Slip flow over a lubricated rotating disk

Abstract

A set of slip-flow boundary conditions for the flow due to a lubricated disk rotating in a Newtonian fluid is derived. Similarity solutions are generally prohibited by the replacement of the conventional no-slip conditions by the new slip-flow conditions, except in the particular case when the power-law index of the non-Newtonian lubricant equals 1/3. The amount of velocity slip is controlled by a single dimensionless slip coefficient. Numerical solutions are presented for this case, showing that the three-dimensional flow field is dramatically affected by accentuated velocity slip. In particular, the axial flow towards the disk, i.e. the pumping efficiency, and the torque required to maintain steady rotation of the disk, decrease monotonically with increasing slip.