离散发热器件基于(火积)耗散率最小和最高温度最小的构形优化比较

王刚; 谢志辉; 范旭东; 陈林根; 孙丰瑞

doi:10.7498/aps.66.204401

摘要

建立了导热基座上圆柱体离散发热器件的三维湍流散热模型，基于构形理论，考虑空气变物性及可压缩性和黏性耗散，研究了器件材料的热导率、热源强度和流体流速对器件最高温度、基于（火积）耗散定义的当量热阻和平均Nu数的影响.结果表明：在总发热功率一定的条件下，以器件最高温度和当量热阻为性能指标进行热设计，均存在最优热源强度分布使得散热性能最优.当各热源强度相同且热源热导率小于基座热导率时，提高热源热导率可明显改善散热性能；将热源热导率沿流动方向从低到高布置可降低器件最高温度，而将热源热导率均匀布置可使当量热阻最小.所得结果可为实际热设计中不同材质和不同发热率的电子器件最优布置提供理论支撑.

关键词:

Abstract

A three-dimensional (3D) turbulent heat dissipation model of cylindrical discrete heat generation components is established on a conductive basis. The whole solid section is set in a square channel with adiabatic walls, and the components, cooled by clean air flowing through the channel, are arranged in a line with equal spacings. The influences of the heat conductivities of the components, intensities of heat sources and velocity of fluid flow on the maximum temperature (MT) of components, the equivalent thermal resistance (ETR) based on entransy dissipation of the heat dissipation system, and the averaged Nu number are investigated with the constructal theory considering variable properties, compressibility and viscous dissipation of air. The total heat generation rate and the total heat conductivity of heat sources are fixed as the constraint conditions. The circumstances in which heat generation rates and heat conductivities of heat sources are unequal are considered. The results show that for the fixed total heat generation rate of heat sources, despite MT or ETR that is taken as the performance index for thermal design, there exists an optimal intensity distribution of heat sources for the best thermal performance of the system. In fact, for different objectives, the optimal intensity distributions of heat sources are corresponding to the best match between the distributions of heat sources and the distributions of temperature gradient. There are different optimal distributions for different velocities of the fluid flow and different optimization objectives. Besides, the averaged Nu number increases with the increase of intensity difference in heat sources, which means that the convective heat transfer is enhanced, but this phenomenon is relatively weak when the velocity of fluid flow is low. For the fixed total heat generation rate of heat sources, when the intensities of heat sources are equal and the thermal conductivities of heat sources are lower than that of the conductive basis, increasing heat conductivities of the heat sources can evidently improve thermal performance of the system; the MT can be lowest when the conductivities of heat sources increase along the fluid flow; and the ETR is lowest when the conductivities of heat sources are equal. Both the MT and the ETR decrease with the increasing velocity of fluid flow. The results can provide some theoretical guidelines for the practical thermal design of the electronic components with different materials and different heat generation rates.

Keywords:

constructal theory /
entransy dissipation extremum principle /
cooling of electronic components /
generalized thermodynamic optimization

作者及机构信息

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

通信作者: 陈林根, lingenchen@hotmail.com

基金项目: 国家自然科学基金（批准号：51579244，51206184）和海军工程大学自主立项课题（批准号：20160134）资助的课题.

Authors and contacts

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

Corresponding author: Chen Lin-Gen, lingenchen@hotmail.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51579244, 51206184) and the Independent Project of Naval University of Engineering (Grant No. 20160134).

参考文献

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[37]	Chen Q, Liang X G, Guo Z Y 2013 Int. J. Heat Mass Transfer 63 65
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[46]	Wang H G, Wu D, Rao Z H 2015 Acta Phys. Sin. 64 244401 (in Chinese)[王焕光, 吴迪, 饶中浩2015物理学报64 244401]
[47]	Chen G M, Tso C P 2012 Int. J. Heat Mass Transfer 55 3744
[48]	Jia H, Liu Z C, Liu W, Nakayama A 2014 Int. J. Heat Mass Transfer 73 124
[49]	Wu J, Cheng X 2013 Int. J. Heat Mass Transfer 58 374
[50]	Yuan F, Chen Q 2012 Chinese Sci. Bull. 57 687
[51]	Zheng Z J, He Y L, Li Y S 2014 Sci. China Tech. Sci. 57 773
[52]	Xia S J, Chen L G, Sun F R 2009 Chinese Sci. Bull. 54 3587
[53]	Guo J F, Huai X L, Li X F, Cai J, Wang Y W 2013 Energy 63 95
[54]	Wei S H, Chen L G, Sun F R 2008 Sci. China Ser. E Tech. Sci. 51 1283
[55]	Chen L G, Feng H J, Xie Z H 2016 Entropy 18 353
[56]	Chen L G, Yang A B, Xie Z H, Feng H J, Sun F R 2017 Int. J. Therm. Sci. 111 168
[57]	Xie Z H, Chen L G, Sun F R 2009 Sci. China Ser. E Tech. Sci. 52 3504
[58]	Xie Z H, Chen L G, Sun F R 2009 Chinese Sci. Bull. 54 4418
[59]	Feng H J, Chen L G, Xie Z H, Sun F R 2016 J. Energy Inst. 89 302
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施引文献

