A review of models for effective thermal conductivity of composite materials

The solutions of Maxwell and Rayleigh were the first of many attempts to determine the eective thermal conductivity of heterogeneous material. Early models assumed that no thermal resistance exists between the phases in heterogeneous material. Later studies on solid-liquid and solid-solid boundaries revealed that a temperature drop occurs when heat flows through a boundary between two phases and, as a consequence, the interfacial thermal resistance should be included in the heat transfer model. This paper is a review of the most popular expressions for predicting the eective thermal conductivity of composite materials using the properties and volume fractions of constituent phases. Subject to review were empirical, analytical and numerical models, among others.

[1]  J. Maxwell.  A Treatise on Electricity and Magnetism , 1873, Nature.

[2]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[3]  L. Rayleigh,et al.  LVI. On the influence of obstacles arranged in rectangular order upon the properties of a medium , 1892 .

[4]  A. Eucken.  Die Wärmeleitfähigkeit keramischer feuerfester Stoffe : ihre Berechnung aus der Wärmeleitfähigkeit der Bestandteile , 1932 .

[5]  D. A. G. Bruggeman.  Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen , 1935 .

[6]  Rolf Landauer,et al.  The Electrical Resistance of Binary Metallic Mixtures , 1952 .

[7]  O. K. Crosser,et al.  Thermal Conductivity of Heterogeneous Two-Component Systems , 1962 .

[8]  P. L. Kapitza,et al.  THE STUDY OF HEAT TRANSFER IN HELIUM II , 1971 .

[9]  L. Nielsen.  The Thermal and Electrical Conductivity of Two-Phase Systems , 1974 .

[10]  O. Hunderi,et al.  Optical properties of Ag-SiO 2 Cermet films: A comparison of effective-medium theories , 1978 .

[11]  O. Hunderi,et al.  Conductivity of inhomogeneous materials: Effective-medium theory with dipole-dipole interaction , 1978 .

[12]  D. Hasselman,et al.  Effect of Thermal Expansion Mismatch on the Thermal Diffusivity of Glass‐Ni Composites , 1980 .

[13]  Touvia Miloh,et al.  The effective conductivity of composites with imperfect thermal contact at constituent interfaces , 1986 .

[14]  R. Pohl,et al.  Thermal Boundary Resistance from 0.5–300K , 1986 .

[15]  Y. Benveniste,et al.  Effective thermal conductivity of composites with a thermal contact resistance between the constituents: Nondilute case , 1987 .

[16]  D. Hasselman,et al.  Effective Thermal Conductivity of Composites with Interfacial Thermal Barrier Resistance , 1987 .

[17]  N. J. A. Sloane,et al.  Sphere Packings, Lattices and Groups , 1987, Grundlehren der mathematischen Wissenschaften.

[18]  T. Miloh,et al.  An exact solution for the effective thermal conductivity of cracked bodies with oriented elliptical cracks , 1989 .

[19]  M. Tanaka,et al.  Thermal conductivity of a polymer filled with particles in the wide range from low to super‐high volume content , 1990 .

[20]  Tungyang Chen,et al.  The effective thermal conductivity of composites reinforced by coated cylindrically orthotropic fibers , 1990 .

[21]  T. Miloh,et al.  On the effective thermal conductivity of coated short‐fiber composites , 1991 .

[22]  Rishi Raj,et al.  The effect of particle size on the thermal conductivity of ZnS/diamond composites , 1992 .

[23]  Martin L. Dunn,et al.  The effective thermal conductivity of composites with coated reinforcement and the application to imperfect interfaces , 1993 .

[24]  D. Hasselman,et al.  Effective Thermal Conductivity of Uniaxial Composite with Cylindrically Orthotropic Carbon Fibers and Interfacial Thermal Barrier , 1993 .

[25]  B. E. Artz,et al.  Thermal conductivity of metal‐matrix composites , 1995 .

[26]  A. Hunt,et al.  Geometric Structure and Thermal Conductivity of Porous Medium Silica Aerogel , 1995 .

[27]  Jian Song,et al.  Effective conductivity of composites with spherical inclusions: Effect of coating and detachment , 1996 .

[28]  C. Nan,et al.  Effective thermal conductivity of particulate composites with interfacial thermal resistance , 1997 .

[29]  Thomas C. Hales.  Sphere packings, I , 1997, Discret. Comput. Geom..

[30]  Patrick E. Phelan,et al.  Percolation theory applied to the analysis of thermal interface materials in flip-chip technology , 2000, ITHERM 2000. The Seventh Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (Cat. No.00CH37069).

