Non-Darcy effects in buoyancy driven flows in an enclosure filled with vertically layered porous media

Natural convection in an enclosure filled with two layers of porous media is investigated numerically. Constant heat flux is imposed on the left vertical wall and the right wall is assumed to be at a low temperature. The focus of the work is on the validity of the Darcy model when various combinations of fluid Rayleigh number, Darcy number and permeability ratios are considered for fixed values of the modified Rayleigh numbers. It is found that the boundary effects (Brinkman term) have significant importance at higher modified Rayleigh numbers (Rayleigh number based on permeability, Ram). Calculations are performed for a modified Rayleigh number up to 105. The results showed that, for the investigated range of parameters, the flow structure and heat transfer could be different than what Darcy model predicts. Two circulations are predicted for Raf=1×108, for two different cases, Da=1×10−3, Kr=1000 and Da=1×10−4, Kr=100 (Kr=K1/K2). For Kr>1, increasing permeability ratio decreases flow penetration from layer 1 to layer 2 while reverse is true for Kr<1. For low Ram (Ram⩽103) and Kr=1000, the heat transfer is conductive in the right layer, while this is true for the left layer for Kr=0.001. It is possible to obtain no-slip velocity boundary conditions both at the walls and at the interface between the porous layers even for very low permeability.