Semi analytical solution of MHD asymmetric flow between two porous disks

Abstract

In this paper, we study MHD asymmetric steady incompressible viscous flow of an electrically conducting fluid between two large stationary coaxial porous disks of different permeability in the presence of \u00a0uniform \u00a0transverse \u00a0magnetic \u00a0field. \u00a0The \u00a0governing \u00a0nonlinear \u00a0momentum \u00a0equations \u00a0in \u00a0cylindrical \u00a0co- ordinates together with relevant boundary conditions are reduced to nonlinear ordinary differential equation (NODE) \u00a0using \u00a0similarity \u00a0transformations. \u00a0The \u00a0resulting \u00a0NODE \u00a0is \u00a0solved \u00a0by \u00a0Computer \u00a0Extended \u00a0Series Solution (CESS) and Homotopy Analysis Method (HAM). The analytical solutions are explicitly expressed by \u00a0recurrence \u00a0relation \u00a0for \u00a0determining \u00a0the \u00a0universal \u00a0coefficients. \u00a0The \u00a0nearest \u00a0singularity \u00a0is \u00a0obtained \u00a0at R=4.2981 \u00a0with \u00a0help \u00a0of \u00a0Domb-Sykes \u00a0plot \u00a0which \u00a0restricts \u00a0the \u00a0convergence \u00a0of \u00a0the \u00a0series, \u00a0using \u00a0Euler transformation \u00a0the \u00a0singularity \u00a0is \u00a0mapped \u00a0to \u00a0infinity. \u00a0The \u00a0obtained \u00a0solutions \u00a0are \u00a0valid \u00a0for \u00a0all \u00a0values \u00a0of \u00a0the Reynolds number, magnetic parameter and permeability parameter are presented through graphs and tabular forms \u00a0to \u00a0discuss \u00a0the \u00a0important \u00a0features \u00a0of \u00a0the \u00a0flow. \u00a0The \u00a0resulting \u00a0solutions \u00a0are \u00a0compared \u00a0with \u00a0the \u00a0earlier literatures which are found to be in good agreement. Further, the region of validity of the series is extended for much larger values of R up to infinity by Pade\u2019 approximants. \u00a0