Abstract
Theoretical prediction research on thermal contact resistance is reviewed in this paper. In general, modeling or simulating the thermal contact resistance involves several aspects, including the descriptions of surface topography, the analysis of micro mechanical deformation, and the thermal models. Some key problems are proposed for accurately predicting the thermal resistance of two solid contact surfaces. We provide a perspective on further promising research, which would be beneficial to understanding mechanisms and engineering applications of the thermal contact resistance in heat transport phenomena.
Similar content being viewed by others
References
Viswanath R, Wakharkar V, Watwe A, et al. Thermal performance challenges from silicon to systems. Int Technol J, 2000, 4(3): 1–16
Min G R, Guo S. Thermal Control of Spacecraft (in Chinese). Beijing: Science Press, 1998
Geng Y B, Wei Y M, Pan H L, et al. The thermal control technologies for electric thrusters (in Chinese). In: The Symposium on Electric Propulsion in China, Beijing, China, 2007. 6–11
Ramamurthi K, Kumar S S, Ahilash P M. Thermal contact conductance of molybdenum-sulphide-coated joints at low temperature. J Thermophys Heat Transf, 2007, 21(4): 811–813
Culham J R, Khan W A, Yovanovich M M, et al. The influence of material properties and spreading resistance in the thermal design of plate fin heat sinks. Trans ASME J Electron Pack, 2007, 129: 76–81
Alcock J F. Communications on a review of recent progress in heat transfer. Proc Institution Mech Engineer, 1943, 149: 126–130
Lambert M A, Fletcher L S. Review of models for thermal contact conductance of metals. J Thermophys Heat Transf, 1997, 11(2): 129–140
Lambert M A, Fletcher L S. Thermal contact conductance of non-flat, rough, metallic coated metals. Trans ASME J Heat Transf, 2002, 124: 405: 4–12
Yovanovich M M. Conduction and thermal contact resistances (conductances). In: Rohsenow W M, Hartnett J P, Cho Y I, eds. Hand-hook of Heat Transfer. Chapter 3. New York: McGraw Hill, 1998
Yovanovich M M, Marotha E. Thermal spreading and contact resistance. In: Bejan A, Kraus A D, eds. Heat Transfer Handbook. Chapter 4. New York: Wiley, 2003
Fletcher L S. A review of thermal control materials for metallic junctions. J Spacecraft Rocket, 1972, 9: 849–850
Fletcher L S. A review of thermal enhancement techniques for electronic systems, IEEE T Component Hyhird Manuf Technol, 1990, 13(4): 1012–1021
Kraus A D, Bar-Cohen A. Thermal Analysis and Control of Electronic Equipment. New-York: McGraw-Hill, 1983
Yovanovich M M, Antonetti V W. Application of thermal contact resistance theory to electronic packages. In: Bar-Cohen A, Kraus A D, eds. Advances in Thermal Modeling of Electronic Components and Systems. New York: Hemisphere Publishing, 1988
Madhusudana C V. Thermal Contact Conductance. New York: Springer-Verlag, 1996
Madhusudana C V, Fletcher L S. Contact heat transfer—The last decade. AIAA J, 1986, 24(3): 510–523
Fletcher L S. Recent developments in contact conductance heat transfer. Transa ASME J heat transf, 1988, 110: 1059–1070
Swartz E, Pohl R. Thermal boundary resistance. Rev Mod Phys, 1989, 61: 605–668
Gmelin E, Asen-Palmer M, Reuther M, et al. Thermal boundary resistance of mechanical contacts between solids at sub-ambient temperatures. J Phys D-Appl Phys, 1999, 32: R19–R43
Gu W L. The experimental research on thermal contact resistance (in Chinese). J Nanjing Univ Aeronautics Astronautics, 1992, 24(1): 46–52
Gu W L. The temperature effect on thermal contact resistance (in Chinese). J Nanjing Univ Aeronautics Astronautics, 1994, 26(3): 342–349
Gu W L. A calculation method of thermal contact resistance on random surface (in Chinese). J Aerospace Power, 1995, 10(3): 232–236
Xu L, Xu J M. Research on the thermal contact resistance of solid surface at low temperature (in Chinese). Cryogenics Supercon, 1996, 24(1): 53–58
