Free Convection in a Two-Dimensional Porous Loop

[+] Author and Article Information
L. Robillard, T. H. Nguyen, P. Vasseur

Génie civil, Ecole Polytechnique, Campus de l’Université de Montréal, Montréal, Québec, Canada H3C 3A7

J. Heat Transfer 108(2), 277-283 (May 01, 1986) (7 pages) doi:10.1115/1.3246916 History: Received January 17, 1985; Online October 20, 2009


A study is made of the natural convection in an annular porous layer having an isothermal inner boundary and its outer boundary subjected to a thermal stratification arbitrarily oriented with respect to gravity. For such conditions, no symmetry can be expected for the flow and temperature fields with respect to the vertical diameter and the whole circular region must be considered. Two-dimensional steady-state solutions are sought by perturbation and numerical approaches. Results obtained indicate that the circulating flow around the annulus attains its maximum strength when the stratification is horizontal (heating from the side). This circulating flow is responsible for an important heat exchange between the porous layer and its external surroundings. The flow field is also characterized by the presence of two convective cells near the inner boundary, giving rise to flow reversal on this surface. When the maximum temperature on the outer boundary is at the bottom of the cavity, the convective motion becomes potentially unstable; for a Rayleigh number below 80, there exists a steady-state solution symmetrical with respect to both vertical and horizontal axes; for a Rayleigh number above 80, an unsteady periodic situation develops with the circulating flow alternating its direction around the annulus.

Copyright © 1986 by ASME
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