Analysis of dual solution for MHD flow of Williamson fluid with slippage
This study investigates the numerical solutions of MHD boundary layer and heat transfer of the Williamson fluid flow on the exponentially vertical shrinking sheet, having variable thickness and thermal conductivity under effects of the velocity and thermal slip parameters. It is also assumed that sh...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier B.V.
2019
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| Subjects: | |
| Online Access: | https://repo.uum.edu.my/id/eprint/27937/1/H%205%203%202019%201%2020.pdf |
| _version_ | 1825805718569091072 |
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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 | This study investigates the numerical solutions of MHD boundary layer and heat transfer of the Williamson fluid flow on the exponentially vertical shrinking sheet, having variable thickness and thermal conductivity under effects of the velocity and thermal slip parameters. It is also assumed that shrinking/stretching velocity, as well as the wall temperature, has the exponential function form. In this study, the continuity, momentum and energy equations with buoyancy parameter and Hartmann number are incorporated especially in the Williamson fluid flow case. Similarity transformation variables have been employed to formulate the ordinary differential equations (ODEs) from partial differential equations (PDEs). The resultant ODEs are solved by shooting method with Runge Kutta of fourth order method in Maple software. The effects of the different applied non-dimensional physical parameters on the boundary layer and heat transfer flow problems are presented in graphs. The effects of Williamson parameter, Prandtl number, and slip parameters on velocity and temperature profiles have been thoroughly demonstrated and discussed. The numerical results show that the buoyancy force and the slip parameters contribute to the occurrence of the dual solutions on the boundary layer and heat transfer flow problems. Furthermore, the stability analysis suggests that the first solution is stable and physically possible. |
| first_indexed | 2024-07-04T06:36:51Z |
| format | Article |
| id | uum-27937 |
| institution | Universiti Utara Malaysia |
| language | English |
| last_indexed | 2024-07-04T06:36:51Z |
| publishDate | 2019 |
| publisher | Elsevier B.V. |
| record_format | eprints |
| spelling | uum-279372020-12-01T05:59:57Z https://repo.uum.edu.my/id/eprint/27937/ Analysis of dual solution for MHD flow of Williamson fluid with slippage Lund, Liaquat Ali Omar, Zurni Khan, Ilyas QA75 Electronic computers. Computer science This study investigates the numerical solutions of MHD boundary layer and heat transfer of the Williamson fluid flow on the exponentially vertical shrinking sheet, having variable thickness and thermal conductivity under effects of the velocity and thermal slip parameters. It is also assumed that shrinking/stretching velocity, as well as the wall temperature, has the exponential function form. In this study, the continuity, momentum and energy equations with buoyancy parameter and Hartmann number are incorporated especially in the Williamson fluid flow case. Similarity transformation variables have been employed to formulate the ordinary differential equations (ODEs) from partial differential equations (PDEs). The resultant ODEs are solved by shooting method with Runge Kutta of fourth order method in Maple software. The effects of the different applied non-dimensional physical parameters on the boundary layer and heat transfer flow problems are presented in graphs. The effects of Williamson parameter, Prandtl number, and slip parameters on velocity and temperature profiles have been thoroughly demonstrated and discussed. The numerical results show that the buoyancy force and the slip parameters contribute to the occurrence of the dual solutions on the boundary layer and heat transfer flow problems. Furthermore, the stability analysis suggests that the first solution is stable and physically possible. Elsevier B.V. 2019 Article PeerReviewed application/pdf en https://repo.uum.edu.my/id/eprint/27937/1/H%205%203%202019%201%2020.pdf Lund, Liaquat Ali and Omar, Zurni and Khan, Ilyas (2019) Analysis of dual solution for MHD flow of Williamson fluid with slippage. Heliyon, 5. pp. 1-20. ISSN 24058440 http://doi.org/10.1016/j.heliyon.2019.e01345 doi:10.1016/j.heliyon.2019.e01345 doi:10.1016/j.heliyon.2019.e01345 |
| spellingShingle | QA75 Electronic computers. Computer science Lund, Liaquat Ali Omar, Zurni Khan, Ilyas Analysis of dual solution for MHD flow of Williamson fluid with slippage |
| title | Analysis of dual solution for MHD flow of Williamson fluid with slippage |
| title_full | Analysis of dual solution for MHD flow of Williamson fluid with slippage |
| title_fullStr | Analysis of dual solution for MHD flow of Williamson fluid with slippage |
| title_full_unstemmed | Analysis of dual solution for MHD flow of Williamson fluid with slippage |
| title_short | Analysis of dual solution for MHD flow of Williamson fluid with slippage |
| title_sort | analysis of dual solution for mhd flow of williamson fluid with slippage |
| topic | QA75 Electronic computers. Computer science |
| url | https://repo.uum.edu.my/id/eprint/27937/1/H%205%203%202019%201%2020.pdf |
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