Flow restrictive and shear reducing effect of magnetization relaxation in ferrofluid cavity flow

In this study, we report the effects of a uniform stationary magnetic field on the flow of ferrofluid (FF) inside a boundary driven cavity. A coupled set of conservation equations for the flow field, the Maxwell's magnetostatic equations, and the constitutive magnetization equation are solved numerically. The non-dimensional groups primarily influencing the phenomenon are first systematically identified through the normalization of the complete set of equations. We find the magnetization relaxation effects, under the stationary uniform field, to be flow restrictive in nature. The misalignment between the local magnetic field and the magnetization suppresses the vorticity field in the cavity, shifts the primary central vortex, and reduces the average shear stress at the boundaries. As a consequence, it becomes apparent that at a given Reynolds number, the application of uniform magnetic field can reduce the shear drag at the boundaries of the cavity, of course at an expense of reduced flow rate in their vicinity. Our study uniquely reveals that the relaxation time effects are dominant in the regions of ferrofluid flow where the change in the magnitude of the vorticity takes place over a length scale which is much smaller than the characteristic length scale of the flow geometry. Depending on the magnitudes of influencing parameters, the solution exhibits anomalous characteristics, such as creeping and saturating behavior.