A New Approach in Differential transformation method with application on MHD flow in non-Darcy medium between porous parallel plates considering hall current

Abstract

The study of fluid flow in non-Darcy porous medium subjected to Hall current is very important in scientific and engineering applications such as water filters, groundwater discharge in aquifers, petroleum engineering, MHD generators and chemical engineering. Forchheimer model is needed at high flow rate, where, flow will exhibit non-linearity with respect to velocity which make Darcy law inapplicable at these conditions. In this case, the momentum equations become non-linear. The classical differential transformation method transforms the non-linear differential equations to a non-linear algebraic system which gives more than one solution and may be unstable that leads to divergence of the required solution. The novelty of present method that it is a power series solution avoiding solution multiplicity and divergence by a linearization technique that is applied on non-linear governing equations to obtain the unique and convergent solution. The uniqueness, convergence and stability of the new technique are tested by comparisons with previously available works and it is also verified by a fourth order accurate finite difference (FOFDM) solution. The effects flow parameters on the velocity and friction factor are illustrated. The values of parameters in the present work are chosen according to: the available previous results, the power of the persent method to compute over a lagre range of parameters and the distinctiveness between curves in figures.