Dual-Phase-Lag Diffusion Model for Thomson's Phenomenon on Electromagneto-thermoelastic an Infinitely Long Solid Cylinder

The electromagneto-thermoelastic problem along an infinitely solid cylinder is solved analytically using the dual-phase-lag diffusion model (DPL). The modified Ohm's law, including the temperature gradient (Thomson's phenomenon) and charge density effects, and the generalized Fourier's law, including the current density effect is introduced. The curved surface of the cylinder is subjected to a thermal shock and its adjoining vacuum is placed in a uniform axial magnetic field. The interaction between the deformation and the magnetic field vector is considered by adding a Lorentz's electromagneto-force into the equation of thermoelastic motion is investigated. The Laplace transform and numerical Laplace inversion techniques are applied to solve the problem. Numerical computations for the temperature, displacement and stress distributions as well as for the induced magnetic and electric fields are carried out and displayed graphically. a comparisons have been shown in figures to estimate the effects of the Thomson's coefficient and the applied magnetic field on all the studied fields.