A case study of non-Fourier heat conduction using Internal Variables and GENERIC

TL;DR

This paper combines Non-Equilibrium Thermodynamics with Internal Variables and GENERIC framework to derive and compare various heat conduction models, offering insights for multiscale understanding and numerical simulation improvements.

Contribution

It demonstrates the interpretation of entropy current multipliers as relaxed state variables within both NET-IV and GENERIC frameworks, deriving multiple heat conduction equations and comparing the two approaches.

Findings

Derived Fourier and extended heat conduction equations in both frameworks

Interpreted entropy current multipliers as relaxed state variables

Provided a comparison between NET-IV and GENERIC formulations

Abstract

Applying simultaneously the methodology of Non-Equilibrium Thermodynamics with Internal Variables (NET-IV) and the framework of General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC), we demonstrate that, in heat conduction theories, entropy current multipliers can be interpreted as relaxed state variables. Fourier's law and its various extensions -- the Maxwell-Cattaneo-Vernotte, Guyer-Krumhansl, Jeffreys type, Ginzburg-Landau (Allen-Cahn) type and ballistic-diffusive -- heat conduction equations are derived in both formulations. Along these lines, a comparison of NET-IV and GENERIC is also performed. Our results may pave the way for microscopic/multiscale understanding of beyond-Fourier heat conduction, and open new ways for numerical simulations of heat-conduction problems.