Effect of Electric Nusselt number on Electro-Thermo-Convection in dielectric liquid subjected to unipolar injection

In this article we analyse the results of a numerical simulation of an electro-thermo-convective flow induced in a dielectric liquid layer by the simultaneous action of an external electric field and a thermal gradient. A low conductivity liquid is placed between two horizontal electrodes and subjected to strong unipolar charge injection which set the fluid in motion under the combined action of Coulomb and buoyancy forces. The motion induced by the charge injection has a vigorous character and strongly increases the electric charge transfer and heat transfer between the electrodes. The full set of governing equations including Navier-Stokes equation, the conservation equations of electric charge and energy and Poisson equation for electric potential is solved by a finite volume method. We define an electric Nusselt number (Ne) as the ratio of the effective current and the current existing without liquid motion, number which can be considered as the analog of Nusselt number (Nu) for a pure thermal problem. The case of heating and strong injection of electric charges from lower electrode is considered. The variation of the electric Nusselt number Ne with electrical parameter T for different values of the non-dimensional parameter mobility number M and Rayleigh number is then analyzed. It is shown that the mobility number M is a parameter which plays an important role in the characterization of electro-thermo-convective flows and also that the physical mechanisms of the different instability regimes can be better understood considering the electric Nusselt number Ne.