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The stability of the laminar natural convection boundary layer

Published online by Cambridge University Press:  28 March 2006

C. P. Knowles  and
B. Gebhart
C. P. Knowles
Affiliation:
Sibley School of Mechanical Engineering, Cornell University, Ithaca, N.Y. Now at Systems, Science and Software, La Jolla, California
B. Gebhart
Affiliation:
Sibley School of Mechanical Engineering, Cornell University, Ithaca, N.Y.
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Abstract

This paper concerns the stability characteristics of laminar natural convection in external flows. Until recently, very little was known about such stability because of the inherent complexity of temperature-coupled flows and because of the complicated mechanisms of disturbance propagation. In this work the stability of the laminar natural convection boundary layer is examined more closely in an attempt to predict the experimental results recently obtained. In particular, it is shown that an important thermal capacity coupling exists between the fluid and the wall which generates the flow. This thermal capacity coupling is shown to have a first-order effect for particular Grashof-number wave-number products. Solutions are obtained for a Prandtl number of 0·733 and several values of relative wall thermal capacity. These solutions indicate the important role of this wall coupling. In particular, the results predict the experimental data previously obtained.

In addition, solutions with ‘zero wall storage’ are obtained for a range of Prandtl numbers from 0·733 to 6·9. The relative disturbance u-velocity and temperature amplitudes and their phases are shown for Pr = 0·733 and several wall-storage parameters, and for Pr = 6·9 with zero wall storage. A comparison between the disturbance temperature distribution and the data obtained from a recent experimental investigation shows close agreement when the thermal capacity of the wall is taken into account.

In the appendix, it is shown that for temperature-coupled flows and wall-coupled boundary conditions the flow is unstable at a lower Grashof number for two-dimensional disturbances than it is for three-dimensional disturbances. This result has been supported by the recent experimental observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 34 , Issue 4 , 23 December 1968 , pp. 657 - 686
Copyright
© 1968 Cambridge University Press

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