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The Quarterly Journal of Mechanics and Applied Mathematics 1985 38(2):277-295; doi:10.1093/qjmam/38.2.277
© 1985 by Oxford University Press
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NON-DARCY NATURAL CONVECTION FROM ARBITRARILY INCLINED HEATED SURFACES IN SATURATED POROUS MEDIA

D. S. RILEY and D. A. S. REES

( School of Mathematics, University Walk Bristol BS8 1TW )

An analysis is presented of steady free convection in a saturated porous medium bounded by a heated flat surface and a second thermally insulated (or cold) flat surface, which forms a wedge of angle {alpha}. The flow is induced by the heated surface, which is at an angle {delta} to the gravity vector, where -1/{pi} <{delta}lequal1/2{pi} The pressure gradient-velocity relation is taken to be nonlinear, with departure from the linear Darey situation measured by a parameter G. Matched asymptotic expansions are employed in analysing two distinct cases: the heated surface is (i) horizontal and (ii) at a finite angle above the horizontal. In the former case the flow is driven along by a buoyancy-induced pressure gradient, whilst in the latter it is the direct action of buoyancy forces that drives the flow. Extensive consideration is given to the effects of varying {alpha} {delta} and G.


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