Magnetothermoelasticity with thermal relaxation in a conducting medium with variable electrical and thermal conductivity

The equations of magnetothermoelasticity with one relaxation time and with variable electrical and thermal conductivity for one-dimensional problems including heat sources are cast into matrix form using the state-space and Laplace transform techniques. The resulting formulation is applied to a problem for the whole conducting space with a plane distribution of heat sources. It also is applied to a semispace problem with a traction-free surface and plane distribution of heat sources located inside the conducting medium. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results for the temperature, displacement, and stress distributions are given and illustrated graphically for both problems. A comparison is made with the results obtained in the following cases: (i) the electrical and thermal conductivities have constant values, (ii) the absence of magnetic field, and (iii) the coupled theory in magnetothermoelasticity.