A Comparison of the Semi Analytical and Numerical Method in Solving the Problem of Magnetohydrodynamics Flow of a Third Grade Fluid between Two Parallel Plates

The main purpose of this study is to compare a semi-analytical method and numerical method namely the homotopy perturbation method (HPM) and finite difference method (FDM) respectively. These methods were employed for solving the nonlinear problem of the magnetohydrodynamic (MHD) couette flow of third-grade fluid between the two parallel plates. The comparison was made between a solution of HPM and FDM against a solution obtained from regular perturbation and the results are tabulated. From a computational viewpoint, it is revealed that the HPM is more reliable and efficient than FDM. Also, the results show that the FDM requires slightly more computational effort than the HPM, although the HPM yields more accurate results than the FDM. &nbsp

Finite Element Solution of an Unsteady MHD Flow through Porous Medium between Two Parallel Flat Plates

Finite element solution of unsteady magnetohydrodynamics (MHD) flow of an electrically conducting, incompressible viscous fluid past through porous medium between two parallel plates is presented in the presence of a transverse magnetic field and Hall effect. The results obtained from some test cases are then compared with previous published work using the finite difference method (FDM). Numerical examples show that the finite element method (FEM) gives more accurate results in comparison with the finite difference method (FDM)