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基于构形理论, 以基于(火积)耗散率定义的当量热阻最小为优化目标对复杂肋片进行构形优化, 得到同时考虑肋片导热和对流换热(火积)耗散性能的肋片最优构形, 并比较不同形状和不同优化目标下的肋片最优构形. 结果表明: 存在最佳单元级直肋、中部空腔以及肋片末梢高度和长度比使得复杂肋片当量热阻取得三重最小值. 当量热阻最小的复杂肋片最优构形与T-Y形肋片最优构形相比, 复杂肋片结构使得肋片整体传热性能大大提高. 当肋片传热为二维传热且根部较宽时, 肋片根部温度越不均匀, 当量热阻最小和最大热阻最小的复杂肋片最优构形差别越大. 在保证热安全性的前提下, 工程上对肋片进行优化设计时可选择当量热阻最小的肋片构形设计方案以降低其平均传热温差、提高整体传热性能. 本文从传热优化角度为复杂肋片的优化设计提供了参考.Based on the constructal theory, the constructal optimization of a complex fin is carried out by taking the minimum equivalent thermal resistance, which is defined according to entransy dissipation rate, as the optimization objective. Optimal constructal of the complex fin is obtained by tsking into consideration the entransy dissipation performance caused by heat conduction and heat convection. Comparisons between the optimal constructal with different shapes and optimization objectives of the fins are performed. Results show that there exist the optimal ratios of the height to the length of the elemental fin, central cavity and fin tip which lead to the triple minimum equivalent thermal resistance of the complex fin. By comparing the optimal constructal of the complex fin with that of the T-Y shaped fin, the structure of the complex fin will greatly improve its global heat transfer performance. When the heat transfer of the fin is two-dimensional and the root of the fin is broader, the more non-uniform the temperature at the fin root, the bigger difference of the optimal constructs the complex fin obtains, based on the minimizations of the equivalent thermal resistance and maximum thermal resistance. For the optimal design of the fin in pracuice, when the thermal safety of the fin is ensured, the constructal design scheme of the fin with minimum equivalent thermal resistance can be adopted to reduce temperature difference in the average heat transfer and improves the global heat transfer performance. This paper provides some guidelines for the optimal design of the complex fin from the point of view of heat transfer optimization.
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Keywords:
- constructal theory /
- entransy dissipation rate minimization /
- complex fin /
- generalized thermodynamic optimization
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[2] Bejan A 2000 Shape and Structure, from Engineering to Nature (Cambridge: Cambridge University Press) pp1–314
[3] Bejan A, Lorente S 2008 Design with Constructal Theory (New Jersey: Wiley) pp1–516
[4] Lorenzini G, Moretti S 2011 Fin Shape Thermal Optimization Using Bejan's Constructal Theory (USA: Morgan & Claypool Publishers) pp1–219
[5] Chen L G 2012 Sci. China: Tech. Sci. 55 802
[6] Bejan A 2013 Convection Heat Transfer (4th edition) (New Jersey: Wiley) pp1–605
[7] Bejan A, Lorente S 2013 J. Appl. Phys. 113 151301
[8] Bejan A 2014 Sci. Rep. 4 4017
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[17] Guo Z Y, Cheng X G, Xia Z Z 2003 Chin. Sci. Bull. 48 406
[18] Chen L G 2012 Chin. Sci. Bull. 57 4404
[19] Chen Q, Liang X G, Guo Z Y 2013 Int. J. Heat Mass Transfer 63 65
[20] Cheng X T, Liang X G, Xu X H 2011 Acta Phys. Sin. 60 060512 (in Chinese) [程雪涛, 梁新刚, 徐向华 2011 物理学报 60 060512]
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[26] Feng H J, Chen L G, Xie Z H, Sun F R 2014 Int. Comm. Heat Mass Transfer 52 26
[27] Tao Y B, He Y L, Liu Y K, Tao W Q 2014 Int. J. Heat Mass Transfer 77 695
[28] Wu J, Guo Z Y 2014 Entropy 16 1089
[29] Jia H, Liu Z C, Liu W, Nakayama A 2014 Int. J. Heat Mass Transfer 73 124
[30] Chen Q, Xu Y C, Hao J H 2014 Appl. Energy 113 982
[31] Chen L G, Xiao Q H, Xie Z H, Sun F R 2012 Int. Comm. Heat Mass Transfer 39 1556
[32] Xie Z H, Chen L G, Sun F R 2011 Sci. China: Tech. Sci. 54 1249
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[35] Feng H J, Chen L G, Xie Z H, Sun F R J. Engng. Thermophys. in press
[36] Xiao Q H, Chen L G, Sun F R 2011 Sci. China: Tech. Sci. 54 211
