Velocity Profile of a Ferrofluid in the Presence of Rotating Magnetic Fields. Pseudo-Analytical and Numerical Solutions.

From the beginning of ferro-hydrodynamics, several authors have proposed analytical models to describe the movement of ferrofluids in the presence of rotating external magnetic fields. To this effect they have made valid simplifications in certain and very restricted physical situations. In this work we analyze the effects of these approaches against numerical solutions that do not make use of them. A sample of ferrofluid immersed in containers with three types of geometries was considered: one of flat and parallel plates, one cylindrical and another coaxial cylindrical. Velocity profiles were obtained by these two strategies. The analytical solution leads to a linear model with several simplifications, while the second, numerical in nature, generates a non-linear model, but without approximations. The simulation results showed that the simplifications made in the analytical strategy generate profiles that are valid only for magnetic field intensities lower than the respective ferrofluid saturation values. Additionally, and given the level of development of analytical modeling, it was found that the numerical solution is currently the most appropriate to evaluate the ferro-hydrodynamic model, since it does not have restrictions related to the intensity of the magnetic field. In the same way, it allows to evidence the phenomenon of saturation in the velocity profiles by increasing the intensity of the magnetic field, a situation observed experimentally, and unpredictable by means of these currently available pseudo-analytical solutions.