Fractional Heat Conduction with Variable Thermal Conductivity of Infinite Annular Cylinder Under Thermoelasticity Theorem of Moore–Gibson–Thompson

To discuss the fractional order heat conduction based on Youssef’s model, a new mathematical model of a thermoelastic annular cylinder with variable thermal conductivity will be constructed in this work. The Moore–Gibson– Thompson theorem of generalized thermoelasticity will be considered and the governing equations will be derived in dimensionless forms. The Laplace transform technique will be used for a one-dimensional thermoelastic, isotropic, and homogeneous annular cylinder in which the interior surrounded surface is thermally shocked and there is an axial traction-free environment, while the outer surrounded surface has neither heat increment nor cubical deformation. The numerical results will be computed for the Laplace transform inversions by using Tzou’s iteration approach. The distributions of the cubical deformation, invariant average stress, axial stress, and temperature increment will be represented in figures to analyze and discuss. The results show that the fractional-order and variable thermal conductivity parameters have significant effects on all the studied functions. The physical behaviour of the thermal conductivity is closely aligned with the classification of thermal conductivity into weak, normal, and strong categories, which is essential.