Collective Working Regimes for Coupled Heat Engines

Cisneros, B. Jiménez de; Hernández, A. Calvo

doi:10.1103/physrevlett.98.130602

Cited by 90 publications

(111 citation statements)

References 9 publications

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“…The obtained result η CA = 1 − T c /T h for the efficiency at maximum power (EMP) seemingly exhibits the same degree of generality as the Carnot's formula and also it describes well the efficiency of some actual thermal plants [6][7][8]. Although it turned out that η CA is not a universal result, neither it represents an upper or lower bound for the EMP [9][10][11], its close agreement with EMP for several model systems [12][13][14][15][16][17][18][19][20][21][22][23][24] ignited search for universalities in performance of heat engines.…”

Section: Introductionmentioning

confidence: 99%

Efficiency at and near maximum power of low-dissipation heat engines

Holubec

Ryabov

2015

Phys. Rev. E

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A new universality in optimization of trade-off between power and efficiency for low-dissipation Carnot cycles is presented. It is shown that any trade-off measure expressible in terms of efficiency and the ratio of power to its maximum value can be optimized independently of most details of the dynamics and of the coupling to thermal reservoirs. The result is demonstrated on two specific trade-off measures. The first one is designed for finding optimal efficiency for a given output power and clearly reveals diseconomy of engines working at maximum power. As the second example we derive universal lower and upper bounds on the efficiency at maximum trade-off given by the product of power and efficiency. The results are illustrated on a model of a diffusion-based heat engine. Such engines operate in the low-dissipation regime given that the used driving minimizes the work dissipated during the isothermal branches. The peculiarities of the corresponding optimization procedure are reviewed and thoroughly discussed.

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Section: Introductionmentioning

confidence: 99%

Efficiency at and near maximum power of low-dissipation heat engines

Holubec

Ryabov

2015

Phys. Rev. E

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“…[4,5]. It would be an interesting problem to construct and study the collective behavior of the Carnot cycles coupled with each other by using the property of the Onsager coefficients derived in this paper [6,18,19,20,21].…”

Section: Discussionmentioning

confidence: 99%

Onsager coefficients of a finite-time Carnot cycle

2009

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We study a finite-time Carnot cycle of a weakly interacting gas which we can regard as a nearly ideal gas in the limit of T h − Tc → 0 where T h and Tc are the temperatures of the hot and cold heat reservoirs, respectively. In this limit, we can assume that the cycle is working in the linearresponse regime and can calculate the Onsager coefficients of this cycle analytically using the elementary molecular kinetic theory. We reveal that these Onsager coefficients satisfy the so-called tight-coupling condition and this fact explains why the efficiency at the maximal power ηmax of this cycle can attain the Curzon-Ahlborn efficiency from the viewpoint of the linear-response theory.

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“…(29), the lower bound ε q− maxχ = 0 can be realized also at the lower endpoint of eq. (29), that is, in the limit fig. 2 (a).)…”

Section: P-3mentioning

confidence: 99%

“…Thus additional research work [27][28][29][30] has been devoted to obtain model-independent results on efficiency and COP using the well founded formalism of linear irreversible thermodynamics (LIT) for both cyclic and steadystate models including explicit calculations of the Onsager coefficients using molecular kinetic theory [31][32][33]. Beyond the linear regime a further improvement was reported by Izumida and Okuda [34] by proposing a model of minimally nonlinear irreversible heat engines described by extended Onsager relations with nonlinear terms accounting for power dissipation.…”

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Coefficient of performance under optimized figure of merit in minimally nonlinear irreversible refrigerator

Izumida¹,

Okuda²,

Hernández³

et al. 2013

EPL

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-We apply the model of minimally nonlinear irreversible heat engines developed by Izumida and Okuda [EPL 97, 10004 (2012)] to refrigerators. The model assumes extended Onsager relations including a new nonlinear term accounting for dissipation effects. The bounds for the optimized regime under an appropriate figure of merit and the tight-coupling condition are analyzed and successfully compared with those obtained previously for low-dissipation Carnot refrigerators in the finite-time thermodynamics framework. Besides, we study the bounds for the nontight-coupling case numerically. We also introduce a leaky low-dissipation Carnot refrigerator and show that it serves as an example of the minimally nonlinear irreversible refrigerator, by calculating its Onsager coefficients explicitly.Introduction. -Nowadays, the optimization of thermal heat devices is receiving a special attention because of its straightforward relation with the depletion of energy resources and the concerns of sustainable development. A number of different performance regimes based on different figures of merit have been considered with special emphasis in the analysis of possible universal and unified features. Among them, the efficiency at maximum power (EMP) η maxP for heat engines working along cycles or in steady-state is largely the issue most studied independently of the thermal device nature (macroscopic, stochastic or quantum) and/or the model characteristics [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Even theoretical results have been faced with an experimental realization for micrometre-sized stochastic heat engines performing a Stirling cycle [15].For most of the Carnot-like heat engine models analyzed in the finite-time thermodynamics (FTT) framework [5,6] the EMP regime allows for valuable and simple expressions of the optimized efficiency, which under endoreversible assumptions (i.e., all considered irreversibilities coming from the couplings between the working system and the external heat reservoirs through linear heat transfer laws) recover the paradigmatic Curzon-Ahlborn value [16] η maxP = 1 − √ τ ≡ η CA using τ ≡ T c /T h , where T c and T h denote the temperature of the cold and hot heat

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Collective Working Regimes for Coupled Heat Engines

Cited by 90 publications

References 9 publications

Efficiency at and near maximum power of low-dissipation heat engines

Efficiency at and near maximum power of low-dissipation heat engines

Onsager coefficients of a finite-time Carnot cycle

Coefficient of performance under optimized figure of merit in minimally nonlinear irreversible refrigerator

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