1 International Journal of Basic Sciences & Applied Research. Vol., 5 (1), 1-12, 2016 Available online at http://www.isicenter.org ISSN 2147-3749 ©2016 Numerical Analysis for a Parametric Study of a Steady Non-darcian Flow over a Rotating Disk in a Porous Medium H.A. Attia 1 , M.A.I. Essawy 2* 1 Department of Engineering Mathematics and Physics, Faculty of Engineering, Fayoum University, El-Fayoum- 63415, Egypt 2 Higher Technological Institute (HTI), 3rd zone, 7th section – P.O Box NO. 4 - 6th of October City, Giza, Egypt * Corresponding Author Email: mohamed.essawy@hti.edu.eg Abstract The steady non-darcian flow of an incompressible viscous fluid above an infinite rotating disk in a porous medium is studied. The Forchheimer extension (non-Darcy term) is considered in the flow equations. The governing set of non-linear partial differential equations was non-dimensional zed and reduced to a set of ordinary differential equations for which Finite-Difference numerical technique is implemented. Numerical results for the details of the velocity components profiles were presented in graphs. The effects of the porosity of the medium and the inertial effects on the velocity and both the radial and tangential wall shear stresses are considered. Keywords: Non-Darcian flow, Rotating Disk, Porous Medium, Forchheimer Equation, Numerical Solution. Introduction Rotating disk flows are of both theoretical and practical value. In spite of its apparent simplicity, the flow due to a rotating disk is rich in the information it contains. It is a prototype of many three dimensional fluid flow problems. This is why it has attracted the attention of many researchers to study its different aspects over the years. The boundary layer induced by a rotating disk is of great scientific importance owing to its relevance to applications in many areas such as rotating machinery, lubrication, oceanography, computer storage devices, viscometers, turbo- machinery, crystal growth processes, and chemical vapor deposition reactor. The hydrodynamic flow due to the rotation of an infinite disk is one of the classical problems of fluid mechanics. The pioneering study of fluid flow due to an infinite rotating disk was carried out by von Karman in 1921 that gave a formulation of the problem, discovered its self-similar nature and then introduced his famous transformations which reduced the governing continuity and Navier-Stokes partial differential equations to ordinary differential equations. This simplified the problem considerably and made it amenable to analysis. The approximate solution of these coupled non-linear ODEs provided by Von Karman was based on the momentum integral method approach and more accurate solutions have been deduced by Cochran (1934). Cochran was able to determine the asymptotic limit as the similarity coordinate ζ measuring lateral distances normal to the disk, tends to infinity by patching two series expansions. It is found that the disk acts like a centrifugal fan, the fluid near the disk being thrown radially outwards, this in turn impulses an axial flow towards the disk to maintain continuity. Cochran (1934) obtained