The Optimal Auxiliary Functions Method for Semi-Analytical Solutions of the MHD Mixed Convection Stagnation-Point Flow Problem

The present paper treats the problem of steady laminar MHD flow of an incompressible viscous fluid for mixed convection stagnation-point flow over a vertical stretching sheet in the presence of an externally magnetic field. By means of the Optimal Auxiliary Functions Method (OAFM), the resulting nonlinear ODEs are semi-analytically solved. The impact of various physical parameters, such as the velocity ratio parameter A, the Prandtl number Pr, and the Hartmann number Ha, on the behavior of velocity and temperature profiles is analyzed. Both assisting (λ>0) and opposing (λ<0) flows are considered. The influence of these parameters is tabulated and graphically presented. The originality of this work lies in the development of effective semi-analytical solutions and in the excellent agreement between these solutions and the corresponding numerical solutions. This highlights the accuracy of the proposed method applied to steady laminar MHD flow. A comparative analysis underlines the advantages of the OAFM compared to the iterative method. The obtained results confirm that the OAFM represents a competitive mathematical tool to explore a large class of nonlinear problems with applications in engineering.