Conflicting Aspects in the Flat Plate Boundary Layer Conventional Solution

Abstract

The solution of the steady-state isothermal gas flow with zero-pressure gradient over a flat plate is classical and was presented by Blasius in 1908. Despite being reduced to a third-order Ordinary Differential Equation, nobody has solved it using just three boundary conditions. In consequence, the “solutions” (exact or numerical) are not unique, do not satisfy Prandtl’s boundary layer concept, and give rise to imprecise criteria of the boundary layer thickness definition (0.99.U∞, where U∞ is the free stream velocity) and to idealizations such as the displacement thickness, δ∗, and the momentum thickness, δI. Even though η, the similarity parameter, is defined as a function of x, it is surprising that it is seen as a constant, η∞, at the limit of the boundary layer, being valid for the entire plate. It is shown that uncountable “solutions” satisfying the classical equation and its three natural boundary layer conditions can be built. The reduction technique of the Boundary Value Problem, BVP, to an Initial Value Problem, IVP, and the Perturbation Analysis Technique, used as an attempt to incorporate a fourth boundary condition to the differential equation, are discussed. A more general and direct method to deduce the classical Blasius’s flat plate equation is considered, as one of the steps to rectify its solution, and shed light on the origin of the conflicting issues involved.