A novel mathematical model on generalized thermoelastic diffusion theory

In this work, a new linear model of thermo-diffusion in elastic solids has been proposed in the context of generalized thermo-elasticity. The theories of coupled thermoelastic diffusion and of generalized thermoelastic diffusion problem with one relaxation time and also of generalized thermoelastic diffusion in GN models as well as Lord-Shulman, Green-Nagdhi, two-phase-lag and three-phase-lag models on thermo-elasticity follow as limit cases. A uniqueness theorem of the proposed model followed by the reciprocity theorem for diffusion is derived. The variational theorem for the governing equations has also been derived. Also, some applications of the model in dynamic and quasi-static problems are considered.