Influence of the dielectric force on a thermoelectric convection phenomena in case of weak injection

The electro thermal convection in a plane layer of dielectric liquid subjected to simultaneous action of electric field and thermal gradient is studied. The influence of the dielectric forces on the convective flow is analyzed in the case of a weak charge injection. The set of equations associated with the thermo-electro convective phenomena is solved directly using a finite volume method. The results are analyzed in the configuration of a cavity heating from below and with charge injection from below. The values of EHD instability criteria T_c with and without dielectric forces for different values of parameter L are presented. L provides a measure of the temperature variations of the dielectric constant. Our results are compared with theoretical and experimental ones obtained by other authors. The time evolution of Nusselt number, associated with heat transfer, in terms of various non dimensional electrical parameters (instability criteria T, Rayleigh number Ra and L) is given and analyzed.