Advances in Materials

| Peer-Reviewed |

Validations of a Model to Estimate Thermal Conductivities of Ceramics

Received: 06 September 2016    Accepted: 18 September 2016    Published: 11 October 2016
Views:       Downloads:

Share This Article

Abstract

The Effective Medium Theory Model (EMTM) used in this work is based on the assumption that every phase of the matrix is embedded in a homogeneous medium with conductivity keff to be determined self-consistently. It is based on dilute spherical inclusions of one phase embedded in a matrix of a second phase. Several Samples of composite ceramics that are mechanically strong, relatively non-porous and anisotropic have been investigated. A comparison between the measured data and the results predicted by EMTM were made to validate the model for these ceramic samples. In particular, we investigate the effect of mineralogy (constituents) in ceramics and their spatial distribution profile to validate the homogeneity conditions of the model. Preliminary indicators of validation were used to check the bulk and surface homogeneities. This can be done either by roughly estimating Wiener bounds or by examining microscopically the surfaces of the samples. It turns out that the EMTM is a suitable one to estimate keff provided that the homogeneity conditions are satisfied.

DOI 10.11648/j.am.20160505.13
Published in Advances in Materials (Volume 5, Issue 5, October 2016)
Page(s) 44-50
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Thermal Conductivity, Effective Medium Theory, Ceramics, Composites