[1]	Guo Z Y, Li D Y, Wang B X 1998 Int. J. Heat Mass Transfer 41 2221
[2]	Tao W Q, Guo Z Y, Wang B X 2002 Int. J. Heat Mass Transfer 45 3849
[3]	Xuan Y M 2014 Sci. China Tech. Sci. 44 269 (in Chinese)[宣益民2014中国科学:技术科学44 269]
[4]	Chen L G, Meng F K, Sun F R 2016 Sci. China Tech. Sci. 59 442
[5]	Chen Y P, Yao F, Shi M H 2012 Int. J. Heat Mass Transfer 55 4476
[6]	Xie G N, Liu J, Liu Y Q, Sunden B, Zhang W H 2013 Trans. ASME J. Electron. Packag. 135 021008
[7]	Zhao D L, Tan G 2014 Appl. Thermal Eng. 66 15
[8]	Kang N, Wu H Y, Xu F Y 2015 J. Engng. Thermophys. 36 1572 (in Chinese)[康宁, 吴慧英, 徐发尧2015工程热物理学报36 1572]
[9]	Green C, Kottke P, Han X F, Woodrum C, Sarvey T, Asrar P, Zhang X C, Joshi Y, Fedorov A, Sitaraman S, Bakir M 2015 J. Electron. Packag. 137 040802
[10]	Luo X B, Hu R, Liu S, Wang K 2016 Prog. Energ. Combust. Sci. 56 1
[11]	Chen K, Wang S F, Song M X 2016 Int. J. Heat Mass Transfer 93 108
[12]	Zhang X C, Han X F, Sarvey T E, Green C E, Kottke P A, Fedorov A G, Joshi Y, Bakir M S 2016 J. Electron. Packag. 138 010910
[13]	Bejan A 1997 Int. J. Heat Mass Transfer 40 799
[14]	Bejan A 2000 Shape and Structure, from Engineering to Nature (Cambridge:Cambridge University Press) pp1-314
[15]	Bejan A, Lorente S 2008 Design with Constructal Theory (New Jersey:Wiley) pp1-62
[16]	Chen L G, Feng H J 2016 Multi-objective Constructal Optimization for Flow and Heat and Mass Transfer Processes (Beijing:Science Press) pp1-23(in Chinese)[陈林根, 冯辉君2016流动和传热传质过程的多目标构形优化(北京:科学出版社)第123页]
[17]	Bejan A 2016 The Physics of Life:The Evolution of Everything (New York:St. Martin' s Press) pp1-27
[18]	Chen L G 2012 Sci. China Tech. Sci. 55 802
[19]	Bejan A, Errera M R 2016 J. Appl. Phys. 119 074901
[20]	Bejan A, Fowler A J, Stanescu G 1995 Int. J. Heat Mass Transfer 38 2047
[21]	Stanescu G, Fowler A J, Bejan A 1996 Int. J. Heat Mass Transfer 39 311
[22]	Jassim E, Muzychka Y S 2010 J. Heat Transfer 132 011701
[23]	Hajmohammadi M R, Poozesh S, Nourazar S S 2012 Proc. IMechE Part E J. Process Mech. Eng. 226 324
[24]	Hajmohammadi M R, Poozesh S, Nourazar S S, Manesh A H 2013 Mech. Sci. Tech. 27 1143
[25]	Pedrotti V A, Souza J A, Isoldi J A, dos Santos E D, Isoldi L A 2015 Engenharia Termica ( Thermal Engineering) 14 16
[26]	Shi Z Y, Dong T 2015 Energ. Convers. Manage. 106 300
[27]	Singh D K, Singh S N 2015 Int. J. Heat Mass Transfer 89 444
[28]	Fan X D, Xie Z H, Sun F R, Yang A B 2016 J. Eng. Therm. 37 1994 (in Chinese)[范旭东, 谢志辉, 孙丰瑞, 杨爱波2016工程热物理学报37 1994]
