Effect of Geometry of Filler Particles on the Effective Thermal Conductivity of Two-Phase Systems

Affiliation(s)

Department of Physics, Heat Transfer Laboratory, University of Rajasthan, Jaipur, India.

Department of Physics, Heat Transfer Laboratory, University of Rajasthan, Jaipur, India.

ABSTRACT

The present paper deals with the effect of geometry of filler particles on the effective thermal conductivity for polymer composites. In the earlier models, less emphasis has been given on the shape of filler particles. In this paper, expressions for effective thermal conductivity has been derived using the law of minimal thermal resistance and equal law of the specific equivalent thermal conductivity for three different shapes i.e. spherical, elliptical and hexagonal of filler particles respectively. Calculated values of effective thermal conductivity for various samples using the derived expressions then compared with experimental data available and other models developed in the literature. The results calculated are in good agreement with the earlier experimental data and the deviation, is least in our expressions showing the success of the model.

The present paper deals with the effect of geometry of filler particles on the effective thermal conductivity for polymer composites. In the earlier models, less emphasis has been given on the shape of filler particles. In this paper, expressions for effective thermal conductivity has been derived using the law of minimal thermal resistance and equal law of the specific equivalent thermal conductivity for three different shapes i.e. spherical, elliptical and hexagonal of filler particles respectively. Calculated values of effective thermal conductivity for various samples using the derived expressions then compared with experimental data available and other models developed in the literature. The results calculated are in good agreement with the earlier experimental data and the deviation, is least in our expressions showing the success of the model.

KEYWORDS

Effective Thermal Conductivity; Polymer Composites; Minimal Thermal Resistance; Shape of Filler

Effective Thermal Conductivity; Polymer Composites; Minimal Thermal Resistance; Shape of Filler

Cite this paper

nullD. Chauhan, N. Singhvi and R. Singh, "Effect of Geometry of Filler Particles on the Effective Thermal Conductivity of Two-Phase Systems,"*International Journal of Modern Nonlinear Theory and Application*, Vol. 1 No. 2, 2012, pp. 40-46. doi: 10.4236/ijmnta.2012.12005.

nullD. Chauhan, N. Singhvi and R. Singh, "Effect of Geometry of Filler Particles on the Effective Thermal Conductivity of Two-Phase Systems,"

References

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[3] H. Tavman, “Thermal and Mechanical Properties of Copper Powder Filled Poly (Ethylene) Composites,” Powder Technology, Vol. 91, No. 1, 1997, pp. 63-67. doi:10.1016/S0032-5910(96)03247-0

[4] A. Boudenne, L. Ibos, E. Gehin, M. Fois and J. C. Majeste, “Anomalous Behavior of Thermal Conductivity and Diffusivity in Polymeric Materials Filled with Metallic Particles,” Journal of Material Science, Vol. 40, No. 16, 2005, pp. 4163-4167. doi:10.1007/s10853-005-3818-2

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[10] J. Z. Liang and G. S. Liu, “A New Heat Transfer Model of Inorganic Particulate-Filled Polymercomposites,” Journal of Material Science, Vol. 44, No. 17, 2009, pp. 47154720. doi:10.1007/s10853-009-3729-8

[11] J. Z. Liang and F. H. Li, “Measurement of Thermal Conductivity of Hollow Glass-Bead-Filled Polypropylene Composites,” Polymer Testing, Vol. 25, No. 4, 2006, pp. 527531. doi:10.1016/j.polymertesting.2006.02.007

[12] H. S. Tekce, D. Kumlutas and I. H. Tavman, “Effect of Particle Shape on Thermal Conductivity of Copper Reinforced Polymer Composites,” Journal of Reinforced Plastics and Composites, Vol. 26, No. 1, 2007, pp. 113-121. doi:10.1177/0731684407072522

[13] L. E. Nielson, “Thermal Conductivity of Particulate-Filled Polymers,” Journal of Applied Polymer Science, Vol. 17, No. 12, 1973, pp. 3819-3820. doi:10.1002/app.1973.070171224

[14] S. Cheng and R. Vachon, “A Technique for Predicting the Thermal Conductivity of Suspensions, Emulsions and Porous Materials,” International Journal of Heat Mass Transfer, Vol. 13, No. 3, 1970, pp. 537-546. doi:10.1016/0017-9310(70)90149-3

[15] Y. Agari, A. Ueda and S. Nagai, “Thermal Conductivity of a Polymer Composite,” Journal of Applied Polymer Science, Vol. 49, No. 9, 1993, pp. 1625-1634. doi:10.1002/app.1993.070490914

[16] J. Z. Liang and F. H. Li, “Simulation of Heat Transfer in Hollow GlassBead-Filled Polypropylene Composites by Finite Element Method,” Polymer Testing, Vol. 26, No. 3, 2007, pp. 419-424. doi:10.1016/j.polymertesting.2006.12.014