References
[1] M. Zhang, P. C. Zhai, Y. Li, J. T. Zhang, Q. J. Zhang, “Effective Thermal Conductivity of Particulate Composites with Different Particle Configurations” AIP Conf. Proc. 973, 2008, p141.
[2] S.-Y. Zhao, B.-M. Zhang, X.-D. He, “Temperature and pressure dependent effective thermal conductivity of fibrous insulation Int. J. Therm. Sci. 48(2), 2009, p 440.
[3] L. Chaffron, C. Sauder, C. Lorrette, L. Briottet, A. Michaux, L. Gélébart, A. Coupé, M. Zabiego, M. Le Flem, And J.-L. Séran, “Innovative SiC/SiC Composite for Nuclear Applications” EPJ Web of Conferences 51, 2013, 01003.
[4] F. Brigaud, D. S. Chapman, S. Le Douaran, “Estimating thermal conductivity in sedimentary basins using lithologic ...” AAPG Bull. 74, 1990, P1459.
[5] A. Correia, F. W. Jones, A. Fricker, “Terrestrial heat‐flow density estimates for the Jeanne D’Arc Basin, offshore eastern Canada” Geophysics 55, 1990, P 1625.
[6] S. Suresh & A. Mortensen, “Fundamentals of Functionally Graded Materials”IOM Communication” Ltd., London. 1998.
[7] Y. Xu & K. Yagi “Automatic FEM model generation for evaluating thermal conductivity of composite with random materials arrangement” Comput. Mater. Sci. 30 2004, P242–252.
[8] S.J. Zinkle & L.L. Snead “Thermophysical and Mechanical Properties of SiC/SiC” Composites an upcoming version of the fusion Materials Properties Handbook (MPH) J.W. Davis ed. (Boeing, St. Louis). Oak Ridge National Laboratory, 1999.
[9] O.Wiener,” Abhandlungen der Mathematish-Physischen Klasse der K6niglichen Sachsischen Gesellschaft der Wissenschaften”, Leipzig, 1912, p. 509.
[10] B. M Suleiman1, S. E. Gustafsson1, E. Karawacki1, R. Glamheden' and U. Lindblom', “Effective Thermal Conductivity of Amulti-Phase Sys'iem” Journal of thermal Analysis, Vol. 51, 1998.
[11] (a) M. Koizumi “The concept of FGM, in: J. B. Holt, M. Koizumi, T. Hirai, Z. A. Munir (Eds.),” Ceramic Transactions, Functionally Graded Materials”, vol. 34, The American Ceramic Society, 1993.
[12] (b) M. Koizumi, M. Niino, Overview of FGM Research in Japan, MRS Bulletin, 1 1995, p 19-21.
[13] X.-Q, Fang J-X LIU & T. Zhang “Dynamic effective thermal properties of functionally graded. fibrous composites using non-Fourier heat conduction Computational” Journal of Composite Materials Vol. 43, No. 21, 2009, P2351-2369.
[14] Gray L. J., Kaplan T. & Richardson J. D., Paulino G. H., and Mem. ASME “Green’s Functions and Boundary Integral Analysis for Exponentially Graded Materials: Heat Conduction” J. Appl. Mech. 70 2003,-P543.
[15] Kuo H.-Y. & Chen T. “Steady and transient Green's functions for anisotropic conduction in an exponentially graded solid”. Int. J. Solids Struct. 42: 2005, P1111–1128.
[16] Cahill D. G., Braun Paul V., Chen G., Clarke D. R., Fan S., Goodson K. E., Keblinski P., King W. P., Mahan G. D., Majumdar A., Maris H. J., Phillpot S. R., Pop E., and Shi Li,” Nanoscale thermal transport II” Applied Physics Reviews 1, 2014, 011305.
[17] J. C.Maxwell (1892), A Treatise on Electricity and Magnetism, third ed., vol. 1, Dover, NewYork. Oxford: Clarendon 1954, p 435-41.
[18] Rayleigh, L. On the influence of obstacles arranged in rectangular order upon the properties of the medium. Philosophical Magazines 34 481-502, 1892.
[19] D. Polder & J H Van Santen” The effective permeability of mixtures of solids “Physica 12 257-71, 1946.
[20] A. Baldan, “Progress in Ostwald Ripening Theories and Their Applications to Nickel-Base.” Journal of Materials Science 37 2002, p2171-2202.
[21] J. A. Reynolds & J. M. Hough “Formulae for Dielectric Constant of Mixtures” Proc. Phys. Soc. B 70, 1957, P769-75.
[22] R. L. Hamilton & O. K. Crosser, “Thermal Conductivity of Heterogeneous Two-Component Systems” Ind. Eng. Chem. Fundamen., 1 (3), 1962, pp 187–191.
[23] A 
Rocha & A Acrivos “Experiments on the Effective Conductivity of Dilute Dispersions Containing Highly Conducting Slender Inclusions” Proc. R. Soc. A 337, 1974, P123-33.
[24] R. McPhedran & D. McKenzie “The conductivity of lattices of spheres. in the simple cubic lattice” Proceeding of the Royal Society of London: A 359 1978, P45–63.
[25] .A. Sangani & A. Acrivos “Effective Conductivity Of A Periodic Array of Spheres” Proceeding of the Royal Society of London: A 386 1983, P263–275.
[26] Z. Hashin “Assessment of the self-consistent scheme approximation: conductivity of particulate composites” Journal of Composite Materials 2 1968, 284–300,
[27] Y. Benveniste & T. Miloh” On the effective thermal-conductivity of coated short-fiber composites.” Journal of Applied Physics 69, 1991, 1337–1344.
[28] J.D. Felske “Effective thermal conductivity of composite spheres in a continuous medium with contact resistance, Int. Heat Mass Transfer 47 2004, p 3453–3461.
[29] P. K. Samantray, P. Karthikeyan & K. S Reddy. “Estimating effective thermal conductivity of two-phase materials.” International Journal of Heat and Mass Transfer 49, 2006, P 4209–4219.
[30] Jinzao Xu, Benzheng Gao, Hongda Du, Feiyu Kang “A statistical model for effective thermal conductivity of composite materials” International Journal of Thermal Sci., 104, 2016, P 348–356.
[31] T W Noh, P H Song & A J Sievers “Self-consistency conditions for the effective-medium approximation in composite materials: Phys. Rev. B 44 1991, P 123-165.
[32] G. W. Milton, “The coherent potential approximation is a realizable effective medium scheme” Commun. Math. Phys., 99 1985, P463.
[33] L. Tan, “Multiple Length and Time-scale Approaches in Materials Modeling”, Advances in Materials Volume 6, Issue 1-1, (2017), P 1-9.
[34] S.Tang, B. Zhu, M. Jia, Q. He, S. Sun, Y. Mei, and L. Zhou, “Effective-medium theory for one-dimensional gratings” Phys. Rev. B 91, 2015, P174201.
[35] J.-B. Vaney, A. Piarristeguyb, V. Ohorodniichucka, O. Ferry, A. Pradel, E. Alleno, J. Monnier, E. B. Lopes, A. P. Gonçalves, G. Delaizir, C. Candolfi, A. Dauschera and B. Lenoira “Effective medium theory based modeling of the thermoelectric properties of composites: comparison between predictions and experiments in the glass–crystal composite system Si10As15Te75–Bi0.4Sb1.6Te3”, J. Mater. Chem. C, 3, 2015, P11090-11098.
[36] T H. Jordan, “An effective medium theory for three-dimensional elastic heterogeneities” Geophysical Journal International Volume 203, Issue 2, 2015, P. 1343-1354.
[37] M. Siddiqui and A. M. Arif, “Generalized Effective Medium Theory for Particulate Nanocomposite Materials”, Materials, 9, 2016, P694.
[38] http://www.compositesworld.com/articles/composites-2016-materials-and-processes.
[39] G. Angenheister (ed.), Landolt-Börnstein, Numerical Data and Functional Relationships in Science and Technology, vol. 1/a (Springer, Berlin, 1982, p. 311.
[40] B. M. Suleiman, “Effective Thermal Conduction in Composite Materials” Applied Physics A, Material Sciences & Processing, 2010, 99 P223–228.
Author Information
  • Department of Applied Physics and Astronomy, College of Sciences, University of Sharjah, Sharjah, United Arab Emirates

