Investigation of harmonic plane waves: detailed analysis of recent thermoplastic model with single delay term

Abstract

This work is concerned with a recent thermoelastic model. We investigate the propagation of plane harmonic waves in the context of this very recently proposed heat conduction model, an exact heat conduction model with a single delay term, established by Quintanilla. This model attempted to reformulate the heat conduction model that takes into account microstructural effects in heat transport phenomena and provided an alternative heat conduction theory with a single delay term. We aim to study the harmonic plane waves propagating in a thermoelastic medium by employing this new model and derive the exact dispersion relation solution. We mainly focus on a longitudinal wave coupled to a thermal field and find two different modes of this wave. We derive asymptotic expressions for several important characterizations of the wave fields: phase velocity, specific loss, penetration depth, and amplitude ratio. Analytical expressions for these wave characteristics are obtained for different cases of very-high- and low-frequency regions for elastic- and thermal-mode longitudinal waves. To verify the analytical results, we also carry out computational work to obtain numerical results of the wave characterizations for intermediate values of frequency and illustrate the results graphically. We show that our analytical and numerical results are in perfect match. On the basis of the analytical and numerical results, a thorough analysis of the effects of the single delay parameter on various wave characteristics is presented. We highlight several characteristic features of the new thermoelastic model, as compared with other models.

Numerical Resolution of an Exact Heat Conduction Model With a Delay Term

“…This heat conduction equation has been complemented with other equations to obtain a thermoelastic problem and several contributions has been dedicated to study it. We recall some of them [13][14][15][16][17][18]22].…”