Low-dissipation heat devices: Unified trade-off optimization and bounds

Abstract

We apply a unified and trade-off based optimization for low-dissipation models of cyclic heat devices which accounts for both useful energy and losses. The resulting performance regime lies between those of maximum first-law efficiency and maximum χ (a unified figure of merit corresponding to power output of heat engines). The bounds available for both symmetric and extremely asymmetric heat devices are explicitly obtained. The similarities for heat engines and refrigerators and the energetic advantages of the trade-off optimization are specially stressed.

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

“…In the present paper we reveal a new universality in optimization of trade-off between power and efficiency for low-dissipation Carnot cycles [32,[49][50][51]. As our main result, we show that any trade-off measure expressible in terms of efficiency and the ratio of power to its maximum value exhibits the same degree of universality as the EMP (see Sec.…”

“…This result was further precised [27] and recently a similar argumentation was successfully used for general thermodynamic devices [28]. Further universalities were obtained for the class of heat engines working in the regime of "low dissipation" [15,[29][30][31][32][33], where the work dissipated during the * viktor.holubec@mff.cuni.cz isothermal branches of the Carnot cycle grows in inverse proportion to the duration of these branches. 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].…”

Anomalous Brownian refrigerator

“…On the other hand, many optimization criteria were proposed in case of refrigerator. Widely used target function was introduced in [60,61,62,63,64] by giving equal footing for COP and cooling rate, known as χ-criterion [62,63]. In view of new findings in Brownian refrigerators, it will be of immense interest to study these quantities in our system.…”

Geometric Heat Engines Featuring Power that Grows with Efficiency

“…Heat engines that attain their maximal power and maximal efficiency (which is either the Carnot efficiency or a lower value) at different working conditions are here defined as heat engines with a power-efficiency trade-off. The power-efficiency trade-off is the subject of many recent studies [3,[6][7][8][9][10][11].Less is known about the efficiency and power of cyclic heat engines, but a lot of research effort has been devoted to understanding them in recent years [12][13][14][15][16][17][18][19]. The operation of a cyclic engine is characterized by a protocol that describes the time dependence of key variables along the cycle -e.g.…”

“…Less is known about the efficiency and power of cyclic heat engines, but a lot of research effort has been devoted to understanding them in recent years [12][13][14][15][16][17][18][19]. The operation of a cyclic engine is characterized by a protocol that describes the time dependence of key variables along the cycle -e.g.…”