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.

No abstract

No abstract