Analytical Solution of Viscous Flow in Porous Media Using ADM and Comparison with the Numerical Runge-Kutta Method

In this article, the problem of laminar viscous flow in a semi-porous channel in the presence of a transverse magnetic field is presented, and the Adomian decomposition method is employed to compute an approximation for the solution of the system of nonlinear differential equations governing on the problem. Then, we consider the influence of the two dimensionless numbers: the Hartmann number (Ha) for the description of the magnetic forces and the Reynolds number (Re) for the dynamic forces. The results of the Adomian decomposition method (ADM) were compared with the numerical method (NM) solution, homotopy perturbation method (HPM), and variation iteration method (VIM). The results reveal that this method is very effective and simple and can be applied for other nonlinear problems.