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Khader MM, Megahed AM, Eid A. Numerical treatment of the radiated and dissipative power-law nanofluid flow past a nonlinear stretched sheet with non-uniform heat generation. Sci Rep 2023; 13:22691. [PMID: 38114528 PMCID: PMC10730838 DOI: 10.1038/s41598-023-49547-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2023] [Accepted: 12/09/2023] [Indexed: 12/21/2023] Open
Abstract
The main aim of this paper is to investigate the effect of non-uniform heat generation and viscous dissipation on the boundary layer flow of a power-law nanofluid over a nonlinear stretching sheet. Within the thermal domain, the analysis considers both thermal radiation and variable thermal conductivity. Through the use of similarity transformations, the governing boundary layer equations are transformed into a system of ODEs. The spectral collocation method (SCM) with shifted Vieta-Lucas polynomials (VLPs) is implemented to give an approximate expression for the derivatives and then use it to numerically solve the proposed system of equations. By employing this technique, the system of ODEs is converted into a system of nonlinear algebraic equations. The dimensionless temperature, concentration, and velocity are graphically presented and analyzed for various values of the relevant governing parameters. Through the presented graphical solutions, we can see that the main outcomes indicate that an increase in the power law index, thermal conductivity parameter, and radiation parameter leads to a noticeable decrease in the local Nusselt number, with reductions of around 0.05 percent, 0.23 percent, and 0.11 percent, respectively. In contrast, the Prandtl parameter demonstrates an opposing effect, elevating the local Nusselt number by about 0.1 percent. We validated the accuracy of the numerical solutions by comparing them in some special cases with existing literature.
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Affiliation(s)
- M M Khader
- Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11566, Saudi Arabia.
- Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt.
| | - Ahmed M Megahed
- Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
| | - A Eid
- Department of Physics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11566, Saudi Arabia
- Department of Astronomy, Faculty of Science, Cairo University, Giza, Egypt
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Srivastava HM, Saad KM, Khader MM. An efficient spectral collocation method for the dynamic simulation of the fractional epidemiological model of the Ebola virus. Chaos Solitons Fractals 2020; 140:110174. [PMID: 32834654 PMCID: PMC7409997 DOI: 10.1016/j.chaos.2020.110174] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Revised: 07/03/2020] [Accepted: 07/27/2020] [Indexed: 05/04/2023]
Abstract
This article investigates a family of approximate solutions for the fractional model (in the Liouville-Caputo sense) of the Ebola virus via an accurate numerical procedure (Chebyshev spectral collocation method). We reduce the proposed epidemiological model to a system of algebraic equations with the help of the properties of the Chebyshev polynomials of the third kind. Some theorems about the convergence analysis and the existence-uniqueness solution are stated. Finally, some numerical simulations are presented for different values of the fractional-order and the other parameters involved in the coefficients. We also note that we can apply the proposed method to solve other models.
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Affiliation(s)
- H M Srivastava
- Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
- Department of Medical Research, China Medical University Hospital, China Medical University, Taiwan, Taichung 40402, Republic of China
- Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
| | - Khaled M Saad
- Department of Mathematics, College of Arts and Sciences, Najran University, Najran, Kingdom of Saudi Arabia
- Department of Mathematics, Faculty of Applied Science, Taiz University, Taiz, Yemen
| | - M M Khader
- Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Kingdom of Saudi Arabia
- Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
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Khader MM, Saad KM. Numerical Studies of the Fractional Korteweg-de Vries, Korteweg-de Vries-Burgers’ and Burgers’ Equations. Proc Natl Acad Sci , India, Sect A Phys Sci 2020. [DOI: 10.1007/s40010-020-00656-2] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Saad KM, Khader MM, Gómez-Aguilar JF, Baleanu D. Numerical solutions of the fractional Fisher's type equations with Atangana-Baleanu fractional derivative by using spectral collocation methods. Chaos 2019; 29:023116. [PMID: 30823705 DOI: 10.1063/1.5086771] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2018] [Accepted: 01/11/2019] [Indexed: 06/09/2023]
Abstract
The main objective of this paper is to investigate an accurate numerical method for solving a biological fractional model via Atangana-Baleanu fractional derivative. We focused our attention on linear and nonlinear Fisher's equations. We use the spectral collocation method based on the Chebyshev approximations. This method reduced the nonlinear equations to a system of ordinary differential equations by using the properties of Chebyshev polynomials and then solved them by using the finite difference method. This is the first time that this method is used to solve nonlinear equations in Atangana-Baleanu sense. We present the effectiveness and accuracy of the proposed method by computing the absolute error and the residual error functions. The results show that the given procedure is an easy and efficient tool to investigate the solution of nonlinear equations with local and non-local singular kernels.
