The equations of generalized thermoelastic diffusion, based on the theory of Lord and Shulman with one relaxation time, are given in anisotropic media. A variational principle for the governing equations is obtained. Then we show that the variational principle can be used to obtain a uniqueness theorem under suitable conditions. A reciprocity theorem for these equations is given. The obtained results are valid for some special cases that can be deduced from our generalized model.

The equations of generalized thermoelastic diffusion, based on the theory of Lord and Shulman, are given. Using Laplace transforms, a uniqueness theorem for these equations is proved. Also, a reciprocity theorem is obtained.

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.