Optimization on the performance of a harmonic quantum Brayton heat engine

The cycle model of an irreversible quantum heat engine working with many noninteracting harmonic oscillators is established. The engine cycle consists of two adiabatic and two constant-frequency processes and is referred to as the harmonic quantum Brayton cycle. The general performance characteristics of the cycle are investigated, based on the quantum master equation and semigroup approach. Expressions for several important performance parameters, such as the efficiency, power output, and rate of the entropy production, are derived. By using numerical solutions, the power output of the heat engine subject to finite cycle duration is optimized. The maximum power output and the corresponding parameters are calculated numerically. The optimal regions of the efficiency and the optimal ranges of temperatures of the working substance and times spent on the two constant-frequency processes are determined. Moreover, the optimal performance of the cycle in the high-temperature limit is compared with that of a classical Brayton heat engine working with an ideal gas. The results obtained here show that in the high-temperature limit, a harmonic quantum Brayton cycle may be equivalent to a classical Brayton cycle.