Start up Flow with Velocity slip in the Entrance Region of a Porous Circular Tube Start up Flow with Velocity slip in the Entrance Region of a Porous Circular Tube

Abstract

Suddenly started laminar flow of an incompressible viscous fluid in the entrance region of a porous circular tube is studied analytically, taking into account the tangential velocity slip at its surface. Adopting a similarity velocity profile of the form of nth.degree parabola in the boundary layer, the integrated forms of the equations of continuity, momentum and energy are solved by the method of characteristics. The entry length is seen reduced by the fluid injection across the wall of the tube and increased by the tangential velocity slip at it. Both these factors are found increasing the start-up time required for the full development of the flow.