In this paper it is analysed the case of an oscillatory flow in a round pipe in which a magnetic flow is applied. In magnetorheological flows (MRF) the fluid develops yield stress, the strength of which depends on the intensity of the magnetic field. The analysis considers an oscillatory pressure gradient and an oscillatory magnetic field of different frequencies. It is investigated the effect of a cyclical yield stress on the frequency and amplitude of the flow velocity, including the phenomenon of resonance. In this study, the MFR is modelled as a Bingham fluid with time- dependent yield stress.

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