### Abstract

The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindelöf theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curvature of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 <n ⩽ 1, the solution has a positive curvature, while for n > 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.

Original language | English |
---|---|

Pages (from-to) | 1155-1166 |

Number of pages | 12 |

Journal | Applied Mathematics and Mechanics (English Edition) |

Volume | 35 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2014 |

Externally published | Yes |

### Fingerprint

### Keywords

- boundary layer flow
- existence
- non-linear boundary value problem
- power law fluid
- uniqueness

### ASJC Scopus subject areas

- Applied Mathematics
- Mechanics of Materials
- Mechanical Engineering

### Cite this

*Applied Mathematics and Mechanics (English Edition)*,

*35*(9), 1155-1166. https://doi.org/10.1007/s10483-014-1854-6

**Similarity solutions for non-Newtonian power-law fluid flow.** / Wei, D. M.; Al-Ashhab, S.

Research output: Contribution to journal › Article

*Applied Mathematics and Mechanics (English Edition)*, vol. 35, no. 9, pp. 1155-1166. https://doi.org/10.1007/s10483-014-1854-6

}

TY - JOUR

T1 - Similarity solutions for non-Newtonian power-law fluid flow

AU - Wei, D. M.

AU - Al-Ashhab, S.

PY - 2014

Y1 - 2014

N2 - The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindelöf theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curvature of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.

AB - The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindelöf theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curvature of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.

KW - boundary layer flow

KW - existence

KW - non-linear boundary value problem

KW - power law fluid

KW - uniqueness

UR - http://www.scopus.com/inward/record.url?scp=84920249615&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84920249615&partnerID=8YFLogxK

U2 - 10.1007/s10483-014-1854-6

DO - 10.1007/s10483-014-1854-6

M3 - Article

VL - 35

SP - 1155

EP - 1166

JO - Applied Mathematics and Mechanics

JF - Applied Mathematics and Mechanics

SN - 0253-4827

IS - 9

ER -