Abstract This paper numerically investigates the effect of unipolar charge injection on the onset of Rayleigh-Benard convection (RBC) in a layer of insulating liquid contained between two parallel plates. A recent developed unified model on the basis of the mesoscopic lattice Boltzmann method (LBM) is employed to solve the entire macro control equations. Two different cases of charge injection from above and from below are considered. It is interesting to find that the charge injection advances the onset of convection regardless of the injection direction. Besides, the decrease of critical Rayleigh number, along with the increase of flow intensity and the enhancement of heat transfer resulting from charge injection remain the same for different injection directions. However, the results show that the charge injection directions have significant effect on temperature and charge density distribution, as well as the evolution of flow motion, especially for the case of larger electric Rayleigh number. In addition, the effects of Prandtl number, the mobility number and the injection number are also studied.

中文翻译：

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单极电荷注入方向对 Rayleigh-Bénard 对流开始的影响：格子 Boltzmann 研究

摘要 本文数值研究了单极电荷注入对两个平行板之间绝缘液体层中瑞利-贝纳对流 (RBC) 开始的影响。最近开发的基于介观格子玻尔兹曼方法 (LBM) 的统一模型用于求解整个宏观控制方程。考虑了从上方和从下方注入电荷的两种不同情况。有趣的是，无论注入方向如何，电荷注入都会提前对流开始。此外，临界瑞利数的降低，随着流动强度的增加和电荷注入引起的传热增强，对于不同的注入方向保持不变。然而，结果表明，电荷注入方向对温度和电荷密度分布以及流动运动的演化有显着影响，尤其是在电瑞利数较大的情况下。此外，还研究了Prandtl数、迁移数和注入数的影响。