Flows Between Stationary Surfaces of Revolution, Having Similarity Solutions

Abstract

Laminar flow of an incompressible, Newtonian fluid is considered, in a narrow space between two stationary surfaces of revolution having a common axis of symmetry. 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 are found for which similarity solutions exist; the shapes are delineated and the similarity problems are formulated. Finally, a method for solving the similarity problem is discussed and the solution is tabulated from the results of calculations conducted on a digital computer.