### Abstract

Two dimensional natural convection of a nonlinear fluid of the differential type, in an inclined cavity of arbitrary aspect ratio is solved by a regular perturbation for small Grashof numbers. We show that the series are asymptotic in character. Non-Newtonian effects appear at the third order of the analysis even though the Giesekus-Tanner theorem is not valid. The relative contributions of the elastic and shear rate dependent viscosity characteristics of the liquid to the non-Newtonian behavior are investigated through a parametric study, together with the dependence of the Nusselt number on the nonlinear properties of the fluid. The effects of the aspect ratio and the inclination of the enclosure on the flow field and the heat transfer coefficient are also investigated. An interesting instability of the fluid of grade three triggered by elastic effects is discussed together with the implications concerning heat transfer characteristics.

Original language | English |
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Title of host publication | Numerical Methods for Non-Newtonian Fluid Dynamics |

Publisher | Publ by ASME |

Pages | 31-39 |

Number of pages | 9 |

Volume | 179 |

ISBN (Print) | 0791813622 |

Publication status | Published - 1994 |

Event | Proceedings of the 1994 ASME Fluids Engineering Division Summer Meeting. Part 9 (of 18) - Lake Tahoe, NV, USA Duration: Jun 19 1994 → Jun 23 1994 |

### Other

Other | Proceedings of the 1994 ASME Fluids Engineering Division Summer Meeting. Part 9 (of 18) |
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City | Lake Tahoe, NV, USA |

Period | 6/19/94 → 6/23/94 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*Numerical Methods for Non-Newtonian Fluid Dynamics*(Vol. 179, pp. 31-39). Publ by ASME.

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*Numerical Methods for Non-Newtonian Fluid Dynamics.*vol. 179, Publ by ASME, pp. 31-39, Proceedings of the 1994 ASME Fluids Engineering Division Summer Meeting. Part 9 (of 18), Lake Tahoe, NV, USA, 6/19/94.

**Natural convection of viscoelastic liquids.** / Siginer, D. A.; Valenzuela-Rendon, A.

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

TY - GEN

T1 - Natural convection of viscoelastic liquids

AU - Siginer, D. A.

AU - Valenzuela-Rendon, A.

PY - 1994

Y1 - 1994

N2 - Two dimensional natural convection of a nonlinear fluid of the differential type, in an inclined cavity of arbitrary aspect ratio is solved by a regular perturbation for small Grashof numbers. We show that the series are asymptotic in character. Non-Newtonian effects appear at the third order of the analysis even though the Giesekus-Tanner theorem is not valid. The relative contributions of the elastic and shear rate dependent viscosity characteristics of the liquid to the non-Newtonian behavior are investigated through a parametric study, together with the dependence of the Nusselt number on the nonlinear properties of the fluid. The effects of the aspect ratio and the inclination of the enclosure on the flow field and the heat transfer coefficient are also investigated. An interesting instability of the fluid of grade three triggered by elastic effects is discussed together with the implications concerning heat transfer characteristics.

AB - Two dimensional natural convection of a nonlinear fluid of the differential type, in an inclined cavity of arbitrary aspect ratio is solved by a regular perturbation for small Grashof numbers. We show that the series are asymptotic in character. Non-Newtonian effects appear at the third order of the analysis even though the Giesekus-Tanner theorem is not valid. The relative contributions of the elastic and shear rate dependent viscosity characteristics of the liquid to the non-Newtonian behavior are investigated through a parametric study, together with the dependence of the Nusselt number on the nonlinear properties of the fluid. The effects of the aspect ratio and the inclination of the enclosure on the flow field and the heat transfer coefficient are also investigated. An interesting instability of the fluid of grade three triggered by elastic effects is discussed together with the implications concerning heat transfer characteristics.

UR - http://www.scopus.com/inward/record.url?scp=0027983390&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027983390&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0027983390

SN - 0791813622

VL - 179

SP - 31

EP - 39

BT - Numerical Methods for Non-Newtonian Fluid Dynamics

PB - Publ by ASME

ER -