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Research Papers

Optimal Ecological Performance Investigation of a Quantum Harmonic Oscillator Brayton Refrigerator

[+] Author and Article Information
Xiaowei Liu

College of Power Engineering,
Naval University of Engineering,
Wuhan 430033, China
e-mail: pkumass@126.com

Lingen Chen

Institute of Thermal Science and Power Engineering,
Wuhan Institute of Technology,
Wuhan 430205, China;
School of Mechanical and Electrical Engineering,
Wuhan Institute of Technology,
Wuhan 430205, China
e-mail: lingenchen@hotmail.com

Shuhuan Wei

College of Power Engineering,
Naval University of Engineering,
Wuhan 430033, China
e-mail: weishuhuan1@qq.com

Fankai Meng

College of Power Engineering,
Naval University of Engineering,
Wuhan 430033, China
e-mail: 782601028@qq.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Thermal Science and Engineering Applications. Manuscript received September 29, 2018; final manuscript received March 7, 2019; published online June 6, 2019. Assoc. Editor: Ibrahim Hassan.

J. Thermal Sci. Eng. Appl 12(1), 011007 (Jun 06, 2019) (7 pages) Paper No: TSEA-18-1474; doi: 10.1115/1.4043186 History: Received September 29, 2018; Accepted March 08, 2019

A model for the quantum Brayton refrigerator that takes the harmonic oscillator system as the working substance is established. Expressions of cooling load, coefficient of performance (COP), and ecological function are derived. With numerical illustrations, the optimal ecological performance is investigated. At the same time, effects of heat leakage and quantum friction are also studied. For the case with the classical approximation, the optimal ecological performance, and effects of heat leakage and quantum friction are also investigated. For both general cases and the case with classical approximation, the results indicate that the ecological function has a maximum. The irreversible losses decrease the ecological performance, while having different effects on the optimal ecological performance. For the case with classical approximation, numerical calculation with friction coefficient μ = 0.02 and heat leakage coefficient Ce = 0.01 shows that the cooling load (RE) at the maximum ecological function is 6.23% smaller than the maximum cooling load (Rmax). The COP is also increased by 12.1%, and the exergy loss rate is decreased by 27.6%. Compared with the maximum COP state, the COP (ɛE) at the maximum ecological function is 0.55% smaller than the maximum COP (ɛmax) and that makes 7.63% increase in exergy loss rate, but also makes 6.17% increase in cooling load and 6.20% increase in exergy output rate.

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Figures

Grahic Jump Location
Fig. 1

Irreversible quantum Brayton refrigeration cycle

Grahic Jump Location
Fig. 2

E/Emax,μ = 0,Ce = 0 versus β2 and β4

Grahic Jump Location
Fig. 3

Effects of µ and Ce on E/Emax,μ = 0,Ce = 0 versus COP

Grahic Jump Location
Fig. 4

RE/Rmax and RE/Rɛ versus µ

Grahic Jump Location
Fig. 5

ɛE/ɛmax and ɛE/ɛmax versus µ

Grahic Jump Location
Fig. 6

(A/τ)E/(A/τ)R and (A/τ)E/(A/τ)ɛ versus µ

Grahic Jump Location
Fig. 7

[σ/(kBβ0)]E/[σ/(kBβ0)]R and [σ/(kBβ0)]E/[σ/(kBβ0)]ɛ versus µ

Grahic Jump Location
Fig. 8

E/Emax,μ = 0,Ce = 0 versus β2 and β4 for classical approximation

Grahic Jump Location
Fig. 9

Effects of µ and Ce on E/Emax,μ = 0,Ce = 0 versus COP for classical approximation

Grahic Jump Location
Fig. 10

RE/Rmax and RE/Rɛ versus µ for classical approximation

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