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基于构形理论, 以(火积)耗散率最小为优化目标, 对冷却流道的“盘点”传热问题进行构形优化, 得到冷却流道的圆盘构造体最优构形. 结果表明: 对于扇形单元体, 在其泵功率给定的条件下, 存在最佳展弦比使得扇形单元体无量纲当量热阻取得最小值; 对于一级树状圆盘, 在其总泵功率给定的条件下, 存在一级与单元级最佳流道宽度比和扇形单元体最佳无量纲半径使 得一级树状圆盘无量纲当量热阻取得最小值, 且一级与单元级最佳流道宽度比仅与单元体分支数有关. 当中心圆盘半径等于0时, 一级树状圆盘最终退化成辐射状圆盘, 此时一级树状圆盘半径为临界半径. 当一级树状圆盘半径大于临界半径时, 需对圆盘冷却流道采用树状布置, 反之则采用辐射状布置. 存在最佳单元体分支数使得无量纲当量热阻取得最小值, 这与高导热材料通道的“盘点”导热构形优化结果有明显区别. (火积)耗散率最小和最大温差最小的一级树状冷却流 道圆盘构造体最优构形是不同的. 与最大温差最小的冷却流道圆盘构造体相比, (火积)耗散率最小的冷却流道圆盘构造体当量热阻得到极大降低, 其整体传热性能得到明显提高. 因此, (火积)耗散极值原理与对流构形优化相结合, 有助于进一步揭示(火积)耗散极值原理在传热优化方面的优越性.Based on configucation theory, the construction of a “disc-point” heat transfer with cooling channels can be optimized by taking minimum entransy dissipation rate. Thus an optimal construction of the disc-shaped assembly with cooling channels is obtained. The results show that there exists an optimal aspect ratio of the elemental sector which leads to the minimum dimensionless equivalent thermal resistance of the elemental sector at the fixed pumping power; there also exists an optimal width ratio of the elemental and first-order cooling channel to the optimal dimensionless radius of the elemental sector, which leads to the minimum dimensionless equivalent thermal resistance of the first-order branched-pattern disc at the fixed total pumping power. Moreover, the optimal width ratio of the elemental and first-order cooling channels is only relative to the number of elemental tributaries. When the radius of the central disc tends to zero, the branch-pattern disc is simplified into a radial-pattern disc, and the radius of the first-order branch-pattern disc becomes the critical radius at this point. When the radius of the branch-pattern disc is higher than the critical radius, the branch-pattern design should be adopted, otherwise the radial-pattern design should be adopted. There exists an optimal number of elemental tributaries which lead to the minimum dimensionless equivalent thermal resistance of the first-order branch-pattern disc, which is obviously different from the results of the “disc-point” heat conduction constructional optimization with high-conductivity channels. The optimal constructions of the first-order branch-pattern disc based on the minimizations of entransy dissipation rate and maximum temperature difference are different. The dimensionless equivalent thermal resistance of the disc with cooling channels based on the minimization of entransy dissipation rate is greatly reduced as compared with that based on the minimization of maximum temperature difference, and its global heat transfer performance is obviously improved simultaneously. Therefore, the combination of the entransy dissipation extremum principle and the heat convection constructional optimization further illustrates the advantages of minimization of entransy dissipation rate for heat transfer optimizations.
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Keywords:
- constructal theory /
- entransy dissipation rate /
- cooling channels /
- generalized thermodynamic optimization
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[26] Xu M T, Guo J F, Cheng L 2009 Front. Energy Power Engng. China 3 402
[27] Xu M 2011 Energy 36 4272
[28] Xia S J, Chen L G, Sun F R 2011 Sci. China: Tech. Sci. 54 352
[29] Liu W, Liu Z C, Jia H, Fan A W, Nakayama A 2011 Int. J. Heat Transfer 54 3049
[30] Hu G J, Cao B Y, Guo Z Y 2011 Chin. Sci. Bull. 56 2974
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[33] 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]
[34] Chen Q, Xu Y C 2012 Energy 37 571
[35] Guo J F, Huai X L 2012 Energy 41 335
[36] Chen L G, Xiao Q H, Xie Z H, Sun F R 2012 Int. Comm. Heat Mass Transfer 39 1556
[37] Feng H J, Chen L G, Xie Z H, Sun F R 2013 Sci. China Tech. Sci. 56 299
[38] Wu J, Cheng X T 2013 Int. J. Heat Mass Transfer 58 374
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[1] Bejan A 1997 Int. J. Heat Mass Transfer 40 799
[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] Chen L G 2012 Sci. China: Tech. Sci. 55 802
[5] Ledezma G, Bejan A, Errera M 1997 J. Appl. Phys. 82 89
[6] Rocha L A O, Lorente S, Bejan A 2002 Int. J. Heat Mass Transfer 45 1643
[7] Ghodoossi L, Egrican N J 2003 Appl. Phys. 93 4922
[8] Wu W, Chen L, Sun F 2007 Energy Convers. Mgmt. 48 101
[9] Wei S H, Chen L G, Sun F R 2009 Sci. China Ser. E: Tech. Sci. 52 2981
[10] Xiao Q H, Chen L G, Sun F R 2011 Chin. Sci. Bull. 56 102
[11] Chen L G, Wei S H, Sun F R 2011 Int. J. Heat Mass Transfer 54 210
[12] Feng H J, Chen L G, Sun F R 2012 Sci. China: Tech. Sci. 55 779
[13] Bejan A, Errera M R 2000 Int. J. Heat Mass Transfer 43 3105
[14] Xiao Q H, Chen L G, Sun F R 2010 Sci. China: Tech. Sci. 53 2458
[15] Wechsatol W, Lorente S, Bejan A 2003 Int. J. Heat Mass Transfer 46 4381
[16] Wechsatol W, Lorente S, Bejan A 2004 Int. J. Exergy 1 2
[17] Daguenet-Frick X, Bonjour J, Revellin R 2010 IEEE Trans. Components & Packag. Tech. 33 115
[18] Guo Z Y, Zhu H Y, Liang X G 2007 Int. J. Heat Mass Transfer 50 2545
[19] 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]
[20] Guo Z Y, Cheng X G, Xia Z Z 2003 Chin. Sci. Bull. 48 406
[21] 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]
[22] 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]
[23] Zhu 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]
[24] Chen L G 2012 Chin. Sci. Bull. 57 4404
[25] Liu X B, Guo Z Y 2009 Acta Phys. Sin. 58 4766 (in Chinese) [柳雄斌, 过增元 2009 58 4766]
[26] Xu M T, Guo J F, Cheng L 2009 Front. Energy Power Engng. China 3 402
[27] Xu M 2011 Energy 36 4272
[28] Xia S J, Chen L G, Sun F R 2011 Sci. China: Tech. Sci. 54 352
[29] Liu W, Liu Z C, Jia H, Fan A W, Nakayama A 2011 Int. J. Heat Transfer 54 3049
[30] Hu G J, Cao B Y, Guo Z Y 2011 Chin. Sci. Bull. 56 2974
[31] 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]
[32] 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]
[33] 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]
[34] Chen Q, Xu Y C 2012 Energy 37 571
[35] Guo J F, Huai X L 2012 Energy 41 335
[36] Chen L G, Xiao Q H, Xie Z H, Sun F R 2012 Int. Comm. Heat Mass Transfer 39 1556
[37] Feng H J, Chen L G, Xie Z H, Sun F R 2013 Sci. China Tech. Sci. 56 299
[38] Wu J, Cheng X T 2013 Int. J. Heat Mass Transfer 58 374
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