Three-dimensional generalized thermoelastic diffusion and application for a thermoelastic half-space subjected to rectangular thermal pulse

In this article, a model of three-dimensional generalized thermo-diffusion in a half-space thermoelastic medium subjected to permeating gas and the rectangular thermal pulse has been constructed. The half-space is considered to be made of an isotropic homogeneous thermoelastic material. The chemical potential is also assumed to be known on the bounding plane. Laplace transform techniques have been applied, and the solution is obtained in the Laplace transform domain using a direct approach. The solution of the problem in the physical domain is obtained numerically using a numerical method based on a Riemann-sum approximation for the inversion of Laplace transform. The temperature increment, stress, strain, diffusion concentration, and chemical potential distributions are represented graphically. The nonzero value of the relaxation time parameter predicts the finite speed of thermal, mechanical, diffusion waves.