This paper presents a numerical-analytic solution for the fow of a ferrofuid in the annular gap between two concentric cylinders induced by a rotating magnetic feld. Unlike analytical solutions presented in the literature, this analysis takes into account the effect of the terms ω×M and in the magnetization equation which are commonly disregarded in order to decouple the magnetic hydrodynamic problem obtaining in this way an analytical solution. However, it was found that its effect is negligible under the assumption that the magnetization vector of the ferrofuid is proportional to magnetic feld vector. The numerical results show a good agreement with the asymptotic solution reported by Chaves et al. 2010. We also review the range of application of this analysis and others reported in the literature made under assumption of proportionality of the vectors of magnetization and magnetic feld.