### Abstract

Conduction in thin discs can be modelled using the finequation, and there are analytical solutions of this equation for a circular disc with a constant heat-transfer coefficient. However, convection (particularly free convection) in rotating-disc systems is a conju gate problem: the heat transfer in the fluid and the solid are coupled, and the relative effects of conduction and convection are related to the Biot number, Bi, which in turn is related to the Nusselt number. In principle, if the radial distribution of the disc temperature is known then Bi can be determined numerically. But the determina tion of heat flux from temperature measurements is an example of an inverse problem where small uncertainties in the temperatures can create large uncertainties in the computed heat flux. In this pa per, Bayesian statistics are applied to the inverse solution of the cir cular fin equation to produce reliable estimates of Bi for rotating discs, and numerical experiments using simulated noisy tempera ture measurements are used to demonstrate the effectiveness of the Bayesian method. Using published experimental temperature measurements, the method is also applied to the conjugate problem of buoyancy-induced flow in the cavity between corotating com pressor discs.

Original language | English |
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Title of host publication | Proceedings ASME Turbo Expo, 2015 |

Subtitle of host publication | Turbine Technical Conference and Exposition, Volume 5C, Heat Transfer |

Publisher | American Society of Mechanical Engineers (ASME) |

Pages | V05CT00A001 |

Number of pages | 1 |

ISBN (Print) | 9780791856734 |

DOIs | |

Publication status | Published - 2015 |

Event | ASME Turbo Expo 2015: Turbine Technical Conference and Exposition, GT 2015 - Montreal, Canada Duration: 15 Jun 2015 → 19 Jun 2015 |

### Conference

Conference | ASME Turbo Expo 2015: Turbine Technical Conference and Exposition, GT 2015 |
---|---|

Country | Canada |

City | Montreal |

Period | 15/06/15 → 19/06/15 |

### Fingerprint

### Cite this

*Proceedings ASME Turbo Expo, 2015: Turbine Technical Conference and Exposition, Volume 5C, Heat Transfer*(pp. V05CT00A001). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/GT2015-42029

**Use of fin equation to calculate nusselt numbers for rotating discs.** / Tang, Hui; Shardlow, Tony; Owen, J. Michael.

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

*Proceedings ASME Turbo Expo, 2015: Turbine Technical Conference and Exposition, Volume 5C, Heat Transfer.*American Society of Mechanical Engineers (ASME), pp. V05CT00A001, ASME Turbo Expo 2015: Turbine Technical Conference and Exposition, GT 2015, Montreal, Canada, 15/06/15. https://doi.org/10.1115/GT2015-42029

}

TY - GEN

T1 - Use of fin equation to calculate nusselt numbers for rotating discs

AU - Tang, Hui

AU - Shardlow, Tony

AU - Owen, J. Michael

N1 - Paper No. GT2015-NS5C

PY - 2015

Y1 - 2015

N2 - Conduction in thin discs can be modelled using the finequation, and there are analytical solutions of this equation for a circular disc with a constant heat-transfer coefficient. However, convection (particularly free convection) in rotating-disc systems is a conju gate problem: the heat transfer in the fluid and the solid are coupled, and the relative effects of conduction and convection are related to the Biot number, Bi, which in turn is related to the Nusselt number. In principle, if the radial distribution of the disc temperature is known then Bi can be determined numerically. But the determina tion of heat flux from temperature measurements is an example of an inverse problem where small uncertainties in the temperatures can create large uncertainties in the computed heat flux. In this pa per, Bayesian statistics are applied to the inverse solution of the cir cular fin equation to produce reliable estimates of Bi for rotating discs, and numerical experiments using simulated noisy tempera ture measurements are used to demonstrate the effectiveness of the Bayesian method. Using published experimental temperature measurements, the method is also applied to the conjugate problem of buoyancy-induced flow in the cavity between corotating com pressor discs.

AB - Conduction in thin discs can be modelled using the finequation, and there are analytical solutions of this equation for a circular disc with a constant heat-transfer coefficient. However, convection (particularly free convection) in rotating-disc systems is a conju gate problem: the heat transfer in the fluid and the solid are coupled, and the relative effects of conduction and convection are related to the Biot number, Bi, which in turn is related to the Nusselt number. In principle, if the radial distribution of the disc temperature is known then Bi can be determined numerically. But the determina tion of heat flux from temperature measurements is an example of an inverse problem where small uncertainties in the temperatures can create large uncertainties in the computed heat flux. In this pa per, Bayesian statistics are applied to the inverse solution of the cir cular fin equation to produce reliable estimates of Bi for rotating discs, and numerical experiments using simulated noisy tempera ture measurements are used to demonstrate the effectiveness of the Bayesian method. Using published experimental temperature measurements, the method is also applied to the conjugate problem of buoyancy-induced flow in the cavity between corotating com pressor discs.

UR - http://www.scopus.com/inward/record.url?scp=84954342235&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1115/GT2015-42029

U2 - 10.1115/GT2015-42029

DO - 10.1115/GT2015-42029

M3 - Conference contribution

SN - 9780791856734

SP - V05CT00A001

BT - Proceedings ASME Turbo Expo, 2015

PB - American Society of Mechanical Engineers (ASME)

ER -