On the reflection of thermoelastic waves under an exact heat conduction model with a delay and temperature-dependent elastic parameters

Abstract

The present work aims at describing the reflection of thermoelastic waves under a recently proposed thermoelasticity theory by Quintanilla [Some solutions for a family of exact phase-lag heat conduction problems. Mech Res Commun. 2011;38:355–360.]. Here the author has highlighted the condition for well-posedness by treating the three-phase-lag heat conduction theory differently and extended the results to obtain an alternative thermoelasticity theory with a single-delay term. In the present work, we formulate a mathematical model under this new theory to investigate the reflection of thermoelastic waves at the boundary of an elastic medium. The work is discussed for an isotropic medium with temperature-dependent elastic parameters. Unified field equations for Quintanilla's theory along with three other theories, namely, classical thermoelasticity theory, Lord-Shulman theory and Green-Naghdi theory, are considered for the analysis. The three waves, i.e. elastic-mode longitudinal wave, thermal-mode wave and transverse wave are found, among which only the first two are observed to be coupled. The amplitude ratio and phase velocity for various waves are obtained for incident longitudinal and incident transverse wave cases. The results are presented graphically for various angles of incidence and temperature dependence index parameter. Some important observations are highlighted and comparison between the considered theories is presented.