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基于构形理论, 以(火积)耗散率最小为优化目标, 在微、纳米尺度下对圆盘导热问题进行构形优化, 得到尺寸效应影响下的无量纲当量热阻最小的圆盘构造体最优构形. 结果表明: 在微、纳米尺度下, 尺寸效应影响下的圆盘构造体最优构形与无尺寸效应影响时的圆盘构造体最优构形有明显区别. 存在最佳无量纲高导热材料通道长度使无量纲当量热阻取得最小值; 随着扇形单元体数目的增大, 最小无量纲当量热阻先减小后增大, 存在最佳的扇形单元体数目使得无量纲当量热阻取得双重最小值, 这与常规尺度下圆盘构造体相应的性能特性明显不同. (火积)耗散率最小的圆盘构造体(火积)耗散率比最大温差最小的构造体(火积)耗散率降低了7.31%, 也即圆盘构造体的平均传热温差降低了7.31%. 微、纳米尺度下基于(火积)耗散率最小的圆盘构造体最优构形能够降低圆盘构造体的平均传热温差, 同时有助于提高其整体传热性能. 本文工作有助于进一步拓展(火积)耗散极值原理的应用范围.Based on constructal theory, the constructal optimization of a disc on micro and nanoscales is carried out by taking minimum entransy dissipation rate as optimization objective; and the optimal construction of the disc with minimum dimensionless equivalent thermal resistance is obtained. The result shows that the optimal construction of the disc when the size effectis taken into account is obviously different from that without considering the size effect. There exists an optimal dimensionless channel length of the high conductivity material which leads to the minimum dimensionless equivalent thermal resistance. With the increase in the number of the elemental sectors, the minimum dimensionless equivalent thermal resistance decreases first and then increases, and there exists an optimal number of the elemental sectors which leads to the double minimum dimensionless equivalent thermal resistance, which is different from the performance characteristic of the disc on a conventional scale. The entransy dissipation rate of the disc, based on the minimization of entransy dissipation rate, is reduced by 7.31% as compared with that based on maximum temperature difference, that is, the average heat transfer temperature difference of the disc is reduced by 7.31%. The optimal construction on micro and nanoscales, obtained based on minimum entransy dissipation rate, can reduce the average heat transfer temperature difference of a disc, and improves its global heat transfer performance simultaneously. The work in this paper can help to further extend the application range of the entransy dissipation extremum principle.
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Keywords:
- constructal theory /
- entransy dissipation rate minimization /
- micro and nanoscales /
- generalized thermodynamic optimization
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[2] Bejan A, Lorente S 2008 Design with Constructal Theory (New Jersey: Wiley) pp1-516
[3] Chen L G 2012 Sci. China: Tech. Sci. 55 802
[4] Bejan A 1997 Int. J. Heat Mass Transfer 40 799
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[6] Wu W J, Chen L G, Sun F R 2006 Sci. China Ser. E Tech. Sci. 49 332
[7] Wei S H, Chen L G, Sun F R 2009 Sci. China Ser. E Tech. Sci. 52 2981
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[27] Chen L G 2012 Chin. Sci. Bull. 57 4404
[28] Chen L G 2013 J. Naval University Engng 25 1 (in Chinese) [陈林根 2013 海军工程大学学报 25 1]
[29] Liu X B, Guo Z Y 2009 Acta Phys. Sin. 58 4766 (in Chinese) [柳雄斌, 过增元 2009 58 4766]
[30] Xu M 2011 Energy 36 4272
[31] Guo J F, Xu M T, Cheng L 2011 Sci. China Tech. Sci. 54 1267
[32] Cheng X T, Xu X H, Liang X G 2011 Acta Phys. Sin. 60 118103 (in Chinese) [程雪涛, 徐向华, 梁新刚 2011 60 118103]
[33] Cheng X T, Dong Y, Liang X G 2011 Acta Phys. Sin. 60 114402 (in Chinese) [程雪涛, 董源, 梁新刚 2011 60 114402]
[34] 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 60 060512]
[35] Hu G J, Cao B Y, Guo Z Y 2011 Chin. Sci. Bull. 56 2974
[36] Xu Y C, Chen Q 2012 Int. J. Heat Mass Transfer 55 5148
[37] Chen Q, Xu Y C, Guo Z Y 2012 Chin. Sci. Bull. 57 4646
[38] Guo J F, Huai X L 2012 Energy 43 355
[39] Feng H J, Chen L G, Sun F R 2012 Sci. China: Tech. Sc. 55 779
