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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

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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  • 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.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51206184, 51176203, 51356001, 51579244).
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    [2]

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

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

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    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

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

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

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

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

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

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

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

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    Xu Y C, Chen Q 2013 Energy 60 464

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

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

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

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

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

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

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    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]

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    [53]

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

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    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]

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

  • [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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  • Received Date:  30 January 2015
  • Accepted Date:  24 May 2015
  • Published Online:  05 October 2015

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

  • 1. Institute of Thermal Science and Power Engineering, Naval University of Engineering, Wuhan 430033, China;
  • 2. Military Key Laboratory for Naval Ship Power Engineering, Naval University of Engineering, Wuhan 430033, China;
  • 3. College of Power Engineering, Naval University of Engineering, Wuhan 430033, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 51206184, 51176203, 51356001, 51579244).

Abstract: 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.

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