Promotion of ferrofluid microchannel flows by gradient magnetic fields

•Ferrofluid Couette-Poiseuille flows subject to gradient magnetic field are analyzed.•Steady gradient magnetic fields promote the ferrofluid Couette-Poiseuille flows.•The backflow is completely suppressed and the flow separation disappears.•The gradient magnetic field enhances the effect of magnetization relaxation.•The gradient magnetic field increases magnetic stress and reduces shear stress.