[40] Wu J, Cheng X T 2013 Int. J. Heat Mass Transfer 58 374
[41] Cheng X T, Zhang Q Z, Xu X H, Liang X G 2013 Chin. Phys. B 22 020503
[42] Bejan A 1982 Entropy Generation through Heat and Fluid Flow (New York: Wiley) pp1-240
[43] Dong Y, Guo Z Y 2012 Acta Phys. Sin. 61 030507 (in Chinese) [董源, 过增元 2012 61 030507]
[44] Cheng X T, Liang X G 2013 Chin. Phys. B 22 010508
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[1] Bejan A 2000 Shape and Structure, from Engineering to Nature (Cambridge: Cambridge University Press) pp1-314
[2] Bejan A, Lorente S 2008 Design with Constructal Theory (New Jersey: Wiley) pp1-516
[3] Chen L G 2012 Sci. China: Tech. Sci. 55 802
[4] Bejan A 1997 Int. J. Heat Mass Transfer 40 799
[5] Ghodoossi L, Egrican N 2003 J. Appl. Phys. 93 4922
[6] Wu W J, Chen L G, Sun F R 2006 Sci. China Ser. E Tech. Sci. 49 332
[7] Wei S H, Chen L G, Sun F R 2009 Sci. China Ser. E Tech. Sci. 52 2981
[8] Xiao Q H, Chen L G, Sun F R 2011 Chin. Sci. Bull. 56 2400
[9] Rocha L A O, Lorente S, Bejan A 2002 Int. J. Heat Mass Transfer 45 1643
[10] Rocha L A O, Lorente S, Bejan A 2006 Int. J. Heat Mass Transfer 49 2626
[11] Xiao Q H, Chen L G, Sun F R 2011 Chin. Sci. Bull. 56 102
[12] Xiao Q H, Chen L G, Sun F R 2011 Int. J. Therm. Sci. 50 1031
[13] da Silva A K, Vasile C, Bejan A 2004 Int. J. Heat Mass Transfer 47 4257
[14] Chen L G, Wei S H, Sun F R 2011 Int. J. Heat Mass Transfer 54 210
[15] Duncan A B, Peterson G P 1994 Appl. Mech. Rev. 47 397
[16] Guo Z Y 2000 Advances In Mechanics 30 1 (in Chinese) [过增元 2000 力学进展 30 1]
[17] Guo Z Y, Li Z X 2003 Int. J. Heat Mass Transfer 46 149
[18] Guo Z Y, Li Z X 2003 Int. J. Heat Fluid Flow 24 284
[19] Liu T, Ji J, Guo Z Y, Li Z X 2004 Chin. Sci. fund 6 349 (in Chinese) [刘涛, 纪军, 过增元, 李志信 2004 中国科学基金 6 349]
[20] Gosselin L, Bejan A 2004 J. Appl. Phys. 96 5852
[21] Guo Z Y, Zhu H Y, Liang X G 2007 Int. J. Heat Mass Transfer 50 2545
[22] 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]
[23] Guo Z Y, Cheng X G, Xia Z Z 2003 Chin. Sci. Bull. 48 406
[24] Han G Z, Zhu H Y, Cheng X X, Guo Z Y 2005 J. Engng. Thermophys 26 1022 (in Chinese) [韩光泽, 朱宏晔, 程新广, 过增元 2005 工程热 26 1022]
[25] Han G, Guo Z Y 2007 Proc. CSEE 27 98 (in Chinese) [韩光泽, 过增元 2007 中国电机工程学报 27 98]
[26] hu H Y, Chen Z J, Guo Z Y 2007 Pro. Natural Sci. 17 1692 (in Chinese) [朱宏晔, 陈泽敬, 过增元 2007 自然科学进展 17 1692]
[27] Chen L G 2012 Chin. Sci. Bull. 57 4404
[28] Chen L G 2013 J. Naval University Engng 25 1 (in Chinese) [陈林根 2013 海军工程大学学报 25 1]
[29] Liu X B, Guo Z Y 2009 Acta Phys. Sin. 58 4766 (in Chinese) [柳雄斌, 过增元 2009 58 4766]
[30] Xu M 2011 Energy 36 4272
[31] Guo J F, Xu M T, Cheng L 2011 Sci. China Tech. Sci. 54 1267
[32] Cheng X T, Xu X H, Liang X G 2011 Acta Phys. Sin. 60 118103 (in Chinese) [程雪涛, 徐向华, 梁新刚 2011 60 118103]
[33] Cheng X T, Dong Y, Liang X G 2011 Acta Phys. Sin. 60 114402 (in Chinese) [程雪涛, 董源, 梁新刚 2011 60 114402]
[34] 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 60 060512]
[35] Hu G J, Cao B Y, Guo Z Y 2011 Chin. Sci. Bull. 56 2974
[36] Xu Y C, Chen Q 2012 Int. J. Heat Mass Transfer 55 5148
[37] Chen Q, Xu Y C, Guo Z Y 2012 Chin. Sci. Bull. 57 4646
[38] Guo J F, Huai X L 2012 Energy 43 355
[39] Feng H J, Chen L G, Sun F R 2012 Sci. China: Tech. Sc. 55 779
[40] Wu J, Cheng X T 2013 Int. J. Heat Mass Transfer 58 374
[41] Cheng X T, Zhang Q Z, Xu X H, Liang X G 2013 Chin. Phys. B 22 020503
[42] Bejan A 1982 Entropy Generation through Heat and Fluid Flow (New York: Wiley) pp1-240
[43] Dong Y, Guo Z Y 2012 Acta Phys. Sin. 61 030507 (in Chinese) [董源, 过增元 2012 61 030507]
[44] Cheng X T, Liang X G 2013 Chin. Phys. B 22 010508
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