Electro-thermo-convection is a typical interdisciplinary problem, that has been widely studied in terms of its physical phenomena in Newtonian fluids. As an essential supplement to the study of electrohydrodynamics, electro-thermo-convection in power-law fluids within rectangular enclosures is investigated in this paper. Two geometrical configurations are considered, namely differentially heated vertical and horizontal wall configurations. The governing equations are discretized using the finite volume scheme, and the bifurcations, flow patterns, and heat transfer efficiency under different power-law indexes are studied. A comprehensive comparison between the Newtonian and non-Newtonian cases is presented. The results indicate that electro-thermo-convection in power-law fluids exhibits more complicated hydrodynamic behavior than in Newtonian fluids. The shear-thinning characteristic decreases the criterion of subcritical bifurcation and corresponds to a smaller hysteresis loop, whereas the shear-thickening characteristic has an opposite effect. The bifurcation diagrams exhibit various features under different power-law indexes, and some of which have not been observed in Newtonian fluids. Additionally, the effects of the non-Newtonian behavior on the temporal evolution of the flow are discussed, and the fluid motion is found to be sensitive to the power-law index.

电热对流是一个典型的跨学科问题，已在牛顿流体中对其物理现象进行了广泛研究。作为电流体动力学研究的必要补充，本文研究了矩形外壳内幂律流体中的电热对流。考虑了两种几何构型，即差热垂直壁构型和水平壁构型。利用有限体积法离散了控制方程，研究了不同幂律指标下的分叉，流型和传热效率。提出了牛顿和非牛顿情况之间的全面比较。结果表明，与牛顿流体相比，幂律流体中的电热对流表现出更复杂的流体动力学行为。剪切变稀特性降低了亚临界分叉的标准，并且对应于较小的磁滞回线，而剪切变厚特性具有相反的效果。分叉图在不同的幂律指数下表现出各种特征，其中一些尚未在牛顿流体中观察到。此外，讨论了非牛顿行为对流动时间演化的影响，发现流体运动对幂律指数敏感。而剪切增稠特性则相反。分叉图在不同的幂律指数下表现出各种特征，其中一些尚未在牛顿流体中观察到。此外，讨论了非牛顿行为对流动时间演化的影响，发现流体运动对幂律指数敏感。而剪切增稠特性则相反。分叉图在不同的幂律指数下表现出各种特征，其中一些尚未在牛顿流体中观察到。此外，讨论了非牛顿行为对流动时间演化的影响，发现流体运动对幂律指数敏感。