Xu L, Zhang T, Xiong W, et al. The contact surface effect on thermal contact resistance at low temperature and vacuum (in Chinese). Vacuum Cryogenics, 1998, 4(1): 1–4
Zhang T, Xu L, Xiong W, et al. Comparison and analysis of theoretical models in the research of thermal contact conductance (in Chinese). Cryogenics Supercon, 1998, 26(2): 58–64
Xu L, Zhang T, Zhao L P, et al. Using double heat-flux meter method to measure the thermal contact resistance of solid material at low temperature and vacuum (in Chinese). Cryogenics, 1999, (4): 185–189
Zhao L P, Xu L. Using profile discrimination method to investigate thermal contact conductance between rough interfaces (in Chinese). Cryogenics, 2000, 118(6): 52–57
Zhao L P, Xu L, Li Z C, et al. Research on the relationship between thermal contact conductance of solid interfaces and cycling load at low temperatures (in Chinese). Cryogenics Supercon, 2000, 28(1): 51–54
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: 811–818
Chen J. Investigation on the computer simulation of boundary heat transfer process between solids at low temperature (in Chinese). Dissertation of Doctoral Degree. Wuhan: Huazhong University of Science and Technology, 2004
Shi L. Investigation of heat transport on the solid-solid contact interface at low temperature (in Chinese). Dissertation of Doctoral Degree. Wuhan: Huazhong University of Science and Technology, 2006
Han Y G, Xuan Y M, Tang R F. Heat transfer on the contact surfaces with frictional heating (in Chinese). J Nanjing Univ Sci Technol, 1998, 22(3): 260–263
Ying J. The evaluation of thermal contact resistance in heat transfer effect (in Chinese). J Zhejiang Univ, 1996, 30(4): 415-4–21
Ying J. The theoretical and experimental research of thermal contact resistance on roughness surface (in Chinese). J Zhejiang Univ (Sci Ed), 1997, 31(1): 104–109
Zhao H L, Huang Y M, Xu J L, et al. Experiment research on thermal contact resistance of normal used joints (in Chinese). J Xi’an Univ Technol, 1999, 15(3): 26–29
Zhu D C. Experiment research on solid interface thermal contact conductance coefficient (in Chinese). Dissertation of Master Degree. Dalian: Dalian University of Technology, 2007
Bahrami M, Culham J R, Yovanovich M M, et al. Thermal contact resistance of nonconforming rough surfaces. Part 1: Contact mechanics model. J Thermophys Heat Transf, 2004, 18(2): 209–217
Bahrami M, Culham J R, Yovanovich M M, et al. Thermal contact resistance of nonconforming rough surfaces. Part 2: Thermal model. J Thermophys Heat Transf, 2004, 18(2): 218–227
Carslaw H S, Jaeger J C. Conduction of Heat in Solids. 2nd ed. Oxford: Clarendon Press, 1959
Gibson R D. The contact resistance for a semi-infinite cylinder in a vacuum. Appi Energ, 1976, 2: 57–65
Yovanovich M M. Thermal constriction resistance of contacts on a half-space: Intergral formulation. In: Progress in Astronautics and Aeronautics: Radiative Transfer and Thermal Control. New York: AIAA, 1976. 397–418
Mikic B B, Rohsenow W M. Thermal Contact Resistance. Mech Eng RepDSP74542-41, MIT. 1966
Cooper M G, Mikic B B, Yovanovich M M. Thermal contact conductance. Int J Heat Mass Transf, 1969, 12: 279–300
Yovanovich M M. General thermal constriction resistance parameter for annular contacts on circular flux tubes. AIAA J, 1976, 14(6): 822–824
Negus K J, Yovanovich M M. Constriction resistance of circular flux tubes with mixed boundary conditions by linear superposition of Neumann solutions. ASME-84-HT-84, ASME. 1984
Mao Q G. The Evaluation and Measurement of Surface Roughness (in Chinese). Beijing: Mechanical Industry Press, 1991
Zhou Z R. Advancing of Tribology Development (in Chinese). Beijing: Science Press, 2006
Guo F Y, Chen Z H. The Theory and Application of Electric Contact (in Chinese). Beijing: China Electric Power Press, 2008
Clausing A M, Chao B T. Thermal contact conductance in a vacuum environment. Trans ASME J Heat Transf, 1965, 87: 243–251
Greenwood J A, Tripp J H. The elastic contact of rough spheres. J Appi Mech, 1967, 89(1): 153–159
