Dual Phase Lag Model on Magneto-Thermoelasticity Infinite Non-Homogeneous Solid Having a Spherical Cavity

Abstract

In this article, the induced displacement, temperature and stress fields in an infinite non-homogeneous elastic medium with a spherical cavity are obtained in the context dual-phase-lag model. The surface of the cavity is stress free and is subjected to a thermal shock. The material is assumed to be elastic and has an inhomogeneity in the radial direction. The type of non-homogeneity is such that the elastic constants, thermal conductivity and density are proportional to the n th power of the radial distance. The solutions are obtained analytically employing the Laplace transforms technique. The numerical inversion of the transforms is carried out using Fourier series expansions. The stresses components, temperature and displacement are computed numerically and presented graphically. A comparison of the results is made for different theories. If the magnetic field is neglected, the results obtained are deduced as a special case from this study.