Numerical analysis of natural convection heat transfer in a square enclosure horizontally or vertically divided into fluid and porous regions

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This paper describes an analytical study of laminar natural convection heat transfer in a square enclosure horizontally or vertically divided into fluid and porous regions. The Navier-Stokes equation governs the fluid motion in the fluid region, while Brinkman's extension of Darcy's law is assumed to hold within the porous region. These equations are solved using the Galerkin finite element method in the range 10^3<Ra_f<10^5 and 10^<-3><Da<10^<-5>. The flow patterns are similar for horizontal and vertical divisions. There are two flow modes in the enclosure: circulation over the enclosure and circulation in the fluid region only. Although the flow penetration into the porous region is influenced substantially by the Rayleigh number and the Darcy number, the effect of the Darcy number is more significant. The magnitude of the flow penetration is found to be larger for the vertical division than for the horizontal division.
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