Holm R. Electric Contacts: Theory and Applications. New York: Springer-Verlag, 1967
Yovanovich M M. Overall constriction resistance between contacting rough, wavy surfaces. Int J Heat Mass Transf, 1969, 12: 1517–1520
Bürde S S, Yovanovich M M. Thermal resistance at smooth sphere/rough flat contacts: Theoretical analysis. AIAA 78–871. 1978
Lambert M A. Thermal contact conductance of spherical rough surfaces. Dissertation of Doctoral Degree. Houston: Texas A & M University, 1995
Kumar S S, Ramamurthi K. Influence of flatness and waviness of rough surfaces on surface contact conductance. Trans ASME J Heat Transf, 2003, 125: 394–402
Greenwood J A, Wiliamson J B P. Contact of nominally flat surfaces. Proc Roy Soc A, 1966, 295: 300–319
Greenwood J A. The area of contact between rough surfaces and flats. J Lubricant Technol, 1967, 81: 81–91
Greenwood J A, Tripp J H. The contact of two nominally flat rough surfaces. Proc Inst Mech Eng, 1970, 185: 625–633
Mikic B B. Thermal contact conductance: Theoretical considerations. Int J Heat mass transfer, 1974, 17: 205–214
Bush A W, Gibson R D, Thomas T R. The elastic contact of rough surface. Wear, 1975, 35: 87–111
Sayles R S, Thomas T R. Thermal conductance of a rough elastic contact. J Appi Energ, 1976, 2: 249–267
McCool J I. Comparison of models for the contact of rough surfaces. Wear, 1986, 107: 37–60
Yovanovich M M. Thermal contact correlations. In: AIAA 16th Thermophysics Conference, Palo Alto, California, USA, 1981. 83–95
Sridhar M R, Yovanovich M M. Review of elastic and plastic contact conductance models: Comparison with experiment. J Thermophys HeatTransf, 1994, 8(4): 633–640
Polycarpou A A, Etsion I. Analytical approximations in modeling contacting rough surfaces. Trans ASME J Trihol, 1999, 121: 234–239
Greenwood J A, Wu J J. Surface roughness and contact: An apology. Meccanica, 2001, 36(6): 617–630
Sayles R S, Thomas T R. Surface topography as a nonstationary random process. Nature, 1978, 271(2): 431 434
Mandelbrot B B. Fractal, Form, Chance and Dimension. Freeman: Sanfacisco, 1977
Majumdar A, Bhushan B. Role of fractal geometry in roughness characterization and contact mechanics of surfaces. ASME J Trihol, 1990, 112(1): 205–216
Majumdar A, Bhushan B. Fractal model of elastic-plastic contact between rough surfaces. ASME J Tribol, 1991, 113(1): 1–11
Majumdar A, Tien C L. Fractal characterization and simulation of rough surface. Wear, 1990, 136: 313–324
Warren T L, Krajcinovic D. Fractal models of elastic-perfectly plastic contact of rough surfaces based on the Contor set. Int J Solid Struct, 1995, 32(19): 2907–2922
Warren T L, Krajcinovic D. Random cantor set models for the elastic-perfectly plastic contact of rough surfaces. Wear, 1996, 196: 1–15
Warren T L, Majumdar A, Krajcinovic D. A fractal model for the rigid-perfectly plastic contact of rough surfaces. Trans ASME J Appi Mech, 1996, 63: 47–54
Dubuc B, Tricot C, Zucker S W. Evaluating the fractal dimension of profiles. Phys Rev A, 1989, 39(3): 1500–1512
Hasegawa M, Liu J, Okuda K, et al. Calculation of the fractal dimensions of machined surface profiles. Wear, 1996, 192: 40–45
Ge S R, Suo S F. The method of calculation the fractal dimension of surface roughness profiles (in Chinese). Tribology, 1997, 17(4): 354–362
Wang A L, Yang C X. Wavelet transform method evaluate the fractal characterization of profiles (in Chinese). Chinese J Mech Eng, 2002, 38(5): 80–85
Wang A L, Yang C X. The calculation methods for the fractal characterization of surface topography (in Chinese). Chinese Mech Eng, 2002, 13(8): 714–718
Wang A L, Yang C X. Wavelet transform method evaluate the fractal characterization of profiles (in Chinese). Chinese J Mech Eng, 2002, 38(5): 80–85
Wang A L, Yang C X, Yuan X G. Evaluation of the wavelet transform method for machined surface topography II: Fractal characteristic analysis. Tribol Int, 2003, 36(7): 527–535
