Linear irreversible thermodynamics and coefficient of performance

Cisneros, B. Jiménez de; Arias-Hernandez, L. A.; Hernández, A. Calvo

doi:10.1103/physreve.73.057103

Cited by 47 publications

(42 citation statements)

References 8 publications

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“…Practically since the beginning of FTT as an active discipline, the limited validity of the CA-efficiency was established [3][4][5][6][7]. Nonetheless, at the end of the 1980's the CAefficiency was found linked to MW reversible cycles [13,14] and recently with its role in microscopic [11], mesoscopic [12] and macroscopic thermal cycles [8,9], and therefore the CA-efficiency has gained new insights, that have to do with a possible universality at least at the first few terms in the Taylor expansion of the efficiency as a function of η C = 1 − τ [12,19,21,23]. Clearly, Eq.…”

Section: ∆S =ˆTmentioning

confidence: 99%

“…Through their papers on reversible cycles performing at MW, LL [13,14] established a bridge with FTT-MPcycles, basically by means of the CA-efficiency. In recent years several authors [8][9][10][19][20][21][22][23] have renewed the interest on the CA-efficiency. The discussion on this famous formula has been mainly turned on to its possible universal nature within the context of finite-time cycles.…”

Section: ∆S =ˆTmentioning

confidence: 99%

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Connection between maximum-work and maximum-power thermal cycles

2013

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We propose a new connection between maximum-power Curzon-Ahlborn thermal cycles and maximum-work reversible cycles. This linkage is built through a mapping between the exponents of a class of heat transfer laws and the exponents of a family of heat capacities depending on temperature. This connection leads to the recovery of known results and to a wide and interesting set of new results for a class of thermal cycles. Among other results we find that it is possible to use analytically closed expressions for maximum-work efficiencies to calculate good approaches to maximum-power efficiencies.PACS numbers: 05.70.Ln Non-equilibrium and irreversible thermodynamics; 05.70.-a Thermodynamics; 84.60.Bk Performance characteristics of energy conversion systems, figure of merit.As it is well known, in 1975 [1] Curzon-Ahlborn (CA) found that an endoreversible Carnot-like thermal engine in which the isothermal branches of the cycle are not in thermal equilibrium with their corresponding heat reservoirs at absolute temperatures T 1 and T 2 < T 1 has an efficiency at the maximum-power (MP) regime given byThis equation was obtained by using the so-called Newton law of cooling to model the heat exchanges between the heat reservoirs and the working fluid along the isothermal branches of the cycle. In fact, Eq. (1) The square root term (SRT) observed in the CA-efficiency can be found in other processes of energy conversion, such as the so-called water powered machine, which mixes two steady streams of hot and cold water to produce an output stream of warm water at maximum kinetic energy [16]. In fact, the role of the SRT of temperatures is more general and it appears also in some irreversible processes such as the irreversible cooling or heating of an ideal gas initially at temperature T i in contact with a series of auxiliary reservoirs to reach the final temperature T f of a main heat reservoir, the SRT appears when the generation of entropy of this process is minimized [17]. As it can be seen, the SRT is found in several thermal processes (reversible or irreversible) subject to some extremal conditions. A result less known is that corresponding to the way the square root is lost in the case of reversible cycles operating at MW regime. In 1989 [14], LL first studied a cycle formed by two adiabatic processes and two paths with constant heat capacities C > 0 of the working fluid (see Fig. 1). This reversible cycle operating under MW conditions has an efficiency given by η CA = 1 − √ τ , where τ = T − /T + is the ratio between the minimum and maximum temperatures of the cycle (see Fig. 1). Actually, the first author in finding this expression for a MW engine was Chambadal [18]. LL [14] generalized the model of Fig. 1, to encompass a family of symmetric and asymmetric reversible cycles which have a MW efficiency that do no deviate from η CA more than 14%. This behavior was referred to as a near universality property of η CA . However, for the case of reversible cycles performing at MW, we will demonstrate that the CA-effici...

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Section: ∆S =ˆTmentioning

confidence: 99%

Section: ∆S =ˆTmentioning

confidence: 99%

Connection between maximum-work and maximum-power thermal cycles

2013

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“…A heat pump must transfer heat in a finite time and similar to the efficiency at maximum power for the motor we must find the coefficient of performance of the heat pump, under conditions of maximum heat transfer from the cold to the hot bath. Following Van den Broeck's work [18], regarding the efficiency at maximum power for the motor, some authors have investigated the coefficient of performance of the refrigerator at maximumQ 1→2 (∆T /T ) [20]. This quantity is maximum at a temperature difference ∆T * , given by…”

Section: (F/t and ∆T /Tmentioning

confidence: 99%

“…In a recent work, Van den Broeck [18] has shown that in the linear response regime, the efficiency at maximum power of a Brownian engine reaches the efficiency of an endoreversible engine when it operates at maximum power, namely the Curzon-Ahlborn efficiency [19]. Corresponding to the efficiency at maximum power, some authors have studied the equivalent quantity for the heat pump using linear irreversible thermodynamics [20]. Analytical expressions for the efficiency at maximum power [18,[21][22][23] and the corresponding quantity for a heat pump have been derived but the validity of these expressions have not been confirmed for the BL heat engine/heat pump for a finite mass of the Brownian particle.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Energetics of a Brownian Motor and Refrigerator Driven by Nonuniform Temperature

BENJAMIN

2014

Int. J. Mod. Phys. B

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The energetics of a Brownian heat engine and heat pump driven by position dependent temperature, known as the Büttiker-Landauer heat engine and heat pump, is investigated by numerical simulations of the inertial Langevin equation. We identify parameter values for optimal performance of the heat engine and heat pump. Our results qualitatively differ from approaches based on the overdamped model. The behavior of the heat engine and heat pump, in the linear response regime is examined under finite time conditions and we find that the efficiency is lower than that of an endoreversible engine working under the same condition. Finally, we investigate the role of different potential and temperature profiles to enhance the efficiency of the system. Our simulations show that optimizing the potential and temperature profile leads only to a marginal enhancement of the system performance due to the large entropy production via the Brownian particle's kinetic energy.

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“…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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Linear irreversible thermodynamics and coefficient of performance

Cited by 47 publications

References 8 publications

Connection between maximum-work and maximum-power thermal cycles

Connection between maximum-work and maximum-power thermal cycles

Stochastic Energetics of a Brownian Motor and Refrigerator Driven by Nonuniform Temperature

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

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