·1246· 工程科学学报.第41卷，第10期 在一定的理论假设和试验测量之上，在工程应用上 [11]Lambert MA,Fletcher L S.Review of models for thermal contact 具有一定的局限性.同时，试验测量系统的精确性 conductance of metals.J Thermophys Heat Transfer,1997,11 和试验方法的科学性直接影响接触热阻理论计算的 (2):129 12]Lambert M A,Fletcher L S.Thermal contact conductance of non- 准确性，如何更为高效、准确的测量接触表面的形貌 flat,rough,metallic coated metals.J Heat Transfer,2002,124 特征，能否建立一套具有普适性的接触热阻理论是 (3):405 未来的努力方向. [13] Fletcher L.S.A review of thermal enhancement techniques for (2)数值模拟法计算接触热阻具有快捷、高效 electronic systems.IEEE Trans Comp Hybrids Mfg,1990,13 等优点，但是仿真模型往往人为假定接触峰形状和 (4):1012 [14]Kraus A D,Bar-Cohen A.Thermal Analysis Control of Elec- 接触间隙比，实际上由于接触表面形貌的复杂性和 tronic Equipment.Florida:MeGraw-Hill,1983 接触点分布的随机性，为了更加准确的获知接触点 [15]Madhusudana C V,Fletcher L S.Contact heat transfer-the last 大小和空间分布信息，需要开展更为精确的三维表 decade.AlAA J,1986,24(3):510 面测量和表征. [16]Fletcher L S.Recent developments in contact conductance heat (3)接触热阻的各影响因素往往是相互耦合 transfer.J Heat Transfer,1988,110(4B):1059 的，基于多场耦合理论借助大型仿真软件采用直接 [17]Gmelin E,Asen-Palmer M,Reuther M,et al.Thermal boundary resistance of mechanical contacts between solids at sub-ambient 耦合法开展多耦合分析有助于更加的准确预测接触 temperatures.J Phys D Appl Phys,1999,32(6):R19 热阻. [18]Gu W L.Experiment on thermal contact resistance.J Nanjing (4)接触热阻是一个多学科交叉的跨尺度问 4 eron Inst,1992,24(1):46 题，在微尺度领域傅里叶定律不再适用，为了准确预 (顾慰兰.接触热阻的试验研究.南京航空学院学报，1992， 测接触热阻需要宏观和微观相结合，进一步深入开 24(1):46) 展跨尺度研究 [19]Gu WL.Yang Y S.The influence of temperature on contact re- sistance of metallic surfaces temperature.J Nanjing Unir Aeron 参考文献 4sron,1994,26(3):342 (顾慰兰，杨燕生.温度对接触热阻的影响.南京航空航天 [1]Lambert M A,Fletcher L S.Thermal contact conductance of 大学学报，1994,26(3)：342) spherical rough metals.J Heat Transfer,1997,119(4):684 [20]Xu L,Yang J,Xu J M,et al.The research of contact thermal [2]Adrian Bejan,Allan D K.Heat Transfer Handbook.New Jersey: resistance of solid surface at low temperature.Cryog Supercond, Wiley.2003 1996,24(1):53 [3]Song C Y,Luan T,Wu J B,et al.Research progress on the inter- (徐烈，杨军，徐佳梅，等.低温下固体表面接触热阻的研 face thermal resistance of polymer based thermal interface materi- 究.低温与超导，1996,24(1)：53) als.J Integr Technol,2019.8(1):56 [21]Xu L,Zhang T,Xiong W,et al.The effect of contact interfaces (宋成轶，栾添，邬剑波，等.聚合物基热界面材料界面接触 on thermal contact resistance at low temperature and vacuum.Vac 热阻的研究进展.集成技术，2019,8(1)：56) Cog,1998,4(1)1) [4]Dter Haar.Collected Papers of P.L.Kapitza.London:Pergamon (徐烈，张涛，熊炜，等.真空低温下接触表面对接触热阻的 Press,1965 影响.