Unsteady Stokes Flow through a Porous Pipe with Periodic Suction and Injection with Slip Conditions

The problem of unsteady Stokes flow of certain Newtonian fluids in a circular pipe of uniform cross section is discussed. The pipe is uniformly porous. The unsteady Navier-Stokes equations for the system in cylindrical polar coordinates have been solved analytically to obtain a complete description of the flow. The solution of the flow equations subject to the slip boundary-conditions leads to the detailed expressions for axial and radial components of velocity and the pressure distribution depending on position coordinates and time. As a special case we have presented the situation when no-slip boundary conditions are implemented. The velocity profile is analyzed for different values of the flow parameters like Womersley number, slip length and time.