Abstract
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.