Abstract
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.
Highlights
Due to various applications in relevant subjects, including the field of geophysics, growing attention is being paid to the interaction between thermoelastic solids and fluids such as porothermoelastic fields and water
Hobiny [22] studied the impacts of relaxation time and porosity in porothermoelastic materials under a hybrid finite element method
The numerical results are graphically presented to show the impacts of the porosity and fractional parameter in porothermoelastic medium for all considered variables
Summary
Due to various applications in relevant subjects, including the field of geophysics, growing attention is being paid to the interaction between thermoelastic solids and fluids such as porothermoelastic fields and water. Their theory is called the of thermoelastic theory with one relaxation time They obtained their model by modifying the Fourier’s law of heating conduction. Derived the governing equations of the thermoelastic theory with two thermal relaxation times. Sherief and Hussein [8] studied porothermoelasticity and obtained equations for a model predicting the finite speed of wave propagation. Sherief et al [11] studied a 2D axisymmetric thermoelastic problem for an infinite medium containing cylindrical heat sources of different materials with two time delays. Hobiny [22] studied the impacts of relaxation time and porosity in porothermoelastic materials under a hybrid finite element method. Saeed et al [25] applied the finite element scheme to discuss thermoelastic interaction in a poroelastic medium under the Green and Lindsay model. The numerical results are graphically presented to show the impacts of the porosity and fractional parameter in porothermoelastic medium for all considered variables
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