Analytic solution of Guyer-Krumhansl equation for laser flash experiments

TL;DR

This paper derives an analytical solution to the Guyer-Krumhansl heat conduction equation tailored for laser flash experiments, validating it against numerical simulations to better model non-Fourier heat transfer in complex materials.

Contribution

It provides the first analytical solution to the Guyer-Krumhansl equation with boundary conditions specific to laser flash experiments, enhancing modeling accuracy for non-Fourier heat conduction.

Findings

Analytical solution matches numerical simulations.

Validates non-Fourier heat conduction models.

Applicable to heterogeneous materials.

Abstract

The existence of non-Fourier heat conduction is known for a long time in small and low temperature systems. The deviation from Fourier's law has been found at room temperature in heterogeneous materials like rocks and metal foams \cite{Botetal16, Vanetal17}. These experiments emphasized that the so-called Guyer-Krumhansl equation is adequate for modeling complex materials. In this paper an analytic solution of Guyer-Krumhansl equation is presented considering boundary conditions from laser flash experiment. The solutions are validated with the help of a numerical code \cite{KovVan15} developed for generalized heat equations.