Magnetorheological fluids (MRF) are increasingly used for the design of dampers in many cases when a given response is critical for desired performance. Some recent examples are self-powered magnetorheological dampers, cable vibration control and wheeled vehicle dampers. Loads of this type can be very big, especially in the case of seismic-dampers as well as in heavy vehicles and aircraft landing gear. This problem can be more efficiently dealt with by using an inverse-problem strategy, where the required performance is specified a priori, and the fluid parameters are changed accordingly by means of a variable magnetic field. The effect on the flow of the time-variation of the parameters of the Herschel-Bulkley constitutive model is analyzed in this paper. In this way, the influence of a varying magnetic field on the unsteady flow of a magnetic fluid is explored. Yield stress, viscosity and power index are assumed time-dependent. In particular, linear variations in time of these parameters are considered, and the case where the yield stress and viscosity oscillate in time is explored in detail. The characteristics of the velocity field are analyzed for different values of the constants that determine the time structure of the constitutive parameters.

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