The unsteady viscous flow between two parallel disks with a time-varying gap width and a central fluid source.

Abstract

This paper analyizes an unsteady viscous incompressible fluid flow between two parallel disks. The gap-width between the two disks in varied arbitrarily with time, and a fluid source is located at the center of one disk. The Navier-Stokes equations have been solved using a new multifold power series expansion method. Experiments were carried out for the case of the sinusoidal gap-width variation, and the theory is in good agreement with the experimental result. Especially, it is noted that the theory can describe precisely the effect of a non-linear interaction between the two flows due to the gap-width variation and to the central fluid source.