A generalized electromagneto-thermoelastic problem for an infinitely long solid cylinder

The theory of generalized thermoelasticity, based on the theory of Lord and Shulman with one relaxation time, is used to study the electromagneto-thermoelastic interactions in an infinitely long perfectly conducting solid cylinder subjected to a thermal shock on its surface when the cylinder and its adjoining vacuum is subjected to a uniform axial magnetic field. The cylinder deforms because of thermal shock, and due to the application of the magnetic field, there result an induced magnetic and an induced electric field in the cylinder. The Maxwellʹs equations are formulated and the generalized electromagneto-thermoelastic coupled governing equations are established. By means of the Laplace transform and numerical Laplace inversion the problem is solved. The distributions of the considered temperature, stress, displacement, induced magnetic and electric field are represented graphically. From the distributions, it can be found the electromagnetic-thermoelastic coupled effects and the wave type heat propagation in the medium. This indicates that the generalized heat conduction mechanism is completely different from the classic Fourierʹs in essence. In generalized thermoelasticity theory heat propagates as a wave with finite velocity instead of infinite velocity in medium.