Ecological optimisation of irreversible harmonic oscillator Carnot refrigerator

A model of a quantum harmonic oscillator Carnot refrigerator with heat resistance, internal irreversibility and heat leakage is established in this paper. Based on the quantum master equation and semigroup approach, equations of some important performance parameters, such as cooling load, coefficient of performance (COP), exergy output rate, entropy generation rate and ecological function (a criterion E=A/tau - T-0 sigma representing the optimal compromise between exergy output rate A/tau and exergy loss rate T-0 sigma), for the irreversible quantum Carnot refrigerator are derived. The optimal ecological performance of the refrigerator at high temperature limit is analysed using numerical examples. The effects of internal irreversibility and heat leakage on the optimal ecological performance are discussed. Performance comparisons of the quantum refrigerator under maximum ecological function, maximum COP and maximum cooling load conditions are also performed. Some special cases, i.e. endoreversible, frictionless and without heat leakage, are discussed. Taking ecological optimisation criterion as the objective makes larger improvement of the COP and the reduction in the exergy loss rate at the cost of smaller cooling load drop.