Effective magnetoviscosity of planar-Couette magnetic fluid flow

Magnetic fluid spin velocity, shear stress, and magnetoviscosity were calculated for a planar-Couette magnetic fluid flow, with applied uniform dc magnetic field transverse to the duct axis and by using Shliomis' first magnetization relaxation equation, generally valid for low magnetic fields. For simplicity, the magnetic fluid was assumed to be linearly magnetizable with constant magnetic susceptibility. Using the assumption of incompressible flow and the symmetry of the geometry, the solution for the axial flow is a linear function of position within the channel while the spin velocity is spatially constant, where both the spin velocity and the change in viscosity, obey a third order algebraic torque equation due to an imposed magnetic field H or a fifth order algebraic torque equation due to the imposed magnetic flux density B. This analysis describes the conditions for multivalued effective magnetoviscosity and spin velocity.