Dynamic robustness of endoreversible Carnot refrigerator working in the maximum performance per cycle time

Lü, Ke; Nie, Wenjie; He, Jizhou

doi:10.1038/s41598-018-30847-2

Cited by 4 publications

(3 citation statements)

References 46 publications

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“…Under FPDT, finite dimensions of, say, heat exchangers are recognized as optimizable variables [2,3,6,[17][18][19][20] in the presence of finite rates of heat transfer. Thus, the total heat transfer area to be allocated on the hot and cold sides of the energy conversion system is constrained:…”

Section: Thermoelectric Generator Modelmentioning

confidence: 99%

Thermoelectric generator in endoreversible approximation: the effect of heat-transfer law under finite physical dimensions constraint

Kaur,

Johal,

Feidt

2021

Preprint

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We revisit the optimal performance of a thermoelectric generator within the endoreversible approximation, while imposing a finite physical dimensions constraint (FPDC) in the form of a fixed total area of the heat exchangers. Our analysis is based on the linear-irreversible law for heat transfer between the reservoir and the working medium, in contrast to Newton's law usually assumed in literature. The optimization of power output is performed with respect to the thermoelectric current as well as the fractional area of the heat exchangers. We describe two alternate designs for allocating optimal areas to the heat exchangers. Interestingly, for each design, the use of linear-irreversible law yields the efficiency at maximum power in the well-known form, 2η C /(4 − η C ), earlier obtained for the case of thermoelectric generator under exoreversible approximation, i.e. assuming only the internal irreversibility due to Joule heating. On the other hand, the use of Newton's law yields Curzon-Ahlborn efficiency. I. INTRODUCTIONThe real-world energy convertors perform under finitesize and finite-time constraints on the resources. In recent years, finite-time thermodynamics [1] has been popular in the study of irreversible processes. Finite physical dimensions thermodynamics (FPDT) is another approach, which considers, for example, the physical size of heat exchanger between heat reservoir and working substance, to study irreversible processes in actual devices. This approach was started by Chambadal [2] in 1957, followed by Novikov [3] and further illustrated by other authors [4][5][6]. For instance, Chambadal and Novikov started with a steady-state heat engine which is simultaneously in contact with hot and cold reservoirs. It was coupled to the hot reservoir through a finite heat transfer conductance and in perfect contact with the cold reservoir. Its efficiency at maximum power (EMP) comes out in the now well-known form, known as Curzon-Ahlborn (CA) efficiency:where θ = T c /T h is the ratio of cold to hot bath temperatures. This EMP is independent of any other model parameters like the Carnot efficiency η C = 1 − θ. The exact efficiency was reproduced in an elegant way by assuming the so-called endoreversible approximation where

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Section: Thermoelectric Generator Modelmentioning

confidence: 99%

Thermoelectric generator in endoreversible approximation: the effect of heat-transfer law under finite physical dimensions constraint

Kaur,

Johal,

Feidt

2021

Preprint

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“…Especially in the realm of finite-time thermodynamics, endoreversible and irreversible models have, in their assets, a good number of works in this regard. From the pioneering work of Santillan et al [10], a number of studies have analyzed the local and global stability of a variety of operation regimes [11][12][13][14][15][16][17][18], including economic factors [19], and have extended the analysis to heat pumps, refrigerators, and generalized heat engines [17,[20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Optimization, Stability, and Entropy in Endoreversible Heat Engines

González-Ayala

Roco

Medina

et al. 2020

Entropy

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The stability of endoreversible heat engines has been extensively studied in the literature. In this paper, an alternative dynamic equations system was obtained by using restitution forces that bring the system back to the stationary state. The departing point is the assumption that the system has a stationary fixed point, along with a Taylor expansion in the first order of the input/output heat fluxes, without further specifications regarding the properties of the working fluid or the heat device specifications. Specific cases of the Newton and the phenomenological heat transfer laws in a Carnot-like heat engine model were analyzed. It was shown that the evolution of the trajectories toward the stationary state have relevant consequences on the performance of the system. A major role was played by the symmetries/asymmetries of the conductance ratio σhc of the heat transfer law associated with the input/output heat exchanges. Accordingly, three main behaviors were observed: (1) For small σhc values, the thermodynamic trajectories evolved near the endoreversible limit, improving the efficiency and power output values with a decrease in entropy generation; (2) for large σhc values, the thermodynamic trajectories evolved either near the Pareto front or near the endoreversible limit, and in both cases, they improved the efficiency and power values with a decrease in entropy generation; (3) for the symmetric case (σhc=1), the trajectories evolved either with increasing entropy generation tending toward the Pareto front or with a decrease in entropy generation tending toward the endoreversible limit. Moreover, it was shown that the total entropy generation can define a time scale for both the operation cycle time and the relaxation characteristic time.

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“…Especially relevant is the energetic optimization of heat devices, either heat engines (HE) or refrigerators (RE). And key aspects in the optimization of energy converters related with the second law of thermodynamics are the entropy generation and the thermal efficiency/power output for HE's or coefficient of performance/cooling rate for RE's [1][2][3][4][5] .…”

mentioning

confidence: 99%

Thermodynamic optimization subsumed in stability phenomena

González-Ayala

Medina

Roco

et al. 2020

Sci Rep

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in the present paper the possibility of an energetic self-optimization as a consequence of thermodynamic stability is addressed. this feature is analyzed in a low dissipation refrigerator working in an optimized trade-off regime (the so-called Omega function). The relaxation after a perturbation around the stable point indicates that stability is linked to trajectories in which the thermodynamic performance is improved. furthermore, a limited control over the system is analyzed through consecutive external random perturbations. The statistics over many cycles corroborates the preference for a better thermodynamic performance. endoreversible and irreversible behaviors play a relevant role in the relaxation trajectories (as well as in the statistical performance of many cycles experiencing random perturbations). A multi-objective optimization reveals that the well-known endoreversible limit works as an attractor of the system evolution coinciding with the pareto front, which represents the best energetic compromise among efficiency, entropy generation, cooling power, input power and the omega function. Meanwhile, near the stable state, performance and stability are dominated by an irreversible behavior.

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Dynamic robustness of endoreversible Carnot refrigerator working in the maximum performance per cycle time

Cited by 4 publications

References 46 publications

Thermoelectric generator in endoreversible approximation: the effect of heat-transfer law under finite physical dimensions constraint

Thermoelectric generator in endoreversible approximation: the effect of heat-transfer law under finite physical dimensions constraint

Optimization, Stability, and Entropy in Endoreversible Heat Engines

Thermodynamic optimization subsumed in stability phenomena

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