Implicit finite difference solution for the magneto-hydro-dynamic unsteady free convective flow and heat transfer of a third-grade fluid past a porous vertical plate

Magneto-hydro-dynamic (MHD) unsteady flow and heat transfer of a third grade fluid passing an infinite vertical porous plate with uniform suction applied at the plate has been studied. The governing nonlinear partial differential equations are reduced to a system of nonlinear algebraic equations using implicit finite difference schemes and then the system is solved using damped-Newton method. The effect of the various physical parameters on the velocity and temperature are studied. One of the important observations is that when the third order elastic parameter increases the velocity decreases, whereas an opposite effect is observed when second order elastic parameter increases. Present method is valid for all values of elastic parameters where as the earlier approximation methods like perturbation and power series methods are valid for small values of elastic parameter. Further the advantage of our method is that it does not require repeated derivation for every change in the boundary conditions.