Effects of Hall current and two temperatures in transversely isotropic magnetothermoelastic with and without energy dissipation due to ramp-type heat

Abstract

The present article is concerned with the investigation of disturbances in a homogeneous transversely isotropic thermoelastic rotating medium with two temperatures, in the presence of the combined effects of Hall currents and magnetic field. The formulation is applied to the thermoelasticity theories developed by Green-Naghdi theories of type-II and type-III. Laplace and Fourier transform techniques are applied to solve the problem. The analytical expressions of displacements, stress components, temperature change, and current density components are obtained in the transformed domain. A numerical inversion technique has been applied to obtain the results in the physical domain. Numerical simulated results are depicted graphically to show the effect of Hall current and two temperatures on resulting quantities. Some special cases are also deduced from the present investigation.