The magnetoviscosity of a ferrofluid flowing down a circular tube in the pr
esence of a magnetic field oscillating in the direction of the axis is stud
ied on the basis of ferrohydrodynamics, Maxwell's equations of magnetostati
cs, and a relaxation equation for the magnetization. Three different relaxa
tion equations, proposed in the literature, are considered. For large ampli
tude of the oscillating field the three equations lead to different values
of the magnetoviscosity. For large magnetic permeability the self-consisten
t magnetic field generated by the magnetization has significant effect.