We investigate by direct numerical simulation (DNS) the dynamics of a liquid metal in a cylindrical cell under the conjugate effects of a temperature gradient and an ac magnetic field. These numerical simulations are performed for a range of Hartmann and shielding parameters, $30\le \mathrm{Ha}\le 301$ and $1\le S_{\omega }\le 68$, which correspond to intermediate regimes between low and high frequency of the applied magnetic field. The scales of the physical parameters are discussed in order to analyze the DNS results. In our simulations, the Lorentz force overbalances the buoyancy force and is responsible for the flow patterns made of two tori. Each torus is characterized by a different average temperature which leads to different temperature gradients at the bottom and the top walls, and consequently different heat transfer to the outside. Thermal plumes advected between the two tori appear intermittently. The Lorentz force enhances the thermal exchanges even at a low Ha. We establish that a single master curve represents the evolution of the heat transfer characteristic of the different cases by plotting the $\mathrm{Nu}/\mathrm{Pe}$ vs $Q_J/Q_c$, where Nu and Pe are the Nusselt and Péclet numbers, and $Q_J$ and $Q_c$ are the total power deposited by the Joule effect and the total power transferred without motion, respectively.

Close

PrevNext

View figure in article

• Magnetohydrodynamics
• Rayleigh-Bénard convection
• Thermal convection