Two-dimensional problem for a half-space with axi-symmetric distribution in the theory of generalized thermoelastic diffusion

In this work, we study a two-dimensional problem of axi-symmetric distribution of temperatures in a half-space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time. The surface of the half-space is taken as traction free and subjected to axi-symmetric time-dependent thermal shock. The chemical potential is also assumed to be a known function of time on the bounding plane. The Laplace and Hankel transform techniques are used. The analytical solution in the transform domain is obtained by using a direct approach. The inverse of the double transform is obtained by using a numerical method based on Fourier expansion techniques. Numerical results for the temperature, displacement, stress, concentration, and chemical potential are carried out and represented graphically.