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矩形肋片热沉(火积)耗散率最小与最大热阻最小构形优化的比较研究

杨爱波 陈林根 谢志辉 孙丰瑞

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矩形肋片热沉(火积)耗散率最小与最大热阻最小构形优化的比较研究

杨爱波, 陈林根, 谢志辉, 孙丰瑞

Comparative study on constructal optimizations of rectangular fins heat sink based on entransy dissipation rate minimization and maximum thermal resistance minimization

Yang Ai-Bo, Chen Lin-Gen, Xie Zhi-Hui, Sun Feng-Rui
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  • 针对矩形肋片热沉, 分别以最大热阻最小化和基于(火积)耗散定义的当量热阻最小化为优化目标, 采用二维传热模型并结合有限元数值仿真对其进行构形优化, 比较了两种目标下的热沉最优构形, 并分析了全局参数(综合了对流换热系数、肋片占据的总面积及其热导率的函数)和材料占比对两种目标(最大热阻、当量热阻)及其对应最优构形的影响. 结果表明: 热沉外形固定时, 两种目标下均不存在最优的肋片厚度; 热沉外形自由变化时, 两种目标下的最优构形存在一定的差异. 此外, 全局参数对两种目标下的最优构形均没有影响, 而材料占比对两种目标下的最优构形均有较大影响. 提高全局参数和材料占比均可以减小最大热阻最小值和当量热阻最小值, 但对两种目标的减小程度不同. 总体上, 调节热沉结构参数使当量热阻最小, 可以同时获得很好的局部极限性能; 而调节热沉结构参数使最大热阻最小, 获得的整体平均散热性能却较差. 因此, 对本文热沉模型进行优化时, 以当量热阻最小化为优化目标更合理.
    Constructal optimization of a rectangular fin heat sink with two-dimensional heat transfer model is carried out through using numerical simulation by finite element method, in which the minimized maximum thermal resistance and the minimized equivalent thermal resistance based on entransy dissipation are taken as the optimization objectives, respectively. The optimal constructs based on the two objectives are compared. The influences of a global parameter (a) which integrates convective heat transfer coefficient, overall area occupied by fin and its thermal conductivity, and the volume fraction (φ), on the minimized maximum thermal resistance, the minimized equivalent thermal resistances and their corresponding optimal constructs are analyzed. The results show that there does not exist optimal thickness of fins for the two objectives when the shape of the heat sink is fixed, and the optimal constructs based on the two objectives are different when the shape of the heat sinks can be changed freely. Besides, the global parameter has no influence on the optimal constructs based on the two objectives, but the volume fraction does. The increases of the global parameter and the volume fraction reduce the minimum values of the maximum thermal resistance and the equivalent thermal resistance, but the degrees are different. The reduce degree of the global parameter to the minimized equivalent thermal resistance is larger than that to the minimized maximum thermal resistance. The minimized equivalent thermal resistance and the minimized maximum thermal resistance are reduced by 40.03% and 41.42% for a= 0.5, respectively, compared with those for a = 0.3. However, the reduce degree of the volume fraction to the minimized maximum thermal resistance is larger than that to the minimized equivalent thermal resistance. The minimized equivalent thermal resistance and the minimized maximum thermal resistance are reduced by 59.69% and 32.80% for φ= 0.4, respectively, compared with those for φ= 0.3. As a whole, adjusting the parameters of the heat sink to make the equivalent thermal resistance minimum can make the local limit performance good enough at the same time; however, the overall average heat dissipation performance of the heat sink becomes worse when the parameters of the heat sink are adjusted to make the maximum thermal resistance minimum. Thus, it is more reasonable to take the equivalent thermal resistance minimization as the optimization objective when the heat sink is optimized.
    • 基金项目: 国家自然科学基金(批准号: 51206184, 51176203, 51356001, 51579244)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51206184, 51176203, 51356001, 51579244).
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  • [1]

    Harahap F, Mcmanus H N 1967 Trans. ASME J. Heat Transfer 89 32

    [2]

    Ahmed I, Krane R J, Parsons J R1994 Trans. ASME J. Electr. Pack. 116 60

    [3]

    Baskaya S, Sivrioglu M, Ozek M 2000 Int. J. Therm. Sci. 39 797

    [4]

    Narasimhan S, Bar-Cohen A, Nair R 2003 IEEE Trans. Compon. Pack. Tech. 26 136

    [5]

