A modified Moore-Gibson-Thompson fractional model for mass diffusion and thermal behavior in an infinite elastic medium with a cylindrical cavity

Abstract

This article discussed a new fractional model that included governing equations describing mass and thermal diffusion in elastic materials. We formulated the thermal and mass diffusion equations using the Atangana-Baleanu-Caputo (ABC) fractional derivative and the Moore-Gibson-Thomson (MGT) equation. In addition to the fractional operators, this improvement included incorporating temperature and diffusion relaxation periods into the Green and Naghdi model (GN-Ⅲ). To verify the proposed model and analyze the effects of the interaction between temperature and mass diffusion, an infinite thermoelastic medium with a cylindrical hole was considered. We analyzed the problem under boundary conditions where the concentration remained constant, the temperature fluctuated and decreased, and the surrounding cavity was free from any external forces. We applied Laplace transform techniques and Mathematica software to generate calculations and numerical results for various field variables. We then compared the obtained results with those from previous relevant models. We have graphically depicted the results and extensively examined and evaluated them to understand the effects of the relationship between temperature and mass diffusion in the system.

Keywords

• fractional derivative
• thermoelastic
• diffusion
• mgt equation
• infinite medium