This paper establishes a model of an irreversible two-stage combined thermal Brownian refrigerator with an intermediate heat reservoir by combining finite time thermodynamics with non-equilibrium thermodynamics. The model is composed of two irreversible thermal Brownian refrigerators working in series. The combined thermal Brownian refrigerator works among three constant temperature heat reservoirs. There exist finite rate heat transfer processes among heat reservoirs and refrigerators. Considering heat leakage, heat transfer losses, and heat flows via kinetic energy change of particles, expressions of cooling load and the coefficient of performance (COP) are derived. The effects of design parameters on system performance are studied. The optimal performance of the irreversible combined thermal Brownian refrigerator is studied. The cooling load and COP are higher when the temperature of the intermediate heat reservoir is close to that of the bottom heat reservoir. Compared with the single-stage thermal Brownian refrigerator, which works between the heat source and sink with the same temperatures, the cooling load of the combined thermal Brownian refrigerator is greater, whereas the COP is smaller.

中文翻译：

---

不可逆两阶段组合式热布朗制冷机的建模及其最佳性能

通过将有限时间热力学与非平衡热力学相结合，建立了带有中间储热器的不可逆两阶段组合布朗布朗制冷机模型。该模型由两个串联的不可逆热布朗制冷机组成。组合式布朗热式制冷机在三个恒温储热器之间工作。在储热器和冰箱之间存在有限速率的传热过程。考虑到颗粒的热泄漏，传热损失和动能变化引起的热流，得出了冷却负荷和性能系数（COP）的表达式。研究了设计参数对系统性能的影响。研究了不可逆组合布朗咖啡制冷机的最佳性能。当中间储热器的温度接近底部储热器的温度时，冷却负荷和COP较高。与在相同温度下在热源和散热器之间工作的单级布朗尼制冷机相比，联合布朗尼制冷机的冷却负荷更大，而COP较小。