Numerical Solution of the Newtonian Plane Couette Flow with Linear Dynamic Wall Slip

Abstract

An efficient numerical approach based on weighted-average finite differences is used to solve the Newtonian plane Couette flow with wall slip, obeying a dynamic slip law that generalizes the Navier slip law with the inclusion of a relaxation term. Slip is exhibited only along the fixed lower plate, and the motion is triggered by the motion of the upper plate. Three different cases are considered for the motion of the moving plate, i.e., constant speed, oscillating speed, and a single-period sinusoidal speed. The velocity and the volumetric flow rate are calculated in all cases and comparisons are made with the results of other methods and available results in the literature. The numerical outcomes confirm the damping with time and the lagging effects arising from the Navier and dynamic wall slip conditions and demonstrate the hysteretic behavior of the slip velocity in following the harmonic boundary motion.