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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.
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Keywords:
- double-peak structure /
- spreading characteristic /
- heat flux density /
- thermocapillary force
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[2] Li T, Liu J 2004 J. Refrig. 03 22 (in Chinese)[李腾, 刘静2004制冷学报03 22]
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[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 62 174702]
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[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]
[20] 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 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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[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 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 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 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]
[20] 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 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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