A two-dimensional generalized thermoelastic diffusion problem for a half-space

• The dynamic response of a two-dimensional generalized thermoelastic diffusion problem for a half-space is investigated.
• Due to the complexity of the governing equations, they are solved by hybrid Laplace transform-finite element method.
• The results show that the non-zero values of all the considered variables are only in a bounded region.
• The results also show that the propagating speed of diffusive wave is larger than that of thermoelastic wave.

The dynamic response of a two-dimensional generalized thermoelastic diffusion problem for a half-space is investigated in the context of the generalized thermoelastic diffusion theory. The half-space is subjected to a thermal shock and a chemical potential shock on its bounding surface. The governing equations of this problem are formulated, and due to the complexity of the equations, a numerical method, i.e., hybrid Laplace transform-finite element method, is used to solve them. The non-dimensional temperature, displacement and chemical potential are obtained and illustrated graphically. The results show that the non-zero values of all the considered variables are only in a bounded region and vanish identically beyond this region, and the propagating speed of diffusive wave is larger than that of thermoelastic wave.