Abstract
Conduction in thin disks can be modeled using the fin equation, and there are analytical solutions of this equation for a circular disk with a constant heattransfer coefficient. However, convection (particularly free convection) in rotatingdisk systems is a conjugate 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 disk temperature is known then Bi can be determined numerically. But the determination 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 paper, Bayesian statistics are applied to the inverse solution of the circular fin equation to produce reliable estimates of Bi for rotating disks, and numerical experiments using simulated noisy temperature 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 buoyancyinduced flow in the cavity between corotating compressor disks.
Original language  English 

Article number  121003 
Pages (fromto)  110 
Number of pages  10 
Journal  Journal of Turbomachinery: Transactions of the ASME 
Volume  137 
Issue number  12 
Early online date  23 Sept 2015 
DOIs  
Publication status  Published  1 Dec 2015 
Bibliographical note
Paper No: TURBO151123Fingerprint
Dive into the research topics of 'Use of fin equation to calculate Nusselt numbers for rotating disks'. Together they form a unique fingerprint.Profiles

Hui Tang
 Department of Mechanical Engineering  Lecturer
 EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
 Centre for Sustainable Energy Systems (SES)
 IAAPS: Propulsion and Mobility
Person: Research & Teaching, Core staff, Affiliate staff