Numerical Study of Transient High Rayleigh Number Convection in an Attic-Shaped Porous Layer

Scaling arguments and numerical analysis are used to document the transient and steady-state regimes of natural convection in a triangular porous layer cooled from above (along the sloping wall). The numerical simulations are conducted in the high Rayleigh number domain, Ra = 100, 1000, where Ra is the Darcy-modified Rayleigh number based on height, H. The scale analysis predicts the existence of distinct thermal boundary layers if Ra^1/2 (H/L) > 1, where H/L is the height/length geometric ratio of the attic-shaped porous layer. The numerical simulations confirm the scaling results, as well as the prediction that the flow consists primarily of an elongated horizontal counterflow driven by the cold wall. In addition, the numerical solutions show the presence of a Be´nard-type instability at high enough Rayleigh numbers. For example, if H/L = 0.2, the instability is present when Ra > 620; this critical Rayleigh number is found to increase as H/L increases.