Transient Disturbance in a Half-Space under Generalized Magneto-Thermoelasticity with Internal Heat Source

The transient waves caused by a line heat source with a uniform velocity inside isotropic homogeneous thermoelastic perfectly conducting half-space permeated into a uniform magnetic field are studied. The formulation is applied under three theories of generalized thermoelasticity: Lord-Shulman theory with one relaxation time, Green-Lindsay theory with two relaxation times, as well as the classical dynamical coupled theory. The problem is reduced to the solution of three differential equations by introducing the elastic and thermoelastic potentials. The normal mode analysis is used to obtain the expression for the temperature, displacement components and the thermal stresses. Numerical results are given and illustrated graphically. Comparisons are made with the results predicted by the three theories in the presence and absence of magnetic field and the internal heat source.