Wang A L, Yang C X, Yuan X G. Evaluation of the wavelet transform method for machined surface topography I: Methodology validation. Tribol Int, 2003, 36(7): 517–526
Ge S R, Zhu H. Fractal in Tribology (in Chinese). Beijing: China Machine Press, 2005
Chang W R, Etsion I, Bogy D B. An elastic-plastic model for the contact of rough surfaces. Trans ASME J Tribol, 1987, 109: 257–263
Zahouani H, Vargiolu R, Loubet J L. Fractal models of surface topography and contact mechanics. Math Comp Model, 1998, 28(4–8): 517–534
Blyth M G, Pozrikidis C. Heat conduction across irregular and fractal-like surfaces. Int J Heat Mass Transf, 2003, 46: 1329–1339
Zou M Q, Yu B M, Cai J C, et al. Fractal model for thermal contact conductance. J Heat Transf, 2008, 130: 101301
Ciavarella M, Dibello S, Demelio G. Conductance of rough random profiles. Int J Solid Struct, 2008, 45(3–4): 879–893
Wang A L, Wu Y T, Yang C X. The size distribution characteristic of cavities and active nucleation sites in pool boiling surface (in Chinese). J Eng Therm Energ Power, 2003, 18(3): 291–296
Li Y Z, Madhusudana C V, Leonardi E. Experimental investigation of thermal contact conductance: Variations of surface microhardness and roughness. Int J Thermophys, 1998, 19(6): 1691–1704
Singhal V, Garimella S V. Prediction of thermal contact conductance by surface deformation analysis. In: Proceedings of 2001 ASME International Mechanical Engineering Congress and Exposition, New York, USA, 2001. 43–50
Zhao J F, Wang A L, Yang C X. The statistical characteristic of roughness profiles on thermal contact conductance surface (in Chinese). Cryogenics, 2003, 134(4): 49–56
Zhao J F, Wang A L, Yang C X. A model of thermal contact conductance based on the statistic characteristic of roughness profile (in Chinese). J Eng Thermophys, 2004, 25(1): 145–147
Zhao J F, Wang A L, Yang C X. Prediction of thermal contact conductance based on the statistics of the roughness profile characteristics. Int J Heat Mass Transf, 2005, 48: 974–985
Patir N. A numerical procedure for random generation of rough surfaces. Wear, 1978, 47: 63–277
Waton W, Spedding T A. The time series modeling of non-Gaussian engineering processes. Wear, 1982, 83: 215–231
Whitehouse D J. The generation of two-dimensional random surfaces having a specified function. Ann CIRP, 1983, 32(1): 495–498
Newland D E. An Introduction to Random Vibration and Spectral Analysis. 2nd ed. London: Longman, 1984
Hu Y Z, Tonder K. Simulation of 3-D random rough surface by 2-D digital filter and Fourier analysis. Int J Mach Tools Manuf, 1992, 32: 83–99
Chilamankuri S K, Bhushan B. Contact analysis of non-Gaussian random surfaces. Proc Inst Mech Eng, 1998, 212: 19–32
Mihailidis A, Bakolas V. Numerical simulation of real 3-D rough surface. J Balk Tribol Assoc, 1999, 5: 247–231
Wu J J. Simulation of rough surface with FFT. Tribol Int, 2000, 33: 47–58
Bakolas V. Numerical generation of arbitrarily oriented non-Gaussian three-dimensional rough surfaces. Wear, 2003, 254: 546–554
Zhou X K, Zhou H, Li D L. Fractal Iconography (in Chinese). Beijing: Higher Education Press, 1995
McGaughey D, Atiken G J M. Generating two-dimensional Brownian motion using the fraction Gaussian process (FGP) algorithm. Physica A, 2002, 311: 369–380
Yovanovich M M. Thermal contact correlations. In: AIAA 16th Thermophysics Conference, Palo Alto, California, USA, 1981. 83–95
Hegazy A A. Thermal joint conductance of conforming rough surfaces: Effect of surface microhardness variation. Dissertation of Doctoral Degree. Waterloo: University of Waterloo, 1985
Liu J. Micro/Nano-Scale Heat Transfer (in Chinese). Beijing: Science Press, 2001
National Nature Science Foundation Council. Engineering Thermophysics and Energy Utilization (2006–2010)(in Chinese). Beijing: Science Press, 2007
Sridhar M R, Yovanovich M M. Elastoplastic contact conductance model for isotropic conforming rough surfaces and comparison with experiments. Trans AMSE J Heat Transf, 1996, 118: 3–9
Rostami A A, Hassan A Y, Lim P C. Parametric study of thermal constriction resistance. Heat Mass Transf, 2001, 37(1): 5–10
