The Effect of Fractional Time Derivative on Two-Dimension Porous Materials Due to Pulse Heat Flux
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 pr...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/3/207 |
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| author | Tareq Saeed Ibrahim A. Abbas |
| author_facet | Tareq Saeed Ibrahim A. Abbas |
| author_sort | Tareq Saeed |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T04:12:03Z |
| format | Article |
| id | doaj.art-d739acba6bfa4464a874eb27770331c9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T04:12:03Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d739acba6bfa4464a874eb27770331c92023-12-03T13:59:30ZengMDPI AGMathematics2227-73902021-01-019320710.3390/math9030207The Effect of Fractional Time Derivative on Two-Dimension Porous Materials Due to Pulse Heat FluxTareq Saeed0Ibrahim A. Abbas1Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaMathematics Department, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaIn 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.https://www.mdpi.com/2227-7390/9/3/207Fourier-Laplace transformsporous materialeigenvalues methodfractional time derivative |
| spellingShingle | Tareq Saeed Ibrahim A. Abbas The Effect of Fractional Time Derivative on Two-Dimension Porous Materials Due to Pulse Heat Flux Mathematics Fourier-Laplace transforms porous material eigenvalues method fractional time derivative |
| title | The Effect of Fractional Time Derivative on Two-Dimension Porous Materials Due to Pulse Heat Flux |
| title_full | The Effect of Fractional Time Derivative on Two-Dimension Porous Materials Due to Pulse Heat Flux |
| title_fullStr | The Effect of Fractional Time Derivative on Two-Dimension Porous Materials Due to Pulse Heat Flux |
| title_full_unstemmed | The Effect of Fractional Time Derivative on Two-Dimension Porous Materials Due to Pulse Heat Flux |
| title_short | The Effect of Fractional Time Derivative on Two-Dimension Porous Materials Due to Pulse Heat Flux |
| title_sort | effect of fractional time derivative on two dimension porous materials due to pulse heat flux |
| topic | Fourier-Laplace transforms porous material eigenvalues method fractional time derivative |
| url | https://www.mdpi.com/2227-7390/9/3/207 |
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