Fractional Moore-Gibson-Thomson model for mass diffusion and thermal dynamics: Application to an infinite viscoelastic medium with a cylindrical cavity

Abstract

This article presented an innovative fractional model that integrated mass diffusion and thermal diffusion equations within thermo-viscoelastic Kelvin-Voigt materials, providing a deeper understanding of material behavior. The model employed the Atangana-Baleanu-Caputo (ABC) fractional derivative in conjunction with the Moore-Gibson-Thomson (MGT) equation, effectively capturing non-local and memory-dependent processes that were often overlooked in traditional models. By incorporating these advanced concepts, the model offered a more accurate representation of material responses, particularly in scenarios involving complex thermal and mass diffusion effects. The model utilized advanced mathematical techniques, including Laplace transforms and Mathematica, to solve the resulting complex differential equations, ensuring computational efficiency and accuracy. Validation of the model was conducted through comparisons with previous studies, demonstrating its improvements over existing approaches, and confirming its practical applicability. The article also provided graphical results and analysis, emphasizing the significant effects of heat transfer, viscoelasticity, and mass diffusion on material performance. These contributions were crucial for advancing engineering applications, especially in systems where traditional models fell short, such as in microelectronics, aerospace, and energy systems. The novelty of this work lay in its ability to address the limitations of conventional models by incorporating memory-dependent effects and non-local interactions, which significantly enhanced the prediction and design of materials under complex loading conditions.

Keywords

• ABC fractional derivative
• Thermal diffusion
• Viscoelasticity
• MGT heat equation
• Kelvin–Voigt materials