### Abstract

Flow of Bingham plastics through straight, long tubes is studied by means of a versatile analytical method that allows extending the study to a large range of tube geometries. The equation of motion is solved for general non-circular cross-sections obtained via a continuous and one-to-one mapping called the shape factor method. In particular the velocity field and associated plug and stagnant zones in tubes with equilateral triangular and square cross-section are explored. Shear stress normal to equal velocity lines, energy dissipation distribution and rate of flow are determined. Shear-thinning and shear-thickening effects on the flow, which cannot be accounted for with the Bingham model, are investigated using the Hershey-Bulkley constitutive formulation an extension of the Bingham model. The existence and the extent of undeformed regions in the flow field in a tube with equilateral triangular cross-section are predicted in the presence of shear-thinning and shear-thickening as a specific example. The mathematical flexibility of the analytical method allows the formulation of general results related to viscoplastic fluid flow with implications related to the design and optimization of physical systems for viscoplastic material transport and processing.

Original language | English |
---|---|

Pages (from-to) | 1-10 |

Number of pages | 10 |

Journal | International Journal of Non-Linear Mechanics |

Volume | 88 |

DOIs | |

Publication status | Published - Jan 1 2017 |

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### All Science Journal Classification (ASJC) codes

- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics

### Cite this

*International Journal of Non-Linear Mechanics*,

*88*, 1-10. https://doi.org/10.1016/j.ijnonlinmec.2016.09.012

}

*International Journal of Non-Linear Mechanics*, vol. 88, pp. 1-10. https://doi.org/10.1016/j.ijnonlinmec.2016.09.012

**On the physics of viscoplastic fluid flow in non-circular tubes.** / Letelier, Mario F.; Siginer, Dennis A.; Hinojosa, Cristian Barrera.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the physics of viscoplastic fluid flow in non-circular tubes

AU - Letelier, Mario F.

AU - Siginer, Dennis A.

AU - Hinojosa, Cristian Barrera

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Flow of Bingham plastics through straight, long tubes is studied by means of a versatile analytical method that allows extending the study to a large range of tube geometries. The equation of motion is solved for general non-circular cross-sections obtained via a continuous and one-to-one mapping called the shape factor method. In particular the velocity field and associated plug and stagnant zones in tubes with equilateral triangular and square cross-section are explored. Shear stress normal to equal velocity lines, energy dissipation distribution and rate of flow are determined. Shear-thinning and shear-thickening effects on the flow, which cannot be accounted for with the Bingham model, are investigated using the Hershey-Bulkley constitutive formulation an extension of the Bingham model. The existence and the extent of undeformed regions in the flow field in a tube with equilateral triangular cross-section are predicted in the presence of shear-thinning and shear-thickening as a specific example. The mathematical flexibility of the analytical method allows the formulation of general results related to viscoplastic fluid flow with implications related to the design and optimization of physical systems for viscoplastic material transport and processing.

AB - Flow of Bingham plastics through straight, long tubes is studied by means of a versatile analytical method that allows extending the study to a large range of tube geometries. The equation of motion is solved for general non-circular cross-sections obtained via a continuous and one-to-one mapping called the shape factor method. In particular the velocity field and associated plug and stagnant zones in tubes with equilateral triangular and square cross-section are explored. Shear stress normal to equal velocity lines, energy dissipation distribution and rate of flow are determined. Shear-thinning and shear-thickening effects on the flow, which cannot be accounted for with the Bingham model, are investigated using the Hershey-Bulkley constitutive formulation an extension of the Bingham model. The existence and the extent of undeformed regions in the flow field in a tube with equilateral triangular cross-section are predicted in the presence of shear-thinning and shear-thickening as a specific example. The mathematical flexibility of the analytical method allows the formulation of general results related to viscoplastic fluid flow with implications related to the design and optimization of physical systems for viscoplastic material transport and processing.

UR - http://www.scopus.com/inward/record.url?scp=84993991952&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84993991952&partnerID=8YFLogxK

U2 - 10.1016/j.ijnonlinmec.2016.09.012

DO - 10.1016/j.ijnonlinmec.2016.09.012

M3 - Article

AN - SCOPUS:84993991952

VL - 88

SP - 1

EP - 10

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

SN - 0020-7462

ER -