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

摘要

A new similarity transformation applies to the boundary layer equations, which governnlaminar, steady, and incompressible flows. This transformation is proved to be morenconsistent and more complete than the well known Falkner–Skan transformation. It appliesnto laminar, incompressible, and steady boundary layer flows with a power-lawnueu0001xu0002u0001cxm or exponential profile ueu0001xu0002u0001cemx of the outer velocity. This family of “similarnsolutions” is resolved for various values of the exponent m. A physical interpretationnof these velocity profiles is presented, and conclusions are drawn regarding the tolerancenof these boundary layers to flow separation under an adverse pressure gradient.