Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis
Steady incompressible magnetohydrodynamic mixed convection boundary layer flow of a Casson fluid on an exponentially vertical shrinking sheet using the non‐Newtonian heating equation is investigated in this paper. There are three main objectives of this study, namely, to develop a new mathematical m...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Published: |
John Wiley & Sons, Inc
2019
|
| Subjects: |
| _version_ | 1803629143334584320 |
|---|---|
| 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 | Steady incompressible magnetohydrodynamic mixed convection boundary layer flow of a Casson fluid on an exponentially vertical shrinking sheet using the non‐Newtonian heating equation is investigated in this paper. There are three main objectives of this study, namely, to develop a new mathematical model, to obtain multiple solutions, and to perform stability analysis. The governing partial differential equations have been changed into nonlinear ordinary differential equations. The resultant equations of boundary value problems are then converted into the equivalent initial value problems using the shooting method before they can be solved using Runge‐Kutta of order four. The numerical results are obtained and found to be in good agreement with the published literature. The results also indicate that the velocity boundary layer becomes thinner as the magnetic, slip, and Casson parameters increase. Dual solutions for temperature and velocity distributions are obtained. Furthermore, the results suggest that the presence of the force of buoyancy (opposing flow case) would cause the occurrence of dual solutions. However, based on the stability analysis, only the first solution is stable. |
| first_indexed | 2024-07-04T06:33:10Z |
| format | Article |
| id | uum-26535 |
| institution | Universiti Utara Malaysia |
| last_indexed | 2024-07-04T06:33:10Z |
| publishDate | 2019 |
| publisher | John Wiley & Sons, Inc |
| record_format | dspace |
| spelling | uum-265352019-10-29T01:45:13Z https://repo.uum.edu.my/id/eprint/26535/ Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis Lund, Liaquat Ali Omar, Zurni Khan, Ilyas QA75 Electronic computers. Computer science Steady incompressible magnetohydrodynamic mixed convection boundary layer flow of a Casson fluid on an exponentially vertical shrinking sheet using the non‐Newtonian heating equation is investigated in this paper. There are three main objectives of this study, namely, to develop a new mathematical model, to obtain multiple solutions, and to perform stability analysis. The governing partial differential equations have been changed into nonlinear ordinary differential equations. The resultant equations of boundary value problems are then converted into the equivalent initial value problems using the shooting method before they can be solved using Runge‐Kutta of order four. The numerical results are obtained and found to be in good agreement with the published literature. The results also indicate that the velocity boundary layer becomes thinner as the magnetic, slip, and Casson parameters increase. Dual solutions for temperature and velocity distributions are obtained. Furthermore, the results suggest that the presence of the force of buoyancy (opposing flow case) would cause the occurrence of dual solutions. However, based on the stability analysis, only the first solution is stable. John Wiley & Sons, Inc 2019-08 Article PeerReviewed Lund, Liaquat Ali and Omar, Zurni and Khan, Ilyas (2019) Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis. Heat Transfer-Asian Research. ISSN 10992871 http://doi.org/10.1002/htj.21554 doi:10.1002/htj.21554 doi:10.1002/htj.21554 |
| spellingShingle | QA75 Electronic computers. Computer science Lund, Liaquat Ali Omar, Zurni Khan, Ilyas Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis |
| title | Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis |
| title_full | Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis |
| title_fullStr | Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis |
| title_full_unstemmed | Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis |
| title_short | Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis |
| title_sort | steady incompressible magnetohydrodynamics casson boundary layer flow past a permeable vertical and exponentially shrinking sheet a stability analysis |
| topic | QA75 Electronic computers. Computer science |
| work_keys_str_mv | AT lundliaquatali steadyincompressiblemagnetohydrodynamicscassonboundarylayerflowpastapermeableverticalandexponentiallyshrinkingsheetastabilityanalysis AT omarzurni steadyincompressiblemagnetohydrodynamicscassonboundarylayerflowpastapermeableverticalandexponentiallyshrinkingsheetastabilityanalysis AT khanilyas steadyincompressiblemagnetohydrodynamicscassonboundarylayerflowpastapermeableverticalandexponentiallyshrinkingsheetastabilityanalysis |