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 I0 and temperature difference between the top and bottom walls ΔT0: 15≤f≤1000Hz, 2≤I0≤67 A and 6≤ΔT0≤11 K. In these experiments, the Hartmann number Ha, the shielding parameter Sω and Rayleigh number Ra vary in the following range: 6≤Ha≤200, 1≤Sω≤70, 2.3×106≤Ra≤4.1×106. 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/Peω vs. QJ/Qc allows predicting the evolution of the heat transfer under different conditions of temperature difference and Lorentz force. Here Nu and Peω are the Nusselt number and a Péclet number based on the Lorentz force, and QJ and Qc are the total power deposited by the Joule effect and the total conduction heat flux without motion, respectively. The experiments show that Nu/Peω∼(QJ/Qc)−2/5.