### Abstract

Original language | English |
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Title of host publication | Numerical Analysis and Applied Mathematics, Vols I-III |

Editors | T E Simos, G Psihoyios, C Tsitouras |

Publisher | American Institute of Physics |

Pages | 1680-1683 |

Number of pages | 4 |

Volume | 1281 |

ISBN (Print) | 978-0-7354-0834-0 |

DOIs | |

Publication status | Published - 2010 |

### Publication series

Name | AIP Conference Proceedings |
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Publisher | American Institute of Physics |

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### Cite this

*Numerical Analysis and Applied Mathematics, Vols I-III*(Vol. 1281, pp. 1680-1683). (AIP Conference Proceedings). American Institute of Physics. https://doi.org/10.1063/1.3498165

**The Asymptotic Behaviour at a Re-Entrant Corner for a PTT Fluid in the Limit of Small kappa.** / Evans, Jonathan D; Sibley, David N.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Numerical Analysis and Applied Mathematics, Vols I-III.*vol. 1281, AIP Conference Proceedings, American Institute of Physics, pp. 1680-1683. https://doi.org/10.1063/1.3498165

}

TY - CHAP

T1 - The Asymptotic Behaviour at a Re-Entrant Corner for a PTT Fluid in the Limit of Small kappa

AU - Evans, Jonathan D

AU - Sibley, David N

N1 - International Conference on Numerical Analysis and Applied Mathematics. 19-25 September 2010. Rhodes, Greece.

PY - 2010

Y1 - 2010

N2 - We consider the Upper Convected Maxwell (UCM) limit of the Phan-Thien-Tanner (PTT) equations for steady planar flow around re-entrant comers. The PTT equations give the UCM equations in the limit of vanishing model parameter kappa, this dimensionless parameter being associated with the quadratic stress terms in the PTT model. The critical length scale local to the comer is r = O(kappa (1/2(1-alpha))) as kappa -> 0, where pi/alpha a is the re-entrant comer angle with alpha is an element of [1/2, 1) and r the radial distance. On distances far smaller than this we obtain the PTT kappa = 1 problem, whilst on distances greater (but still small) we obtain the UCM problem kappa = 0. This critical length scale is that on which intermediate behaviour of the PTT model is obtained where both linear and quadratic stress terms are present in the wall boundary layer equations. The double limit kappa -> 0, r -> 0 thus yields a nine region local asymptotic structure.

AB - We consider the Upper Convected Maxwell (UCM) limit of the Phan-Thien-Tanner (PTT) equations for steady planar flow around re-entrant comers. The PTT equations give the UCM equations in the limit of vanishing model parameter kappa, this dimensionless parameter being associated with the quadratic stress terms in the PTT model. The critical length scale local to the comer is r = O(kappa (1/2(1-alpha))) as kappa -> 0, where pi/alpha a is the re-entrant comer angle with alpha is an element of [1/2, 1) and r the radial distance. On distances far smaller than this we obtain the PTT kappa = 1 problem, whilst on distances greater (but still small) we obtain the UCM problem kappa = 0. This critical length scale is that on which intermediate behaviour of the PTT model is obtained where both linear and quadratic stress terms are present in the wall boundary layer equations. The double limit kappa -> 0, r -> 0 thus yields a nine region local asymptotic structure.

UR - http://dx.doi.org/10.1063/1.3498165

U2 - 10.1063/1.3498165

DO - 10.1063/1.3498165

M3 - Chapter

SN - 978-0-7354-0834-0

VL - 1281

T3 - AIP Conference Proceedings

SP - 1680

EP - 1683

BT - Numerical Analysis and Applied Mathematics, Vols I-III

A2 - Simos, T E

A2 - Psihoyios, G

A2 - Tsitouras, C

PB - American Institute of Physics

ER -