Shallow cavity flow in a porous medium driven by differential heating

Abstract

This is the unspecified version of the paper.This version of the publication may differ from the final published version. This paper describes steady flow through a porous medium in a shallow twodimensional cavity driven by differential heating of the upper surface. The lower surface and sidewalls of the cavity are thermally insulated. The main emphasis is on the situation where the Darcy-Rayleigh number R is large and the aspect ratio of the cavity L (length/depth) is of order R 1/2 . For a monotonic temperature distribution at the upper surface, the leading-order problem consists of an interaction involving the horizontal boundary-layer equations, which govern the flow throughout most of the cavity, and the vertical boundary-layer equations which govern the flow near the colder sidewall. This problem is solved using numerical and asymptotic methods. The limiting cases where L R Permanent repository link

On the boundary layer structure of differentially heated cavity flow in a stably stratified porous medium

“…Similarity solutions of the horizontal boundary layer equations on a heated horizontal wall have been discussed by Cheng & Chang (1976) and Chang & Cheng (1983). More recently, the flow generated by differential heating of the upper surface of a rectangular cavity whose other three walls are thermally insulated has been considered by Daniels & Punpocha (2004;2005) and Daniels (2006).…”

Entropy generation in a square cavity

“…He indicated that viscous coupling effect was negligible through out the normalized saturation range. Steady flow through a porous medium in a shallow two-dimensional cavity was studied by Daniels (2006). He showed that for a monotonic temperature distribution at the upper surface, the problem consisted of an interaction involving the horizontal boundary-layer equations and the vertical boundarylayer equations, which governed the flow near the colder sidewall.…”