Magneto-thermoelastic interaction in a functionally graded medium under gravitational field

The main concern of the present contribution is the thermoelastic interactions of displacements, stress and temperature in a functionally graded unbounded medium due to the influence of gravitational field and an induced magnetic field of constant intensity while the medium is rotating with an uniform angular velocity. The governing equations have been formulated in the context of generalized thermoelasticity with energy dissipation (Green Naghdi model III (GN III)) under the influence of periodically varying heat source. Employing Laplace and Fourier transforms as tools, the problem has been solved analytically in the transformed domain. The inversion of the Fourier transform is performed analytically using Mathematica package and the numerical inversion of the Laplace transform has been executed using Zakian method. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed. Excellent predictive capability is demonstrated due to the effect of nonhomogeneity, effect of rotation, influence of magnetic field and gravitational field also.

Automated summary

This study focuses on the thermoelastic interactions of displacements, stress, and temperature in a functionally graded unbounded medium under the influence of gravitational field and induced magnetic field while rotating with uniform angular velocity. The governing equations are formulated using generalized thermoelasticity with energy dissipation, and the problem is solved analytically in the transformed domain using Laplace and Fourier transforms. The results demonstrate excellent predictive capability considering nonhomogeneity, rotation, magnetic field influence, and gravitational field influence.