Effects of Electrical Boundary Configurations on Magnetohydrodynamic Flow and Heat Transfer in a Liquid Metal-filled Annulus

This numerical study investigates magnetohydrodynamic (MHD) flow and heat transfer for liquid metals within a cylindrical annulus subjected to a radial magnetic field. A parametric study compares the thermal behavior of these metals under identical conditions, with particular focus on the influence of the annular wall's electrical boundary conditions on heat transfer. The finite volume method is used to analyze three electrical boundary conditions: electrically insulated walls (EI), electrically conducting vertical walls (EC-V), and electrically conducting horizontal walls (EC-H). The findings show that magnetic field strength, annular gap, aspect ratio, and wall conductivity significantly affect temperature distribution, average Nusselt number, Lorentz force, and induced electric field. The Nusselt number increases when the aspect ratio is below unity but decreases when it is above unity, and it improves consistently with a larger annular gap. Stronger magnetic fields are required to sustain conduction-dominated regimes in thicker annuli. The magnetic field generates characteristic Hartmann and Roberts layers through Lorentz force interactions, with layer dissipation observed in conducting wall cases. Among the configurations, the EC-H case exhibits the highest heat transfer performance compared to EI boundaries, particularly for intermediate gap ratios (R ≈ 0.5–0.87). (EC-H) offers the best heat transfer overall, with up to 10% gains for R<0.87, while (EI) performs better for R>0.87, and (EC-V) remains the least efficient.