Application of the HAM-based Mathematica package BVPh 2.0 on MHD Falkner–Skan flow of nano-fluid

•The MHD Falkner–Skan flow of nano-fluid.•The HAM-based Mathematica package BVPh 2.0 for coupled nonlinear ODEs.•Guaranteed convergence of series solution.

Many boundary-layer flows are governed by one or coupled nonlinear ordinary differential equations (ODEs). Currently, a Mathematica package BVPh 2.0 is issued for nonlinear boundary-value/eigenvalue problems with boundary conditions at multiple points. The BVPh 2.0 is based on an analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM), and is free available online. In this paper, the BVPh 2.0 is successfully applied to solve magnetohydrodynamic (MHD) Falkner–Skan flow of nano-fluid past a fixed wedge in a semi-infinite domain, and the influence of physical parameters on the considered flows is investigated in details. Physically, this work deepens and enriches our understandings about the magnetohydrodynamic Falkner–Skan flows of nano-fluid past a wedge. Mathematically, it illustrates the potential and validity of the BVPh 2.0 for complicated boundary-layer flows.