### Abstract

Unsteady flow in a semi-infinite contracting or expanding pipe is reinvestigated using long series analysis. The proposed series method is useful in analysing the problem for a moderately large constant α (α = aȧ/v, where a = a(t), the radius of the pipe is a function of time, ȧ(t) is the velocity of the wall, and v is kinematic viscosity). For positive values of α (expansion of the pipe) accuracy of the series representing shear stress and pressure gradient is increased from α = 2·89 to α = 6·0 by extracting the singularity followed by completion of the series. For negative values of α (contraction of the pipe), we revert the series which results into the increase of the region of validity of the transposed series from α = -25·0 to α -2·89. Later we use Padé approximants for summing them. Also, the asymptotic solution for large values of α is obtained and it agrees closely with pure numerical values of shear stress at the wall and pressure gradient.

Original language | English |
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Pages (from-to) | 151-165 |

Number of pages | 15 |

Journal | IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) |

Volume | 60 |

Issue number | 2 |

DOIs | |

Publication status | Published - 01-01-1998 |

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### All Science Journal Classification (ASJC) codes

- Applied Mathematics

### Cite this

*IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)*,

*60*(2), 151-165. https://doi.org/10.1093/imamat/60.2.151