[31]  Patrick E. Phelan,et al.  SIZE EFFECTS ON THE THERMAL CONDUCTIVITY OF POLYMERS LADEN WITH HIGHLY CONDUCTIVE FILLER PARTICLES , 2001, Proceeding of Heat Transfer and Transport Phenomena in Microscale.

[32]  Patrick E. Phelan,et al.  A Scattering-Mediated Acoustic Mismatch Model for the Prediction of Thermal Boundary Resistance , 2001 .

[33]  M. Monde,et al.  A new estimation method of thermal diffusivity using analytical inverse solution for one-dimensional heat conduction , 2001 .

[34]  S. Kim,et al.  Determination of mesopore size of aerogels from thermal conductivity measurements , 2002 .

[35]  A. Sánchez-Lavega,et al.  On the effective thermal diffusivity of fiber-reinforced composites , 2002 .

[36]  A. Bejan,et al.  Heat transfer handbook , 2003 .

[37]  R. Prasher,et al.  An Effective Unit Cell Approach to Compute the Thermal Conductivity of Composites With Cylindrical Particles , 2003 .

[38]  Q. Xue.  A percolation model of metal–insulator composites , 2003 .

[39]  J. D. Felske,et al.  EFFECTIVE THERMAL CONDUCTIVITY OF COMPOSITE SPHERES IN A CONTINUOUS MEDIUM WITH CONTACT RESISTANCE , 2004 .

[40]  V. S. Vaidhyanathan,et al.  Transport phenomena , 2005, Experientia.

[41]  Koichi Yagi,et al.  Development of an Internet System for Composite Design and Thermophysical Property Prediction , 2006 .

[42]  J. Molina,et al.  Assessing predictive schemes for thermal conductivity against diamond-reinforced silver matrix composites at intermediate phase contrast , 2007 .

[43]  H. Böhm,et al.  Effect of diamond shapes and associated thermal boundary resistance on thermal conductivity of diamond-based composites , 2007 .

[44]  A. Strachan,et al.  Phonon thermal conductivity in nanolaminated composite metals via molecular dynamics. , 2007, The Journal of chemical physics.

[45]  C. Matt,et al.  Effective Thermal Conductivity of Composite Materials with 3-D Microstructures and Interfacial Thermal Resistance , 2007 .

[46]  X. Fang.  Non-steady effective thermal conductivity of matrix composite materials with high volume concentration of particles , 2008 .

[47]  C. Toulemonde,et al.  Numerical modelling of the effective conductivities of composites with arbitrarily shaped inclusions and highly conducting interface , 2008 .

[48]  X. Fang,et al.  Scattering of thermal waves and non-steady effective thermal conductivity of composites with coated fibers , 2008 .

[49]  Prediction of Material Properties of Nanostructured Polymer Composites Using Atomistic Simulations , 2009 .

[50]  Xue-Qian Fang,et al.  Scattering of thermal waves and non-steady effective thermal conductivity of composites with coated particles , 2009 .

[51]  Xiaopeng Huang,et al.  Thermal transport in Si/Ge nanocomposites , 2009 .

[52]  Jinxi Liu,et al.  Scattering of Thermal Waves and Unsteady Effective Thermal Conductivity of Particular Composites with Functionally Graded Interface , 2009 .

[53]  Guoliang Tao,et al.  A Percolation Model of Thermal Conductivity for Filled Polymer Composites , 2010 .

[54]  Johan Liu,et al.  Modeling of the effective thermal conductivity of composite materials with FEM based on resistor networks approach , 2010 .

[55]  A. Satapathy,et al.  A computational and experimental investigation on thermal conductivity of particle reinforced epoxy composites , 2010 .

[56]  Structure, thermal, and mechanical properties of interfaces in PMC: A molecular simulation study , 2011 .

[57]  Xiao-dong Wang,et al.  Effects of non-ideal structures and high temperatures on the insulation properties of aerogel-based composite materials , 2011 .

[58]  Xiao-dong Wang,et al.  A 3-D numerical heat transfer model for silica aerogels based on the porous secondary nanoparticle aggregate structure , 2012 .

[59]  J. J. Alvarado-Gil,et al.  A model for the effective thermal conductivity of metal-nonmetal particulate composites , 2012 .

[60]  Jun-Jie Zhao,et al.  Effects of solid–gas coupling and pore and particle microstructures on the effective gaseous thermal conductivity in aerogels , 2012, Journal of Nanoparticle Research.

[61]  Xiao-dong Wang,et al.  Experimental and analytical analyses of the thermal conductivities and high-temperature characteristics of silica aerogels based on microstructures , 2013 .