Recent developments in Nernst-Ettingshausen (NE) physical phenomena combined with advances in the performance of rare-earth permanent magnets make thermomagnetic (TM) cryocoolers well suited for practical applications. The device performance of a NE cryocooler depends on both the material and the geometric shape of the device. Despite continued progress in TM materials, the optimum shape is still based on a simplified infinite-stage model derived in 1963 by Harman [Adv. Energy Convers. 3(4), 667–676 (1963)]. Harman's model assumes several nonrealistic assumptions, such as temperature-independent material properties and constant current density. We relax such assumptions and derive a fully-temperature-dependent numerical model to accurately solve for the thermomagnetic features of a NE cooler with arbitrary geometry. We correct Harman's analytical function and compare its performance with the performance of devices of various shapes. The corrected shape has a higher coefficient of performance (COP) at higher temperature differentials, which indicates that when the material resistivity is a strong function of the temperature, the corrected infinite-stage device can provide better performance than Harman's geometry. Moreover, the corrected infinite-shape device can provide higher heat flow density under a similar optimum-COP condition. A case study based on a state-of-the-art TM material, $\mathrm{Bi}$-$\mathrm{Sb}$ alloy, is presented, and the critical parameters for designing an efficient thermomagnetic cooler are discussed in detail.

中文翻译：

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实用的无限级Nernst-Ettingshausen低温冷却器

Nernst-Ettingshausen（NE）物理现象的最新发展以及稀土永磁体性能的提高，使得热磁（TM）低温制冷器非常适合实际应用。NE低温冷却器的设备性能取决于设备的材料和几何形状。尽管TM材料不断取得进步，但最佳形状仍基于Harman [ Adv。能源转换。3（4），667–676（1963）]。Harman模型假设了一些不切实际的假设，例如与温度无关的材料特性和恒定电流密度。我们放宽了这样的假设，并导出了一个完全依赖温度的数值模型，以精确求解具有任意几何形状的NE冷却器的热磁特征。我们更正了Harman的分析功能，并将其性能与各种形状的设备的性能进行了比较。校正后的形状在较高的温差下具有较高的性能系数（COP），这表明，当材料电阻率是温度的强函数时，校正后的无限级器件可以提供比Harman几何形状更好的性能。此外，在相似的最佳COP条件下，校正后的无限形状器件可以提供更高的热流密度。以最先进的TM材料为基础的案例研究，$双$--$锑$ 提出了一种合金，并详细讨论了设计高效热磁冷却器的关键参数。