Magnetic Fluid Flows in Porous Media^*

The seepage law under a magnetic field is obtained by up-scaling the flow at the pore scale of rigid porous media, and the macroscopic equivalent model is also obtained. It is proved that the macroscopic mass flow depends on the macroscopic magnetic force and the gradients of pressure and of magnetic pressure, as Zahn and Rosensweig have described in their experiments. The permeability tensor is symmetric and positive.