### Abstract

Non-isothermal flows with convective heat transfer through a curved duct of square cross section are numerically studied by using a spectral method, and covering a wide range of curvature, δ, 0<δ≤0.5 and the Dean number, Dn, 0≤Dn≤6000. A temperature difference is applied across the vertical sidewalls for the Grashof number Gr= 100, where the outer wall is heated and the inner one cooled. Steady solutions are obtained by the Newton-Raphson iteration method and their linear stability is investigated. It is found that the stability characteristics drastically change due to an increase of curvature from δ = 0.23 to 0.24. When there is no stable steady solution, time évolution calculations as well as their spectral analyses show that the steady flow turns into chaos through periodic or multi-periodic flows if Dn is increased no matter what δ is. The transition to a periodic or chaotic state is retarded with an increase of S. Nusselt numbers are calculated as an index of horizontal heat transfer and it is found that the convection due to the secondary flow, enhanced by the centrifugal force, increases heat transfer significantly from the heated wall to the fluid. If the flow becomes periodic and then chaotic, as Dn increases, the rate of heat transfer increases remarkably.

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

Pages (from-to) | 1013-1022 |

Number of pages | 10 |

Journal | Journal of Fluids Engineering, Transactions of the ASME |

Volume | 128 |

Issue number | 5 |

DOIs | |

Publication status | Published - Sep 2006 |

### Fingerprint

### Keywords

- Curvature
- Curved duct
- Dean number
- Heat transfer
- Secondary flow

### ASJC Scopus subject areas

- Mechanical Engineering
- Fluid Flow and Transfer Processes

### Cite this

*Journal of Fluids Engineering, Transactions of the ASME*,

*128*(5), 1013-1022. https://doi.org/10.1115/1.2236131

**Effects of curvature and convective heat transfer in curved square duct flows.** / Mondal, R. N.; Kaga, Y.; Hyakutake, T.; Yanase, Shinichiro.

Research output: Contribution to journal › Article

*Journal of Fluids Engineering, Transactions of the ASME*, vol. 128, no. 5, pp. 1013-1022. https://doi.org/10.1115/1.2236131

}

TY - JOUR

T1 - Effects of curvature and convective heat transfer in curved square duct flows

AU - Mondal, R. N.

AU - Kaga, Y.

AU - Hyakutake, T.

AU - Yanase, Shinichiro

PY - 2006/9

Y1 - 2006/9

N2 - Non-isothermal flows with convective heat transfer through a curved duct of square cross section are numerically studied by using a spectral method, and covering a wide range of curvature, δ, 0<δ≤0.5 and the Dean number, Dn, 0≤Dn≤6000. A temperature difference is applied across the vertical sidewalls for the Grashof number Gr= 100, where the outer wall is heated and the inner one cooled. Steady solutions are obtained by the Newton-Raphson iteration method and their linear stability is investigated. It is found that the stability characteristics drastically change due to an increase of curvature from δ = 0.23 to 0.24. When there is no stable steady solution, time évolution calculations as well as their spectral analyses show that the steady flow turns into chaos through periodic or multi-periodic flows if Dn is increased no matter what δ is. The transition to a periodic or chaotic state is retarded with an increase of S. Nusselt numbers are calculated as an index of horizontal heat transfer and it is found that the convection due to the secondary flow, enhanced by the centrifugal force, increases heat transfer significantly from the heated wall to the fluid. If the flow becomes periodic and then chaotic, as Dn increases, the rate of heat transfer increases remarkably.

AB - Non-isothermal flows with convective heat transfer through a curved duct of square cross section are numerically studied by using a spectral method, and covering a wide range of curvature, δ, 0<δ≤0.5 and the Dean number, Dn, 0≤Dn≤6000. A temperature difference is applied across the vertical sidewalls for the Grashof number Gr= 100, where the outer wall is heated and the inner one cooled. Steady solutions are obtained by the Newton-Raphson iteration method and their linear stability is investigated. It is found that the stability characteristics drastically change due to an increase of curvature from δ = 0.23 to 0.24. When there is no stable steady solution, time évolution calculations as well as their spectral analyses show that the steady flow turns into chaos through periodic or multi-periodic flows if Dn is increased no matter what δ is. The transition to a periodic or chaotic state is retarded with an increase of S. Nusselt numbers are calculated as an index of horizontal heat transfer and it is found that the convection due to the secondary flow, enhanced by the centrifugal force, increases heat transfer significantly from the heated wall to the fluid. If the flow becomes periodic and then chaotic, as Dn increases, the rate of heat transfer increases remarkably.

KW - Curvature

KW - Curved duct

KW - Dean number

KW - Heat transfer

KW - Secondary flow

UR - http://www.scopus.com/inward/record.url?scp=33750074457&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750074457&partnerID=8YFLogxK

U2 - 10.1115/1.2236131

DO - 10.1115/1.2236131

M3 - Article

AN - SCOPUS:33750074457

VL - 128

SP - 1013

EP - 1022

JO - Journal of Fluids Engineering, Transactions of the ASME

JF - Journal of Fluids Engineering, Transactions of the ASME

SN - 0098-2202

IS - 5

ER -