Flow of ferrofluid within a channel driven by a rotating magnetic field: Implications of surface magnetic stresses and magnetic body couples

This research presents a discussion of the flow of a ferrofluid in a square cross-sectional area channel driven by a rotating magnetic field. The objective was to evaluate the coupled effect of surface magnetic stresses and diffusion of the internal angular momentum as potential mechanisms for generating flow. In many analyses of flow induced by time-dependent magnetic fields, the effect of the diffusion of the internal angular momentum has been dismissed, based on the negligible value of the spin viscosity coefficient estimated from order-of-magnitude analyses. In light of these considerations, we conducted a review of the existing analyses and put forward a new approach of the order-of-magnitude analysis of the spin viscosity coefficient. The paper presents a detailed description of the solution procedure for the flow field, with and without the inclusion of the diffusion of the internal angular momentum. To justify the assumptions involved in the analytical solution of the flow, we expanded a previous scale analysis to define Reynolds and Strouhal numbers in the linear and internal angular momentum balance equations. It was proven that the maximum surface velocity predicted at the ferrofluid–air boundary closely aligns with the reported experimental data for moderate amplitudes of the magnetic field.