Two-phase stratified MHD flows in wide rectangular ducts: analytical and numerical solutions

This study explores the effects of a non-conductive gas layer flowing concurrently with a conductive liquid on the two-phase flow characteristics in wide horizontal ducts under a constant vertical magnetic field. To this end, analytical solutions for the velocity profile and induced magnetic field are presented for laminar gas-liquid stratified magnetohydrodynamic (MHD) flow between two infinite plates of various conductivities. The contributions of the Lorentz force and wall shear stresses to the pressure gradient are examined. To the best of our knowledge, it is shown for the first time that, unlike the single-phase Hartmann flow, the velocity profiles in two-phase flow differ significantly depending on whether the bottom wall is conducting or insulating. In the case of an insulating bottom wall, the gas lubrication effect and potential pumping power savings are significantly greater, regardless of the magnetic Reynolds number. This conclusion also holds for gas-liquid MHD flows in rectangular ducts with finite width-to-height aspect ratios. To assess the applicability of the Two-Plate (TP) model to wide ducts, numerical solutions of the two-dimensional problem are used to investigate the influence of side walls on the two-phase flow characteristics, considering various combinations of bottom and side wall conductivities. In all cases, the results for high aspect ratios converge to the analytical solution obtained from the TP model with the same bottom wall conductivity. However, the influence of insulating side walls remains significant even at large aspect ratios when the bottom wall is conducting. Unexpectedly, in such cases, the change in the induced magnetic field due to the presence of side walls has a dramatic effect on the velocity profile, leading to a reduced pressure gradient compared to that predicted by the TP model.