# On the propagation of temperature-rate waves and traveling waves in rigid conductors of the Graffi--Franchi--Straughan type

## TL;DR

This paper investigates second-sound phenomena in Graffi--Franchi--Straughan type conductors, revealing nonlinear effects like wave blow-up and unique waveforms due to temperature-dependent relaxation times, using analytical and numerical methods.

## Contribution

It introduces a detailed analysis of temperature-rate and traveling waves in a new class of conductors with nonlinear effects caused by temperature-dependent relaxation times.

## Key findings

- Finite-time temperature-rate wave blow-up observed.
- Thermal traveling waves exhibit a 'tongue' waveform.
- Nonlinear effects are significant in these conductors.

## Abstract

We examine second-sound phenomena in a class of rigid, thermally conducting, solids that are described by a special case of the Maxwell--Catteneo flux law. Employing both analytical and numerical methods, we examine both temperature-rate waves and thermal traveling waves in this class of thermal conductor, which have recently been termed Graffi--Franchi--Straughan type conductors. In the present study, the temperature-dependent nature of the thermal relaxation time, which is the distinguishing feature of this class of conductors, gives rise to a variety of nonlinear effects; in particular, finite-time temperature-rate wave blow-up and temperature traveling waveforms which exhibit a "tongue". The presentation concludes with a discussion of possible follow-on studies.