3-D Simulations of Diffusivity Measurements in Liquids with an Applied Magnetic Field

The effect of convective contamination in self-diffusivity experiments of liquid metals is predicted via a three-dimensional (3-D) model that includes an applied magnetic field. A uniform heat flux is applied at the sidewall of the cylindrical ampoule, and heat losses are allowed at the top and bottom walls of the ampoule. A wide range of a uniform, steady, axial magnetic field (from moderate to very strong) is considered in the model. Since the thermal Peclet number, Pe, is very small for the parameters of interest, convective heat transfer is neglected. A large interaction parameter, N, suggests that the flow is inertialess. The temperature and flow problems are solved at steady state while the time-dependent concentration problem is determined for various mass Peclet numbers, P e. In all cases, the output D (i.e., with convective contamination) increases with an increase in the temperature non-uniformity ΔTθ. The radial and azimuthal velocities are much smaller than the axial velocity in each case. A stronger magnetic field can tolerate a higher temperature non-uniformity ΔTθ, but ΔTθ is still less than 0.025 K with a 5 T magnetic field for convective contaminations to be less than 5 of the total mass flux.