Local Equilibrium in Transient Heat Conduction

TL;DR

This paper introduces a new thermodynamic approach that retains the local equilibrium hypothesis while addressing fast heat conduction processes.

Contribution

A novel thermodynamic framework is proposed that retains local equilibrium while addressing non-local and high-frequency heat transfer.

Findings

The new approach uses energy density rate as an additional variable to model transient heat conduction.

The framework is demonstrated on the Cattaneo-type flux model and the two-temperature phonon–electron system.

The method provides a thermodynamically consistent alternative to extended irreversible thermodynamics.

Abstract

Extended irreversible thermodynamics (EIT) has been widely used to overcome the deficiencies of classical irreversible thermodynamics in describing fast transport phenomena. By employing fluxes as additional independent variables and rejecting local equilibrium hypothesis, EIT may provide a thermodynamically consistent framework for high-frequency and non-local processes. Here, we propose an alternative approach to EIT that shares the same objective but does not reject local equilibrium hypothesis. Using the rates of change of the energy density as the additional independent variable, we illustrate this approach for two typical problems of transient heat conduction: the Cattaneo-type flux model with thermodynamic inertia and the two-temperature model of energy transfer in a phonon–electron system.