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热机性能的优化是热力学领域的一个重要问题，而工质与热源之间的传热过程是热机工作时产生不可逆的主要来源.本文在引入功率增益和效率增益两个重要参数的基础上，基于一个简化的Curzon-Ahlborn热机模型并利用合比分比原理，给出了线性与非线性传热过程的热机在任意功率输出时的效率表达式，结合数值计算详细讨论了热机在任意功率输出时的特性.研究表明，参数作为功率增益P的函数存在两个分支：在第一分支上（不利情形），效率呈现出单调变化特征；在第二分支上（有利情形），效率随着的P变化是非单调的且有最大值.随着传热指数的增加，热机的工作区域减小，这源于非线性传热过程包含热辐射所致.进一步发现功率-效率关系曲线存在权衡工作点，热机在该点附近工作能够实现最有效的热功转换.研究结果有助于深入理解具有不同传热过程热机的优化执行.The optimal performance of heat engine is an important issue in thermodynamics, but the heat transfer between the working medium and two heat reservoirs induces the irreversibility during the operation of heat engine. Based on two important parameters introduced in this paper(namely, the power gain and the efficiency gain), for heat engine operating in the linear and nonlinear heat transfer processes, the formula for the efficiency at arbitrary power is achieved in terms of a simplified Curzon-Ahlborn heat engine model and the componendo and dividendo rule. The features of heat engine at arbitrary power output are also discussed in detail based on the numerical calculations. It is indicated that the parameter as a function of the power gain P contains two branches:the efficiency shows the monotonous variation on the first branch (the favorable case); the efficiency exhibits the non-monotonous characteristics and has the maximum value on the second branch(the unfavorable case). The working region of the heat engine is reduced as the heat transfer exponent increases, which results from the radiative contribution in the nonlinear heat transfer process. For the first branch, the contour-line plot of versus TL/TH and P clearly demonstrates that has the decreasing trend with increasing TL/TH and|P|; for the second branch, monotonically deceases as TL/TH increases, but shows the non-monotonic behaviors as|P|increases. The efficiency has the maximum value in the region where TL/TH and|P|have the small values, and the working regime of heat engines in the nonlinear heat transfer process is relatively small due to the complexity of the nonlinear heat transfer process. The curves of the efficiency in two heat transfer processes are loop-shaped, when|P| 0 and|P| 1, the curves of ~P in two heat transfer processes are same. But in other regimes, the efficiency of the heat engine with the linear heat transfer process is bigger than in the nonlinear heat transfer process. Furthermore, it is found that a considerably larger efficiency can be obtained when heat engine working close to the maximum power. This implies that there exists the trade-off working point where the heat engine can perform the most effective heat-work conversion. In addition, the curves of the power gain vs. the efficiency gain also display the loop-shaped characteristics, but there is the weak difference on the second branch. Our results are very conducive to understanding the optimal performance of heat engines in different heat transfer processes.
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Keywords:
- power gain /
- efficiency gain /
- arbitrary power /
- efficiency
[1] Curzon F, Ahlborn B 1975 Am. J. Phys. 43 22
[2] Vaudrey A, Lanzetta F, Feidt M 2014 J. Non-Equil. Therm. 39 199
[3] Andresen B 2011 Angew. Chem. Int. Ed. 50 2690
[4] Chen L G, Sun F R 1998 Acta Phys. Sin. 18 395 (in Chinese)[陈林根, 孙丰瑞 1998 18 395]
[5] van den Broeck C 2005 Phys. Rev. Lett. 95 190602
[6] Angulo-Brown F, Phez-Hernhndez F 1993 J. Appl. Phys. 74 2216
[7] Huleihil M, Andresen B 2006 J. Appl. Phys. 100 014911
[8] Chen L, Sun F, Wu C 1999 J. Phys. D:Appl. Phys. 32 99
[9] Zhou S, Chen L, Sun F, Wu C 2005 Appl. Energy 81 376
[10] Chen L, Li J, Sun F 2008 Appl. Energy 85 52
[11] Chen L, Sun F, Wu C 2006 Appl. Energy 83 71
[12] Cheng X T, Wang W H, Liang X G 2012 Chin. Sci. Bull. 55 2847
[13] Arias-Hernandez L A, Ares de Prarga G, Angulo-Brown F 2003 Open Sys. Informat. Dyn. 10 351
[14] Li J, Chen L, Sun F 2007 Appl. Energy 84 944
[15] Shu L W, Chen L, Sun F 2009 Sci. China Ser. B:Chem. 52 1154
[16] Chimal-Eguia J C, Barranco-Jimenez M A 2006 Open Sys. Informat. Dyn. 13 43
[17] Whitney R S 2014 Phys. Rev. Lett. 112 130601
[18] Whitney R S 2015 Phys. Rev. B 91 115425
[19] Holubec V, Ryabov A 2016 J. Stat. Mech. 2016 073204
[20] Long R, Liu W 2016 Phys. Rev. E 90 052114
[21] Ryabov A, Holubec V 2016 Phys. Rev. E 93 050101
[22] Agrawal D C 2009 Eur. J. Phys. 30 1173
[23] Paez-Hernandz R T, Portillo-Diaz P, Ladino-Luna D 2016 J. Non-Equil. Therm. 41 19
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[1] Curzon F, Ahlborn B 1975 Am. J. Phys. 43 22
[2] Vaudrey A, Lanzetta F, Feidt M 2014 J. Non-Equil. Therm. 39 199
[3] Andresen B 2011 Angew. Chem. Int. Ed. 50 2690
[4] Chen L G, Sun F R 1998 Acta Phys. Sin. 18 395 (in Chinese)[陈林根, 孙丰瑞 1998 18 395]
[5] van den Broeck C 2005 Phys. Rev. Lett. 95 190602
[6] Angulo-Brown F, Phez-Hernhndez F 1993 J. Appl. Phys. 74 2216
[7] Huleihil M, Andresen B 2006 J. Appl. Phys. 100 014911
[8] Chen L, Sun F, Wu C 1999 J. Phys. D:Appl. Phys. 32 99
[9] Zhou S, Chen L, Sun F, Wu C 2005 Appl. Energy 81 376
[10] Chen L, Li J, Sun F 2008 Appl. Energy 85 52
[11] Chen L, Sun F, Wu C 2006 Appl. Energy 83 71
[12] Cheng X T, Wang W H, Liang X G 2012 Chin. Sci. Bull. 55 2847
[13] Arias-Hernandez L A, Ares de Prarga G, Angulo-Brown F 2003 Open Sys. Informat. Dyn. 10 351
[14] Li J, Chen L, Sun F 2007 Appl. Energy 84 944
[15] Shu L W, Chen L, Sun F 2009 Sci. China Ser. B:Chem. 52 1154
[16] Chimal-Eguia J C, Barranco-Jimenez M A 2006 Open Sys. Informat. Dyn. 13 43
[17] Whitney R S 2014 Phys. Rev. Lett. 112 130601
[18] Whitney R S 2015 Phys. Rev. B 91 115425
[19] Holubec V, Ryabov A 2016 J. Stat. Mech. 2016 073204
[20] Long R, Liu W 2016 Phys. Rev. E 90 052114
[21] Ryabov A, Holubec V 2016 Phys. Rev. E 93 050101
[22] Agrawal D C 2009 Eur. J. Phys. 30 1173
[23] Paez-Hernandz R T, Portillo-Diaz P, Ladino-Luna D 2016 J. Non-Equil. Therm. 41 19
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