Trujillo D M, Pappoff C G. A general thermal contact resistance finite element. Finite Eiern Anal Des, 2002, 38: 263–276
Wahid SMS. Numerical analysis of heat flow in contact heat transfer. Int J Heat Mass Transf, 2003, 46: 4751–4754
Black A F, Singhal V, Garimella S V. Analysis and prediction of constriction resistance for contact between rough engineering surface. J Thermophys Heat Transf, 2004, 18(1): 30–36
Salti B, Laraqi N. 3-D numerical modeling of heat transfer between two sliding bodies: Temperature and thermal contact resistance. Int J Heat Mass Transf, 1999, 42: 2363–2374
Laraqi N. Thermal constriction resistance of coated solids-static and sliding contacts. Int Commun Heat Mass Transf, 1999, 26(3): 299–309
Laraqi N, Barri A. New models of thermal resistance at the interface of solids connected by random disk contacts. CR Mecanique, 2002, 330: 39–43
Laraqi N, Barri A. Theory of thermal resistance between solids with randomly sized and located contacts. Int J Heat Mass Transf, 2002, 45:4175–4180
Laraqi N. Change of scale effect in the phenomena of thermal multi-constriction. CR Mecanique, 2002, 330:141–145
Tomimura T, Matsuda Y, Zhang X, et al. Two-dimensional modeling of heat transfer between contacting metal surfaces with spherical waviness: Estimation of thermal contact conductance based on random numbers surface model. In: 5th International Symposium on Heat Transfer, Beijing, China, 2000. 137–142
Zhang X, Cong P, Fujiwara S, et al. A new method for numerical simulation of thermal contact resistance in cylindrical coordinates. Int J Heat Mass Transf, 2004, 47: 1091–1098
Zhang X, Cong P, Fujii M. A study on thermal contact resistance at the interface of two solids. Int J Thermophys, 2006, 27(3): 880–895
Touzellbaev M, Goodson K. Impact of nucleation density on the thermal resistance near diamond-substrate boundaries. J Thermophys Heat Transf, 1997, 11: 506–512
Prasher R S, Phelan P E. A scattering-mediated acoustic mismatch model for the prediction of thermal boundary resistance. J Heat Transf, 2001, 123: 105–112
Chen G. Ballistic-diffusive equations for transient heat conduction from nano to macroscales. J Heat Transf, 2002, 124: 320–328
Liang X G, Yue B. The interface roughness effect on the in-plane thermal conductivity in nanoscale (in Chinese). J Eng Thermophys, 2006, 27(3): 475: 4–77
Liao N, Yang P. Characterizations of interfacial heat transfer for electronic packages by multi-scale modeling. J Thermophys Heat Transf, 2008, 22(4): 581–586
Prasher R S, Phelan P E. Microscopic and macroscopic thermal contact resistances of pressed mechanical contacts. J Appi Phys, 2006, 100:063538
Zhong H, Lukes J R. Interfacial thermal resistance between carbon nanotubes: Molecular dynamics simulations and analytical thermal modeling. Phys Rev B, 2006, 74: 125403
Hu M, Shenogin S, Keblinski P. Molecular dynamics simulation of interfacial thermal conductance between silicon and amorphous polyethylene. Appi Phys Lett, 2007, 91: 241910
Termentzidis K, Chantrenne P, Keblinski P. Nonequilibrium molecular dynamics simulation of the in-plane thermal conductivity of superlattices with rough interfaces. Phys Rev B, 2009, 79: 214307
Landry E S, McGaughey A J H. Thermal boundary resistance predictions from molecular dynamics simulations and theoretical calculations. Phys Rev B, 2009, 80: 165304
Lyver J W, Blaisten-Barojas E. Effects of the interface between two Lennard-Jones crystals on the lattice vibrations: A molecular dynamics study. J Phys-Condens Mat, 2009, 21: 345402
Gu W L. The Semi-Empirical Correlation of Contact Heat Transfer Research and Other Problems (in Chinese). CSAA-99-006. 1999
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, A., Zhao, J. Review of prediction for thermal contact resistance. Sci. China Technol. Sci. 53, 1798–1808 (2010). https://doi.org/10.1007/s11431-009-3190-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-009-3190-6