Transient responses to an infinite solid with a spherical cavity according to the MGT thermo-diffusion model with fractional derivatives without nonsingular kernels
Ahmed E. Abouelregal, Alanazi Rayan, Doaa M. Mostafa
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.