Generalized heat conduction in heat pulse experiments

TL;DR

This paper introduces a generalized heat conduction equation derived from entropy principles, unifying various classical models and demonstrating unique solution properties with a new numerical method.

Contribution

It presents a novel generalized heat conduction equation compatible with kinetic theory, unifying multiple classical models and analyzing solution behaviors.

Findings

Derivation of a generalized heat conduction equation encompassing classical models.

Demonstration of faster-than-Fourier pulse propagation in over-diffusion regimes.

Development and stability proof of a simple numerical solution method.

Abstract

A novel equation of heat conduction is derived with the help of a generalized entropy current and internal variables. The obtained system of constitutive relations is compatible with the momentum series expansion of the kinetic theory. The well known Fourier, Maxwell-Cattaneo-Vernotte, Guyer-Krumhansl, Jeffreys-type, and Cahn-Hilliard type equations are derived as special cases. Some remarkable properties of solutions of the general equation are demonstrated with heat pulse initial and boundary conditions. A simple numerical method is developed and its stability is proved. Apparent faster than Fourier pulse propagation is calculated in the over-diffusion regime.