The flow of a ferrofluid between two parallel infinitely long plates generated by a rotating magnetic field has been studied analytically and numerically using spin diffusion theory for a broad range of frequencies and intensities of the magnetic field. This work was motivated by interest in obtaining better agreement between the theoretical predictions and the experimental observations of the dependence of the flow magnitude on the amplitude and frequency of the magnetic field. These discrepancies have been attributed to the use of asymptotic solutions to assess velocity profiles obtained to moderate magnetic field strength and to the need to use a more accurate magnetization equation to high amplitudes and frequencies of the magnetic field. For such reasons, the objective of this work was to evaluate the effect of the magnetization equations derived by Shliomis [Sov. Phys. JETP 34, 1291 (1972)] (Sh-72) and by Martsenyuk, Raikher, and Shliomis [Sov. Phys. JETP 38, 413 (1974)] (MRSh-74) on the flow predictions of the spin diffusion theory using a simple geometry. It was found that the flow predictions for the two cases studied match with an asymptotic solution in the limit of low field strength when the Langevin parameter α is less than 0.1, for any value of the dimensionless frequency (Ω̃). Marked differences were found in the predictions of flow magnitude dependence on the amplitude and frequency of the magnetic field when Sh-72 or MRSh-74 was used for α>1. Results also show that there is a critical value of frequency above which the velocity of the ferrofluid decreases with increasing magnetic field amplitude. Whereas the value of the critical frequency predicted by the Sh-72 magnetization equation is approximately unity for any value of the magnetic field amplitude, the MRSh-74 equation predicts that the critical frequency increases with increasing magnetic field amplitude. Predictions of the MRSh-74 equation are in qualitative agreement with previously reported experimental velocity profiles in other geometries.