Generalized thermoelastic responses in an infinite solid cylinder under the thermoelastic-diffusion model with four lags

Understanding thermal diffusion through elastic materials is an important process that links the fields of temperature, strain, and mass diffusion. Certain mathematical and experimental models have been developed to explain this phenomenon, and defects flaws in the traditional theories have been discovered. In this context, a new and improved model of thermal diffusion has been introduced in which Fourier and Fick's laws are replaced by more general formulas. The equations for heat conduction and mass diffusion in the proposed model are extended to incorporate higher-order time derivatives and four lag phases. In special cases, some classical and generalized thermoelastic diffusion models may be obtained. The suggested model has been applied to investigate the thermoelastic diffusion processes in a solid cylinder caused by a possible thermal and chemical shock to its surface. The numerical findings of the thermodiffusion fields are shown and described graphically. The influence of the four-phase delay parameters on the various investigated fields has been compared between different models of thermal diffusion.