Hydromagnetic stagnation point flow of a viscous fluid over a stretching or shrinking sheet

We establish the existence and uniqueness results over the semi-infinite interval [0,∞) for a class of nonlinear third order ordinary differential equations of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{array}{l}f'''( \eta) + f( \eta)f''( \eta) - ( f'( \eta) )^{2} - Mf'( \eta)\\[6pt]\quad {}+ C(C + M ) = 0,\\[6pt]f( 0 ) = s ,\qquad f'( 0 ) = \chi ,\qquad \displaystyle\lim\limits_{\eta \to \infty} f'( \eta) = C.\end{array}$$\end{document} Such nonlinear differential equations arise in the stagnation point flow of a hydromagnetic fluid. In particular, we establish the existence and uniqueness results, and properties of physically meaningful solutions for all values of the physical parameters M, s, χ and C. Furthermore, a method of obtaining analytical solutions for this general class of differential equations is outlined. From such a general method, we are able to obtain an analytical expression for the shear stress at the wall in terms of the physical parameters of the model. Numerical solutions are then obtained (by using a boundary value problem solver) and are validated by the analytical solutions. Also the numerical results are used to illustrate the properties of the velocity field and the shear stress at the wall. Some exact solutions are also obtained in certain special cases.