真空与低温，1998,4(1)：1) [5]Thomas T R,Probert S D.Correlations for thermal contact con- [22]Xu R P,Feng H D,Zhao L P,et al.Experimental investigation ductance in vacuo.J Heat Transfer,1972.94(3):276 of thermal contact conductance at low temperature based on fractal [6] Swartz E T,Pohl R 0.Thermal boundary resistance.Rer Mod description.Int Commun Heat Mass Transfer,2006,33(7):811 Phs,1989,61(3):605 [23]Chen J.Inrestigation on the Computer Simulation of Boundary [7]Hmina N,Scudeller Y.Thermal interface resistance and subsur- Heat Transfer Process betwceen Solids at Low Temperature [Disser- face effusivity of submicron metallic films on dielectric substrates: tation ]Wuhan:Huazhong University of Science and Technolo- an experimental method for simultaneous determination.Int Heat ,2004 Mass Transfer,1998,41(18):2781 (陈进.低温固体界面传热过程计算机仿真研究[学位论 [8]Rostami AA,Hassan A Y,Lim PC.Parametric study of thermal 文].武汉：华中科技大学，2004) constriction resistance.Heat Mass Transfer,2001,37(1):5 [24]Ying J.Chen WQ.Chen ZC.Effect of heat transfer on the esti- [9]Yovanovich MM.Four decades of research on thermal contact, mation of contact resistance.JZhejiang Unie Nat Sci,1996,30 gap,and joint resistance in microelectronies.IEEE Trans Compon (4):415) Packag Technol,2005,28(2):182 (应济，陈伟球，陈子辰.换热影响下的接触热阻估计.浙江 [10]Prasher R.Thermal boundary resistance and thermal conductivity 大学学报：自然科学版，1996,30(4)：415) of multiwalled carbon nanotubes.Phys Rev B,2008.77(7): [25]Ying J.Jia Y.Chen Z C.et al.Theoretical and experimental re- 075424 search on the contact thermal resistance between real surface.工程科学学报,第 41 卷,第 10 期 在一定的理论假设和试验测量之上,在工程应用上 具有一定的局限性. 同时,试验测量系统的精确性 和试验方法的科学性直接影响接触热阻理论计算的 准确性,如何更为高效、准确的测量接触表面的形貌 特征,能否建立一套具有普适性的接触热阻理论是 未来的努力方向. (2)数值模拟法计算接触热阻具有快捷、高效 等优点,但是仿真模型往往人为假定接触峰形状和 接触间隙比,实际上由于接触表面形貌的复杂性和 接触点分布的随机性,为了更加准确的获知接触点 大小和空间分布信息,需要开展更为精确的三维表 面测量和表征. (3)接触热阻的各影响因素往往是相互耦合 的,基于多场耦合理论借助大型仿真软件采用直接 耦合法开展多耦合分析有助于更加的准确预测接触 热阻. (4)接触热阻是一个多学科交叉的跨尺度问 题,在微尺度领域傅里叶定律不再适用,为了准确预 测接触热阻需要宏观和微观相结合,进一步深入开 展跨尺度研究. 参 考 文 献 [1] Lambert M A, Fletcher L S. Thermal contact conductance of spherical rough metals. J Heat Transfer, 1997, 119(4): 684 [2] Adrian Bejan, Allan D K. Heat Transfer Handbook. New Jersey: Wiley, 2003 [3] Song C Y, Luan T, Wu J B, et al. Research progress on the inter鄄 face thermal resistance of polymer based thermal interface materi鄄 als. J Integr Technol, 2019, 8(1): 56 (宋成轶, 栾添, 邬剑波, 等. 聚合物基热界面材料界面接触 热阻的研究进展. 集成技术, 2019, 8(1): 56) [4] Dter Haar. Collected Papers of P. L. Kapitza. London: Pergamon Press, 1965 [5] Thomas T R, Probert S D. Correlations for thermal contact con鄄 ductance in vacuo. J Heat Transfer, 1972, 94(3): 276 [6] Swartz E T, Pohl R O. Thermal boundary resistance. Rev Mod Phys, 1989, 61(3): 605 [7] Hmina N, Scudeller Y. Thermal interface resistance and subsur鄄 face effusivity of submicron metallic films on dielectric substrates: an experimental method for simultaneous determination. Int J Heat Mass Transfer, 1998, 41(18): 2781 [8] Rostami A A, Hassan A Y, Lim P C. Parametric study of thermal constriction resistance. Heat Mass Transfer, 2001, 37(1): 5 [9] Yovanovich M M. Four decades of research on thermal contact, gap, and joint resistance in microelectronics. IEEE Trans Compon Packag Technol, 2005, 28(2): 182 [10] Prasher R. Thermal boundary resistance and thermal conductivity of multiwalled carbon nanotubes. Phys Rev B, 2008, 77 ( 7 ): 075424 [11] Lambert M A, Fletcher L S. Review of models for thermal contact conductance of metals. J Thermophys Heat Transfer, 1997, 11 (2): 129 [12] Lambert M A, Fletcher L S. Thermal contact conductance of non鄄 flat, rough, metallic coated metals. J Heat Transfer, 2002, 124 (3): 405 [13] Fletcher L S. A review of thermal enhancement techniques for electronic systems. IEEE Trans Comp Hybrids Mfg, 1990, 13 (4): 1012 [14] Kraus A D, Bar鄄Cohen A. Thermal Analysis & Control of Elec鄄 tronic Equipment. Florida: McGraw鄄Hill, 1983 [15] Madhusudana C V, Fletcher L S. Contact heat transfer鄄the last decade. AIAA J, 1986, 24(3): 510 [16] Fletcher L S. Recent developments in contact conductance heat transfer. J Heat Transfer, 1988, 110(4B): 1059 [17] Gmelin E, Asen鄄Palmer M, Reuther M, et al. Thermal boundary resistance of mechanical contacts between solids at sub鄄ambient temperatures. J Phys D Appl Phys, 1999, 32(6): R19 [18] Gu W L. Experiment on thermal contact resistance. J Nanjing Aeron Inst, 1992, 24(1): 46 (顾慰兰. 接触热阻的试验研究. 南京航空学院学报, 1992, 24(1): 46) [19] Gu W L, Yang Y S. The influence of temperature on contact re鄄 sistance of metallic surfaces temperature. J Nanjing Univ Aeron Astron, 1994, 26(3): 342 (顾慰兰, 杨燕生. 温度对接触热阻的影响. 南京航空航天 大学学报, 1994, 26(3): 342) [20] Xu L, Yang J, Xu J M, et al. The research of contact thermal resistance of solid surface at low temperature. Cryog Supercond, 1996, 24(1): 53 (徐烈, 杨军, 徐佳梅, 等. 低温下固体表面接触热阻的研 究. 低温与超导, 1996, 24(1): 53) [21] Xu L, Zhang T, Xiong W, et al. The effect of contact interfaces on thermal contact resistance at low temperature and vacuum. Vac Cryog, 1998, 4(1): 1) (徐烈, 张涛, 熊炜, 等. 真空低温下接触表面对接触热阻的 影响. 真空与低温, 1998, 4(1): 1) [22] Xu R P, Feng H D, Zhao L P, et al. Experimental investigation of thermal contact conductance at low temperature based on fractal description. Int Commun Heat Mass Transfer, 2006, 33(7): 811 [23] Chen J. Investigation on the Computer Simulation of Boundary Heat Transfer Process between Solids at Low Temperature [Disser鄄 tation]. Wuhan: Huazhong University of Science and Technolo鄄 gy, 2004 (陈进. 低温固体界面传热过程计算机仿真研究[ 学位论 文]. 武汉: 华中科技大学, 2004) [24] Ying J, Chen W Q, Chen Z C. Effect of heat transfer on the esti鄄 mation of contact resistance. J Zhejiang Univ Nat Sci, 1996, 30 (4): 415) (应济, 陈伟球, 陈子辰. 换热影响下的接触热阻估计. 浙江 大学学报:自然科学版, 1996, 30(4): 415) [25] Ying J, Jia Y, Chen Z C, et al. Theoretical and experimental re鄄 search on the contact thermal resistance between real surface. J ·1246·