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

Abstract

This paper describes the boundary-layer structure of flow through a porous medium in a two-dimensional rectangular cavity driven by differential heating of the upper surface. The lower surface and sidewalls of the cavity are thermally insulated. In the limit of large Darcy–Rayleigh number, the solution involves a horizontal boundary layer near the upper surface where the main thermal gradients occur. For a monotonic temperature distribution at the upper surface, these drive fluid to the colder end of the cavity where it descends within a narrow vertical boundary layer before returning to the horizontal layer. The horizontal and vertical layers form an interactive system which is solved by a combination of asymptotic analysis and numerical computation. A complete solution is obtained for the case of a quadratic temperature distribution at the upper surface. The solution of the interactive boundary-layer system determines the almost constant temperature in the core region below the horizontal and vertical layers, which contains relatively weak variations in both the thermal and velocity fields.