Cite This Article
  • APA Style

    Bashir M. Suleiman. (2016). Validations of a Model to Estimate Thermal Conductivities of Ceramics. Advances in Materials, 5(5), 44-50. https://doi.org/10.11648/j.am.20160505.13

    Copy | Download

    ACS Style

    Bashir M. Suleiman. Validations of a Model to Estimate Thermal Conductivities of Ceramics. Adv. Mater. 2016, 5(5), 44-50. doi: 10.11648/j.am.20160505.13

    Copy | Download

    AMA Style

    Bashir M. Suleiman. Validations of a Model to Estimate Thermal Conductivities of Ceramics. Adv Mater. 2016;5(5):44-50. doi: 10.11648/j.am.20160505.13

    Copy | Download

  • @article{10.11648/j.am.20160505.13,
      author = {Bashir M. Suleiman},
      title = {Validations of a Model to Estimate Thermal Conductivities of Ceramics},
      journal = {Advances in Materials},
      volume = {5},
      number = {5},
      pages = {44-50},
      doi = {10.11648/j.am.20160505.13},
      url = {https://doi.org/10.11648/j.am.20160505.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.am.20160505.13},
      abstract = {The Effective Medium Theory Model (EMTM) used in this work is based on the assumption that every phase of the matrix is embedded in a homogeneous medium with conductivity keff to be determined self-consistently. It is based on dilute spherical inclusions of one phase embedded in a matrix of a second phase. Several Samples of composite ceramics that are mechanically strong, relatively non-porous and anisotropic have been investigated. A comparison between the measured data and the results predicted by EMTM were made to validate the model for these ceramic samples. In particular, we investigate the effect of mineralogy (constituents) in ceramics and their spatial distribution profile to validate the homogeneity conditions of the model. Preliminary indicators of validation were used to check the bulk and surface homogeneities. This can be done either by roughly estimating Wiener bounds or by examining microscopically the surfaces of the samples. It turns out that the EMTM is a suitable one to estimate keff provided that the homogeneity conditions are satisfied.},
     year = {2016}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Validations of a Model to Estimate Thermal Conductivities of Ceramics
    AU  - Bashir M. Suleiman
    Y1  - 2016/10/11
    PY  - 2016
    N1  - https://doi.org/10.11648/j.am.20160505.13
    DO  - 10.11648/j.am.20160505.13
    T2  - Advances in Materials
    JF  - Advances in Materials
    JO  - Advances in Materials
    SP  - 44
    EP  - 50
    PB  - Science Publishing Group
    SN  - 2327-252X
    UR  - https://doi.org/10.11648/j.am.20160505.13
    AB  - The Effective Medium Theory Model (EMTM) used in this work is based on the assumption that every phase of the matrix is embedded in a homogeneous medium with conductivity keff to be determined self-consistently. It is based on dilute spherical inclusions of one phase embedded in a matrix of a second phase. Several Samples of composite ceramics that are mechanically strong, relatively non-porous and anisotropic have been investigated. A comparison between the measured data and the results predicted by EMTM were made to validate the model for these ceramic samples. In particular, we investigate the effect of mineralogy (constituents) in ceramics and their spatial distribution profile to validate the homogeneity conditions of the model. Preliminary indicators of validation were used to check the bulk and surface homogeneities. This can be done either by roughly estimating Wiener bounds or by examining microscopically the surfaces of the samples. It turns out that the EMTM is a suitable one to estimate keff provided that the homogeneity conditions are satisfied.
    VL  - 5
    IS  - 5
    ER  - 

    Copy | Download

  • Sections