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The Instability of Fluids with Time Dependent Heating


Currie, Iain George (1966) The Instability of Fluids with Time Dependent Heating. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/TH7H-TH69.


The stability of a fluid having a non-uniform temperature stratification is examined analytically for the response of infinitesimal disturbances. The growth rates of disturbances have been established for a semi-infinite fluid for Rayleigh numbers of 103, 104, and 105 and for Prandtl numbers of 7.0 and 0.7.

The critical Rayleigh number for a semi-infinite fluid, based on the effective fluid depth, is found to be 32, while it is shown that for a finite fluid layer the critical Rayleigh number depends on the rate of heating. The minimum critical Rayleigh number, based on the depth of a fluid layer, is found to be 1340.

The stability of a finite fluid layer is examined for two special forms of heating. The first is constant flux heating, while in the second, the temperature of the lower surface is increased uniformly in time. In both cases, it is shown that for moderate rates of heating the critical Rayleigh number is reduced, over the value for very slow heating, while for very rapid heating the critical Rayleigh number is greatly increased. These results agree with published experimental observations.

The question of steady, non-cellular convection is given qualitative consideration. It is concluded that, although the motion may originate from infinitesimal disturbances during non-uniform heating, the final flow field is intrinsically non-linear.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Applied Mechanics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Rannie, W. Duncan
Thesis Committee:
  • Unknown, Unknown
Defense Date:20 May 1966
Funding AgencyGrant Number
Record Number:CaltechTHESIS:09102015-161601825
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9149
Deposited On:11 Sep 2015 14:19
Last Modified:28 Feb 2024 00:34

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