Numerical solution to the flow of a second grade fluid over a stretching sheet using the method of quasi-linearization

In this short work we look at the flow of a second grade fluid due to a stretching sheet coinciding with the plane y=0. Two equal and opposite forces are applied along the x-axis (horizontal plane) in such a way that the origin remains fixed and the velocity of stretching is proportional to the distance from the origin. This problem was studied by Rajagopal et al. [Rheol. Acta 23 (1984) 213; Meccanica 19 (1984) 158] where a perturbation scheme was used to obtain the solution. Using the same similarity transformation given by Rajagopal et al., we solve the full equation numerically, using the method of quasi-linearization of Bellman and Kalaba [Quasilinearization and Non-Linear Boundary Value Problems, American Elsevier, New York, 1965]. Results will be given for the velocity distribution and the shear stress at the wall.