- Poulikakos, D. and Bejan, A., The departure from Darcy flow in natural convection in a vertical porous layer,
Phys. Fluids (USA), vol. 28 no. 12
pp. 3477 - 84 [1.865301] .
(last updated on 2007/04/08)
An analytical and numerical study is reported of steady-state natural convection in a two-dimensional porous layer heated from the side. Contrary to previous investigations of the phenomenon, which were all based on the Darcy flow model, a vector generalization of Forchheimer's one-dimensional model is used in the present study, which is valid for all values of local Reynolds number based on pore size. A matched boundary layer solution of the type developed by Weber (1975) for Darcy flow is developed for the limit of large-pore Reynolds numbers (the `non-Darcy' limit). It is shown that the natural convection phenomenon in the non-Darcy limit is governed by a new dimensionless group, the Rayleigh number for the higher Reynolds number limit, Ra∞. Numerical experiments are reported in the range 1.6×105⩽Ra∞⩽1.6×109, in a porous layer with height/thickness ratio equal to 2, and with a high value of Darcy modified Rayleigh number (Ra=4000). The numerical experiments confirm the flow features and scales anticipated by the matched boundary layer solution for the non-Darcy limit. The experiments also document the transition from the well-known Darcy flow to the large-pore Reynolds-number limit treated in this paper
boundary layers;convection;flow through porous media;