Development lengths in Newtonian Poiseuille flows with wall slip

The effect of wall slip on the development of planar and axisymmetric Newtonian Poiseuille flows is studied by means of finite element simulations. The Navier slip law is employed. i.e., it is assumed that the slip velocity varies linearly with the wall shear stress. In addition to the standard definition of the development length, L, as the length required for the maximum velocity to attain 99% of its fully-developed value, the wall development length Lw is also relevant in the presence of slip. This is defined as the length required for the slip velocity to decrease to 1.01% of its fully-developed value. The numerical simulations for the planar and the axisymmetric geometries showed that both L and Lw increase with slip passing through a maximum and vanish at a critical value of the slip parameter corresponding to the full slip case. Moreover, the velocity overshoots and the axial pressure minimum near the entrance become less pronounced as slip becomes stronger. The calculations of L for the planar flow are in good agreement with available results in the literature. An interesting result is that in contrast to the axisymmetric flow in which Lw < L, the planar flow develops more slowly at the wall than at the midplane, i.e. Lw > L in the planar case.