The Effects of Fractional Time Derivatives in Porothermoelastic Materials Using Finite Element Method

In this work, a new model for porothermoelastic waves under a fractional time derivative and two time delays is utilized to study temperature increments, stress and the displacement components of the solid and fluid phases in porothermoelastic media. The governing equations are presented under Lord-Shulman theory with thermal relaxation time. The finite element method has been adopted to solve these equations due to the complex formulations of this problem. The effects of fractional parameter and porosity in porothermoelastic media have been studied. The numerical outcomes for the temperatures, the stresses and the displacement of the fluid and the solid are presented graphically. These results will allow future studies to gain a detailed insight into non-simple porothermoelasticity with various phases.

Automated summary

A new model for porothermoelastic waves with fractional time derivative and two time delays was used to study temperature increments, stress, and displacement components in porothermoelastic media. The governing equations were presented under Lord-Shulman theory with thermal relaxation time, and the finite element method was adopted due to the complex formulations. The effects of fractional parameter and porosity in porothermoelastic media were studied, and numerical outcomes were presented graphically for future detailed studies on non-simple porothermoelasticity with various phases.