Laminar magnetohydrodynamic flow of liquid metal in an annulus under an axial magnetic field driven by direct current

This paper investigates the behavior of electrically driven liquid metal flow in an annular cylindrical domain subjected to a strong axial magnetic field. The flow is induced by a radial electric current passing through liquid metal, generating an azimuthal Lorentz force that drives motion in the θ-direction. Starting with the full set of axisymmetric magnetohydrodynamic (MHD) equations, we derive an analytical solution based on the assumptions of a strong magnetic field and negligible secondary flows. This axisymmetric model captures the dominant electric potential fields and corresponding azimuthal velocity distribution, which enables the convenient prediction of velocity profiles. The analysis focuses on the axisymmetric regime where curvature effects are negligible. To validate the model, we construct an experimental system using electric potential velocimetry for accurate velocity measurements. A consistency in the velocity profiles is observed between the experiment and model predictions, although some deviations appear at higher Reynolds numbers (or lower Hartmann numbers) due to the onset of nonlinearity. The present model serves as a benchmark for MHD systems of annular configurations and provides the exact base flow required for future investigations into flow instabilities and turbulence.