Thermally driven tall cavity flows in porous media: the convective régime

Abstract

Thermally driven flows in a two-dimensional rectangular cavity filled with a fluid-saturated porous medium are considered when the applied temperature difference is perpendicular to the gravity vector. The flow depends on two non-dimensional parameters, the Darcy-Rayleigh number, A , and the cavity aspect ratio, h (height / width). Steady motion is generated by maintaining the vertical sidewalls at different constant temperatures and the horizontal boundaries are assumed to be thermally insulating. The present study is concerned with the limit of large aspect ratio, h → ∞. and Darcy-Rayleigh numbers A of order h , such that convection is important throughout the cavity. The main properties of the flow and heat transfer are obtained by considering a vertical boundary-layer approximation to the motion in the main body of the cavity. This leads, in particular, to the prediction of a position of minimum heat transfer across the cavity, of interest in the thermal insulation of buildings and other areas of technology.

On the boundary-layer structure of cavity flow in a porous medium driven by differential heating

“…A numerical solution of the vertical boundary-layer problem was obtained by Daniels (1983). Further asymptotic structures for shallow cavities (L = O(R) and L = O(R 1/2 ) as R → ∞) have been discussed by Daniels, Blythe & Simpkins (1986, 1989 and for tall cavities (L = O(R −1 ) and L = O(R −1/2 ) as R → ∞) by Ansari & Daniels (1993, 1994. Although the present investigation is motivated partly by applications to differential heating in groundwater flows and geothermal energy systems, it is also designed to provide fundamental insight into general flow structures in cavities where the horizontal surfaces are thermally conducting.…”