Magneto-thermoelastic wave propagation in a finitely conducting medium: A comparative study for three types of thermoelasticity I, II, and III

Abstract

The present work is concerned with the propagation of magneto-thermoelastic plane waves of assigned frequency in a homogeneous isotropic finitely conducting elastic medium permeated by a uniform magnetic field. The problem has been formulated under the purview of Green and Naghdi theory of thermoelasticity of type-III (GN-III). Interactions among elastic, thermal and magnetic fields have been taken into account. A dispersion relation is derived to investigate the nature of waves propagating in the medium. Perturbation technique has been employed to obtain the solution of the dispersion relation, when the magneto-thermoelastic coupling parameter is small. This enables to identify three different types of waves. Phase velocity, specific loss and penetration depth have been discussed. Using derived analytical expressions, numerical results have been computed for the variation of several physical quantities of interest. The impact of the magnetic field has been studied. Computational results have been presented graphically for all the three cases GN-I, GN-II, GN-III. A comparative study has been performed for these three cases. The study reveals that in the case of GN-II theory, coupled magneto-thermoelastic waves are unattenuated and non-dispersive in contrast to the cases of GN-I and GN-III theories. © 2021 Taylor & Francis Group, LLC.