Analytical Solutions of Axial Annular Newtonian Flows with Dynamic Wall Slip

We consider the cessation of annular Poiseuille and annular Couette flows of a Newtonian fluid, under the assumption that wall slip occurs following a dynamic slip law, i.e., a law involving a slip-relaxation parameter. The relaxation time-dependent term forces the eigenvalue parameter to appear in the boundary conditions and, thus, the resulting spatial problems correspond to Sturm-Liouville problems different from their static-Navier slip counterparts. The orthogonality conditions of the associated eigenfunctions for both flows of interest are derived and analytical closed-form solutions are then obtained. For comparison purposes, the analytical solutions corresponding to the static Navier slip condition, are derived. Comparisons are also made with the plane Poiseuille and Couette flows when the annular gap becomes small. As expected, flow dynamics becomes slower in the presence of wall slip and this effect is accentuated by increasing the slip-relaxation parameter.