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受热基底上的液滴铺展及换热特性

叶学民 李永康 李春曦

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受热基底上的液滴铺展及换热特性

叶学民, 李永康, 李春曦

Spreading and heat transfer characteristics of droplet on a heated substrate

Ye Xue-Min, Li Yong-Kang, Li Chun-Xi
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  • 液滴在受热基底上的铺展特征将直接影响其传热特性.基于润滑理论建立了单液滴在受热基底上的演化模型,模拟了壁温均匀和自中心向两侧呈指数规律衰减两种情形下液滴的铺展历程,提出了一种针对二维液滴表面热流密度和传热量的计算方法,借助该方法分析了液滴铺展特征及外部对流换热条件对传热特性的影响,所得结果与已有文献有较好的一致性.结果表明:当壁温均匀时,液滴在重力驱动下呈现具有“单峰”结构的对称铺展特征,表面热流密度由两侧向中心递减;液滴表面积随时间小幅增大,传热能力有所增强.当壁温自中心向两侧呈指数规律衰减时,液滴铺展明显呈现三个阶段特征,厚度剖面由“单峰”结构渐变为“双峰”结构,且“双峰”峰值随时间先增大后减小,该变化源于重力和热毛细力的复杂博弈及在演化过程中的交替主导地位;液滴中心处热流密度不断增大,“双峰”处热流密度则持续减小;接触线处热流密度相比邻近有一明显跃升;液滴表面积随时间显著增大,传热能力有效提高.增强外部对流换热条件虽将减缓液滴铺展过程,抑制其表面积增大,但总体上有利于提高其传热能力,且随时间增长,该现象愈加显著;增大毕渥数使液滴动态接触角及接触线移动速率的变化发生延迟,但并不改变其总体特征.
    The spreading characteristics of a droplet on a heated substrate have direct influences on its spreading area and heat transfer, so the exploration in this aspect is of important significance for cooling electronic and aerospace equipments. In the present paper, the evolution model of a droplet on a heated solid substrate is established based on the lubrication theory, and spreading processes are simulated respectively when the wall temperature is uniform and decreases exponentially from the center to both sides. A method of assessing the heat flux and heat transfer capacity of a two-dimensional liquid droplet is proposed. Influences of spreading characteristics and heat convective condition at the liquid-gas interface on heat transfer feature of the droplet are examined, and the results are in good agreement with the published ones in the literature. The simulated results show that in the case of uniform wall temperature, the evolution of the droplet is dominated mainly by gravity and illustrates symmetrical spreading characteristics, and the thickness profile presents a single-peak feature of which the value diminishes with time. The heat flux across the droplet surface decreases from both sides to the center, and the surface area of the droplet increases with time slightly, so the performance of heat transfer is strengthened to a certain extent. When the wall temperature decreases exponentially from the center to both sides, the spreading process of the droplet manifests three obvious stages, in which a single-peak feature of thickness profile gradually evolutes into a double-peak feature after surviving for a short period of time, and the peak values of the double-peak first increase firstly and then decrease, resulting from the complex game of gravity and thermocapillary force and their alternative dominance in the evolution. The variations of the dynamic contact angle and travelling speed of the contact line with time can also reflect the above characteristics. The heat flux in the center of the droplet increases, while its values at the double-peak and contact lines decrease with time. In addition, the heat flux at the contact line has a distinct jump feature compared with that at the adjacent position. The droplet surface area expands significantly with time, so the heat transfer capability is improved apparently. Enhancing heat convective condition at the liquid-gas interface, namely greater Biot number, slows the droplet spreading process, which inhibits the expansion of the droplet surface area. However, it enables the droplet to stay in a higher temperature region, resulting in the enhancement of heat dissipation of the droplet. Therefore, the comprehensive interactions of the above aspects strengthen the heat transfer capability, and this phenomenon tends to be increasingly significant over time. Greater Biot number delays the variations of the dynamic contact angle and the travelling speed of the contact line, without changing their general characteristics.
      通信作者: 叶学民, yexuemin@163.com
    • 基金项目: 国家自然科学基金(批准号:11202079)和河北省自然科学基金(批准号:A2015502058)资助的课题.
      Corresponding author: Ye Xue-Min, yexuemin@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11202079) and the Natural Science Foundation of Hebei Province, China (Grant No. A2015502058).
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    Cheng W L, Han F Y, Liu Q N, Zhao R, Fan H 2011 Energy 36 249

    [18]

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    Cheng Y L, Ye X M, Yan W P 2002 J. North Chin. Electr. Power Univ. 29 50 (in Chinese)[程友良, 叶学民, 阎维平2002华北电力大学学报29 50]

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    Wang L, Huai X L, Tao Y J, Wang L 2010 J. Eng. Therm. 06 987 (in Chinese)[王磊, 淮秀兰, 陶毓伽, 王立2010工程热物理学报06 987]

    [21]

