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The Effect of Fractional Time Derivative on Two-Dimension Porous Materials Due to Pulse Heat Flux

Author

Listed:
  • Tareq Saeed

    (Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Ibrahim A. Abbas

    (Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt)

Abstract

In the present article, the generalized thermoelastic wave model with and without energy dissipation under fractional time derivative is used to study the physical field in porous two-dimensional media. By applying the Fourier-Laplace transforms and eigenvalues scheme, the physical quantities are presented analytically. The surface is shocked by heating (pulsed heat flow problem) and application of free traction on its outer surface (mechanical conditions) by the process of temperature transport (diffusion) to observe the full analytical solutions of the main physical fields. The magnesium (Mg) material is used to make the simulations and obtain numerical outcomes. The basic physical field quantities are graphed and discussed. Comparisons are made in the results obtained under the strong (SC), the weak (WC) and the normal (NC) conductivities.

Suggested Citation

  • Tareq Saeed & Ibrahim A. Abbas, 2021. "The Effect of Fractional Time Derivative on Two-Dimension Porous Materials Due to Pulse Heat Flux," Mathematics, MDPI, vol. 9(3), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:207-:d:483809
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    References listed on IDEAS

    as
    1. Manuela Carini & Vittorio Zampoli, 2020. "On Porous Matrices with Three Delay Times: A Study in Linear Thermoelasticity," Mathematics, MDPI, vol. 8(3), pages 1-16, March.
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    Cited by:

    1. A. V. Sedelnikov & D. I. Orlov & V. V. Serdakova & A. S. Nikolaeva, 2023. "Investigation of the Stress-Strain State of a Rectangular Plate after a Temperature Shock," Mathematics, MDPI, vol. 11(3), pages 1-12, January.

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