Modelling of coupled convective and magneto-thermoelectric phenomena for a sphere immersed in liquid metal using finite element method and adaptive meshes

N. Bernabeu¹ - O. Budenkova¹ - A. Gagnoud¹ - S. Rukolaine² - Y. Du Terrail Couvat¹ - Y. Fautrelle¹

¹ University Grenoble Alpes, CNRS, Grenoble INP, SIMaP, F-38000 Grenoble, France
² Ioffe Institute, St. Petersburg 194021, Russian Federation

Abstract
Thermoelectric phenomena which occur if an electrically conducting sphere is immersed in a liquid metal and subjected to a thermal gradient and an external static magnetic field are studied numerically and analytically for small Hartmann numbers. Such configuration can happen during solidification of metallic alloys under a static magnetic field, then the sphere would correspond to an equiaxed dendrite grain. The numerical model includes the Ohm's law accounting for the thermoelectric and eddy currents, the stationary Navier-Stokes equations with the Lorentz force and the diffusion-advection equation for the temperature. A finite element method with an adaptive mesh is used to solve the problem. It is found that for the Hartmann number Ha < 1 analytical solutions for a decoupled problem and numerical solutions of a fully coupled one are similar, whereas for Ha=O(1) the thermoelectric current in the system is attenuated by the eddy current in the liquid. Consequently, with increase of the magnetic field the intensity of thermoelectric convection remains bounded not only due to the braking effect of the magnetic field, but also because of the decrease of the thermoelectric force in the liquid. Tables 1, Figs 7, Refs 16.