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Natural convection in an infinite porous medium with a concentrated heat source

Published online by Cambridge University Press:  19 April 2006

Adrian Bejan
Adrian Bejan
Affiliation:
Department of Mechanical Engineering, University of Colorado, Boulder
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Abstract

The phenomenon of buoyancy-induced convection in an infinite porous medium with a concentrated heat source is studied analytically. The transient and steady-state temperature distribution and flow pattern around the source are determined using a perturbation analysis in the Rayleigh number based on the heat generation rate at the source. The first-order transient solution derived in the paper is valid for Rayleigh numbers less than 10. The transient flow pattern consists of an expanding vortex ring situated in the horizontal plane containing the source. The steady-state solution, valid for Rayleigh numbers of the order of 20 or less, reveals an upward flow pattern which becomes very intense near the source. The upward flow extends throughout the medium. Both solutions show that as the Rayleigh number increases the region situated above the source is effectively heated by natural convection in addition to direct heat conduction from the source.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 89 , Issue 1 , 14 November 1978 , pp. 97 - 107
Copyright
© 1978 Cambridge University Press

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