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Affiliation(s)
- K M Saad
- Department of Mathematics, Faculty of Arts and Sciences, Najran University, P.O. Box 1988, Najran City, Saudi Arabia
| | - M M Khader
- Department of Mathematics and Statistics, College of Science, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 1440, Riyadh, Saudi Arabia
| | - J F Gómez-Aguilar
- CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, 62490 Cuernavaca, Morelos, Mexico
| | - Dumitru Baleanu
- Department of Mathematics, Faculty of Sciences, Cankaya University, Balgat, P.O. Box 06530, Ankara, Turkey
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Al-Marri MJ, Khader MM, Tawfik M, Qi G, Giannelis EP. CO₂ sorption kinetics of scaled-up polyethylenimine-functionalized mesoporous silica sorbent. Langmuir 2015; 31:3569-3576. [PMID: 25764385 DOI: 10.1021/acs.langmuir.5b00189] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Two CO2 solid sorbents based on polyethylenimine, PEI (M(n) ∼ 423 and 10K), impregnated into mesoporous silica (MPS) foam prepared in kilogram quantities via a scale-up process were synthesized and systematically characterized by a range of analytical and surface techniques. The mesoporous silica sorbent impregnated with lower molecular weight PEI, PEI-423/MPS, showed higher capacity toward CO2 sorption than the sorbent functionalized with the higher molecular weight PEI (PEI-10K/MPS). On the other hand, PEI-10K/MPS exhibited higher thermal stability than PEI-423/MPS. The kinetics of CO2 adsorption on both PEI/MPS fitted well with a double-exponential model. According to this model CO2 adsorption can be divided into two steps: the first is fast and is attributed to CO2 adsorption on the sorbent surface; the second is slower and can be related to the diffusion of CO2 within and between the mesoporous particles. In contrast, the desorption process obeyed first-order kinetics with activation energies of 64.3 and 140.7 kJ mol(-1) for PEI-423/MPS and PEI-10K/MPS, respectively. These studies suggest that the selection of amine is critical as it affects not only sorbent capacity and stability but also the energy penalty associated with sorbent regeneration.
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Affiliation(s)
- M J Al-Marri
- †Gas Processing Center, College of Engineering, Qatar University, P.O. Box 2713, Doha, Qatar
| | - M M Khader
- †Gas Processing Center, College of Engineering, Qatar University, P.O. Box 2713, Doha, Qatar
| | - M Tawfik
- †Gas Processing Center, College of Engineering, Qatar University, P.O. Box 2713, Doha, Qatar
| | - G Qi
- ‡Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14853, United States
| | - E P Giannelis
- ‡Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14853, United States
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Khader MM, Al-Marri MJ, Ali S, Qi G, Giannelis EP. Adsorption of CO<sub>2</sub> on Polyethyleneimine 10k—<i>Mesoporous silica</i> Sorbent: XPS and TGA Studies. ACTA ACUST UNITED AC 2015. [DOI: 10.4236/ajac.2015.64026] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Khader MM, Megahed AM. Effect of Viscous Dissipation on the Boundary Layer Flow and Heat Transfer Past a Permeable Stretching Surface Embedded in a Porous Medium with a Second-Order Slip Using Chebyshev Finite Difference Method. Transp Porous Media 2014. [DOI: 10.1007/s11242-014-0380-x] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Khader MM, Sweilam NH. Approximate solutions for the fractional advection–dispersion equation using Legendre pseudo-spectral method. ACTA ACUST UNITED AC 2013. [DOI: 10.1007/s40314-013-0091-x] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Khader MM. The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations. J Comput Nonlinear Dyn 2013; 8:41018-NaN. [PMID: 24891846 PMCID: PMC4011031 DOI: 10.1115/1.4024852] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2012] [Revised: 04/02/2013] [Indexed: 06/03/2023]
Abstract
In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.
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Affiliation(s)
- M M Khader
- Department of Mathematics and Statistics , College of Science, Al-Imam Mohammed Ibn Saud, Islamic University (IMSIU), Riyadh 11566, Saudi Arabia e-mail:
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Sweilam NH, Khader MM, Adel M. On the stability analysis of weighted average finite difference methods for fractional wave equation. ACTA ACUST UNITED AC 2012. [DOI: 10.7153/fdc-02-02] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Khader MM, Vurens GH, Kim IK, Salmeron M, Somorjai GA. Photoassisted catalytic dissociation of water to produce hydrogen on partially reduced .alpha.-iron(III) oxide. J Am Chem Soc 2002. [DOI: 10.1021/ja00246a014] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Soliman AT, Al Suweid AR, Gamil H, Khader MM, Afour MG. Glucose tolerance, C-peptide response to glucagon, and thyroid and adrenal functions in relation to auto-antibodies in vitiligo. J Trop Pediatr 1996; 42:60. [PMID: 8820627 DOI: 10.1093/tropej/42.1.60] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
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El-Anadouli BE, Khader MM, Saleh MM, Ateya BG. Application of porous flow through electrodes: IV. Hydrogen evolution on packed bed electrodes of iron spheres in flowing alkaline solutions. J APPL ELECTROCHEM 1991. [DOI: 10.1007/bf01464298] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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