Axisymmetric Thermal Response of a Nonlocal Visco-Thermoelastic Medium under MGT Heat Conduction with HTT and Fractional-Order Effects

Abstract

This paper investigates a two-dimensional axisymmetric thermal source problem in a homogeneous and isotropic visco-thermoelastic half-space governed by the Moore-Gibson-Thompson (MGT) heat equation. The model includes nonlocal effects, hyperbolic two temperature (HTT) theory, viscosity and fractional-order derivative (FOD) effects. A circular thermal source is prescribed on the bounding plane, while the surface is assumed to be mechanically traction free. The governing equations are written in nondimensional form and reduced by introducing suitable potential functions. The Laplace transform with respect to time and the Hankel transform with respect to the radial coordinate are applied to obtain the transformed expressions for the displacement components, stress components, conductive temperature and thermodynamic temperature. The transformed solutions are inverted numerically to study the effect of the nonlocal parameter, HTT parameter, viscosity and fractional-order parameter on the field quantities generated by the circular thermal loading. The numerical results show that these parameters have a clear influence on the normal stress, tangential stress, conductive temperature and temperature distribution. Several limiting cases are also obtained, which confirms the generality of the present formulation.