A revised exposition of the Green-Naghdi theory of heat propagation

DOI10.1007/s10659-013-9431-8zbMath1284.35433arXiv1211.4481OpenAlexW2070983482MaRDI QIDQ2434109

Paolo Podio-Guidugli, Swantje Bargmann, Antonino Favata

Publication date: 17 February 2014

Published in: Journal of Elasticity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.4481

zbMATH Keywords

hyperbolic heat propagationthermomechanics without energy dissipationthree types of heat-propagation theories

Mathematics Subject Classification ID

Thermal effects in solid mechanics (74F05) Heat equation (35K05) Thermodynamics of continua (80A17) PDEs in connection with classical thermodynamics and heat transfer (35Q79)

Related Items (6)

For a statistical interpretation of Helmholtz' thermal displacement ⋮ Nonlinear heat wave propagation in a rigid thermal conductor ⋮ On thermo-electro-mechanical simple materials with fading memory. Restrictions of the constitutive equations in a Green-Naghdi type theory ⋮ A mechanical model for heat conduction ⋮ A non-local dissipative Lagrangian modelling for generalized thermoelasticity in solids ⋮ An unconditionally stable algorithm for generalized thermoelasticity based on operator-splitting and time-discontinuous Galerkin finite element methods

Cites Work

• Unnamed Item
• A virtual power format for thermomechanics
• Heat waves.
• On entropy flux of transversely isotropic elastic bodies
• Classical results for a non-classical theory: Remarks on thermodynamic relations in Green-Naghdi thermo-hyperelasticity
• The thermodynamics of elastic materials with heat conduction and viscosity
• Thermoelasticity without energy dissipation
• A demonstation of consistency of an entropy balance with balance of energy
• On entropy flux-heat flux relation in thermodynamics with Lagrange multipliers
• Entropy flux relation for viscoelastic bodies
• The coldness, a universal function in thermoelastic bodies
• Die Kältefunktion, eine universelle Funktion in der Thermodynamik viskoser wärmeleitender Flüssigkeiten. (The coldness function, a universal function in the thermodynamic of viscouse heat-conducting fluids)
• Method of Lagrange multipliers for exploitation of the entropy principle
• A re-examination of the basic postulates of thermomechanics
• The behavior of hyperbolic heat equations’ solutions near their parabolic limits
• On energy and entropy influxes in the Green–Naghdi Type III theory of heat conduction
• Heat waves
• ON A GLOBAL ENTROPY PRODUCTION INEQUALITY
• Thermodynamics

This page was built for publication: A revised exposition of the Green-Naghdi theory of heat propagation