[29]	Fan X D 2015 M. S. Thesis (Wuhan:Naval University of Engineering) (in Chinese)[范旭东2015硕士学位论文(武汉:海军工程大学)]
[30]	Gong S W, Chen L G, Feng H J, Xie Z H, Sun F R 2015 Int. Commun. Heat Mass Transfer 68 1
[31]	Gong S W, Chen L G, Feng H J, Xie Z H, Sun F R 2014 Chinese Sci. Bull. 59 3609 (in Chinese)[龚舒文, 陈林根, 冯辉君, 谢志辉, 孙丰瑞2014科学通报59 3609]
[32]	Gong S W, Chen L G, Feng H J, Xie Z H, Sun F R 2016 Sci. China Tech. Sci. 59 631
[33]	Gong S W 2014 M. S. Thesis (Wuhan:Naval University of Engineering) (in Chinese)[龚舒文2014硕士学位论文(武汉:海军工程大学)]
[34]	Guo Z Y, Zhu H Y, Liang X G 2007 Int. J. Heat Mass Transfer 50 2545
[35]	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7897页]
[36]	Chen L G 2012 Chinese Sci. Bull. 57 4404
[37]	Chen Q, Liang X G, Guo Z Y 2013 Int. J. Heat Mass Transfer 63 65
[38]	Cheng X T, Liang X G 2014 Chinese Sci. Bull. 59 5309
[39]	Chen L G 2014 Sci China Tech. Sci. 57 2305
[40]	Cheng X T, Liang X G, Guo Z Y 2011 Chinese Sci. Bull. 56 847
[41]	Hu G J, Cao B Y, Guo Z Y 2011 Chinese Sci. Bull. 56 2974
[42]	Cheng X T, Zhang Q Z, Xu X H, Liang X G 2013 Chin. Phys. B 22 020503
[43]	Zhao T, Chen Q 2013 Acta Phys. Sin. 62 234401 (in Chinese)[赵甜, 陈群2013物理学报62 234401]
[44]	Cheng X T, Liang X G 2014 Acta Phys. Sin. 63 190501 (in Chinese)[程雪涛, 梁新刚2014物理学报63 190501]
[45]	Liu W, Liu Z C, Jia H, Fan A W, Nakayama A 2011 Int. J. Heat Mass Transfer 54 3049
[46]	Wang H G, Wu D, Rao Z H 2015 Acta Phys. Sin. 64 244401 (in Chinese)[王焕光, 吴迪, 饶中浩2015物理学报64 244401]
[47]	Chen G M, Tso C P 2012 Int. J. Heat Mass Transfer 55 3744
[48]	Jia H, Liu Z C, Liu W, Nakayama A 2014 Int. J. Heat Mass Transfer 73 124
[49]	Wu J, Cheng X 2013 Int. J. Heat Mass Transfer 58 374
[50]	Yuan F, Chen Q 2012 Chinese Sci. Bull. 57 687
[51]	Zheng Z J, He Y L, Li Y S 2014 Sci. China Tech. Sci. 57 773
[52]	Xia S J, Chen L G, Sun F R 2009 Chinese Sci. Bull. 54 3587
[53]	Guo J F, Huai X L, Li X F, Cai J, Wang Y W 2013 Energy 63 95
[54]	Wei S H, Chen L G, Sun F R 2008 Sci. China Ser. E Tech. Sci. 51 1283
[55]	Chen L G, Feng H J, Xie Z H 2016 Entropy 18 353
[56]	Chen L G, Yang A B, Xie Z H, Feng H J, Sun F R 2017 Int. J. Therm. Sci. 111 168
[57]	Xie Z H, Chen L G, Sun F R 2009 Sci. China Ser. E Tech. Sci. 52 3504
[58]	Xie Z H, Chen L G, Sun F R 2009 Chinese Sci. Bull. 54 4418
[59]	Feng H J, Chen L G, Xie Z H, Sun F R 2016 J. Energy Inst. 89 302
[60]	COMSOL 2012 COMSOL Multiphysics User' s Guide (Version 4.3b) (Sweden:COMSOL Incorporated) pp103-147

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