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.

Using magnetohydrodynamics (MHD), the thermal energy and mass transport boundary layer flow parameters of Reiner–Philippoff fluid (non-Newtonian) are numerically investigated. In terms of energy and mass transfer, non-linear radiation, Cattaneo–Christov double diffusions, convective conditions at the surface, and the species reaction pertaining to activation energy are all addressed. The stated governing system of partial differential equations (PDEs) is drained into a non-linear differential system using appropriate similarity variables. Numerical solutions are found for the flow equations that have been determined. Two-dimensional charts are employed to demonstrate the flow field, temperature and species distributions, and rate of heat and mass transfers for the concerned parameters for both Newtonian and Reiner–Philippoff fluid examples. The stream line phenomenon is also mentioned in this paper. A table has also been utilized to illustrate the comparison with published results, which shows that the current numerical data are in good accord. The findings point to a new role for heat and mass transfer. According to the findings, increasing values of solutal and thermal relaxation time parameters diminish the associated mass and thermal energy layers. The current study has significant ramifications for chemical engineering systems.