An electrically insulating layer of a dielectric liquid confined between horizontal conducting electrodes, the upper of which is warmer, becomes unstable with respect to the onset of steady convection when the voltage between the plates reaches a critical value. In a rapidly varying ac field this instability is due to the Kelvin body force which depends on the polarization P and the gradient of the electric field E. Our recent linear stability analysis [Chem. Phys. Letters 179, 311 (1991)] for the critical voltage showed that as the gravitational Rayleigh number becomes increasingly negative the critical wave number at the onset of convection becomes very large. We now extend this analysis to examine how the Nusselt number depends on the extent of supercriticality in the weakly nonlinear regime. As the temperature drop between the plates increases the fraction of the heat transfer associated with convection is found to pass through a maximum value when the critical horizontal wave number is close to 4 times its value when gravity is absent.

中文翻译：

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通过极化介电液体的对流传热

绝缘层 介电液 限于水平之间 进行 电极 鞋面较热，相对于稳定的发作变得不稳定 对流当极板之间的电压达到临界值时。在迅速变化中交流电 场的不稳定性是由于开尔文体力决定的 极化 P和梯度电场 Ë。我们最近的线性稳定性分析[Chem。物理 临界电压的字母179，311（1991）]表明，随着重力瑞利数变得越来越负，临界电压波 发病数 对流变得很大。现在，我们扩展此分析以检查Nusselt数如何取决于弱非线性状态中的超临界程度。随着板间温度的下降，传播热量 有关联 对流 当临界水平线被发现通过最大值时 波 缺少重力时，数值接近其值的4倍。