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The heat transfer process inevitably occurs in the operation of real heat engine. In this article, a low-dissipation heat engine with generic heat transfer process is proposed based on the low-dissipation Carnot model. The formulas for the power and the efficiency of heat engine with generic heat transfer law are derived, and the low-dissipation heat engine performance is also optimized by the trade-off optimization method, which offers a unified scheme to understand the behaviors of heat engines with generic heat transfer processes. Furthermore, the characteristics of the power as well as the efficiencies for thermal engines with the different heat transfer processes are discussed in detail, and it is found that the power and the efficiency without heat transfer process are independent of heat leak, but are related to contact time, heat dissipation and Carnot efficiency. The power output of heat engine monotonically increases as Carnot efficiency increases, but the large contact time ratio and the large dissipation ratio make it difficult to provide the big power output. When the heat leak is absent and () is fixed, the efficiency of heat engine decreases (increases) with the increase of (). It is noted that the heat transfer process greatly influences the performance of heat engine, and /C versus displays the similar properties under three heat transfer laws. It is clearly shown that /C versus shows the transition from the monotonic decrease to monotonic increase with increasing, but /C versus is opposite to the former, and the maximum value of /C also shifts rightwards with the increase of . Additionally, the corresponding efficiency of heat engine diminishes significantly as m decreases and n increases. When heat engines are dominated by different heat transfer laws, the curves of versus C are consistent as C is relatively large or small, but it is observed that there exist the evident differences among three characteristic curves in the middle regime. The relatively large or small will also lead to the reduction of the working regime where heat engine can function normally. Our results are very helpful in understanding the design principle and the optimization mechanism for actual thermal engines and refrigerators.
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Keywords:
- low-dissipation heat engines /
- heat transfer laws /
- trade-off criterion /
- efficiency of the heat engine
[1] Curzon F, Ahlborn B 1975 Am. J. Phys. 43 22
[2] van den Broeck C 2005 Phys. Rev. Lett. 95 190602
[3] Li J, Chen L G, Ge Y L, Sun F R 2013 Acta Phys. Sin. 62 130501 (in Chinese)[李俊, 陈林根, 戈延林, 孙丰瑞2013 62 130501]
[4] Andresen B 2011 Angew. Chem. Int. Ed. 50 2690
[5] Hernandez A C, Medina A, Roco J M M, White J A, Velasco S 2001 Phys. Rev. E 63 037102
[6] de Tomas C, Roco J M M, Hernandez A C, Wang Y, Tu Z C 2013 Phys. Rev. E 87 012105
[7] Long R, Liu Z C, Liu W 2014 Phys. Rev. E 89 062119
[8] Long R, Liu W 2015 Phys. Rev. E 91 042127
[9] Zhang Y C, Huang C K, Lin G X, Chen J C 2016 Phys. Rev. E 93 032152
[10] Esposito M, Kawai R, Lindenberg K, van den Broeck C 2010 Phys. Rev. Lett. 105 150603
[11] Izumida Y, Okuda K 2012 Europhys. Lett. 97 10004
[12] Izumida Y, Okuda K, Hernandez A C, Roco J M M 2013 Europhys. Lett. 101 10005
[13] Izumida Y, Okuda K, Roco J M M, Hernandez A C 2015 Phys. Rev. E 91 052140
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[1] Curzon F, Ahlborn B 1975 Am. J. Phys. 43 22
[2] van den Broeck C 2005 Phys. Rev. Lett. 95 190602
[3] Li J, Chen L G, Ge Y L, Sun F R 2013 Acta Phys. Sin. 62 130501 (in Chinese)[李俊, 陈林根, 戈延林, 孙丰瑞2013 62 130501]
[4] Andresen B 2011 Angew. Chem. Int. Ed. 50 2690
[5] Hernandez A C, Medina A, Roco J M M, White J A, Velasco S 2001 Phys. Rev. E 63 037102
[6] de Tomas C, Roco J M M, Hernandez A C, Wang Y, Tu Z C 2013 Phys. Rev. E 87 012105
[7] Long R, Liu Z C, Liu W 2014 Phys. Rev. E 89 062119
[8] Long R, Liu W 2015 Phys. Rev. E 91 042127
[9] Zhang Y C, Huang C K, Lin G X, Chen J C 2016 Phys. Rev. E 93 032152
[10] Esposito M, Kawai R, Lindenberg K, van den Broeck C 2010 Phys. Rev. Lett. 105 150603
[11] Izumida Y, Okuda K 2012 Europhys. Lett. 97 10004
[12] Izumida Y, Okuda K, Hernandez A C, Roco J M M 2013 Europhys. Lett. 101 10005
[13] Izumida Y, Okuda K, Roco J M M, Hernandez A C 2015 Phys. Rev. E 91 052140
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