Finite Difference Modeling of Time Fractal Impact on Unsteady Magneto-hydrodynamic Darcy–Forchheimer Flow in Non-Newtonian Nanofluids with the <i>q</i>-Derivative
This contribution addresses a fractal numerical scheme that can be employed for handling fractal time-dependent parabolic equations. The numerical scheme presented in this contribution can be used to discretize integer order and fractal derivatives in a given differential equation. Therefore, the sc...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/1/8 |
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| author | Amani S. Baazeem Yasir Nawaz Muhammad Shoaib Arif |
| author_facet | Amani S. Baazeem Yasir Nawaz Muhammad Shoaib Arif |
| author_sort | Amani S. Baazeem |
| collection | DOAJ |
| description | This contribution addresses a fractal numerical scheme that can be employed for handling fractal time-dependent parabolic equations. The numerical scheme presented in this contribution can be used to discretize integer order and fractal derivatives in a given differential equation. Therefore, the scheme and results can be used for both cases. The proposed finite difference scheme is based on two stages. Fractal time derivatives are discretized by employing the proposed approach. For the scalar convection–diffusion equation, we derive the stability condition of the proposed fractal scheme. Using a nonlinear chemical reaction, the approach is also used to solve the Quantum Calculus model of a Williamson nanofluid’s unsteady Darcy–Forchheimer flow over flat and oscillatory sheets. The findings indicate a negative correlation between the velocity profile and the porosity parameter and inertia coefficient, with an increase in these factors resulting in a drop in the velocity profile. Additionally, the fractal scheme under consideration is being compared to the fractal Crank–Nicolson method, revealing that the proposed scheme exhibits a superior convergence speed compared to the fractal Crank–Nicolson method. Several problems involving the motion of non-Newtonian nanofluids through magnetic fields and porous media can be investigated with the help of the proposed numerical scheme. This research has implications for developing more efficient heat transfer and energy conversion devices based on nanofluids. |
| first_indexed | 2024-03-08T10:55:21Z |
| format | Article |
| id | doaj.art-74bb70300c084e958847099e5322d76e |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-08T10:55:21Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-74bb70300c084e958847099e5322d76e2024-01-26T16:35:08ZengMDPI AGFractal and Fractional2504-31102023-12-0181810.3390/fractalfract8010008Finite Difference Modeling of Time Fractal Impact on Unsteady Magneto-hydrodynamic Darcy–Forchheimer Flow in Non-Newtonian Nanofluids with the <i>q</i>-DerivativeAmani S. Baazeem0Yasir Nawaz1Muhammad Shoaib Arif2Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11623, Saudi ArabiaDepartment of Mathematics, Air University, PAF Complex E-9, Islamabad 44000, PakistanDepartment of Mathematics, Air University, PAF Complex E-9, Islamabad 44000, PakistanThis contribution addresses a fractal numerical scheme that can be employed for handling fractal time-dependent parabolic equations. The numerical scheme presented in this contribution can be used to discretize integer order and fractal derivatives in a given differential equation. Therefore, the scheme and results can be used for both cases. The proposed finite difference scheme is based on two stages. Fractal time derivatives are discretized by employing the proposed approach. For the scalar convection–diffusion equation, we derive the stability condition of the proposed fractal scheme. Using a nonlinear chemical reaction, the approach is also used to solve the Quantum Calculus model of a Williamson nanofluid’s unsteady Darcy–Forchheimer flow over flat and oscillatory sheets. The findings indicate a negative correlation between the velocity profile and the porosity parameter and inertia coefficient, with an increase in these factors resulting in a drop in the velocity profile. Additionally, the fractal scheme under consideration is being compared to the fractal Crank–Nicolson method, revealing that the proposed scheme exhibits a superior convergence speed compared to the fractal Crank–Nicolson method. Several problems involving the motion of non-Newtonian nanofluids through magnetic fields and porous media can be investigated with the help of the proposed numerical scheme. This research has implications for developing more efficient heat transfer and energy conversion devices based on nanofluids.https://www.mdpi.com/2504-3110/8/1/8fractal numerical scheme<i>q</i>-derivativestabilityconvergencefluid flow model |
| spellingShingle | Amani S. Baazeem Yasir Nawaz Muhammad Shoaib Arif Finite Difference Modeling of Time Fractal Impact on Unsteady Magneto-hydrodynamic Darcy–Forchheimer Flow in Non-Newtonian Nanofluids with the <i>q</i>-Derivative Fractal and Fractional fractal numerical scheme <i>q</i>-derivative stability convergence fluid flow model |
| title | Finite Difference Modeling of Time Fractal Impact on Unsteady Magneto-hydrodynamic Darcy–Forchheimer Flow in Non-Newtonian Nanofluids with the <i>q</i>-Derivative |
| title_full | Finite Difference Modeling of Time Fractal Impact on Unsteady Magneto-hydrodynamic Darcy–Forchheimer Flow in Non-Newtonian Nanofluids with the <i>q</i>-Derivative |
| title_fullStr | Finite Difference Modeling of Time Fractal Impact on Unsteady Magneto-hydrodynamic Darcy–Forchheimer Flow in Non-Newtonian Nanofluids with the <i>q</i>-Derivative |
| title_full_unstemmed | Finite Difference Modeling of Time Fractal Impact on Unsteady Magneto-hydrodynamic Darcy–Forchheimer Flow in Non-Newtonian Nanofluids with the <i>q</i>-Derivative |
| title_short | Finite Difference Modeling of Time Fractal Impact on Unsteady Magneto-hydrodynamic Darcy–Forchheimer Flow in Non-Newtonian Nanofluids with the <i>q</i>-Derivative |
| title_sort | finite difference modeling of time fractal impact on unsteady magneto hydrodynamic darcy forchheimer flow in non newtonian nanofluids with the i q i derivative |
| topic | fractal numerical scheme <i>q</i>-derivative stability convergence fluid flow model |
| url | https://www.mdpi.com/2504-3110/8/1/8 |
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