Lattice Boltzmann analysis for electro-thermo-convection with a melting boundary in horizontal concentric annuli

In this paper, we perform a two-dimensional numerical investigation into the electro-thermoconvection with a melting boundary in horizontal concentric annuli filled with a dielectric phase change material. The whole set of coupled equations is solved by lattice Boltzmann method: Navier-Stokes equations, electrohydrodynamics (EHD) equations, and the energy equation. It is found that there exist three regimes during melting with EHD, namely, diffusive regime, thermal convection regime, and electroconvection regime, and the augmentation of melting heat transfer is due to the radial electroconvective flow induced by Coulomb force in the third regime. Moreover, the continuous melting of solid leads to the dynamical transition between the different flow patterns of electro-thermo-convection, as well as the interesting evolutions of temperature and charge density distribution. In different regimes of melting, the liquid fraction fl and Nusselt number Nu follow different power laws. In detail, before the onset of radial flow motion, fl scales as Fo1/2 whereas Nu scales as fl-4/5 (Fo represents the Fourier number), and in the electroconvection dominated regime, we have fl ∼Fo and Nu ∼fl0.