Numerical analysis of electro-thermo-convection in a differentially heated square cavity with electric conduction

Natural convection with an electric field in the classic differentially heated square cavity is numerically studied. The electric conduction model for the generation of free space charges, which applies to weak and moderate electric field with weakly conducting liquids, is specially considered. The whole set of governing equations is implemented in the open-source finite-volume framework of OpenFOAM. Thorough investigation has been undertaken to analyze the thermal and flow characteristics of electro-thermo convection. The results reveal that the introduction of an electric field leads to a suppressive influence on flow motion across all considered Rayleigh numbers (Ra), aligning with recent experimental findings. This effect becomes more pronounced with increasing conduction number (C ₀), resulting in the reduction of flow intensity and a thicker thermal boundary layer. Consequently, heat transfer is subdued due to the electric field, causing a decrease in the Nusselt number (Nu) as C ₀ increases. To elucidate the mechanism how the electric field impacts natural convection, the torques induced by the electric and buoyancy forces are computed. Higher C ₀ will lead to a lower buoyancy torque and stronger electric torque, where the electric torque is opposite to the buoyancy torque, thus the weaker flow strength is shown at higher C ₀. Finally, to quantify the reduction in heat loss, the relative Nusselt number (Rnu) is introduced. It is found that there is a critical Ra corresponding to minimal Rnu, and for the parameters considered in this study, the minimum Rnu of 0.563 is observed at C ₀ = 0.2 and Ra = 1.2 × 10⁴. For large Ra, the Rnu almost keeps constant with increasing Ra.