Predictor homotopy analysis method (PHAM) for nano boundary layer flows with nonlinear navier boundary condition: Existence of four solutions

Abstract

In the present work, the classical laminar boundary layer equation of the flow away from the origin past a wedge with the no-slip boundary condition replaced by a nonlinear Navier boundary condition is considered. This boundary condition contains an arbitrary index parameter, denoted by n > 0, which appears in the di_erential equation to be solved. Predictor homotopy analysis method (PHAM) is applied to this problem and more, it is proved corresponding to the value (fourmula presented), there exist four solutions. Furthermore, these solutions are approximated by analytical series solution using PHAM for further physical interpretations.