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Geomechanics and Engineering Volume 23, Number 3, November10 2020 , pages 217-225 DOI: https://doi.org/10.12989/gae.2020.23.3.217 |
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Fractional order GL model on thermoelastic interaction in porous media due to pulse heat flux |
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Faris S. Alzahrani and Ibrahim A. Abbas
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| Abstract | ||
| In this paper, the thermoelastic interactions in a two-dimension porous body are studied. This problem is solved by using the Green and Lindsay (GL) generalized thermoelasticity model under fractional time derivative. The derived approaches are estimated. with numeral results which are applied to the porous mediums in simplifying geometrical. The bounding plane surface of the present half-space continuum is subjected to a pulse heat flux. We use the Laplace-Fourier transforms methods with the eigenvalues approach to solve the problem. The numerical solutions for the field functions are obtained numerically using the numerical Laplace inversion technique. The effects of the fractional parameter and the thermal relaxation times on the temperature field, the displacement field, the change in volume fraction field of voids distribution and the stress fields have been calculated and displayed graphically and the obtained results are discussed. | ||
| Key Words | ||
| Laplace-Fourier transforms; Green and Lindsay model; porous medium; eigenvalues approach; fractional derivative | ||
| Address | ||
| Faris S. Alzahrani: Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia Ibrahim A. Abbas: 1.) Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia 2.) Department of mathematics, Faculty of Science, Sohag University, Sohag, Egypt | ||