In this paper, we solve numerically the entire set of equations associated with the electro-thermo-convective phenomena that take place in a planar layer of dielectric liquid heated from below and subjected to unipolar injection. For the first time the whole set of coupled equations is solved: Navier-Stokes equations, electrohydrodynamic (EHD) equations and the energy equation. We first validate the numerical simulation by comparing the electro-convection stability criteria with ones obtained with a stability approach. The numerical solution of the electrothermo-convection problem is then presented entirely with a detailed analysis of stability parameters. In particular, the relation between fluid velocity, non-dimensional electrical parameter T, Rayleigh number Ra and Prandtl number Pr is given. An analytical model is presented in order to understand the flow behaviour at some critical conditions. The way that the onset of motion passes from purely electrical convection to purely thermal convection is, in particular, investigated and explained in detail. Finally, a result on the heat transfer enhancement due to electro-convection is exhibited and compared with data from experimental works available in this field.

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An impinging jet in a dielectric liquid is generated by applying a high potential difference to a blade-plane geometry. This kind of jet is both a fluid flow and an electrical phenomenon. In our study, an overview of the flow field is easily obtained by using the classical particle velocity method. Two patterns of electrohydrodynamic velocity profiles of the jet can be observed when the applied high voltage varies. A typical method for a classical impinging jet is used in order to point out the specific characteristics of electrohydrodynamic jets. Electric current measurements and particle-image-velocimetry investigations are conducted synchronously, which contribute to the analysis of this electrohydrodynamic phenomenon. Two electrical current regimes are presented according to the potential difference.Index Terms-Blade-plane geometry, dielectric liquids, electric potential, electrohydrodynamics, fluid flow control, particle image velocimetry (PIV). NOMENCLATUREThree velocity components in Cartesian coordinates and their vector norms. For a 2-D flow in xy plane, V = V 2 x + V 2 y . V c Mean streamwise distribution of centerline velocity. V c,max Maximum value of V c .