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Finite Prandtl number convection with nearly insulating boundaries

Published online by Cambridge University Press:  17 April 2009

N. Riahi
N. Riahi
Affiliation:
Department of Theoretical and Applied Mechanics, College of Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
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Abstract

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Arbitrary Prandtl number convection in a layer with nearly insulating boundaries is investigated. For B1/3 > 3.95P (P is the Prandtl number and B being the ratio between the thermal conductivities of the boundary and of the fluid) two-dimensional rolls are stable. The heat transported by the stable rolls reaches its peak at a critical P = B1/3/5.77 beyond which the heat flux decreases with increasing P. For B1/3 = 3.95P rolls become unstable to disturbances in the form of rolls oriented at a right angle to the original rolls. For B1/3 > 3.95P square pattern convection represents the preferred stable convection. The stable square pattern transports the maximum amount of heat at a critical P = B1/3/3.7.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 24 , Issue 3 , December 1981 , pp. 339 - 347
Copyright
Copyright © Australian Mathematical Society 1981

References

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