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.

The present work is devoted to the derivation of fundamental equations in generalized thermoelastic diffusion with four lags and higher-order time-fractional derivatives. The equations of the heat conduction and the mass diffusion have been modified by using Taylor’s series of time-fractional order. In this new model, the Fourier and the Fick laws have been modified to include a higher time-fractional order of the heat conduction vector, the gradient of temperature, the diffusing mass flux and the gradient of chemical potential. We adopted the definitions of Caputo and Jumarie; for time-fractional derivatives. The work of Nowacki; Sherief, Hamza, and Saleh; and Aouadi; are deduced as limit cases from the current investigation. Applying this formulation, we have discussed a thermoelastic-diffusion problem for a half-space exposed to thermal and chemical shock with a permeable material in contact with the half-surface. We discussed the sensitivity of the different physical parameters in all studied fields in detail and the results are presented graphically as well as in tabular forms.

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.

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.

The present work focuses on the attributes of flow, heat, and mass transfer together with double diffusive Cattaneo–Christov mechanism with regards to their applications. The aim of this study is to investigate the non-Newtonian Powell–Eyring fluid flow, taking into account the twofold impact of the heat generation mechanism and the viscous dissipation due to an extensible sheet. The chemical reaction between the fluid particles and the fluid variable properties is assumed in this study. The motive behind this study is the continuous and great interest in the utilization of non-Newtonian liquids in organic and technical disciplines. This model is administered and governed by the momentum equation, energy equation, and concentration, all of which are in the form of partial differential equations. With the help of the shooting technique, the numerical solution is obtained. Graphs show the characteristics of flow, heat, and mass transfer mechanisms for various governing parameters. Additionally, significant physical non-dimensional quantities have been presented in a tabular form. The outcomes detect that increasing the Deborah number, which is connected with the mass transfer field and the chemical reaction parameter, decreases the concentration distribution.