Magneto-Viscosity and Spin-Up Dynamics of Ferrofluids Between Parallel Plates

Abstract This study examines the ferrohydrodynamic flow between two parallel rigid walls caused by the velocity of the upper plate. The ferrohydrodynamic model for magneto-viscosity is developed using the governing equations of ferrohydrodynamics along with Maxwell's equations. In an externally imposed magnetic field, the resulting magnetic torque introduces additional resistance to the flow, resulting in magneto-viscosity. The results show that magneto-viscosity is driven by the magnetic flux intensity, the frequency of the sinusoidally varying applied magnetic field, and the velocity of the upper plate. Velocity field and microrotation field profiles are presented for different magnitudes of the imposed magnetic field, vortex viscosity, and spin-viscosity parameters. This mathematical model is solved for magnetic-field-dependent viscosity, velocity profiles, and spin-velocity profiles under various magnetic-field frequencies and plate velocities using comsol multiphysics software.