### Abstract

The unsteady flows of an incompressible Oldroyd-B fluid between two infinite parallel plates are considered when the slippage between the plate and the fluid is valid. The relative velocity between the fluid and plate is assumed to be proportional to the shear rate at the plates. The flow is generated by moving one of the plates or application of the constant pressure gradient giving arise to two unsteady boundary value problems. Analytical solutions of the problems are obtained. Effects of various dimensionless parameters emerging in the model on velocity field are presented graphically. It is shown that the solution exists for all values of non-Newtonian parameters. The solutions with no-slip condition for Maxwell, second grade and viscous fluid appear as limiting cases of the present results.

Original language | English (US) |
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Pages (from-to) | 2282-2287 |

Number of pages | 6 |

Journal | World Applied Sciences Journal |

Volume | 13 |

Issue number | 11 |

State | Published - Dec 1 2011 |

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### All Science Journal Classification (ASJC) codes

- General

### Cite this

*World Applied Sciences Journal*,

*13*(11), 2282-2287.

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*World Applied Sciences Journal*, vol. 13, no. 11, pp. 2282-2287.

**Effect of slip condition on unsteady flows of an oldroyd-b fluid between parallel plates.** / Siddiqui, Abdul M.; Haroon, T.; Zahid, M.; Shahzad, A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Effect of slip condition on unsteady flows of an oldroyd-b fluid between parallel plates

AU - Siddiqui, Abdul M.

AU - Haroon, T.

AU - Zahid, M.

AU - Shahzad, A.

PY - 2011/12/1

Y1 - 2011/12/1

N2 - The unsteady flows of an incompressible Oldroyd-B fluid between two infinite parallel plates are considered when the slippage between the plate and the fluid is valid. The relative velocity between the fluid and plate is assumed to be proportional to the shear rate at the plates. The flow is generated by moving one of the plates or application of the constant pressure gradient giving arise to two unsteady boundary value problems. Analytical solutions of the problems are obtained. Effects of various dimensionless parameters emerging in the model on velocity field are presented graphically. It is shown that the solution exists for all values of non-Newtonian parameters. The solutions with no-slip condition for Maxwell, second grade and viscous fluid appear as limiting cases of the present results.

AB - The unsteady flows of an incompressible Oldroyd-B fluid between two infinite parallel plates are considered when the slippage between the plate and the fluid is valid. The relative velocity between the fluid and plate is assumed to be proportional to the shear rate at the plates. The flow is generated by moving one of the plates or application of the constant pressure gradient giving arise to two unsteady boundary value problems. Analytical solutions of the problems are obtained. Effects of various dimensionless parameters emerging in the model on velocity field are presented graphically. It is shown that the solution exists for all values of non-Newtonian parameters. The solutions with no-slip condition for Maxwell, second grade and viscous fluid appear as limiting cases of the present results.

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M3 - Article

VL - 13

SP - 2282

EP - 2287

JO - World Applied Sciences Journal

JF - World Applied Sciences Journal

SN - 1818-4952

IS - 11

ER -