Electro-thermo-capillary-convection in a square layer of dielectric liquid subjected to a strong unipolar injection

In this paper, the effect electric field on the flow induced by the combined buoyancy and thermocapillary forces is carried out. Calculations are performed for a strong unipolar injection (C = 10) and different values of Marangoni number (−10000 ≤ Ma ≤ 10000), thermal Rayleigh number (5000 ≤ Ra ≤ 50,000) and electric Rayleigh number (0 ≤ T ≤ 800). The Prandtl number (Pr) and the mobility parameter (M) are fixed at 116.6 and 49, respectively. These values correspond to the Silicone oil used as working liquid several practical applications. The full set of coupled equations: Navier–Stokes, Electro-hydrodynamic (EHD) and heat transfer equations are directly solved using stream function-vorticity formalism. Obtained results show that the electric forces can control the thermocapillary instabilities. According to the intensity and the direction of the applied electric forces, it is demonstrated that these instabilities can be accentuated, attenuated, or even completely eliminated.