Analytical and numerical modelling of ballistic heat conduction observed in heat pulse experiments

TL;DR

This paper explores physical interpretations and modeling approaches for ballistic heat conduction, including a coupled thermo-mechanical model and an internal variable model, validated through experiments and analytical solutions.

Contribution

It introduces a coupled Maxwell-Cattaneo-Vernotte model with numerical solutions and an analytical approach using internal variables for ballistic heat conduction.

Findings

Numerical solution successfully models heat pulse experiments on NaF.

Analytical solution highlights the importance of boundary conditions.

Validation confirms the effectiveness of the proposed models.

Abstract

Among the three heat conduction modes, the ballistic propagation is the most difficult to model. In the present paper, we discuss its physical interpretations and showing different alternatives to its modeling. We highlight two of them: a thermo-mechanical model in which the generalized heat equation - the so-called Maxwell-Cattaneo-Vernotte equation - is coupled to thermal expansion. At the same time, the other one uses internal variables. For the first one, we developed a numerical solution and tested on the heat pulse experiment performed by McNelly et al.~on NaF samples. For the second one, we found an analytical solution that emphasizes the role of boundary conditions. This analytical method is used to validate the earlier developed numerical code.