Analysis of some magnetohydrodynamic flows of third-order fluid saturating porous space

A hybrid method based on pseudo-spectral collocation in the sense of least-square method is applied to examine the magnetohydrodynamic (MHD) flow of non-Newtonian fluid. The flow equation through constitutive relations of thirdorder fluid is considered. Four illustrative examples of nonlinear flow, namely (i) plane Couette flow, (ii) Plug flow, (iii) fully developed plane Poiseuille flow, and (iv) generalized plane Couette flow, are considered. An incompressible electrically conducting fluid saturates the porous space between two boundaries. The solutions of governing nonlinear problems are obtained and analyzed through numerical method and graphical illustration.