The axially symmetric flow of a viscous fluid between two infinite rotating disks

Abstract

This is a numerical investigation of the similarity solutions of the Navier-Stokes equations describing the steady axially symmetric flow of a viscous incompressible fluid between two infinite rotating disks. Several cases have been examined in detail and the radial and transverse velocity profiles are displayed; value of the torque experienced in these cases are also given. It is found that at high Reynolds numbers, the main core of the fluid is in a state of solid rotation for practically all values of the ratio of angular velocity of the two disks. When the disks are rotating in the same sense, and when one is at rest and the other is rotating, the results show that edge effects must be taken into account in any complete solution to the problem. However, when the disks rotate in opposite directions, the solutions exhibit features which appear unlikely to occur in practice.