Abstract
In this work, the consideration of variable thermal conductivity as a linear function of temperature has been taken into account in the context of two-temperature generalized thermoelasticity (Youssef's model). The governing equations have been derived and used to solve the one-dimensional problems of an elastic half-space. The governing equations have been cast into a matrix form by using Bahar-Hetnarski method, and Laplace transform is used to get the general solution for any set of boundary conditions. The solution has been applied for a thermally shocked medium that has no strain on its bounding plane. The numerical inversion of the Laplace transform has been calculated by using the Riemann-sum approximation method. The distribution of the conductive temperature, the thermo-dynamical temperature, the strain, the displacement, and the stress have been shown graphically with some comparisons.