Gas-Liquid Stratified MHD Flows in Inclined Rectangular Ducts

This study investigates fully developed stratified gas–liquid magnetohydrodynamic (MHD) flow of an electrically conducting liquid and a nonconducting gas in inclined rectangular ducts subjected to a vertical magnetic field. Analytical and numerical solutions for the velocity and induced magnetic fields are obtained in terms of the governing dimensionless parameters for concurrent upward, concurrent downward, and countercurrent flows. Unlike single-phase MHD flow, duct inclination strongly affects two-phase flow by altering the liquid holdup and the relative contributions of gravitational, frictional, and electromagnetic forces.The results reveal a complex interplay among gravity, Lorentz forces, and wall and interfacial shear stresses. These interactions govern the liquid holdup, pressure gradient, multiple steady solutions, flooding limits, local backflow, jet-like velocity structures, and pumping requirements. Wall conductivity critically affects the induced magnetic field and Lorentz-force distribution and therefore cannot be neglected, even at very small magnetic Reynolds numbers. Fully insulating ducts generally exhibit the weakest electromagnetic effects and behavior closest to non-MHD flow. Configurations with a conducting bottom wall exhibit substantially stronger electromagnetic effects and greater sensitivity to side-wall conductivity, leading to pronounced changes in the velocity field, liquid holdup, pressure gradient, gas-lubrication effect, and overall pumping-power requirements.