Universal heat conduction -- the thermodynamics of some weakly nonlocal theories

TL;DR

This paper develops a unified thermodynamic framework for heat conduction that encompasses various classical and modern models, providing a general approach with demonstrative examples.

Contribution

It introduces a universal linear irreversible thermodynamic model for heat conduction, unifying multiple existing theories through a common internal variable approach.

Findings

Derivation of a general heat conduction equation covering multiple models

Demonstration of the universal applicability with two example solutions

Establishment of a thermodynamic basis for weakly nonlocal heat theories

Abstract

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 intensity factor. A general constitutive evolution equation of the current density of the internal energy is derived by introducing linear relationship between the thermodynamic forces and fluxes. The Fourier, Maxwell-Cattaneo-Vernotte, Guyer-Krumhansl, Jeffreys type and Green-Naghdi type equations of heat conduction are obtained as special cases. The universal character of the approach is demonstrated by two examples. Solutions illustrating the properties of the equation with jump boundary conditions are given.