The Effect of an Abrupt Change in the Magnetic Field on Bingham Fluid Flow in a Flat MHD Channel

The study suggests a method for calculating the unsteady flow of conducting Bingham fluid in a MHD channel. The method is based on the possibility for separate descriptions of the flows in the viscous and plastic zones. The independent consideration of flows in viscous and plastic zones in a flat MHD channel enables studying the behavior of the boundary between the zones when an external magnetic field is abruptly changed. We obtained the exact equation that determines the dependence of the zone width of plastic flow on the time and on magnetic field. Moreover, we performed a numerical integration of the equation for some values of parameters to identify the nature of the searched dependence and gave the results in graphs. Theoretical analysis and numerical calculations show that the sudden magnetic field increase causes a sharp increase in the zone width of plastic flow in a short time period, but the transition to the new steady state is complete in infinite time. The proposed method allows determining the position of the boundary of the plastic flow zone as a function of time in the case of an abrupt decrease in the external magnetic field induction.

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