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Optimal Power and Efficiency of Multi-Stage Endoreversible Quantum Carnot Heat Engine with Harmonic Oscillators at the Classical Limit

by Zewei Meng 1,2,3, Lingen Chen 1,2,* and Feng Wu 1,2
1
Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China
2
School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China
3
College of Power Engineering, Naval University of Engineering, Wuhan 430033, China
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(4), 457; https://doi.org/10.3390/e22040457
Received: 2 April 2020 / Revised: 15 April 2020 / Accepted: 16 April 2020 / Published: 17 April 2020
(This article belongs to the Section Quantum Information)
At the classical limit, a multi-stage, endoreversible Carnot cycle model of quantum heat engine (QHE) working with non-interacting harmonic oscillators systems is established in this paper. A simplified combined cycle, where all sub-cycles work at maximum power output (MPO), is analyzed under two types of combined form: constraint of cycle period or constraint of interstage heat current. The expressions of power and the corresponding efficiency under two types of combined constrains are derived. A general combined cycle, in which all sub-cycles run at arbitrary state, is further investigated under two types of combined constrains. By introducing the Lagrangian function, the MPO of two-stage combined QHE with different intermediate temperatures is obtained, utilizing numerical calculation. The results show that, for the simplified combined cycle, the total power decreases and heat exchange from hot reservoir increases under two types of constrains with the increasing number (N) of stages. The efficiency of the combined cycle decreases under the constraints of the cycle period, but keeps constant under the constraint of interstage heat current. For the general combined cycle, three operating modes, including single heat engine mode at low “temperature” (SM1), double heat engine mode (DM) and single heat engine mode at high “temperature” (SM2), appear as intermediate temperature varies. For the constraint of cycle period, the MPO is obtained at the junction of DM mode and SM2 mode. For the constraint of interstage heat current, the MPO keeps constant during DM mode, in which the two sub-cycles compensate each other. View Full-Text
Keywords: finite time thermodynamics; quantum Carnot heat engine; combined cycle; harmonic oscillator system; power; efficiency finite time thermodynamics; quantum Carnot heat engine; combined cycle; harmonic oscillator system; power; efficiency
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Meng, Z.; Chen, L.; Wu, F. Optimal Power and Efficiency of Multi-Stage Endoreversible Quantum Carnot Heat Engine with Harmonic Oscillators at the Classical Limit. Entropy 2020, 22, 457.

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