### Abstract

The fully developed pipe flow of a class of non-linear viscoelastic fluids is investigated. Analytical expressions are derived for the stress components, the friction factor and the velocity field. The friction factor which depends on the Deborah and Reynolds numbers is substantially smaller than the corresponding value for the Newtonian flow field with implications concerning the volume flow rate. We show that non-affine models in the class of constitutive equations considered such as Johnson-Segalman and some versions of the Phan-Thien-Tanner models are not representative of physically realistic flow fields for all Deborah numbers. For a fixed value of the slippage factor they predict physically admissible flow fields only for a limited range of Deborah numbers smaller than a critical Deborah number. The latter is a function of the slippage.

Original language | English |
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Pages (from-to) | 485-493 |

Number of pages | 9 |

Journal | International Journal of Non-Linear Mechanics |

Volume | 40 |

Issue number | 4 |

DOIs | |

Publication status | Published - May 1 2005 |

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### All Science Journal Classification (ASJC) codes

- Mechanical Engineering
- Statistical and Nonlinear Physics

### Cite this

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*International Journal of Non-Linear Mechanics*, vol. 40, no. 4, pp. 485-493. https://doi.org/10.1016/j.ijnonlinmec.2004.07.009

**On the fully developed tube flow of a class of non-linear viscoelastic fluids.** / Letelier, Mario F.; Siginer, Dennis A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the fully developed tube flow of a class of non-linear viscoelastic fluids

AU - Letelier, Mario F.

AU - Siginer, Dennis A.

PY - 2005/5/1

Y1 - 2005/5/1

N2 - The fully developed pipe flow of a class of non-linear viscoelastic fluids is investigated. Analytical expressions are derived for the stress components, the friction factor and the velocity field. The friction factor which depends on the Deborah and Reynolds numbers is substantially smaller than the corresponding value for the Newtonian flow field with implications concerning the volume flow rate. We show that non-affine models in the class of constitutive equations considered such as Johnson-Segalman and some versions of the Phan-Thien-Tanner models are not representative of physically realistic flow fields for all Deborah numbers. For a fixed value of the slippage factor they predict physically admissible flow fields only for a limited range of Deborah numbers smaller than a critical Deborah number. The latter is a function of the slippage.

AB - The fully developed pipe flow of a class of non-linear viscoelastic fluids is investigated. Analytical expressions are derived for the stress components, the friction factor and the velocity field. The friction factor which depends on the Deborah and Reynolds numbers is substantially smaller than the corresponding value for the Newtonian flow field with implications concerning the volume flow rate. We show that non-affine models in the class of constitutive equations considered such as Johnson-Segalman and some versions of the Phan-Thien-Tanner models are not representative of physically realistic flow fields for all Deborah numbers. For a fixed value of the slippage factor they predict physically admissible flow fields only for a limited range of Deborah numbers smaller than a critical Deborah number. The latter is a function of the slippage.

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U2 - 10.1016/j.ijnonlinmec.2004.07.009

DO - 10.1016/j.ijnonlinmec.2004.07.009

M3 - Article

VL - 40

SP - 485

EP - 493

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

SN - 0020-7462

IS - 4

ER -