The MHD boundary layer flow due to a rough rotating disk

The present paper is devoted to the solution of the steady laminar flow of an incompressible viscous electrically conducting fluid over a rotating disk in the presence of a uniform transverse magnetic field. Classical von Karman problem of a rotating disk is extended to the case where the disk surface admits partial slip. Using von Karman similarity transformation the nonlinear equations of motion are reduced to a boundary value problem whose solution is then obtained in terms of a series of exponentially decaying functions for the full range of slip coefficients. The exact numerical method is found to improve as the strength of the magnetic field and the strength of the applied slip are increased. The effects of the magnetic field together with the slip on the physically significant relevant parameters, such as the wall shears, the torque, and the vertical Suction are clarified. Purely explicit analytical expressions for the solution of magnetohydrodynamic equations to support the numerically evaluated solutions are also obtained via the homotopy analysis method. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim