Abstract
The main purpose of this paper is to describe the coupling mechanism between heat transfer and diffusion in thermoelastic materials. This will be investigated by deriving a new thermal diffusion model that allows waves to move at limited speeds, unlike the traditional thermodiffusion models. Based on the thermal relaxation concept, the fractional Moore-Gibson-Thompson equation can be used to describe the equations for heat conduction and mass diffusion. The system of equations is developed using the Green-Naghdi Type III theories and the Atangana-Baleanu-type (AB) fractional differential operator instead of the integer derivatives of time. Under the proposed concept of the fractional thermo-diffusion model, a problem of an unbounded elastic structure with a spherical hole is investigated. The surface within the bore is free of traction and exposed to thermal shock and chemical potential. The system of governing equations was combined into a sixth-order differential equation to determine the analytical results. For this purpose, the Laplace transform was used, and a numerical algorithm to calculate the inversions was applied. The numerical results demonstrate that the improved fractional operator considerably impacts the dynamics of all research fields.