The theoretical analysis of core-annular flow (CAF) holds significant importance in our understanding of fluid transportation, oil extraction, and respiratory airflow dynamics. Here, the linear stability of a CAF comprising of two concentric ferrofluid layers of different magnetic susceptibility, centred on a rod that runs along the axis of a cylindrical pipe is explored. Ferrofluids are stable colloidal fluids, consisting of magnetic particles suspended in a carrier solution. They behave as an ordinary Newtonian fluid, but in the presence of a magnetic field they become magnetised. Originally developed by NASA for vibration dampening purposes, ferrofluids have since been employed in diverse applications ranging from audio speakers to magnetic drug delivery systems. Their widespread use stems from their receptiveness to magnetic fields, which allows for precise control, their remarkable heat transfer qualities, and their adaptability to various shapes and configurations. This talk focuses on the impact of using ferrofluids in a CAF, where an axial pressure gradient drives the flow in both fluids, and the system is subject to an azimuthal field generated from a current running through the rod, or an axial field produced by a suitably placed solenoid in the outer wall. Moreover, upon removing the field, the system reverts to a rod-CAF configuration for two viscous fluids, and novel results are found solely due to the addition of the rod. It will be shown that the introduction of both the rod and magnetic field can have stabilising and destabilising effects on CAF, depending on the parameters of the system.