Many attempts have been made to investigate the classical heat transfer of Fourier, and a number of improvements have been implemented. In this work, we consider a novel thermoelasticity model based on the Moore–Gibson–Thompson equation in cases where some of these models fail to be positive. This thermomechanical model has been constructed in combination with a hyperbolic partial differential equation for the variation of the displacement field and a parabolic differential equation for the temperature increment. The presented model is applied to investigate the wave propagation in an isotropic and infinite body subjected to a continuous thermal line source. To solve this problem, together with Laplace and Hankel transform methods, the potential function approach has been used. Laplace and Hankel inverse transformations are used to find solutions to different physical fields in the space–time domain. The problem is validated by calculating the numerical calculations of the physical fields for a given material. The numerical and theoretical results of other thermoelastic models have been compared with those described previously.

In the current work, a new generalized model of heat conduction has been constructed taking into account the influence of the microscopic structure into the on non-simple thermoelastic materials. The new model was established on the basis of the system of equations that includes three-phase lags of higher-order and two different temperatures, namely thermodynamic and conductive temperature. The two-temperature thermoelastic model presented by Chen and Gurtin (Z Angew Math Phys 19(4):614–627, 1968) and some other previous models have been introduced as special cases from the proposed model. As an application of the new model, we studied the thermoelastic interactions resulting from sudden heating in an isotropic solid subjected to external body force. The influence of the discrepancy parameter and higher-order of the time-derivative has been discussed. This work will enable future investigators to gain insight into non-simple thermoelasticity with different phase delays of higher-order in detail.

No abstract