    Suryawanshi S D, Sane N K 2009 Trans. ASME J. Heat Transfer 131 082501

    [6]

    Song W M, Meng J A, Li Z X 2011 Chin. Sci. Bull. 56 263

    [7]

    Taji S G, Parishwad G V, Sane N K 2014 Int. J. Heat Mass Transfer 72 250

    [8]

    Jones C D, Smith L F 1970 Trans. ASME J. Heat Transfer 2 6

    [9]

    Culham J R, Muzychka Y S 2001 IEEE Trans. Compon. Pack. Tech. 24 159

    [10]

    Shih C J, Liu G C 2004 IEEE Trans. Compon. Pack. Tech. 27 551

    [11]

    Zhou J H, Yang C X, Zhang L N 2009 Appl. Therm. Eng. 29 1872

    [12]

    Zhang X H, Liu D W 2010 Energy Convers. Manage. 51 2449

    [13]

    Arularasan R, Dhanushkodi G, Velraj R 2011 Int. J. Comput. Aid. Eng. Tech. 3 526

    [14]

    Li H Y, Chao S M, Chen J W, Yang J T 2103 Int. J. Heat Mass Transfer 57 722

    [15]

    Lindstedt M, Lampio K, Karvinen R 2015 Trans. ASME J. Heat Transfer 137 61006

    [16]

    Bejan A 1996 J. Adv. Transp. 30 85

    [17]

    Bejan A 1997 Trans. ASME J. Heat Transfer 40 799

    [18]

    Bejan A, Lorente S 2010 Phil. Trans. R. Soc. B: Biol. Sci. 365 1335

    [19]

    Bejan A, Lorente S 2008 Design with Constructal Theory (New Jersey: Wiley)

    [20]

    Bejan A, Lorente S 2103 Phys. Life Rev. 8 209

    [21]

    Bejan A, Zane P J 2012 Design in Nature (New York: Doubleeday)

    [22]

    Chen L G 2012 Sci. China: Tech. Sci. 55 802

    [23]

    Miguel A F 2013 Phys. Life Rev. 10 168

    [24]

    Bejan A, Lorente S 2103 J. Appl. Phys. 113 151301

    [25]

    Luo L 2013 Heat and Mass Transfer Intensification and Shape Optimization (New York: Springer)

    [26]

    Rocha L A O, Lorente S, Bejan A 2013 Constructal Law and the Unifying Principle of Design (Berlin: Springer)

    [27]

    Bejan A 2015 Trans. ASME J. Heat Transfer 137 61003

    [28]

    Muzychka Y S 2005 ASME International Conference on Microchannels and Minichannels Toronto, Canada, June 13-15 2005 p1

    [29]

    Moreno R M, Tao Y X 2006 Trans. ASME J. Heat Transfer 128 740

    [30]

    Muzychka Y S 2007 Int. J. Therm. Sci. 46 245

    [31]

    Bello-Ochende T, Liebenberg L, Meyer J P 2007 Sou. Afr. J. Sci. 103 483

    [32]

    Bello-Ochende T, Meyer J P 2009 Int. J. Emerging Multidiscip. Fluid Sci. 1 61

    [33]

    Xie G N, Zhang F L, Sundén B, Zhang W H 2014 Appl. Therm. Eng. 62 791

    [34]

    Guo Z Y, Liang X G, Zhu H Y 2006 Prog. Natural Sci. 16 1288 (in Chinese) [过增元, 梁新刚, 朱宏晔 2006 自然科学进展 16 1288]

    [35]

    Guo Z Y, Zhu H Y, Liang X G 2007 Int. J. Heat Mass Transfer 50 2545

    [36]

    Guo Z Y, Cheng X G, Xia Z Z 2003 Chin. Sci. Bull. 48 406

    [37]

    Xia S J, Chen L G, Sun F R 2009 Chin. Sci. Bull. 54 3587

    [38]

    Wei S H, Chen L G, Sun F R 2009 Sci. China: Tech.Sci. 52 2981

    [39]

    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 物理学报 60 118103]

    [40]

    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 物理学报 60 114402]

    [41]

    Chen L G 2012 Chin. Sci. Bull. 57 4404

    [42]

    Li Q Y, Chen Q 2012 Chin. Sci. Bull. 57 299

    [43]

    Chen Q, Liang X G, Guo Z Y 2013 Int. J. Heat Mass Transfer 63 65

    [44]

    Xu Y C, Chen Q 2013 Energy 60 464

    [45]

