Fractional Moore-Gibson-Thompson heat transfer model with two-temperature and non-singular kernels for 3D thermoelastic solid

Abstract

A new model of thermoelasticity based on fractional calculus in combination with Fourier's law of heat and dual temperature theory is presented, including the Moore-Gibson-Thomson equation. In the suggested model, the heat equation is represented in a fractional integral form using the Atangana–Baleanu fractional operators. The presence of the concept of the delay parameter in the heat flow vector leads to a finite velocity of heat wave propagation. The model is then applied to investigate the thermoelastic interaction in a homogeneous thermoelastic 3D elastic solid with a thermally loaded and traction-free surface. In the field of Laplace and double Fourier transforms, analytical solutions for thermal variables were derived, which were then reversed to the time-space by means of the Honig-Hirdes procedure. The classical theories of thermoelasticity and some generalized theories as special examples can be derived from the presented model of thermoelasticity with a two-temperature and fractional derivative. Numerical values of the studied field variables were calculated and presented graphically. In order to explore the influences of relaxation time, temperature discrepancy, and fractional order parameters, certain comparisons of thermophysical variables were presented in the figures.