Some Effects of Surface Curvature on Laminar Boundary-Layer Flow

Abstract

The laminar flow of a viscous incompressible fluid over a twodimensional curved surface is investigated for two cases, one in which the curvature is large and the other in which it is moderate. The boundary-layer equations applicable to these cases are obtained as approximations from the exact equations of motion by an order-of-magnitude analysis. These equations are solved for flow over a particular surface with zero surface pressure gradient. In this analysis, the pressure gradient normal to the surface is included, and the boundary conditions are modified in accordance with the requirements of flow over a curved surface. The results indicate tha t for equal Reynolds Numbers, the stress on convex surfaces is less than the flat-plate value, while the stress on concave surfaces is greater than for a flat plate. The most important effect of surface curvature, for the cases considered, is the modification of the shape of the velocity profile near the outer of the boundary layer. The requirement tha t a smooth transition exist between the viscous flow and the potential flow at the edge of the layer causes the profile to have a negative slope near the edge for convex surface curvature and a positive slope for concave surface curvature. X= CONSTANT