Non-Newtonian behaviors of ferrofluid Couette–Poiseuille flows in time-varying magnetic fields

We analyze the fully developed Couette–Poiseuille flows of ferrofluids between two parallel flat walls subject to three types of time-varying magnetic fields. In these scenarios, ferrofluids exhibit diverse non-Newtonian characteristics such as distinct flow velocity distribution, apparent viscosity and shear stress compared to ordinary Couette–Poiseuille flows. The influence of spin viscosity is explored first through the solution of the governing equations with zero and non-zero spin viscosities. It shows that although the value of the spin viscosity is very small, its inviscid limit would have great influence over the velocity and spin velocity distributions. The assumption of zero spin viscosity leads to an exaggerated non-Newtonian behavior induced by time-varying magnetic fields in the ferrofluid Couette–Poiseuille flows. Then the solutions of equations with non-zero spin viscosity are utilized to delve into non-Newtonian behaviors of ferrofluid Couette–Poiseuille flow under the application of the three time-varying magnetic fields. The results indicate that negative rotational viscosity will occur if the dimensionless frequency lies in the range 1–10, which is a distinguishing feature compared with Newtonian flows. At this point, non-Newtonian flow induced by magnetic field arises, although this effect is very tiny. Within the same frequency range, reversed tangential stress appears in strong uniform alternating magnetic fields. The minimum negative rotational viscosity may arrive at up to 20 % of the intrinsic viscosity in the rotating magnetic field when the magnetization relaxation time is 4 ms.