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
differential equation to be solved. Predictor homotopy analysis
method (PHAM) is applied to this problem and more, it is proved
corresponding to the value n=1/3, there exist four
solutions. Furthermore, these solutions are approximated by
analytical series solution using PHAM for further physical
interpretations.