Application of quasilinearization technique to the vertical channel flow and heat convection

The quasilinearization technique, also known as the generalized Newton-Raphson method, is employed to solve the problem of fluid injection through one side of a long vertical channel. With very approximate starting values, only a few iterations are needed to obtain a result with high accuracy. The results are compared with those obtained by the perturbation technique. Although the perturbation technique is perhaps the simplest and the most straight-forward method to achieve solutions to non-linear boundary value problems, the limitation on the magnitude of perturbed parameters hinders its applicability.