Based on the thermosize effects of a confined ideal Maxwellian gas, we established a model of micro/nano-scaled heat pump including two isothermal and two isobaric processes, where the Joule-like heating effect was analyzed in detail by using the nonequilibrium thermodynamic theory. Further, in order to improve the performance of a single thermosize device, a model of two-stage micro/nano-scaled heat pump with multiple micro/nano components is for the first time put forward. The general expressions of heating load and coefficient of performance for the single and the two-stage heat pump are derived. The influences of the internal and external irreversibilities of the system, i.e., Fourier heat flow and the Joule-like heating and the finite rate heat transfer with the reservoirs, on the performance characteristic of thermosize devices are studied in detail. Moreover, we also discuss the effect of the allocation the thermosize components on the optimal performance of the two-stage micro/nano-scaled heat pump cycle. It is found that in the presence of the internal and external irreversibilities, the two kinds of the micro/nano-scaled heat pump can achieve specific heating performance. In particular, when the total number M of the thermosize components is fixed, both the maximum of the optimal coefficient of performance ${\mathrm{\Phi }}^{\mathit{opt},\mathit{max}}$ and the maximum of the heating load ${\mathrm{\Pi }}^{\mathit{opt},\mathit{max}}$ corresponding to the optimal coefficient of performance appear near $n=M/2$ with n being the number of the thermosize elements of the top stage. The results obtained here show several main irreversibility source of the micro/nano-scaled heat pump and have potential applications in the efficient utilization and conversion of energy in the microchannel system using gas.

基于受限理想麦克斯韦气体的热尺寸效应，我们建立了一个包含两个等温和两个等压过程的微纳尺度热泵模型，其中使用非平衡热力学理论详细分析了类似焦耳的热效应。此外，为了提高单个热缩尺寸设备的性能，首次提出了具有多个微纳成分的两级微纳热泵模型。推导了单级和二级热泵的热负荷和性能系数的一般表达式。系统内部和外部不可逆性的影响，即傅立叶热流和焦耳式加热以及与储层的有限速率热传递，对热缩型器件的性能特点进行了详细研究。此外，我们还讨论了分配热尺寸组分对两级微/纳米级热泵循环的最佳性能的影响。发现在存在内部和外部不可逆性的情况下，两种微型/纳米级热泵可以实现特定的加热性能。特别是当总数M的热敏尺寸组件是固定的，两者均具有最佳的最佳性能系数${\mathrm{\Phi }}^{\mathit{选择}，\mathit{最大限度}}$ 和最大的热负荷 ${\mathrm{\Pi }}^{\mathit{选择}，\mathit{最大限度}}$ 对应于最佳性能系数出现在附近 $ñ=\mathrm{中号}/\mathrm{2个}$其中n是顶层热尺寸元件的数量。此处获得的结果显示了微/纳米级热泵的几种主要不可逆性来源，并且在使用气体的微通道系统中有效利用和转换能量方面具有潜在的应用前景。