A numerical investigation of electro-thermo-convection in a $2-D$ differentially heated square cavity filled with a dielectric liquid is presented. Fully coupled governing equations of electric potential, charge transport, Navier–Stokes equations, and the energy equation are implemented in the finite-volume framework of OpenFOAM®. For this kind of electro-thermo-convection, previous studies mainly focused on the strong injection regime. This study extends the analysis to arbitrary injection strengths in weak, medium and strong regimes. Moreover, the flow configuration considered in this study investigates the simultaneous action of buoyancy and Coulomb forces acting in orthogonal direction to each other. For strong and medium injection, the flow transforms from a steady two-cell flow to a periodic two-cell flow and finally evolves into a chaotic flow with multiple cells, as the value of $T$ is increased. In the weak injection regime, chaotic flow with multiple flow cells is observed right from the onset of instability. Heat transfer rates and the maximum velocity are directly proportional to the electric Rayleigh number $T$. Present study gives an insight into different flow structures and the related heat transfer phenomenon at arbitrary injection strengths.

空气中电热对流的数值研究 $\mathrm{2个}--d$提出了一种充满电介质液体的差动加热方腔。完全耦合的电势控制方程，电荷传输，Navier–Stokes方程和能量方程在OpenFOAM®的有限体积框架中实现。对于这种电热对流，以前的研究主要集中在强注入方式上。这项研究将分析扩展到在弱，中和强状态下的任意注入强度。此外，本研究中考虑的流动形态研究了在正交方向上作用的浮力和库仑力的同时作用。对于强注入和中等注入，流量从稳定的两单元流转换为周期性的两单元流，最后演变为具有多个单元的混沌流，其值为$Ť$增加。在弱注入条件下，从不稳定开始就观察到具有多个流动池的混沌流动。传热速率和最大速度与电瑞利数成正比$Ť$。本研究对任意注入强度下的不同流动结构和相关的热传递现象进行了深入研究。