Mathematical analysis of magnetohydrodynamic (MHD) flow of micropolar nanofluid under buoyancy effects past a vertical shrinking surface: dual solutions
In this paper, we explore dual solutions of MHD flow, heat and mass transfer of micropolar nanofluid over a linear vertical shrinking surface with buoyancy effects, which was not considered in the previous works. The governing fluid flow equations of this problem are transformed into nonlinear bound...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier Inc.
2019
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| Subjects: | |
| Online Access: | https://repo.uum.edu.my/id/eprint/26531/1/H%205%202019%20e02432.pdf |
| _version_ | 1825805488566042624 |
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| author | Lund, Liaquat Ali Omar, Zurni Khan, Ilyas |
| author_facet | Lund, Liaquat Ali Omar, Zurni Khan, Ilyas |
| author_sort | Lund, Liaquat Ali |
| collection | UUM |
| description | In this paper, we explore dual solutions of MHD flow, heat and mass transfer of micropolar nanofluid over a linear vertical shrinking surface with buoyancy effects, which was not considered in the previous works. The governing fluid flow equations of this problem are transformed into nonlinear boundary value problems (BVPs) of ordinary differential equations (ODEs) by applying similarity variables. The resultant BVPs are converted into initial value problems (IVPs) by using shooting method which then resolved by employing Runge Kutta of order four. The impacts of the governing parameters, such as suction parameter, material parameter, Richardson number, magnetic parameter, Prandtl number, thermophoresis and Brownian motion parameters on velocity, angular velocity, temperature, and concentration are illustrated graphically. The results indicate that the existence of a range of dual solutions and no-solutions. When Richardson number (delta) is increased, the reduction of the velocity of micropolar nanofluid has occurred in the second solution. The stability analysis on dual solutions, however, reveals that only the first solution is stable. |
| first_indexed | 2024-07-04T06:33:09Z |
| format | Article |
| id | uum-26531 |
| institution | Universiti Utara Malaysia |
| language | English |
| last_indexed | 2024-07-04T06:33:09Z |
| publishDate | 2019 |
| publisher | Elsevier Inc. |
| record_format | eprints |
| spelling | uum-265312019-10-29T01:10:48Z https://repo.uum.edu.my/id/eprint/26531/ Mathematical analysis of magnetohydrodynamic (MHD) flow of micropolar nanofluid under buoyancy effects past a vertical shrinking surface: dual solutions Lund, Liaquat Ali Omar, Zurni Khan, Ilyas QA75 Electronic computers. Computer science In this paper, we explore dual solutions of MHD flow, heat and mass transfer of micropolar nanofluid over a linear vertical shrinking surface with buoyancy effects, which was not considered in the previous works. The governing fluid flow equations of this problem are transformed into nonlinear boundary value problems (BVPs) of ordinary differential equations (ODEs) by applying similarity variables. The resultant BVPs are converted into initial value problems (IVPs) by using shooting method which then resolved by employing Runge Kutta of order four. The impacts of the governing parameters, such as suction parameter, material parameter, Richardson number, magnetic parameter, Prandtl number, thermophoresis and Brownian motion parameters on velocity, angular velocity, temperature, and concentration are illustrated graphically. The results indicate that the existence of a range of dual solutions and no-solutions. When Richardson number (delta) is increased, the reduction of the velocity of micropolar nanofluid has occurred in the second solution. The stability analysis on dual solutions, however, reveals that only the first solution is stable. Elsevier Inc. 2019 Article PeerReviewed application/pdf en https://repo.uum.edu.my/id/eprint/26531/1/H%205%202019%20e02432.pdf Lund, Liaquat Ali and Omar, Zurni and Khan, Ilyas (2019) Mathematical analysis of magnetohydrodynamic (MHD) flow of micropolar nanofluid under buoyancy effects past a vertical shrinking surface: dual solutions. Heliyon, 5 (9). pp. 1-10. ISSN 24058440 http://doi.org/10.1016/j.heliyon.2019.e02432 doi:10.1016/j.heliyon.2019.e02432 doi:10.1016/j.heliyon.2019.e02432 |
| spellingShingle | QA75 Electronic computers. Computer science Lund, Liaquat Ali Omar, Zurni Khan, Ilyas Mathematical analysis of magnetohydrodynamic (MHD) flow of micropolar nanofluid under buoyancy effects past a vertical shrinking surface: dual solutions |
| title | Mathematical analysis of magnetohydrodynamic (MHD) flow of micropolar nanofluid under buoyancy effects past a vertical shrinking surface: dual solutions |
| title_full | Mathematical analysis of magnetohydrodynamic (MHD) flow of micropolar nanofluid under buoyancy effects past a vertical shrinking surface: dual solutions |
| title_fullStr | Mathematical analysis of magnetohydrodynamic (MHD) flow of micropolar nanofluid under buoyancy effects past a vertical shrinking surface: dual solutions |
| title_full_unstemmed | Mathematical analysis of magnetohydrodynamic (MHD) flow of micropolar nanofluid under buoyancy effects past a vertical shrinking surface: dual solutions |
| title_short | Mathematical analysis of magnetohydrodynamic (MHD) flow of micropolar nanofluid under buoyancy effects past a vertical shrinking surface: dual solutions |
| title_sort | mathematical analysis of magnetohydrodynamic mhd flow of micropolar nanofluid under buoyancy effects past a vertical shrinking surface dual solutions |
| topic | QA75 Electronic computers. Computer science |
| url | https://repo.uum.edu.my/id/eprint/26531/1/H%205%202019%20e02432.pdf |
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