A Comparative Study of magneto-thermo-elastic wave propagation in a finitely conducting medium under thermoelasticity of type I, II, III

Abstract

The present work is concerned with the propagation of electro-magneto-thermoelastic plane waves of assigned frequency in a homogeneous isotropic and finitely conducting elastic medium permeated by a primary uniform external magnetic field. We formulate our problem under the theory of Green and Naghdi of type-III (GN-III) to account for the interactions between the elastic, thermal as well as magnetic fields. A general dispersion relation for coupled waves is deduced to ascertain the nature of waves propagating through the medium. Perturbation technique has been employed to obtain the solution of dispersion relation for small thermo-elastic coupling parameter and identify three different types of waves. We specially analyze the nature of important wave components like, phase velocity, specific loss and penetration depth of all three modes of waves. We attempt to compute these wave components numerically to observe their variations with frequency. The effect of presence of magnetic field is analyzed. Comparative results under theories of type GN-I, II and III have been presented numerically in which we have found that the coupled thermoelastic waves are un-attenuated and nondispersive in case of Green-Naghdi-II model which is completely in contrast with the theories of type-I and type-III. Furthermore, the thermal mode wave is observed to propagate with finite phase velocity in case of GN-II model, whereas the phase velocity of thermal mode wave is found to be an increasing function of frequency in other two cases. We achieve significant variations among the results predicted by all three theories.