3D mass diffusivity model of liquid metals in the presence of a magnetic field

The effect of convective contamination for mass diffusivity measurements of liquid germanium with moderate and strong magnetic fields is analyzed in three-dimensional (3D). A steady-state, 3D temperature profile that represents a heat flux at the sidewall varying as cos(θ) in the azimuthal direction is imposed on the cylinder. The temperature non-uniformity-driven convective contamination that leads to approximately 5% greater mass flux, or an allowable temperature non-uniformity is determined for magnetic field strengths of 0.75 and 4.5 T. From the numerical results, the temperature non-uniformity that liquid germanium can tolerate is a tenth of a degree or less for all the cases. The velocities are directly proportional to the temperature non-uniformity in the liquid, with axial velocities usually an order of magnitude higher than the radial and azimuthal velocities. A stronger magnetic field can allow a larger temperature non-uniformity for the same heat transfer condition.