Exergy-based ecological optimization of an irreversible quantum Carnot heat pump with harmonic oscillators

Abstract

This paper studies ecological performance by taking a quantum Carnot heat pump as object. The working substance of the heat pump is harmonic oscillator. Besides heat resistance, this heat pump also has heat leakage and internal friction. This paper derives heating load, coefficient of performance and ecological function and analyse these important parameters with numerical illustrations. At high temperature limit, this paper simplifies these important parameters and deduces the optimal performance by taking ecological function as objective. Also, this paper illustrates effects of irreversibilities with help of numerical calculation. The results reveal that ecological function of the pump has maximum value. Results at high temperature limit reveal that ecological function versus COP characteristic curves are parabolic-like as when heat leakage is absent and ecological function has maximum value. Heat leakage makes characteristic curves become loop-shaped curves and leads to smaller ecological function and COP. With a constant heat leakage, maximum attained ecological function decreases as internal friction increases. Comparison between maximum points of ecological function and COP at high temperature limit reveals that ecological optimization makes COP decrease 16.8%, exergy loss rate increases about 7.20 times, but heating load and exergy output rate greatly increase about 3.18 times and 3.23 times, respectively. Comparison maximum point of ecological function and point where the value of exergy output rate is A∕τ=6.09×10−4 reveals that the second point makes COP decrease 5.21%, exergy output rate increase only 20.9% and heating load increase only 21.1%, but the exergy lose rate increases 40.7%. Taking maximum ecological function as objective makes larger improvement in COP and reduction in exergy loss rate, and the cost is smaller heating load drop.