Internal structure and heat conduction in rigid solids: a two temperature approach

TL;DR

This paper introduces a two-temperature non-Fourier heat conduction model for solids with internal structures, based on non-equilibrium thermodynamics, capturing experimental behaviors across different structured materials.

Contribution

It develops a novel two-temperature model that accounts for internal structure effects in heat conduction, extending thermodynamic theories to non-Fourier regimes.

Findings

Successfully reproduces experimental thermal responses of structured materials.

Highlights the role of coupling parameter in modeling heat transfer.

Provides a framework for understanding non-Fourier heat conduction in complex solids.

Abstract

A non-Fourier thermal transport regime characterizes the heat conduction in solids with internal structure. Several thermodynamic theories attempt to explain the separation from the Fourier regime in such kind of systems. Here we develop a two temperature model to describe the non-Fourier regime from the principles of non-equilibrium thermodynamics. The basic assumption is the existence of two well separated length scales in the system, namely, one related with the matrix dimension (bulk) and the other with the characteristic length of the internal structure. Two Fourier type coupled transport equations are obtained for the temperatures which describe the heat conduction in each of the length scales. Recent experimental results from several groups on the thermal response of different structured materials are satisfactorily reproduced by using the coupling parameter as a fitting parameter. The similarities and differences of the present formalism with other theories are discussed.