Effects of stefan blowing and slip conditions on unsteady MHD casson nanofluid flow over an unsteady shrinking sheet: Dual solutions
In this article, the magnetohydrodynamic (MHD) flow of Casson nanofluid with thermal radiation over an unsteady shrinking surface is investigated. The equation of momentum is derived from the Navier–Stokes model for non-Newtonian fluid where components of the viscous terms are symmetric. The effe...
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| Format: | Article |
| Language: | English |
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Multidisciplinary Digital Publishing Institute (MDPI)
2020
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| Online Access: | https://repo.uum.edu.my/id/eprint/27919/1/S%2012%20487%202020%201%2017.pdf |
| _version_ | 1825805715001835520 |
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| author | Lund, Liaquat Ali Omar, Zurni Raza, Jawad Khan, Ilyas Sherif, El-Sayed M. |
| author_facet | Lund, Liaquat Ali Omar, Zurni Raza, Jawad Khan, Ilyas Sherif, El-Sayed M. |
| author_sort | Lund, Liaquat Ali |
| collection | UUM |
| description | In this article, the magnetohydrodynamic (MHD) flow of Casson nanofluid with thermal
radiation over an unsteady shrinking surface is investigated. The equation of momentum is derived
from the Navier–Stokes model for non-Newtonian fluid where components of the viscous terms
are symmetric. The effect of Stefan blowing with partial slip conditions of velocity, concentration, and temperature on the velocity, concentration, and temperature distributions is also taken into account. The modeled equations of partial differential equations (PDEs) are transformed into the equivalent boundary value problems (BVPs) of ordinary differential equations (ODEs) by employing similarity transformations. These similarity transformations can be obtained by using symmetry analysis. The resultant BVPs are reduced into initial value problems (IVPs) by using the shooting method and then solved by using the fourth-order Runge–Kutta (RK) technique. The numerical results reveal that dual solutions exist in some ranges of different physical parameters such as unsteadiness and suction/injection parameters. The thickness of the velocity boundary layer is enhanced in the second solution by increasing the magnetic and velocity slip factor effect in the boundary layer. Increment in the Prandtl number and Brownian motion parameter is caused by a reduction of the thickness of the thermal boundary layer and temperature. Moreover, stability analysis performed by employing the three-stage Lobatto IIIA formula in the BVP4C solver with the help of MATLAB software reveals that only the first solution is stable and physically realizable. |
| first_indexed | 2024-07-04T06:36:47Z |
| format | Article |
| id | uum-27919 |
| institution | Universiti Utara Malaysia |
| language | English |
| last_indexed | 2024-07-04T06:36:47Z |
| publishDate | 2020 |
| publisher | Multidisciplinary Digital Publishing Institute (MDPI) |
| record_format | eprints |
| spelling | uum-279192020-11-30T00:35:39Z https://repo.uum.edu.my/id/eprint/27919/ Effects of stefan blowing and slip conditions on unsteady MHD casson nanofluid flow over an unsteady shrinking sheet: Dual solutions Lund, Liaquat Ali Omar, Zurni Raza, Jawad Khan, Ilyas Sherif, El-Sayed M. QA75 Electronic computers. Computer science In this article, the magnetohydrodynamic (MHD) flow of Casson nanofluid with thermal radiation over an unsteady shrinking surface is investigated. The equation of momentum is derived from the Navier–Stokes model for non-Newtonian fluid where components of the viscous terms are symmetric. The effect of Stefan blowing with partial slip conditions of velocity, concentration, and temperature on the velocity, concentration, and temperature distributions is also taken into account. The modeled equations of partial differential equations (PDEs) are transformed into the equivalent boundary value problems (BVPs) of ordinary differential equations (ODEs) by employing similarity transformations. These similarity transformations can be obtained by using symmetry analysis. The resultant BVPs are reduced into initial value problems (IVPs) by using the shooting method and then solved by using the fourth-order Runge–Kutta (RK) technique. The numerical results reveal that dual solutions exist in some ranges of different physical parameters such as unsteadiness and suction/injection parameters. The thickness of the velocity boundary layer is enhanced in the second solution by increasing the magnetic and velocity slip factor effect in the boundary layer. Increment in the Prandtl number and Brownian motion parameter is caused by a reduction of the thickness of the thermal boundary layer and temperature. Moreover, stability analysis performed by employing the three-stage Lobatto IIIA formula in the BVP4C solver with the help of MATLAB software reveals that only the first solution is stable and physically realizable. Multidisciplinary Digital Publishing Institute (MDPI) 2020 Article PeerReviewed application/pdf en https://repo.uum.edu.my/id/eprint/27919/1/S%2012%20487%202020%201%2017.pdf Lund, Liaquat Ali and Omar, Zurni and Raza, Jawad and Khan, Ilyas and Sherif, El-Sayed M. (2020) Effects of stefan blowing and slip conditions on unsteady MHD casson nanofluid flow over an unsteady shrinking sheet: Dual solutions. Symmetry, 12. pp. 1-17. ISSN 2073-8994 http://doi.org/10.3390/sym12030487 doi:10.3390/sym12030487 doi:10.3390/sym12030487 |
| spellingShingle | QA75 Electronic computers. Computer science Lund, Liaquat Ali Omar, Zurni Raza, Jawad Khan, Ilyas Sherif, El-Sayed M. Effects of stefan blowing and slip conditions on unsteady MHD casson nanofluid flow over an unsteady shrinking sheet: Dual solutions |
| title | Effects of stefan blowing and slip conditions on unsteady MHD casson nanofluid flow over an unsteady shrinking sheet: Dual solutions |
| title_full | Effects of stefan blowing and slip conditions on unsteady MHD casson nanofluid flow over an unsteady shrinking sheet: Dual solutions |
| title_fullStr | Effects of stefan blowing and slip conditions on unsteady MHD casson nanofluid flow over an unsteady shrinking sheet: Dual solutions |
| title_full_unstemmed | Effects of stefan blowing and slip conditions on unsteady MHD casson nanofluid flow over an unsteady shrinking sheet: Dual solutions |
| title_short | Effects of stefan blowing and slip conditions on unsteady MHD casson nanofluid flow over an unsteady shrinking sheet: Dual solutions |
| title_sort | effects of stefan blowing and slip conditions on unsteady mhd casson nanofluid flow over an unsteady shrinking sheet dual solutions |
| topic | QA75 Electronic computers. Computer science |
| url | https://repo.uum.edu.my/id/eprint/27919/1/S%2012%20487%202020%201%2017.pdf |
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