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The effect of heating rate on the stability of stationary fluids

Published online by Cambridge University Press:  28 March 2006

I. G. Currie
I. G. Currie
Affiliation:
Present address: Department of Mechanical Engineering, University of Toronto, Toronto 5, Ontario, Canada. Daniel and Florence Guggenheim Jet Propulsion Center, Kármán Laboratory of Fluid Mechanics and Jet Propulsion, California Institute of Technology, Pasadena, California
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Abstract

A horizontal fluid layer whose lower surface temperature is made to vary with time is considered. The stability analysis for this situation shows that the criterion for the onset of instability in a fluid layer which is being heated from below, depends on both the method and the rate of heating. For a fluid layer with two rigid boundaries, the minimum Rayleigh number corresponding to the onset of instability is found to be 1340. For slower heating rates the critical Rayleigh number increases to a maximum value of 1707·8, while for faster heating rates the critical Rayleigh number increases without limit.

Two specific types of heating are investigated in detail, constant flux heating and linearly varying surface temperature. These cases correspond closely to situations for which published data exist. The results are in good qualitative agreement.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 29 , Issue 2 , 11 August 1967 , pp. 337 - 347
Copyright
© 1967 Cambridge University Press

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