In this study, the effect of applying a magnetic field resulted from quadrupole magnets on the hydrodynamics and heat transfer of a magnetic Taylor-Couette flow with the axial flow has been investigated numerically for the first time. The studied geometry consists of two vertical concentric cylinders. The inner cylinder rotates with a specific angular velocity to make Taylor-Couette flow and the outer cylinder has been considered stationary. The outer cylinder has also been considered to be under constant heat flux boundary condition. The magnetic nanofluid is a water-based nanofluid consisting Fe3O4 nanoparticles with diameters of 8nm and the magnetic field is produced by quadrupole magnets. The modeling of the problem has been implemented by using the two-phase mixture model and control volume technique. The obtained results indicate that in the absence of magnetic field and in our considered range of Taylor Numbers, the flow consists of lots of vortices which is called the Taylor-Vortex Flow. By applying magnetic field, the ferrofluid flow is pushed toward the outer cylinder wall and the stability of the flow is also increased considerably. Moreover, the local heat transfer coefficient is increased by imposing magnetic field and the increase in heat transfer coefficient by applying magnetic field is decreased as the Taylor number of the flow increases.
