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-B fluid through a porous medium. These equations give rise to a mathematical description in which a modified Darcy's law for an Oldroyd-B 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.