Cavity flow in a porous medium driven by differential heating

Abstract

This paper describes flow through a porous medium in a two-dimensional cavity driven by differential heating of the upper surface. The lower surface and sidewalls of the cavity are thermally insulated and the main emphasis is on the case where the temperature distribution at the upper surface is monotonic, resulting in a single-cell circulation. Numerical results for general values of the Darcy–Rayleigh number R and the cavity aspect ratio L are compared with theoretical predictions for the small Darcy–Rayleigh number limit ( R→0) where the temperature field is conduction-dominated, and an approximate theory for the large Darcy–Rayleigh number limit ( R→∞) where convection is significant. In the latter case a horizontal boundary-layer structure is identified near the upper surface. This conveys fluid to the cold end of the cavity where it descends in a narrow vertical jet in the corner. The temperature is almost constant throughout the remainder of the cavity, and heat transfer arguments and boundary-layer theory are used to predict its value.