The governing equations of thermoelectricity are nonlinear in general. Herein, a first-order linear theory of thermoelectricity for thermoelectric (TE) materials is presented, in which the Joule heating contribution is neglected in the energy balance equation as it is usually at least one order of magnitude smaller than the total thermal energy in TE generator applications. The first-order linear theory is applied to calculate the energy conversion efficiency for homogeneous, functionally graded, and segmented TE generators under 1D heat flow conditions. Energy efficiency for a 2D example is also presented. It is found that the maximum energy efficiencies predicted by the linear theory agree well with those using the general nonlinear theory of thermoelectricity, which indicates that the linear theory is accurate in predicting the energy efficiencies of TE devices. Finally, the peak efficiency for a homogeneous leg under 1D conditions in the linear theory is also characterized by the figure of merit parameter Z as in the nonlinear theory.

中文翻译：

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热电材料的线性热电理论

热电的控制方程一般是非线性的。在此，提出了热电 (TE) 材料的一阶线性热电理论，其中焦耳热贡献在能量平衡方程中被忽略，因为它通常至少比 TE 中的总热能小一个数量级发电机应用。应用一阶线性理论计算一维热流条件下均质、功能分级和分段 TE 发电机的能量转换效率。还提供了 2D 示例的能源效率。发现线性理论预测的最大能量效率与使用一般非线性热电理论的能量效率非常吻合，这表明线性理论在预测 TE 设备的能量效率方面是准确的。最后，线性理论中一维条件下均质支路的峰值效率也由品质因数参数表征Z作为非线性理论。