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 noslip boundary conditions are implemented. the velocity profile is analyzed for different values of the flow parameters like womersley number, slip length and time.