Harmonic Waves Propagation in a Nonlinear Generalized Thermoelasticity with Magnetic Field

Abstract

In this chapter, the homotopy perturbation and Adomain's decomposition methods are applied to obtain the approximate solutions of the equation of motion and heat equation for the harmonic waves propagation in a nonlinear generalized thermoelasticity with magnetic field. The nonlinear coupled system of partial differential equations often appear in the study of circled fuel reactor, high-temperature hydrodynamics and thermo-elasticity problems. The problem is solved in one-dimensional elastic half-space model subjected initially to a prescribed harmonic displacement and the temperature of the medium. The displacement and temperature are calculated for the two methods with the variations of the magnetic field and the relaxation times considering Green Lindsay theory (GL). The results obtained are displayed graphically to show the in uences of the new parameters and the differs between the methods technique. It is obvious that the homotopy perturbation method and adomain decomposition method give the same results that indicates to the origin of the approximate solutions and the methods powerful. The homotopy perturbation method and adomain decomposition method give the same results that indicates to the origin of the approximate solutions and the methods powerful.