The efficiency of a thermoelectric (TE) generator for the conversion of thermal energy into electrical energy can be easily but roughly estimated using a constant properties model (CPM) developed by Ioffe. However, material properties are, in general, temperature (T)-dependent and the CPM yields meaningful estimates only if physically appropriate averages, i.e., spatial averages for thermal and electrical resistivities and the temperature average (TAv) for the Seebeck coefficient (α), are used. Even though the use of αTAv compensates for the absence of Thomson heat in the CPM in the overall heat balance, we find that the CPM still overestimates performance (e.g., by up to 6% for PbTe) for many materials. The deviation originates from an asymmetric distribution of internally released Joule heat to either side of the TE leg and the distribution of internally released Thomson heat between the hot and cold side. The Thomson heat distribution differs from a complete compensation of the corresponding Peltier heat balance in the CPM. Both effects are estimated quantitatively here, showing that both may reach the same order of magnitude, but which one dominates varies from case to case, depending on the specific temperature characteristics of the thermoelectric properties. The role of the Thomson heat distribution is illustrated by a discussion of the transport entropy flow based on the α(T) plot. The changes in the lateral distribution of the internal heat lead to a difference in the heat input, the optimum current and thus of the efficiency of the CPM compared to the real case, while the estimate of generated power at maximum efficiency remains less affected as it is bound to the deviation of the optimum current, which is mostly <1%. This deviation can be corrected to a large extent by estimating the lateral Thomson heat distribution and the asymmetry of the Joule heat distribution. A simple guiding rule for the former is found.

中文翻译：

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热电发电机性能估计的恒定属性模型和温度相关材料属性之间的差异


使用 Ioffe 开发的恒定属性模型 (CPM)，可以轻松但粗略地估计热电 (TE) 发电机将热能转换为电能的效率。然而，材料属性通常与温度 (T) 相关，并且只有在物理上适当的平均值（即热阻和电阻率的空间平均值以及塞贝克系数 (α) 的温度平均值 (TAv)）下，CPM 才会产生有意义的估计，被使用。尽管αTAv的使用弥补了整体热平衡中CPM中汤姆逊热的缺失，但我们发现CPM仍然高估了许多材料的性能（例如，PbTe高出高达6%）。该偏差源自内部释放的焦耳热到 TE 腿两侧的不对称分布以及内部释放的汤姆逊热在热侧和冷侧之间的分布。 Thomson 热分布不同于 CPM 中相应 Peltier 热平衡的完全补偿。这里对两种效应进行了定量估计，表明两者可能达到相同的数量级，但哪一种占主导地位因情况而异，具体取决于热电性能的具体温度特性。汤姆逊热分布的作用通过基于 α(T) 图的传输熵流的讨论来说明。与实际情况相比，内部热量横向分布的变化导致热输入、最佳电流以及 CPM 效率的差异，而最大效率下发电功率的估计受到的影响较小，因为它必然会导致最佳电流的偏差，大多<1%。 通过估计横向汤姆逊热分布和焦耳热分布的不对称性，可以在很大程度上纠正这种偏差。找到了前者的简单指导规则。