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

TL;DR

This paper extends the minimally nonlinear irreversible heat engine model to refrigerators, analyzing bounds under optimized conditions and comparing with low-dissipation Carnot refrigerators, including a numerical study of non-tight coupling cases.

Contribution

It applies the minimally nonlinear irreversible model to refrigerators, deriving bounds under optimization and introducing a leaky low-dissipation Carnot refrigerator as an example.

Findings

Bounds for optimized regimes are derived and compared with previous models.

Numerical analysis of non-tight coupling cases is performed.

A leaky low-dissipation Carnot refrigerator is modeled explicitly.

Abstract

We apply the model of minimally nonlinear irreversible heat engines developed by Izumida and Okuda [EPL {\bf 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.