Convection in a porous cavity 论文

摘要

Convection in a porous cavity driven by heating in the horizontal is analysed by a number of different techniques which yield a fairly complete description of the two-dimensional solutions. The solutions are governed by two dimensionless parameters: the Darcy-Rayleigh number R and the cavity aspect ratio A . We first find solutions valid for shallow cavities, A → 0, by using matched asymptotic expansions. These solutions are given up to O ( A 6 R 4 ). For A fixed, we find regular expansions in R by semi-numerical techniques, up to O ( R 30 ) in some cases. Series-improvement techniques then enable us to cover the range 0 ≤ R ≤ ∞. A limited result regarding bifurcations is noted. Finally, for R → ∞ with A fixed, we propose a self-consistent boundary-layer theory which extends previous approximate work. The results obtained by these different methods of solution are in good agreement with each other and with experiments.