## Abstract

This article considers fully laminar flow of an incompressible viscous fluid in a uniformly porous pipe with suction and injection. An exact solution of the Navier-Stokes equations is given. The velocity filed can be expressed in a series form in terms of the modified Bessel function of the first kind of order n. The volume flux across a plane normal to the flow, the vorticity and the stress on the boundary are presented. The flow properties depend on the cross-Reynolds number, Ua / ν, where U is the suction velocity, a is the radius of the pipe and ν is the kinematic viscosity of the fluid. It is found that for large values of the cross-Reynolds number, the flow near the region of the suction shows a boundary layer character. In this region the velocity and the vorticity vary sharply. Outside the boundary layer, the velocity and the vorticity do not show an appreciable change.

Original language | English |
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Pages (from-to) | 292-301 |

Number of pages | 10 |

Journal | International Journal of Non-Linear Mechanics |

Volume | 43 |

Issue number | 4 |

DOIs | |

Publication status | Published - May 2008 |

## Keywords

- Exact solution
- Injection
- Laminar flow
- Porous pipe
- Suction