A consistent thermodynamic formulation of the field equations for elastic bodies removing the paradox of infinite speed of propagation of thermal signals
Abstract
The classical unsteady heat conduction equation is of parabolic character and consequently predicts an infinite speed of propagation for the thermal disturbances. The purpose of this work is to eliminate this not admissible physical feature. A new fundamental relation between the entropy and the state variables is proposed: besides the classical variables, the entropy is assumed to depend on the heat flux vector. This assumption generalizes the local equilibrium hypothesis which is known to be only valid in the vicinity of equilibrium. A rigid and an elastic heat conductor are respectively considered. Following the lines of Onsager's nonequilibrium thermodynamics, phenomenological laws relating the heat flux to the temperature gradient are derived. They are nonstationary and appear as a straightforward extension of the classical Fourier law.
 Publication:

Journal de Mecanique
 Pub Date:
 1976
 Bibcode:
 1976JMec...15..579L
 Keywords:

 Conductive Heat Transfer;
 Elastic Bodies;
 Nonequilibrium Thermodynamics;
 Propagation Velocity;
 Thermoelasticity;
 Entropy;
 Heat Flux;
 Onsager Relationship;
 State Vectors;
 Temperature Gradients;
 Unsteady State;
 Fluid Mechanics and Heat Transfer