Magnetothermoelastic Interactions in an Infinite Medium upon Hyperbolic Two-Temperature

The general thermoelastic theory, based on Lord-Shulman (LS) theory with hyperbolic two temperatures, is used to analyze the magnetothermoelasticity problem in a semi-infinite material. The medium surface is caused by heat flux and is either taken to be traction-free or constrained as specified. Using Laplace transform techniques, the generalized magnetothermoelastic set of coupled basic equations is rewritten in the series of the matrix-vector differential equations and then solved by the eigenvalues method. The inversion of the transformation solutions is demonstrated in the space-time domains by the Riemann-sum approximation approach and graphically represented in two specific cases. It is demonstrated graphically how the conductive temperature \(\phi \) , thermodynamically temperature T, displacement u, stress \({{\sigma }_{{xx}}}\) , electric \(E\) and induced magnetic h fields were influenced by the hyperbolic two-temperatures parameter and magnetic field.