Hall effect on flows of an Oldroyd-B fluid through porous medium for cylindrical geometries

In this work, the equations are proposed for magnetohydrodynamic (MHD) flows of an Oldroyd-13 fluid through a porous medium. These equations give rise to a mathematical description in which a modified Darcy's law for an Oldroyd-13 fluid is taken into account with Hall effects. This particularly happens when the magnetic field is high. Four flow problems are considered: (i) starting flow in a circular cylinder moving parallel to its length, (ii) starting flow in a circular pipe, (iii) generalized flow in a circular pipe, (iv) starting flow in a rotating cylinder. The problems valid for a small magnetic Reynolds number are solved analytically by applying the Laplace transform method. Graphical results for the velocity are presented and are discussed for various parametric conditions. (c) 2006 Elsevier Ltd. All rights reserved.