[37] Feng H J, Chen L G, Sun F R 2012 Sci. China: Tech. Sci. 55 515
[38] Zheng J L, Luo X B 2011 Proceedings of Chinese Society of Engineering Thermophysics on heat and mass transfer Xi'an, October 14-17, Paper No. 113019 (in Chinese) [郑建林, 罗小兵2011 中国工程热物理学会传热传质学学术会议论文集 西安, 10月14–17日, 论文编号: 113019]
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[40] Cheng X T, Zhang Q Z, Xu X H, Liang X G 2013 Chin. Phys. B 22 020503
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[1] Bejan A 1996 J. Adv. Transp. 30 85
[2] Bejan A 2000 Shape and Structure, from Engineering to Nature (Cambridge: Cambridge University Press) pp1–314
[3] Bejan A, Lorente S 2008 Design with Constructal Theory (New Jersey: Wiley) pp1–516
[4] Lorenzini G, Moretti S 2011 Fin Shape Thermal Optimization Using Bejan's Constructal Theory (USA: Morgan & Claypool Publishers) pp1–219
[5] Chen L G 2012 Sci. China: Tech. Sci. 55 802
[6] Bejan A 2013 Convection Heat Transfer (4th edition) (New Jersey: Wiley) pp1–605
[7] Bejan A, Lorente S 2013 J. Appl. Phys. 113 151301
[8] Bejan A 2014 Sci. Rep. 4 4017
[9] Bejan A, Almogbel M 2000 Int. J. Heat Mass Transfer 43 2101
[10] Lorenzini G, Rocha L A O 2006 Int. J. Heat Mass Transfer 49 4552
[11] Lorenzini G, Rocha L A O 2009 Int. J. Heat Mass Transfer 52 1458
[12] Lorenzini G, Correa R L 2011 Trans. ASME, J. Heat Transfer 133 081902
[13] Xie Z H, Chen L G, Sun F R 2010 Sci. China: Tech. Sci. 53 2756
[14] Lorenzini G, Moretti S 2014 Thermal Sci. 18 339
[15] Guo Z Y, Zhu H Y, Liang X G 2007 Int. J. Heat Mass Transfer 50 2545
[16] Li Z X, Guo Z Y 2010 Field Synergy Principle of Heat Convection Optimization (Beijing: Science Press) pp78-97 (in Chinese) [李志信, 过增元2010 对流传热优化的场协同理论(北京: 科学出版社)第78–97页]
[17] Guo Z Y, Cheng X G, Xia Z Z 2003 Chin. Sci. Bull. 48 406
[18] Chen L G 2012 Chin. Sci. Bull. 57 4404
[19] Chen Q, Liang X G, Guo Z Y 2013 Int. J. Heat Mass Transfer 63 65
[20] Cheng X T, Liang X G, Xu X H 2011 Acta Phys. Sin. 60 060512 (in Chinese) [程雪涛, 梁新刚, 徐向华 2011 物理学报 60 060512]
[21] Chen L G, Feng H J, Xie Z H, Sun F R 2013 Acta Phys. Sin. 62 134401 (in Chinese) [陈林根, 冯辉君, 谢志辉, 孙丰瑞 2013 物理学报 62 134401]
[22] Zhao T, Chan Q 2013 Acta Phys. Sin. 62 234401 (in Chinese) [赵甜, 陈群 2013 物理学报 62 234401]
[23] Wang W H, Cheng X T, Liang X G 2013 Chin. Phys. B 22 110506
[24] Sun C, Cheng X T, Liang X G 2014 Chin. Phys. B 23 050513
[25] Cheng X T, Liang X G 2014 Int. J. Heat Mass Transfer 76 263
[26] Feng H J, Chen L G, Xie Z H, Sun F R 2014 Int. Comm. Heat Mass Transfer 52 26
[27] Tao Y B, He Y L, Liu Y K, Tao W Q 2014 Int. J. Heat Mass Transfer 77 695
[28] Wu J, Guo Z Y 2014 Entropy 16 1089
[29] Jia H, Liu Z C, Liu W, Nakayama A 2014 Int. J. Heat Mass Transfer 73 124
[30] Chen Q, Xu Y C, Hao J H 2014 Appl. Energy 113 982
[31] Chen L G, Xiao Q H, Xie Z H, Sun F R 2012 Int. Comm. Heat Mass Transfer 39 1556
[32] Xie Z H, Chen L G, Sun F R 2011 Sci. China: Tech. Sci. 54 1249
[33] Chen L G, Xiao Q H, Xie Z H, Sun F R 2013 Int. J. Heat Mass Transfer 67 506
[34] Xiao Q H, Chen L G, Xie Z H, Sun F R 2012 J. Engng. Thermophys. 33 1465 (in Chinese) [肖庆华, 陈林根, 谢志辉, 孙丰瑞 2012 工程热物理学报 33 1465]
[35] Feng H J, Chen L G, Xie Z H, Sun F R J. Engng. Thermophys. in press
[36] Xiao Q H, Chen L G, Sun F R 2011 Sci. China: Tech. Sci. 54 211
[37] Feng H J, Chen L G, Sun F R 2012 Sci. China: Tech. Sci. 55 515
[38] Zheng J L, Luo X B 2011 Proceedings of Chinese Society of Engineering Thermophysics on heat and mass transfer Xi'an, October 14-17, Paper No. 113019 (in Chinese) [郑建林, 罗小兵2011 中国工程热物理学会传热传质学学术会议论文集 西安, 10月14–17日, 论文编号: 113019]
[39] Jia L, Mao Z M, Luo X B 2011 Proceedings of Chinese Society of Engineering Thermophysics on heat and mass transfer Xi'an, October 14-17, Paper No. 113537 (in Chinese) [贾琳, 毛章明, 罗小兵2011中国工程热物理学会传热传质学学术会议论文集 西安, 10月14–17日, 论文编号: 113537]
[40] Cheng X T, Zhang Q Z, Xu X H, Liang X G 2013 Chin. Phys. B 22 020503
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