Numerical investigation of electro-thermo-convection with a solid-liquid interface via the lattice Boltzmann method

In this paper, the electro-thermo-convection of a dielectric liquid lying between two parallel planar electrodes with a solid-liquid interface is numerically investigated by using the lattice Boltzmann method. In order to solve the governing equations, four different evolution functions are applied to solve the Navier-Stokes equations, Poisson's equation, charge conservation equation, and the energy equation, respectively. The impacts of some key parameters like the electric Rayleigh number (T), liquid-to-solid thermal conductivity ratio (lambda (r)), thickness of the conducting solid wall (delta), liquid-to-solid permittivity ratio ( epsilon r), and liquid-to-solid mobility ratio (K-r) are investigated in detail. Results indicate that the average heat transfer rate obtained in the presence of the solid substance is always smaller than that obtained for the case of no solid. In addition, we find that the effect of T on heat transfer is weakened with the increasing of lambda (r), and an increase in lambda (r), delta or epsilon r tends to decrease the average Nusselt number and to cause the fluid flow in a steady state. Further, it is observed that the difference of average heat transfer rates gained for different K-r is almost negligible. Moreover, it is noted that the flow characteristics obtained for different ( rho c p ) r at steady state are always identical, while they are largely different for the case of the unsteady state. Finally, the bifurcation types of the linear instability (subcritical or supercritical) and the hysteresis loops in electro-thermo-convection are also investigated and compared with the case without the solid wall.