The natural convection boundary layer adjacent to an inclined plate subject to sudden cooling boundary condition has been studied. It is found that the cold boundary layer adjacent to the plate is potentially unstable to Rayleigh–Bénard instability if the Rayleigh number exceeds a certain critical value. A scaling relation for the onset of instability of the boundary layer is achieved. The scaling relations have been developed by equating important terms of the governing equations based on the development of the boundary layer with time. The flow adjacent to the plate can be classified broadly into a conductive, a stable convective, or an unstable convective regime determined by the Rayleigh number. Proper scales have been established to quantify the flow properties in each of these flow regimes. An appropriate identification of the time when the instability may set in is discussed. A numerical verification of the time for the onset of instability is also presented in this study. Different flow regimes based on the stability of the boundary layer have been discussed with numerical results.
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Research Papers
Scaling of Natural Convection of an Inclined Flat Plate: Sudden Cooling Condition
Suvash C. Saha,
Suvash C. Saha
School of Engineering and Physical Sciences,
e-mail: s_c_saha@yahoo.com
James Cook University
, Townsville, Queensland 4811, Australia
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John C. Patterson,
John C. Patterson
School of Civil Engineering,
University of Sydney
, New South Wales 2006, Australia
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Chengwang Lei
Chengwang Lei
School of Civil Engineering,
University of Sydney
, New South Wales 2006, Australia
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Suvash C. Saha
School of Engineering and Physical Sciences,
James Cook University
, Townsville, Queensland 4811, Australiae-mail: s_c_saha@yahoo.com
John C. Patterson
School of Civil Engineering,
University of Sydney
, New South Wales 2006, Australia
Chengwang Lei
School of Civil Engineering,
University of Sydney
, New South Wales 2006, AustraliaJ. Heat Transfer. Apr 2011, 133(4): 041503 (9 pages)
Published Online: January 11, 2011
Article history
Received:
January 16, 2010
Revised:
November 5, 2010
Online:
January 11, 2011
Published:
January 11, 2011
Citation
Saha, S. C., Patterson, J. C., and Lei, C. (January 11, 2011). "Scaling of Natural Convection of an Inclined Flat Plate: Sudden Cooling Condition." ASME. J. Heat Transfer. April 2011; 133(4): 041503. https://doi.org/10.1115/1.4002982
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