Abstract
A three-dimensional model of the two-temperature generalized thermoelasticity with one relaxation time is established. The resulting non-dimensional coupled equations together with the Laplace and duple Fourier transforms techniques are applied to a specific problem of a half space subjected to ramp-type heating and traction free surface. The inverses of Fourier transforms and Laplace transforms are obtained numerically by using the complex inversion formula of the transform together with Fourier expansion techniques. Numerical results for the conductive temperature, the dynamical temperature, the stress, the strain, and the displacement distributions are represented graphically.