Model for Inertialess Magnetohydrodynamic Flow in Packed Beds

An analytical model for magnetohydrodynamic flow in a porous medium comprised of a packed bed of uniform spheres is developed. A rectangular geometry only is considered. Two distinct cases are studied: an infinite packed bed and a finite packed bed including wall effect. The wall effect is modeled by employing a two-zone porosity model, with a higher porosity wall region inserted between the solid wall and the lower porosity core region. The effect of the conductivity of the packed bed is accounted for by analogy with Hartmann flow in a duct with an external load. A parametric analysis is performed with the completed model to assess the effects of various factors upon the model results.