In this paper it is analyzed the effects on the flow of the time-variation of Herschel-Bulkley model of fluid constitutive parameters. 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. The characteristics of the velocity field is analyzed for different values of the constants that determine the time structure of the constitutive parameters.

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