Negative viscosity effects on ferrofluid flow due to a rotating disk

In this problem, negative viscosity effects are presented on the ferrofluid flow due to a rotating disk. An alternating magnetic field does not single out any direction of the flow but it changes the angular velocity of the particles relative to the vorticity of the flow. The frequency dependent relative magnetization and the angular velocity of the particles are studied here for various dimensionless parameters. Components of ferrofluid velocity and pressure profile are compared with the ordinary case where the frequency of an alternating magnetic field matches with relaxation of magnetization resulting in no effect of negative viscosity on the shear viscosity. The nonlinear coupled differential equations involved here are solved numerically by Shooting Method and the results are graphically expressed.