On the Similarity Conditions of the Three Dimensional Boundary Layer Equations over Bodies of Revolution

Abstract

In this paper similarity conditions of the three dimensional boundary layer flows over bodies of revolution are examined and very general forms of the distributions of the main stream velocity, the radius of the body and the scale factor are found. First, when the fluid at infinity is axially symmetric and the body is rotating about its own axis, the distribution of the outer velocity and others which fulfill the similarity conditions are found to be of the power or the exponential forms. Secondly, when the body is at rest and the main stream has both the meridional and the circumferential velocity components, the general solutions are found to be entirely different from those of the rotating body and are not restricted to the power and the exponential forms. Moreover, it is found that several different flow patterns correspond to one set of similarity constants.