On the flow in a uniformly porous pipe

This article considers fully laminar flow of an incompressible viscous fluid in a uniformly porous pipe with suction and injection. An exact solution of the Navier-Stokes equations is given. The velocity filed can be expressed in a series form in terms of the modified Bessel function of the first kind of order n. The volume flux across a plane normal to the flow, the vorticity and the stress on the boundary are presented. The flow properties depend on the cross-Reynolds number, Ua / ν, where U is the suction velocity, a is the radius of the pipe and ν is the kinematic viscosity of the fluid. It is found that for large values of the cross-Reynolds number, the flow near the region of the suction shows a boundary layer character. In this region the velocity and the vorticity vary sharply. Outside the boundary layer, the velocity and the vorticity do not show an appreciable change.