Generalized magneto-thermoelasticity in a conducting medium with variable material properties

In this paper, we constructed the equations of magneto generalized-thermoelasticity with one relaxation time and each of the electrical conductivity; the thermal conductivity and the modulus of elasticity are taken to be variable. A general one-dimensional problem of a conducting medium has been solved taking into account a constant magnetic field that acts normal to the bounding plane. Laplace and Fourier transforms are used. The resulting formulation is applied to a thermal shock half-space problem that has a constant displacement on the boundary. The inverses Fourier transforms are obtained analytically while the inverses Laplace transforms are obtained numerically. The temperature, displacement and stress distributions are represented graphically.