    Karapetsas G, Sahu K C, Matar O K 2013 Langmuir 29 8892

    [22]

    Yuan Q, Huang X, Zhao Y P 2014 Phys. Fluids 26 092104

    [23]

    Yuan Q, Zhao Y P 2013 J. Fluid Mech. 716 171

    [24]

    Yuan Q, Zhao Y P 2013 Sci. Rep. 3 1944

    [25]

    Roux D C D, Cooper-White J J 2004 J. Colloid Interface. Sci. 277 424

    [26]

    Yang S M, Tao W S 2006 Heat Transfer (4th Ed.) (Beijing:Higher Education Press) pp37-38(in Chinese)[杨世铭, 陶文铨2006传热学(第4版) (北京:高等教育出版社)第37–38页]

  • [1]

    Zhirnov V V, Cavin R K, Hutchby J A 2003 P. IEEE 91 1934

    [2]

    Li T, Liu J 2004 J. Refrig. 03 22 (in Chinese)[李腾, 刘静2004制冷学报03 22]

    [3]

    Liang X Y 2012 M. S. Thesis (Hangzhou:Zhejiang University) (in Chinese)[梁雪艳2012硕士学位论文(杭州:浙江大学)]

    [4]

    Visaria M, Mudawar I 2008 Int. J. Heat Mass Transfer 51 5269

    [5]

    Zhang Z 2013 Ph. D. Dissertation (Beijing:Tsinghua University) (in Chinese)[张震2013博士学位论文(北京:清华大学)]

    [6]

    Gao S, Qu W, Yao W 2007 J. Eng. Therm. 28 221 (in Chinese)[高珊, 曲伟, 姚伟2007工程热物理学报28 221]

    [7]

    Lee K S, Ivanova N, Starov V M, Hilal N, Dutschk V 2008 Adv. Colloid Interface Sci. 144 54

    [8]

    Pasandideh-Fard M, Aziz S D, Chandra S, Mostaghimi J 2001 Int. J. Heat Fluid Flow 22 201

    [9]

    Francois M, Shyy W 2002 Heat Transfer 03 401

    [10]

    Zhu W Y 2007 M. S. Thesis (Dalian:Dalian University of Technology) (in Chinese)[朱卫英2007硕士学位论文(大连:大连理工大学)]

    [11]

    Liu S S, Zhang C H, Zhang H B, Zhou J, He J G, Yin H Y 2013 Chin. Phys. B 22 106801

    [12]

    Karapetsas G, Matar O K, Valluri P, Sefiane K 2012 Langmuir 28 11433

    [13]

    Hu H B, Chen L B, Bao L Y, Huang S H 2014 Chin. Phys. B 23 074702

    [14]

    Xu W, Lan Z, Peng B L, Wen R F, Ma X H 2015 Acta Phys. Sin. 64 216801 (in Chinese)[徐威, 兰忠, 彭本利, 温荣福, 马学虎2015物理学报64 216801]

    [15]

    Wang S L, Li C X, Ye X M 2011 Proc. CSEE. 31 63 (in Chinese)[王松岭, 李春曦, 叶学民2011中国电机工程学报31 63]

    [16]

    Li C X, Pei J J, Ye X M 2013 Acta Phys. Sin. 62 174702 (in Chinese)[李春曦, 裴建军, 叶学民2013物理学报62 174702]

    [17]

    Cheng W L, Han F Y, Liu Q N, Zhao R, Fan H 2011 Energy 36 249

    [18]

    Karapetsas G, Sahu K C, Sefiane K, Matar O K 2014 Langmuir 30 4310

    [19]

    Cheng Y L, Ye X M, Yan W P 2002 J. North Chin. Electr. Power Univ. 29 50 (in Chinese)[程友良, 叶学民, 阎维平2002华北电力大学学报29 50]

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    Wang L, Huai X L, Tao Y J, Wang L 2010 J. Eng. Therm. 06 987 (in Chinese)[王磊, 淮秀兰, 陶毓伽, 王立2010工程热物理学报06 987]

    [21]

    Karapetsas G, Sahu K C, Matar O K 2013 Langmuir 29 8892

    [22]

    Yuan Q, Huang X, Zhao Y P 2014 Phys. Fluids 26 092104

    [23]

    Yuan Q, Zhao Y P 2013 J. Fluid Mech. 716 171

    [24]

    Yuan Q, Zhao Y P 2013 Sci. Rep. 3 1944

    [25]

    Roux D C D, Cooper-White J J 2004 J. Colloid Interface. Sci. 277 424

    [26]

    Yang S M, Tao W S 2006 Heat Transfer (4th Ed.) (Beijing:Higher Education Press) pp37-38(in Chinese)[杨世铭, 陶文铨2006传热学(第4版) (北京:高等教育出版社)第37–38页]

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出版历程
  • 收稿日期:  2016-04-24
  • 修回日期:  2016-09-07
  • 刊出日期:  2016-12-05

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