Hydromagnetic stagnation point flow of a second grade fluid over a stretching sheet

We establish the existence and uniqueness results over the semi-infinite interval [0, ∞) for a class of nonlinear fourth order ordinary differential equations arising in the hydromagnetic stagnation point flow of a second grade fluid over a stretching sheet. In particular, we establish the existence and uniqueness results, and properties of physically meaningful solutions for several sets of values of the parameters M, K, s, χ and C. Then, 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 results are used to illustrate the properties of the velocity field and the shear stress at the wall. We find that the viscoelastic parameter K has a smoothing effect on the flow field. Furthermore, an increase in K results in a decrease in the magnitude of the shear stress at the wall.