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On some general imperfect interface models for conductivity problem

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Authors

  • Nguyen Trung Kien \(^1\) Research and Application Center for Technology in Civil Engineering, University of Transport and Communications, 3 Cau Giay street, Dong Da district, Hanoi, Vietnam https://orcid.org/0000-0003-4342-9125
  • Nguyen Hoang Quan \(^2\) Construction Engineering Faculty, University of Transport and Communications, 3 Cau Giay street, Dong Da district, Hanoi, Vietnam https://orcid.org/0000-0003-2348-4063

DOI:

https://doi.org/10.15625/0866-7136/22333

Keywords:

general imperfect interface, interface parameters, effective conductivity

Abstract

Three general imperfect interface models for thermal conduction are presented. The discontinuity of the microscopic field is described through the interface parameters: one characterizes the temperature jump, and another controls the heat flux jump. These models include the highly and lowly conducting ones as particular cases. The effective conductivity of composite materials with imperfect interfaces is derived from several effective medium approximations. Unlike the perfect interface, the effective conductivity of a composite containing imperfectly bonded inclusions depends on the size of the particles. The results for these models are illustrated by numerical calculations. Some discussions are also presented.

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References

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[2] S.-T. Gu, A.-L. Wang, Y. Xu, and Q.-C. He. Closed form estimates for the effective conductivity of isotropic composites with spherical particles and general imperfect interfaces. International Journal of Heat and Mass Transfer, 83, (2015), pp. 317–326. https://doi.org/10.1016/j.ijheatmasstransfer.2014.12.005.

[3] H. Le Quang. Estimations and bounds of the effective conductivity of composites with anisotropic inclusions and general imperfect interfaces. International Journal of Heat and Mass Transfer, 99, (2016), pp. 327–343. https://doi.org/10.1016/j.ijheatmasstransfer.2016.03.116.

[4] D.-C. Pham and T.-K. Nguyen. General imperfect interface model for spherical-circular inclusion composites. Acta Mechanica, 235, (2024), pp. 2211–2229. https://doi.org/10.1007/s00707-023-03820-y.

[5] Y. Benveniste. A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media. Journal of the Mechanics and Physics of Solids, 54, (2006), pp. 708–734. https://doi.org/10.1016/j.jmps.2005.10.009. Corrigendum: Journal of the Mechanics and Physics of Solids, 55, 666–667 (2007).

[6] 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.

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Published

07-05-2025

How to Cite

Kien, N. T., & Quan, N. H. (2025). On some general imperfect interface models for conductivity problem. Vietnam Journal of Mechanics. https://doi.org/10.15625/0866-7136/22333

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