Numerical simulations of ferrofluid flows through porous media with low column-to-grain diameter ratios are obtained for fluids experiencing external linear-gradient magnetic fields, ferrofluid self-consistent demagnetizing field and induced magnetic field in the non-magnetic granular phase. Analysis of the macroscopic volume-average ferrohydrodynamic model identified the conditions for decoupling magnetostatics from hydrodynamics. Order-of-magnitude calculations of the applied magnetic field versus the self-consistent demagnetizing field and the corresponding Kelvin body force densities showed that such decoupling is fulfilled only for large and positive gradient magnetic field. (c) 2006 Elsevier B.V. All rights reserved.