Darcy–Brinkman Flow through a Tapered Channel or a Cone

Abstract

The Darcy–Brinkman flow through a tapered channel or cone, including the flow through a slit or hole on a plate, is studied for the first time. Assuming small Darcy numbers, the solution is found to third order error using the method of matched asymptotic expansions. There are complex interactions between the outer flow and the boundary layer. Streamlines, velocity, pressure, and shear stress are determined. The results are important for the determination of forces and the modeling of transport phenomena.