Transient thermoelastic response in a semi-infinite medium subjected to a moving heat source: an implementation of the Moore–Gibson–Thompson model with higher-order memory-dependent derivatives

To design and analyze structures and materials that are subjected to changing thermal environments, it is essential to take into account thermal shock events, which are characterized by rapid and dramatic changes in temperature. In this study, a new thermal conductivity model was used to consider the thermal response of an isotropic thermoelastic medium heated by a moving heat source. This model uses memory-dependent higher derivatives and the concept of the Moore–Gibson–Thompson equation. Using the vector-matrix differential equation form, the basic equations are formulated. The model was applied to consider the thermomechanical behavior of a semi-infinite thermoelastic solid. In the field of the Laplace transform, the technique known as the eigenvalue approach deals with the mathematical formulation and solution of the problem. The inversions of Laplace transforms are found numerically using the Honig and Hirdes approximation approach. A graphical representation is provided showing the fluctuation in temperature, displacement, and stress distributions with changing values of kernel functions and higher orders, as well as the velocity of the heat source. Tables are also included to show comparisons and a full analysis of thermomechanical responses and how they affect the way system variables behave.