A generalized thermoelastic diffusion problem for an infinitely long solid cylinder

The theory of generalized thermoelastic diffusion, based on the theory of Lord and Shulman, is used to study the thermoelastic-diffusion interactions in an infinitely long solid cylinder subjected to a thermal shock on its surface which is in contact with a permeating substance. By means of the Laplace transform and numerical Laplace inversion the problem is solved. Numerical results predict finite speeds of propagation for thermoelastic and diffusive waves and the presence of a tensile stress region close to the cylinder surface. The problem of generalized thermoelasticity has been reduced as a special case of our problem.