In this paper we are concerned with a study of the thermoelastic diffusion problem with thermal relaxation in a two-dimensional elastic medium. The bounding surface (isothermal or insulated) of the half-space is taken to be traction free and subjected to a uniformly distributed thermal shock. The fundamental equations of generalized thermoelasticity with diffusion with one relaxation parameter in an elastic medium are obtained as a vector-matrix differential equation form in the Laplace-Fourier transform domain, which is then solved by the eigenvalue approach. A numerical technique is employed to obtain the solution in the physical domain. A comparison is made between the results obtained in a thermoelastic medium with and without diffusion at two different times.
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