The relaxation effects of the volume properties of electrically conducting viscoelastic material

A new model of the equations of generalized thermo-viscoelasticity for an electrically conducting isotropic media permeated by a primary uniform magnetic field, taking into consideration the rheological properties of the volume, is given. The formulation is applied to both generalizations, Lord–Shulman theory and the Green–Lindsay theory, as well as to the coupled theory.The state space approach is adopted for the solution of one-dimensional problems in the absence or presence of heat sources. The Laplace-transform technique is used. A numerical method is employed for the inversion of the Laplace transforms. Numerical results for the stress distribution are given and illustrated graphically for each problem.Comparisons are made with the results predicted by the three theories, or ignoring the viscous effects of the volume. Also, the effect of the magnetic field is studied. It is found that the consideration of these effects is to decrease the thermal stresses.