On the existence of steady solution for flows between rotating conical cylinders

Abstract

The existence of steady solution for flows between two coaxial independently rotating conical cylinders (truncated cones) are considered under condition of small gap and neglecting the effect of the top and bottom boundary. It is proved mathematically that there doesn't exist steady solution of the form: u = u θ (r, z)e + u z (r, z)e Þ and u = u r (r, z)e Ö + u θ (r, z)e with p = p(r, z), for any angular velocities of the conical cylinders. The results of numerical simulation suggest that there exists a statistical three-dimensional steady solution for this configuration with the inner cone rotating and outer one at rest.