Title | Axisymmetric stagnation - Point flow and heat transfer of a viscous fluid on a rotating cylinder with time-dependent angular velocity and uniform transpiration |

Publication Type | Journal Article |

Year of Publication | 2007 |

Authors | Rahimi, A. B., and R. Saleh |

Journal | Journal of Fluids Engineering-Transactions of the ASME |

Volume | 129 |

Pagination | 106-115 |

Date Published | JAN |

Type of Article | Article |

ISSN | 0098-2202 |

Keywords | exact solution, stagnation flow, time-dependent heat transfer, time-dependent rotation, transpiration |

Abstract | {The unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite rotating circular cylinder with transpiration U-0 are investigated when the angular velocity and wall temperature or wall heat flux all vary arbitrarily with time. The free stream is steady and with a strain rate of Gamma. An exact solution of the Navier-Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by the use of appropriate transformations for the most general case when the transpiration rate is also time-dependent but results are presented only for uniform values of this quantity. The general self-similar solution is obtained when the angular velocity of the cylinder and its wall temperature or its wall heat flux vary as specified time-dependent functions. In particular, the cylinder may rotate with constant speed, with exponentially increasing/decreasing angular velocity, with harmonically varying rotation speed, or with accelerating/decelerating oscillatory angular speed. For self-similar flow, the surface temperature or its surface heat flux must have the same types of behavior as the cylinder motion. For completeness, sample semi-similar solutions of the unsteady Navier-Stokes equations have been obtained numerically using a finite-difference scheme. Some of these solutions are presented for special cases when the time-dependent rotation velocity of the cylinder is, for example, a step-function. All the solutions above are presented for Reynolds numbers |

URL | http://dx.doi.org/10.1115/1.2375132%7D |

DOI | 10.1115/1.2375132 |

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