Plume flows in porous media driven by horizontal differential heating

Abstract

AbstractIn this paper we describe flow through a porous medium in a two-dimensional rectangular cavity driven by differential heating of the impermeable lower surface. The upper surface is held at constant pressure and at a constant temperature equal to the minimum temperature of the lower surface, while the sidewalls are impermeable and thermally insulated. Numerical results for general values of the Darcy–Rayleigh number $R$ and the cavity aspect ratio $A$ are compared with theoretical predictions for the small Darcy–Rayleigh number limit $(R\ensuremath{\rightarrow} 0)$ where the temperature field is conduction-dominated, and with a boundary-layer theory for the large Darcy–Rayleigh number limit $(R\ensuremath{\rightarrow} \infty )$ where convection is significant. In the latter case a horizontal boundary layer near the lower surface conveys fluid to the hot end of the cavity where it rises to the upper surface in a narrow plume. Predictions are made of the vertical heat transfer through the cavity.