Axi-Symmetric Problem in the Thermoelastic Medium under Moore-Gibson-Thompson Heat Equation with Hyperbolic Two Temperature, Non-Local and Fractional Order

In this manuscript, a two-dimensional axi-symmetric problem within a thermoelastic medium featuring fractional order derivatives, focusing on the Moore-Gibson-Thompson heat equation (MGT) in response to mechanical loading is investigated. The study assesses the problem's applicability under the influence of hyperbolic two temperature (HTT) and the non-local parameter resulting from ring and disc loads. The governing equations are rendered dimensionless, simplified through the introduction of potential functions, and solved using Laplace and Hankel transforms. Analytical expressions for displacement, stresses, conductive temperature, and temperature distribution components are derived in the transformed domain. Numerical inversion techniques are employed to obtain solutions in the physical domain. The purpose of the manuscript is to analyze the effects of non-local parameters, HTT, and various thermoelasticity theories graphically on resulting stresses, conductive temperature, and temperature distributions. It is observed that the behavior of composite materials under mechanical loading is effected by non-local and HTT. It will provide information about the different constituents of a composite material respond to temperature changes and mechanical stresses, which is crucial for designing and optimizing composite structures. Additionally, specific cases of interest are deduced from the findings of this investigation.