Performance analysis of a refrigerator operating between an infinite-sized hot reservoir and a finite-sized cold one within linear irreversible thermodynamics

Abstract

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 performance 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 time of the refrigerating process, which is a remarkable difference 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 time is large, thus the refrigerating process approaches to the quasistatic operation, which induces the large COP. In particular, when P0, the COP max. The increase of P implies the reduction of , 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, shows the increasing trend with the increase of the exergy E. This is because the increase of E means the enhancement of 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.