### Abstract

In this study, the magnetohydrodynamics (MHD) stagnation-point boundary layer flow of a Carreau fluid towards a permeable stretching/shrinking surface (sheet) is considered. The governing boundary layer equations in the form of nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations by using the similarity transformations, so that they can be solved numerically by the bvp4c function (programme) in Matlab software. The variations of the numerical solutions for the skin friction coefficients as well as the velocity profiles are obtained for several values of the governing parameters. It is found that dual solutions exist when the sheet is stretched and shrunk. Stability analysis is performed to determine which solution is stable and valid physically. Results from the stability analysis show that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable.

Original language | English |
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Title of host publication | Advances in Industrial and Applied Mathematics: Proceedings of 23rd Malaysian National Symposium of Mathematical Sciences, SKSM 2015 |

Publisher | American Institute of Physics Inc. |

Volume | 1750 |

ISBN (Electronic) | 9780735414075 |

DOIs | |

Publication status | Published - 21 Jun 2016 |

Event | 23rd Malaysian National Symposium of Mathematical Sciences: Advances in Industrial and Applied Mathematics, SKSM 2015 - Johor Bahru, Malaysia Duration: 24 Nov 2015 → 26 Nov 2015 |

### Other

Other | 23rd Malaysian National Symposium of Mathematical Sciences: Advances in Industrial and Applied Mathematics, SKSM 2015 |
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Country | Malaysia |

City | Johor Bahru |

Period | 24/11/15 → 26/11/15 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Advances in Industrial and Applied Mathematics: Proceedings of 23rd Malaysian National Symposium of Mathematical Sciences, SKSM 2015*(Vol. 1750). [030031] American Institute of Physics Inc.. https://doi.org/10.1063/1.4954567

**Stability analysis of MHD stagnation-point flow towards a permeable stretching/shrinking surface in a Carreau fluid.** / Naganthran, Kohilavani; Mohd. Nazar, Roslinda.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Advances in Industrial and Applied Mathematics: Proceedings of 23rd Malaysian National Symposium of Mathematical Sciences, SKSM 2015.*vol. 1750, 030031, American Institute of Physics Inc., 23rd Malaysian National Symposium of Mathematical Sciences: Advances in Industrial and Applied Mathematics, SKSM 2015, Johor Bahru, Malaysia, 24/11/15. https://doi.org/10.1063/1.4954567

}

TY - GEN

T1 - Stability analysis of MHD stagnation-point flow towards a permeable stretching/shrinking surface in a Carreau fluid

AU - Naganthran, Kohilavani

AU - Mohd. Nazar, Roslinda

PY - 2016/6/21

Y1 - 2016/6/21

N2 - In this study, the magnetohydrodynamics (MHD) stagnation-point boundary layer flow of a Carreau fluid towards a permeable stretching/shrinking surface (sheet) is considered. The governing boundary layer equations in the form of nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations by using the similarity transformations, so that they can be solved numerically by the bvp4c function (programme) in Matlab software. The variations of the numerical solutions for the skin friction coefficients as well as the velocity profiles are obtained for several values of the governing parameters. It is found that dual solutions exist when the sheet is stretched and shrunk. Stability analysis is performed to determine which solution is stable and valid physically. Results from the stability analysis show that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable.

AB - In this study, the magnetohydrodynamics (MHD) stagnation-point boundary layer flow of a Carreau fluid towards a permeable stretching/shrinking surface (sheet) is considered. The governing boundary layer equations in the form of nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations by using the similarity transformations, so that they can be solved numerically by the bvp4c function (programme) in Matlab software. The variations of the numerical solutions for the skin friction coefficients as well as the velocity profiles are obtained for several values of the governing parameters. It is found that dual solutions exist when the sheet is stretched and shrunk. Stability analysis is performed to determine which solution is stable and valid physically. Results from the stability analysis show that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable.

UR - http://www.scopus.com/inward/record.url?scp=84984535276&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84984535276&partnerID=8YFLogxK

U2 - 10.1063/1.4954567

DO - 10.1063/1.4954567

M3 - Conference contribution

VL - 1750

BT - Advances in Industrial and Applied Mathematics: Proceedings of 23rd Malaysian National Symposium of Mathematical Sciences, SKSM 2015

PB - American Institute of Physics Inc.

ER -