MHD mixed convection slip flow near a stagnation-point on a nonlinearly vertical stretching sheet

The problem of magnetohydrodynamic (MHD) mixed convection flow near a stagnation-point region over a nonlinear stretching sheet with velocity slip and prescribed surface heat flux is investigated; this has not been studied before. Using a similarity transformation, the governing equations are transformed into a system of ordinary differential equations, and then are solved by employing a homotopy analysis method. The effects of the nonlinearity parameter, the magnetic field, mixed convection, suction/injection, and the boundary slip on the velocity and temperature profile are analyzed and discussed. The results reveal that the increasing exponent of the power-law stretching velocity increases the heat transfer rate at the surface. It is also found that the velocity slip and magnetic field increase the heat transfer rate when the free stream velocity exceeds the stretching velocity, i.e.ε<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\varepsilon< 1$\end{document}, and they suppress the heat transfer rate for ε>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\varepsilon> 1$\end{document}.