Effect of phase difference between highly oscillating magnetic field and magnetization on the unsteady ferrofluid flow due to a rotating disk

We have studied the effect of phase difference between the magnetization and the magnetic field intensity on the components of ferrofluid velocity for which the rotational viscosity becomes negative. It is found that for higher angular frequency, the rotational viscosity becomes negative resulting in faster convergence of velocity components as compared to the ordinary case of zero rotational viscosity where the frequency of an alternating magnetic field matches with the relaxation of magnetization. The nonlinear coupled differential equations involved in the problem are solved numerically with the help of Flex PDE.