The energy of a Siemens reduction furnace is provided by the current heating of silicon rods. Further, owing to the temperature gradient in the silicon rod, its center temperature is considerably higher than its surface temperature. The skin effect of alternating current (AC) reduces the temperature gradient within the silicon rod. Therefore, this study essentially establishes an AC heating model of 24 pairs of rod Siemens reactor based on electromagnetic theory. The calculation results are consistent with the industrial production data, indicating that the model is accurate. The results demonstrate that when the AC frequency exceeds 50 kHz, the current density at the center of the silicon rod becomes very small, tending to zero. As the frequency continues to increase, the area where the current density is close to zero expands; further, when the AC frequency exceeds 50 kHz, there exists a constant temperature zone near the central region of the silicon rod, and as the frequency of the AC increases, the range of the constant temperature zone gradually expands outward from the center of the silicon rod. The temperature difference inside the silicon rod increases with the reactor wall emissivity.

中文翻译：

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西门子反应堆中棒的交流电加热模型▴

西门子还原炉的能量由硅棒的电流加热提供。此外，由于硅棒中的温度梯度，其中心温度明显高于其表面温度。交流电（AC）的趋肤效应降低了硅棒内的温度梯度。因此，本研究从本质上基于电磁理论建立了24对棒式西门子电抗器的交流加热模型。计算结果与工业生产数据一致，表明模型是正确的。结果表明，当交流频率超过50 kHz时，硅棒中心的电流密度变得很小，趋于零。随着频率的不断增加，电流密度接近零的区域会扩大；进一步，当AC频率超过50kHz时，在硅棒的中心区域附近存在恒温区，并且随着AC频率的增加，恒温区的范围从硅棒的中心逐渐向外扩展。硅棒内部的温差随反应器壁的发射率而增加。