Thermomagnetic effects on the stability of Taylor-Couette flow of a ferrofluid in the presence of azimuthal magnetic field

A stability analysis is conducted for the non-isothermal Taylor-Couette flow of a non-conductive ferrofluid under the action of an azimuthal magnetic field. The transition from steady flow to Taylor vortex flow is investigated in terms of the critical Taylor number and with respect to the changes in the magnetic field strength, radial temperature gradient, gap ratio, ferroparticle concentration and size. For the linear stability analysis, infinitesimal perturbations to the velocity, temperature and magnetization fields are considered and the resulting linear system of stability equations is solved using Chebyshev collocation method. Also, the original nonlinear system of equations is solved numerically using a finite element analysis software, and the results are compared with the linear stability analysis results. A significant stabilization is observed under strong magnetic fields for all cases. It is also observed that radial temperature difference has a destabilizing effect on the flow and this effect is amplified when the magnetic field strength is increased. Higher ferroparticle volume fraction and size lead to a strong degree of magnetization of the fluid and amplifies the stabilizing effect of magnetic fields. The stabilization under azimuthal magnetic forces is observed to be smaller for the narrow gap case compared to the wide gap case.