Theoretical and experimental study of low conducting fluid MHD flow in an open annular channel

In this paper, we research theoretically and experimentally the 3D laminar flow of an electrolyte in an annular open channel driven by a Lorentz force. The annular duct is formed by two concentric electrically conducting cylinders and limited by an insulating bottom wall. The interaction between a uniform magnetic field along the axial direction and a radial electric current produces a Lorentz force that drives the fluid in the azimuthal direction, producing a Magnetohydrodynamic (MHD) flow. The effect of the three walls is analyzed in detail by considering the gap between the cylinders as well as the depth of the channel. The steady flow is solved using a Galërkin method with orthogonal Bessel-Fourier series. A quasi-analytic approximation for velocity is found. Velocity profiles are explored by varying the depth of the channel and the gap between the cylinders in order to show the effect of the walls on the flow configuration. Results are compared with experimental data provided by PIV technique as well as in those found in scientific literature.