• Reciprocal Relations in Irreversible Processes. II.
• Weakly nonlocal irreversible thermodynamics
• Heat waves
• A thermodynamic theory of thermoelastic and viscoanelastic solids with non-Euclidean structure
• On the mathematical structure of thermodynamics with internal variables

This page was built for publication: Different thermodynamic theories and different heat conduction laws