Effective conductivity of isotropic composite with Kapitza thermal resistance

Nguyen Trung Kien, Nguyen Van Luat, Pham Duc Chinh


A simple method is introduced for computing the effective conductivity of isotropic composite with imperfect interface. Based on the doubly-coated circle assemblage model, one can determine the effective thermal conductivity of the composite. The application of this model to the composite with imperfect interface of the Kapitza's type is proposed. The results obtained were compared with the Fast Fourier Transform simulation and the equivalent inclusion approximation in 2D show the effectiveness of the methods.


effective conductivity; imperfect interface; Kapitza thermal resistance

Full Text:



P. L. Kapitza. The study of heat transfer in helium II. J. Phys. (USSR), 4, (1941), pp. 181–210.

H. Hatta and M. Taya. Thermal conductivity of coated filler composites. Journal of Applied Physics, 59, (6), (1986), pp. 1851–1860. https://doi.org/10.1063/1.336412.

Y. Benveniste and T. Miloh. The effective conductivity of composites with imperfect thermal contact at constituent interfaces. International Journal of Engineering Science, 24, (9), (1986), pp. 1537–1552. https://doi.org/10.1016/0020-7225(86)90162-x.

D. P. H. Hasselman and L. F. Johnson. Effective thermal conductivity of composites with interfacial thermal barrier resistance. Journal of Composite Materials, 21, (6), (1987), pp. 508–515. https://doi.org/10.1177/002199838702100602.

M. L. Dunn and M. Taya. The effective thermal conductivity of composites with coated reinforcement and the application to imperfect interfaces. Journal of Applied Physics, 73, (4), (1993), pp. 1711–1722. https://doi.org/10.1063/1.353206.

S. Torquato and M. D. Rintoul. Effect of the interface on the properties of composite media. Physical Review Letters, 75, (22), (1995), p. 4067. https://doi.org/10.1103/physrevlett.76.3241.

Z. Hashin and S. Shtrikman. A variational approach to the theory of the effective magnetic permeability of multiphase materials. Journal of Applied Physics, 33, (10), (1962), pp. 3125–3131. https://doi.org/10.1063/1.1728579.

D. C. Pham, L. D. Vu, and V. L. Nguyen. Bounds on the ranges of the conductive and elastic properties of randomly inhomogeneous materials. Philosophical Magazine, 93, (18), (2013), pp. 2229–2249. https://doi.org/10.1080/14786435.2013.765992.

T. K. Nguyen, V. L. Nguyen, and D. C. Pham. Estimating effective conductivity of unidirectional transversely isotropic composites. Vietnam Journal of Mechanics, 35, (3), (2013), pp. 203–213. https://doi.org/10.15625/0866-7136/35/3/2767.

D. C. Pham. Bounds on the effective conductivity of statistically isotropic multicomponent materials and random cell polycrystals. Journal of the Mechanics and Physics of Solids, 59, (3), (2011), pp. 497–510. https://doi.org/10.1016/j.jmps.2011.01.006.

D. C. Pham. Solutions for the conductivity of multi-coated spheres and spherically symmetric inclusion problems. Zeitschrift für angewandte Mathematik und Physik, 69, (2018). https://doi.org/10.1007/s00033-017-0905-6.

H. Le Quang, D. C. Pham, G. Bonnet, and Q.-C. He. Estimations of the effective conductivity of anisotropic multiphase composites with imperfect interfaces. International Journal of Heat and Mass Transfer, 58, (1-2), (2013), pp. 175–187. https://doi.org/10.1016/j.ijheatmasstransfer.2012.11.028.

Z. Hashin. Thin interphase/imperfect interface in conduction. Journal of Applied Physics, 89, (4), (2001), pp. 2261–2267. https://doi.org/10.1063/1.1337936.

V. L. Nguyen and T. K. Nguyen. FFT simulations and multi-coated inclusion model for macroscopic conductivity of 2D suspensions of compound inclusions. Vietnam Journal of Mechanics, 37, (3), (2015), pp. 169–176. https://doi.org/10.15625/0866-7136/37/3/5096.

V. Monchiet. FFT based iterative schemes for composites conductors with non-overlapping fibers and Kapitza interface resistance. International Journal of Solids and Structures, 135, (2018), pp. 14–25. https://doi.org/10.1016/j.ijsolstr.2017.10.015.

DOI: https://doi.org/10.15625/0866-7136/12936


  • There are currently no refbacks.

Copyright (c) 2018 Vietnam Academy of Science and Technology



Editorial Office of Vietnam Journal of Mechanics

3rd Floor, A16 Building, 18B Hoang Quoc Viet Street, Cau Giay District, Hanoi, Vietnam

Tel: (+84) 24 3791 7103

Email: vjmech@vjs.ac.vn