Flow patterns and heat transfer in electro-thermo-convection

In this article we study the electro-thermo-convective phenomena in a dielectric liquid layer placed between two electrodes and subjected to the simultaneous action of an electric field and a thermal gradient. The full set of coupled equations: Navier-Stokes, Electro-Hydro-Dynamic (EHD) and Heat Transfer equations are directly solved in a 2D cavity using a finite volume method. In order to characterize the influence of the electric field on heat transfer we first heat the liquid till the thermal steady state is obtained and then apply the electric potential and charge are injected from the lower electrode. Two cases of heating are considered: from the lower electrode and from a lateral wall (left or right). We show that both flow pattern and Nusselt number strongly depend on the following non-dimensional characteristic parameters: electrical parameter, Rayleigh number, Prandtl number and mobility parameter. The development of the convective motion passing from a purely thermal convection to a purely electrical convection is investigated as well as the number of electro-thermo-convective rolls. As a consequence of the analysis of the combined effect of electric and thermal fields on the flow structure and on Nusselt number, we have also evaluated the heat transfer enhancement due to electro-convection.