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.

• Received 27 June 2020
• Revised 23 August 2020
• Accepted 30 November 2020

DOI:https://doi.org/10.1103/PhysRevApplied.15.014011