Throughflows Between Rotating Surfaces of Revolution, Having Similarity Solutions

Abstract

Laminar throughflow of an incompressible, Newtonian fluid is considered, in a narrow space between two surfaces of revolution, rotating with generally different angular velocities about a common axis of rotation. The method of free parameters is used to investigate the existence of similarity solutions. It is found that there are no surface shapes for which similarity solutions exist, when the full Navier-Stokes equations are used to describe the flow. After order-of-magnitude arguments are employed to reduce the equations, surface shapes and spacings are determined for which similarity solutions exist; the shapes and spacings are delineated and the similarity problem is formulated. Finally, a method for solving the similarity problem is discussed and several example solutions are presented.