Thermal convection of a liquid metal under an alternating magnetic field

Abstract

The objective of this work is to measure the heat transfer of a liquid metal in a cylindrical cell under the conjugate effects of a temperature difference and a Lorentz force generated by an alternating current in a coil. The experimental results are compared to recent direct numerical simulations (DNS) (Guillou et al., 2022). 25 experiments are performed for a large range of frequency $f$, ac intensity amplitude $I_0$ and temperature difference between the top and bottom walls $\Delta T_0$: $15\le f\le 1000\mathrm{Hz}$, $2\le I_0\le 67$ A and $6\le \Delta T_0\le 11$ K. In these experiments, the Hartmann number $Ha$, the shielding parameter $S_{\omega }$ and Rayleigh number $Ra$ vary in the following range: $6\le Ha\le 200$, $1\le S_{\omega }\le 70$, $2.3\times 10^6\le Ra\le 4.1\times 10^6$. The experiments with an ac magnetic field are compared with the Rayleigh–Bénard convection (RBC) experiments under the same thermal conditions. Three rings of thermocouples allow characterizing the fluid temperature distribution during the convection. The heat flux at the bottom and top walls are also measured. We observe a very good agreement between the experimental results and the DNS results. As previously shown by numerical simulations, a master curve of $Nu/P{e}_{\omega }$ vs. $Q_J/Q_c$ allows predicting the evolution of the heat transfer under different conditions of temperature difference and Lorentz force. Here $Nu$ and $P{e}_{\omega }$ are the Nusselt number and a Péclet number based on the Lorentz force, and $Q_J$ and $Q_c$ are the total power deposited by the Joule effect and the total conduction heat flux without motion, respectively. The experiments show that $Nu/P{e}_{\omega }\sim {(Q_J/Q_c)}^{-2/5}$.