Generalized magneto-thermoelasticity in a perfectly conducting medium

A model of the equations of generalized magneto-thermoelasticity in a perfectly conducting medium is given. The formulation is applied to generalizations, Lord–Shulman theory with one relaxation time and the Green–Lindsay theory with two relaxation times, as well as to the coupled theory. Laplace transforms and Fourier transforms techniques are used to get the solution. The resulting formulation is used to solve a specific two-dimensional problem. The inverses of Fourier transforms are obtained analytically. Laplace transforms are obtained using the complex inversion formula of the transform together with Fourier expansion techniques. Numerical results for the temperature distribution, thermal stress and displacement components are represented graphically. A comparison was made with the results predicted by the three theories.