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

摘要

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.