On Darcy-Brinkman Equation: Viscous Flow Between Two Parallel Plates Packed with Regular Square Arrays of Cylinders

Effects of the bounding solid walls are examined numerically for slow flow over regular, square arrays of circular cylinders between two parallel plates. A local magnitude of the rate of entropy generation is used effectively to determine the flow region affected by the presence of the solid boundary. Computed axial pressure gradients are compared to the corresponding solution based on the Darcy-Brinkman equation for porous media in which the effective viscosity appears as an additional property to be determined from the flow characteristics. Results indicate that, between two limits of the Darcian porous medium and the viscous flow, the magnitude of μ̂ (the ratio of the effective viscosity to the fluid viscosity) needs to be close to unity in order to satisfy the non-slip boundary conditions at the bounding walls. Although the study deals with a specific geometric pattern of the porous structure, it suggests a restriction on the validity of the Darcy-Brinkman equation to model high porosity porous media. The non-slip condition at the bounding solid walls may be accounted for by introducing a thin porous layer with ˆ 1 μ = near the solid walls.