A Novel Similarity Transformation for the Boundary Layer Equations: Solution of Boundary Layer Flows Subjected to Exponential Outer Velocity Profiles

Abstract

A new similarity transformation applies to the boundary layer equations, which govern laminar, steady, and incompressible flows. This transformation is proved to be more consistent and more complete than the well known Falkner–Skan transformation. It applies to laminar, incompressible, and steady boundary layer flows with a power-law ue(x)=cxm or exponential profile ue(x)=cemx of the outer velocity. This family of “similar solutions” is resolved for various values of the exponent m. A physical interpretation of these velocity profiles is presented, and conclusions are drawn regarding the tolerance of these boundary layers to flow separation under an adverse pressure gradient.