Reflection of thermoelastic waves from the isothermal boundary of a solid half-space under memory-dependent heat transfer

ABSTRACT

In this paper, we investigated the reflection of thermoelastic plane waves from the isothermal stress-free boundary of a homogeneous, isotropic and thermally conducting solid half-space in the context of the new linear theory of generalized thermoelasticity under heat transfer with memory-dependent derivative. It has been found that three types of basic waves consisting of two sets of coupled longitudinal waves and one independent vertically shear type wave may travel with distinct phase speeds. The formulae for various reflection coefficients are determined in case of an incident coupled dilatational elastic wave at an isothermal stress-free boundary of the medium. For an appropriate material, the reflection coefficients are computed numerically and presented graphically for various values of the angle of incidence and discussed the effect of various parameters of interest. At the end, the phase speeds and the attenuations coefficients of the coupled longitudinal waves are shown graphically to compare our results with the existing results.

KEYWORDS:

• Memory-dependent derivative
• plane waves
• dispersion
• phase speeds and attenuation
• reflection

Acknowledgements

The authors would like to gratefully acknowledge the Editor and the anonymous referee for their suggestions and comments to improve the manuscript. They also gratefully acknowledge Professor Samiran Ghosh (Department of Applied Mathematics, University of Calcutta, Kolkata-700009, India.) for his valuable suggestions in preparing the revised version of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).