Optimal low symmetric dissipation Carnot engines and refrigerators

Tomás, Carla de; Hernández, A. Calvo; Roco, J. M. M.

doi:10.1103/physreve.85.010104

Cited by 127 publications

(168 citation statements)

References 21 publications

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“…It was first obtained in FTT for Carnot-like refrigerators by Yan and Chen [22] taking as target function εQ c , whereQ c is the cooling power of the refrigerator, later and independently by Velasco et al [23,24] using a maximum per-unit-time COP and by Allahverdyan et al [25] in the classical limit of a quantum model with two n-level systems interacting via a pulsed external field. Very recent results by Wang et al [26] generalized the previous results for refrigerators [21] and they obtained the following bounds of the COP considering extremely asymmetric dissipation limits:…”

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confidence: 61%

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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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confidence: 61%

“…Thus our model eqs. (12) and (13) under the tight-coupling condition includes the lowdissipation Carnot refrigerator [21,26] in eqs. (30) and (31) as a special case.…”

Section: P-3mentioning

confidence: 99%

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

Izumida¹,

Okuda²,

Hernández³

et al. 2013

EPL

Self Cite

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“…They suggested taking the product of the coefficient of performance (COP) and the heat absorbed by the working substance from the cold bath per unit time as the optimization target function, which was also called the χ−criterion by de Tomás et al in recent work [12]. The COP at maximum χ−criterion was found to be ε Y C ≡ √ ε C + 1 − 1 for endoreversible refrigerators [11] or symmetrically low-dissipation refrigerators [12], where ε C represents the Carnot COP for reversible refrigerators.…”

Section: Introductionmentioning

confidence: 99%

Weighted reciprocal of temperature, weighted thermal flux, and their applications in finite-time thermodynamics

Sheng

2014

Phys. Rev. E

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The concepts of weighted reciprocal of temperature and weighted thermal flux are proposed for a heat engine operating between two heat baths and outputting mechanical work. With the aid of these two concepts, the generalized thermodynamic fluxes and forces can be expressed in a consistent way within the framework of irreversible thermodynamics. Then the efficiency at maximum power output for a heat engine, one of key topics in finite-time thermodynamics, is investigated on the basis of a generic model under the tight-coupling condition. The corresponding results have the same forms as those of low-dissipation heat engines [M. Esposito, R. Kawai, K. Lindenberg, and C. Van den Broeck, Phys. Rev. Lett. 105, 150603 (2010)]. The mappings from two kinds of typical heat engines, such as the low-dissipation heat engine and the Feynman ratchet, into the present generic model are constructed. The universal efficiency at maximum power output up to the quadratic order is found to be valid for a heat engine coupled symmetrically and tightly with two baths. The concepts of weighted reciprocal of temperature and weighted thermal flux are also transplanted to the optimization of refrigerators.

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“…Various optimization criteria [16][17][18][19][20][21][22] have been proposed in optimum analysis of a classical or quantum refrigeration cycle. Chen and Yan [16] introduced the function χ = εQ c /τ , with Q c the heat transported from the cold reservoir and τ the cycle time, as a target function within finite-time-thermodynamics context.…”

Section: Introductionmentioning

confidence: 99%

“…Velasco et al [17] adopted the per-unit-time COP as a target function while Allahverdyan et al [18] introduced εQ c to be the target function. C.de Tomás et al [20] proved the COP at maximum χ for symmetric low-dissipation refrigerators to be ε CA = √ ε C + 1 − 1, where…”

Section: Introductionmentioning

confidence: 99%

Coefficient of performance for a low-dissipation Carnot-like refrigerator with nonadiabatic dissipation

et al. 2013

Phys. Rev. E

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We study the coefficient of performance (COP) and its bounds of the Canot-like refrigerator working between two heat reservoirs at constant temperatures T h and T c , under two optimization criteria χ and Ω. In view of the fact that an "adiabatic" process takes finite time and is nonisentropic, the nonadiabatic dissipation and the finite time required for the "adiabatic" processes are taken into account. For given optimization criteria, we find that the lower and upper bounds of the COP are the same as the corresponding ones obtained from the previous idealized models where any adiabatic process undergoes instantaneously with constant entropy. When the dissipations of two "isothermal" and two "adiabatic" processes are symmetric, respectively, our theoretical predictions match the observed COP's of real refrigerators more closely than the ones derived in the previous models, providing a strong argument in favor of our approach.

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Optimal low symmetric dissipation Carnot engines and refrigerators

Cited by 127 publications

References 21 publications

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

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

Weighted reciprocal of temperature, weighted thermal flux, and their applications in finite-time thermodynamics

Coefficient of performance for a low-dissipation Carnot-like refrigerator with nonadiabatic dissipation

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