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

Abstract

-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

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

“…Our main results are Eqs. (34) and (35) which demonstrate that any trade-off measure expressible in terms of efficiency η and the ratio P/P ⋆ of power to its maximum value exhibits the same degree of universality as the EMP. Consequently, for many systems the tradeoff measure can be optimized independently of most details of the dynamics and of the coupling to thermal reservoirs.…”

“…Namely a general expression for the EMP for these engines has been published [15] and subsequently lower and upper bounds on the EMP were derived [29]. All these results have been confirmed within a minimally nonlinear irreversible thermodynamics framework [34,35]. Another universal result recently appeared in the realm of Brownian motors [36][37][38][39].…”

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

“…The similar issues related to the COP at maximum χ−criterion were also addressed in Ref. [43][44][45][46]. It is quite interesting if one can reproduce these results on the basis of the generic model or some revised version.…”

Heat devices in nonlinear irreversible thermodynamics

“…Although the main theoretical aspects for both HE and RE have been reported previously [27,28], here for the sake of completeness, we give a brief theoretical background emphasizing the unified framework for HE and RE. …”

“…Minimally nonlinear irreversible thermodynamic (MN-LIT) models have also been proposed for cyclic and steady-state heat devices, in order to account for possible thermal dissipation effects in the interaction between the working system and the external heat reservoirs [27,28]. These models incorporate the Onsager relations with an additional nonlinear dissipation term.…”