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Chen J, Wang Y, Chen J, Su S. Optimal figure of merit of low-dissipation quantum refrigerators. Phys Rev E 2023; 107:044118. [PMID: 37198854 DOI: 10.1103/physreve.107.044118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2022] [Accepted: 03/21/2023] [Indexed: 05/19/2023]
Abstract
The Drazin inverse of the Liouvillian superoperator provides a solution to determine the dynamics of a time-dependent system governed by the Markovian master equation. Under the condition of slow driving, the perturbation expansion of the density operator of the system in powers of time can be derived. As an application, a finite-time cycle model of the quantum refrigerator driven by a time-dependent external field is established. The method of the Lagrange multiplier is adopted as a strategy to find the optimal cooling performance. The figure of merit given by the product of the coefficient of performance and the cooling rate is taken as a new objective function, and, consequently, the optimally operating state of the refrigerator is revealed. The effects of the frequency exponent determining dissipation characteristics on the optimal performance of the refrigerator are discussed systemically. The results obtained show that the adjacent areas of the state of the maximum figure of merit are the best operation region of low-dissipative quantum refrigerators.
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Affiliation(s)
- Jingyi Chen
- Department of Physics, Xiamen University, Xiamen 361005, People's Republic of China
| | - Youlin Wang
- Department of Physics, Xiamen University, Xiamen 361005, People's Republic of China
| | - Jincan Chen
- Department of Physics, Xiamen University, Xiamen 361005, People's Republic of China
| | - Shanhe Su
- Department of Physics, Xiamen University, Xiamen 361005, People's Republic of China
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Wang T, Ge Y, Chen L, Feng H, Yu J. Optimal Heat Exchanger Area Distribution and Low-Temperature Heat Sink Temperature for Power Optimization of an Endoreversible Space Carnot Cycle. ENTROPY 2021; 23:e23101285. [PMID: 34682008 PMCID: PMC8534701 DOI: 10.3390/e23101285] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/15/2021] [Accepted: 09/28/2021] [Indexed: 12/24/2022]
Abstract
Using finite-time thermodynamics, a model of an endoreversible Carnot cycle for a space power plant is established in this paper. The expressions of the cycle power output and thermal efficiency are derived. Using numerical calculations and taking the cycle power output as the optimization objective, the surface area distributions of three heat exchangers are optimized, and the maximum power output is obtained when the total heat transfer area of the three heat exchangers of the whole plant is fixed. Furthermore, the double-maximum power output is obtained by optimizing the temperature of a low-temperature heat sink. Finally, the influences of fixed plant parameters on the maximum power output performance are analyzed. The results show that there is an optimal temperature of the low-temperature heat sink and a couple of optimal area distributions that allow one to obtain the double-maximum power output. The results obtained have some guidelines for the design and optimization of actual space power plants.
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Affiliation(s)
- Tan Wang
- Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China; (T.W.); (Y.G.); (H.F.); (J.Y.)
- Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment, Wuhan 430205, China
- School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China
| | - Yanlin Ge
- Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China; (T.W.); (Y.G.); (H.F.); (J.Y.)
- Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment, Wuhan 430205, China
- School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China
| | - Lingen Chen
- Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China; (T.W.); (Y.G.); (H.F.); (J.Y.)
- Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment, Wuhan 430205, China
- School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China
- Correspondence:
| | - Huijun Feng
- Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China; (T.W.); (Y.G.); (H.F.); (J.Y.)
- Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment, Wuhan 430205, China
- School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China
| | - Jiuyang Yu
- Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China; (T.W.); (Y.G.); (H.F.); (J.Y.)
- Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment, Wuhan 430205, China
- School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China
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