Magnetohydrodynamic flow of Bingham fluids in a plane channel: A theoretical study

Abstract

The effect of a fluid's yield stress is numerically investigated on the performance of a DC-operated magnetohydrodynamic (MHD) micro-pump. The test fluid is assumed to be viscoplastic obeying the Papanastasiou–Bingham rheological model. The flow geometry is in the form of a planar channel comprising two long parallel plates of infinite span equipped with two opposing electrodes while the other parts of the channel are assumed to be electrically non-conductive. Having assumed that the isothermal flow generated in this channel by the Lorentz force is laminar and two-dimensional, the effect of Bingham number is investigated on the flow characteristics under steady conditions using the finite-volume method. The numerical results obtained in this work suggest that a fluid's yield stress can dramatically affect the flow kinematics in MHD pumps, even under creeping conditions. It is predicted that, the M-shaped velocity profiles long established in the literature for Newtonian fluids become virtually U-shaped provided that the Bingham number is sufficiently large. This suggests that a fluid's yield stress might have a stabilizing effect on MHD flows with the price being that the maximum wall shear stress is increased for such fluids.