Nonexistence of the reversed flow solutions of the Falkner–Skan equations

Nonexistence of reversed flow solutions of the well-known Falkner–Skan equations arising in the boundary layer theory is considered analytically. A new system of two singular integral equations are proposed and studied, which plays a key role in the study of reversed flow solutions. The properties of the velocity and the shear stress of the reversed flows are provided. These properties describe the shapes and behaviors of the curves of the velocity and the shear stress functions. A new lower bound of the skin-friction which is useful in numerical analysis is given. The results on the nonexistence of reversed flow solutions can be used to estimate the exact critical value which is of importance in aeronautics because separation occurs at this value.

► We study nonexistence of reversed flow solutions of the Falkner–Skan equations.
► The new analytical approach is to propose and study a new systems of two singular integral equations.
► The properties of the velocity and the shear stress of the reversed flow solutions are provided.