如何优化工作在有限尺寸的热源与冷源之间的热设备的性能是有限时间热力学领域的一个重要课题.本文在线性不可热力学框架下,结合有限时间热力学理论,研究了一个无限尺寸热源而有限尺寸冷源的制冷机的工作过程,解析性地推导了紧耦合条件下平均输入功率以及制冷系数表达式,并且进一步讨论了该制冷机的性能.发现平均输入功率与制冷时间不存在明确的优化关系,而且输入功率的增加导致制冷系数单调减小,但辐射能的增加致使制冷系数增强.研究结果对于深入理解实际的热力学过程具有一定的工程实践性价值.%How to optimize the performances of heat devices operating between finite-sized heat sources and sinks has become a very important issue in the field of finite-time thermodynamics. In this paper, a physical model of the refrigerator operating between an infinite-sized hot reservoir and a finite-sized cold one is proposed, and by using the principles of finite-time thermodynamics and the theory of linear irreversible thermodynamics, we present the analytical expressions of the input power and the coefficient of performance (COP) under the tight-coupling condition, and analyze the per-formance characteristics of the refrigerator in detail. When the temperature of the cold reservoir is changed with fixing the environment temperature (the temperature of the hot reservoir), it is found that there does not exist a well-defined optimal relation between the input power and a duration timeτ of the refrigerating process, which is a remarkable dif-ference from the working process of a heat engine operating between a finite-sized hot reservoir and an infinite-sized cold one. We further find that the COP exhibits the monotonically decreasing trend with the increase of the input power, but the increase of the exergy leads to the enhancement of the COP. This feature can be understood as follows: when P is small, this means that the duration timeτ is large, thus the refrigerating process approaches to the quasistatic operation, which induces the large COP. In particular, when P →0, the COP ε→εmax. The increase of P implies the reduction of τ, thus the refrigerating process keeps away from the quasistatic process and approaches to the actual irreversible process, which causes the COP to decrease. On the contrary,εshows the increasing trend with the increase of the exergy E. This is because the increase of E means the enhancement of τ at fixing the input power P , which corresponds to a slow refrigerating process. As a result, E exhibits the increasing behaviors due to the emergence of the quasistatic process. From the above analyses, we can find that an appropriate proposal to optimize the refrigerating performance of heat devices should be based on the actual parameters and the real external environment, thus it is possible to obtain the optimal refrigerating objective at the expense of the suitable input power. These results are not only helpful in the in-depth understanding of the refrigerator operating between an infinite-sized hot reservoir and a finite-sized cold one, but also of great engineering interest in designing realistic heat deices. Our method can also generalize the investigation of heat pumps. In addition, when the tight-coupling condition is false due to the breaking of time-reversal symmetry, there needs to be further consideration about it from the angle of physics.
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