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Convection due to internal heat sources

Published online by Cambridge University Press:  11 April 2006

Morten Tveitereid  and
Enok Palm
Morten Tveitereid
Affiliation:
Department of Mechanics, University of Oslo, Norway
Enok Palm
Affiliation:
Department of Mechanics, University of Oslo, Norway
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Abstract

This paper is concerned with convection generated by uniformly distributed internal heat sources. By a numerical method it is found that the planform is down-hexagons for infinite Prandtl numbers and Rayleigh numbers up to at least 15 times the critical value. The motion is also studied for finite Prandtl numbers and small supercritical Rayleigh numbers by using an amplitude expansion. It turns out that a small subcritical regime exists. Moreover, it also emerges that for Prandtl numbers less than 0.25 the stable planform is up-hexagons. In §3 a necessary condition in order to obtain a hexagonal planform is derived when the coefficients in the differential equations are a function of the vertical co-ordinate z.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 76 , Issue 3 , 11 August 1976 , pp. 481 - 499
Copyright
© 1976 Cambridge University Press

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