    Cheng X T, Liang X G 2013 Energy & Buildings 67 387

    [46]

    Cheng X T, Liang X G 2013 J. Thermal Sci. Tech. 8 337

    [47]

    Cheng X T, Liang X G 2014 Chin. Sci. Bull. 59 5309

    [48]

    Chen L G 2014 Sci. China: Tech. Sci. 57 2305

    [49]

    Wang W H, Cheng X T, Liang X G 2015 Sci. China: Tech. Sci. 58 630

    [50]

    Zhang L, Liu X, Zhao K, Jiang Y 2015 Int. J. Heat Mass Transfer 85 228

    [51]

    Zheng J L, Luo X B 2011 Chinese Society of Engineering Thermophysics Xi'an, China, October, Paper No. 113019 (in Chinese) [郑建林, 罗小兵 2011 中国工程热物理学会论文编号: 113019 西安 10 月]

    [52]

    Jia L, Mao Z M, Luo X B 2011 Chinese Society of Engineering Thermophysics Xi'an, China, October, 2011 Paper No. 113537 (in Chinese) [贾琳, 毛章明, 罗小兵 2011 中国工程热物理学会论文 西安, 中国, 2011年10月 编号: 113537]

    [53]

    Cheng X T, Zhang Q Z, Xu X H, Liang X G 2013 Chin. Phys. B 22 020503

    [54]

    Wu X, Zhang W, Gou Q, Luo Z, Lu Y 2014 Int. J. Heat Mass Transfer 75 414

    [55]

    Xie Z H, Chen L G, Sun F R 2011 Sci. China: Tech. Sci. 54 1249

    [56]

    Xiao Q H, Chen L G, Xie Z H, Sun F R 2012 J. Eng. 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]

    [57]

    Feng H J, Chen L G, Sun F R 2012 Sci. China: Tech. Sci. 55 515

    [58]

    Feng H J, Chen L G, Xie Z H, Sun F R 2015 Acta Phys. Sin. 64 34701 (in Chinese) [冯辉君, 陈林根, 谢志辉, 孙丰瑞 2015 物理学报 64 34701]

    [59]

    Xiao Q H, Chen L G, Sun F R 2011 Sci. China: Tech. Sci. 54 211

    [60]

    Gong S W, Chen L G, Xie Z H, Feng H J, Sun F R 2014 59 3609 Chin. Sci. Bull. (in Chinese) [龚舒文, 陈林根, 谢志辉, 冯辉君, 孙丰瑞 2014 科学通报 59 3609]

    [61]

    Bejan A, Almogbel M 2000 Int. J. Heat Mass Transfer 43 2101

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出版历程
  • 收稿日期:  2015-01-30
  • 修回日期:  2015-05-24
  • 刊出日期:  2015-10-05

矩形肋片热沉(火积)耗散率最小与最大热阻最小构形优化的比较研究

  • 1. 海军工程大学热科学与动力工程研究室, 武汉 430033;
  • 2. 海军工程大学舰船动力工程军队重点实验室, 武汉 430033;
  • 3. 海军工程大学动力工程学院, 武汉 430033
    基金项目: 国家自然科学基金(批准号: 51206184, 51176203, 51356001, 51579244)资助的课题.

摘要: 针对矩形肋片热沉, 分别以最大热阻最小化和基于(火积)耗散定义的当量热阻最小化为优化目标, 采用二维传热模型并结合有限元数值仿真对其进行构形优化, 比较了两种目标下的热沉最优构形, 并分析了全局参数(综合了对流换热系数、肋片占据的总面积及其热导率的函数)和材料占比对两种目标(最大热阻、当量热阻)及其对应最优构形的影响. 结果表明: 热沉外形固定时, 两种目标下均不存在最优的肋片厚度; 热沉外形自由变化时, 两种目标下的最优构形存在一定的差异. 此外, 全局参数对两种目标下的最优构形均没有影响, 而材料占比对两种目标下的最优构形均有较大影响. 提高全局参数和材料占比均可以减小最大热阻最小值和当量热阻最小值, 但对两种目标的减小程度不同. 总体上, 调节热沉结构参数使当量热阻最小, 可以同时获得很好的局部极限性能; 而调节热沉结构参数使最大热阻最小, 获得的整体平均散热性能却较差. 因此, 对本文热沉模型进行优化时, 以当量热阻最小化为优化目标更合理.

English Abstract

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