Heat transfer enhancement analysis of electrohydrodynamic solid-liquid phase change via lattice Boltzmann method

In this study, a lattice Boltzmann method (LBM) is extended for the problem of electrohydrodynamic (EHD) solid-liquid phase change in a square cavity. Four unified lattice Boltzmann equations (LBEs) are used to solve the fully coupled mathematical equations, including the Navier-Stokes equations, the energy conservation equation, the Poisson's equation and the charge conservation equation. We first validate the numerical simulation by three cases in the hydrostatic state and two cases of natural convection melting in a square cavity. The numerical solution of the EHD melting is then presented entirely with a detailed analysis of the mechanisms of EHD enhancement. Results show that, for heating and injection from below, EHD enhances heat transfer by modifying the onset of the flow motion in the liquid zone; whereas for heating and injection from left side, strong enough Coulomb force will lead to the transition of the convection rolls which increases heat transfer at later times of the melting. With the analysis of melting dynamics with varying Rayleigh number Ra, we show that the buoyancy force which was neglected in previous EHD melting problems plays an important role in destabilizing the dynamical system and increasing heat transfer, especially for the case of melting from left. We also investigate the dependence of heat transfer enhancement on electric Rayleigh number Ta, and it is found that the melting time is indeed a decreasing function of Ta. When the values of Ta are high enough, the heat transfer becomes almost independent of Rayleigh number.