Influence of the magnetic field and the conductance ratio on the mass transfer rotating lid driven flow

Abstract

A numerical study of a steady laminar magnetohydrodynamic (MHD) flow driven by a rotating disk at the top of a cylindrical cavity filled with a liquid metal is presented. The fluid flow field was calculated using a finite volume computational fluid dynamics (CFD) model. The effects of the magnetic field, the fluid and wall electrical conductivities, and the wall thickness are investigated. The relevant key parameters for the MHD flows are the Hartmann number M, and the Reynolds number Re. The study was performed for various Re⩾100 and for M in the range 0⩽ M⩽100. This corresponds to a range of interaction parameter N= M 2/ Re of 0⩽ N⩽100. Here the magnetic Reynolds number R m is assumed to be very small but the small-induced magnetic field was taken into account in the formulation of the problem. The work focuses on thin walls, which simplifies the boundary conditions. The thin wall boundary condition is used for the first time for a moving wall. It is shown that for fixed values of the Hartmann and Reynolds numbers, the velocity distribution depends strongly on the conductance ratio k, in spite of the fact that, the Hartmann layer thickness and side layer thickness do not vary with k. The numerical model is also applicable to non-MHD flows, and gives good agreement with previous experiments. The study is destined to predict the influence of a magnetic field on the corrosion rate of a liquid metal on a metallic wall. The results are devoted to analyse the corrosion processes of stainless steels by the Pb–17Li liquid alloy for the fusion reactor. It is assumed that this corrosion is controlled by the near-wall hydrodynamic which is then controlled by an external magnetic field. The concentration equation for the corrosion product is solved, and predicts the evolution of the mass transfer with M. At same magnitude of M the mass transfer is higher for conducting than insulating walls.