[17] T. B. Lewis and L. E. Nielson, “Dynamic Mechanical Properties of Particulate-Filled Composites,” Journal of Applied Polymer Science, Vol. 14, No. 6, 1970, pp. 14491471. doi:10.1002/app.1970.070140604

[1] C. P. Wong and R. S. Bollampally, “Thermal Conductivity, Elastic Modulus, and Coefficient of Thermal Expansion of Polymer Composites Filled with Ceramic Particles for Electronic Packaging,” Journal of Applied Polymer Science, Vol. 74, No. 14, pp. 3396-3403. doi:10.1002/(SICI)1097-4628(19991227)74:14<3396::AID-APP13>3.0.CO;2-3

[2] X. Lu and G. Xu, “Thermally Conductive Polymer Composites for Electronic Packaging,” Journal of Applied Polymer Science, Vol. 65, No. 13, 1997, pp. 2733-2738. doi:10.1002/(SICI)1097-4628(19970926)65:13<2733::AID-APP15>3.0.CO;2-Y

[3] H. Tavman, “Thermal and Mechanical Properties of Copper Powder Filled Poly (Ethylene) Composites,” Powder Technology, Vol. 91, No. 1, 1997, pp. 63-67. doi:10.1016/S0032-5910(96)03247-0

[4] A. Boudenne, L. Ibos, E. Gehin, M. Fois and J. C. Majeste, “Anomalous Behavior of Thermal Conductivity and Diffusivity in Polymeric Materials Filled with Metallic Particles,” Journal of Material Science, Vol. 40, No. 16, 2005, pp. 4163-4167. doi:10.1007/s10853-005-3818-2

[5] N. M. Sofian, M. Rusu, R. Neagu and E. Neagu, “Metal Powder-Filled Polyethylene Composites. V. Thermal Properties,” Journal of Thermoplastic Composite Materials, Vol. 14, No. 1, 2001, pp. 20-33. doi:10.1106/9N6K-VKH1-MHYX-FBC4

[6] B. Weidenfeller, M. Hofer and F. R. Schilling, “Thermal Conductivity, Thermal Diffusivity, and Specific Heat Capacity of Particle Filled Polypropylene,” Composites Part A: Applied Science and Manufacturing, Vol. 35, No. 4, 2004, pp. 423-429. doi:10.1016/j.compositesa.2003.11.005

[7] J. C. Maxwell, “A Treatise on Electricity and Magnetism,” 3rd Edition, Dover, New York, 1954.

[8] G. Bruggeman, “Calculation of Various Physics Constants in Heterogeneous Substances I Dielectricity Constants and Conductivity of Mixed Bodies from Isotropic Substances,” Annalen der Physik, Vol. 416, No. 7, 1935, pp. 636-664. doi:10.1002/andp.19354160705

[9] R. L. Hamilton and O. K. Crosser, “Thermal Conductivity of Heterogeneous Two-Component Systems,” Industrials and Engineering Chemistry Fundamentals, Vol. 1, No. 3, 1962, pp. 187-191. doi:10.1021/i160003a005

[10] J. Z. Liang and G. S. Liu, “A New Heat Transfer Model of Inorganic Particulate-Filled Polymercomposites,” Journal of Material Science, Vol. 44, No. 17, 2009, pp. 47154720. doi:10.1007/s10853-009-3729-8

[11] J. Z. Liang and F. H. Li, “Measurement of Thermal Conductivity of Hollow Glass-Bead-Filled Polypropylene Composites,” Polymer Testing, Vol. 25, No. 4, 2006, pp. 527531. doi:10.1016/j.polymertesting.2006.02.007

[12] H. S. Tekce, D. Kumlutas and I. H. Tavman, “Effect of Particle Shape on Thermal Conductivity of Copper Reinforced Polymer Composites,” Journal of Reinforced Plastics and Composites, Vol. 26, No. 1, 2007, pp. 113-121. doi:10.1177/0731684407072522

[13] L. E. Nielson, “Thermal Conductivity of Particulate-Filled Polymers,” Journal of Applied Polymer Science, Vol. 17, No. 12, 1973, pp. 3819-3820. doi:10.1002/app.1973.070171224

[14] S. Cheng and R. Vachon, “A Technique for Predicting the Thermal Conductivity of Suspensions, Emulsions and Porous Materials,” International Journal of Heat Mass Transfer, Vol. 13, No. 3, 1970, pp. 537-546. doi:10.1016/0017-9310(70)90149-3

[15] Y. Agari, A. Ueda and S. Nagai, “Thermal Conductivity of a Polymer Composite,” Journal of Applied Polymer Science, Vol. 49, No. 9, 1993, pp. 1625-1634. doi:10.1002/app.1993.070490914

[16] J. Z. Liang and F. H. Li, “Simulation of Heat Transfer in Hollow GlassBead-Filled Polypropylene Composites by Finite Element Method,” Polymer Testing, Vol. 26, No. 3, 2007, pp. 419-424. doi:10.1016/j.polymertesting.2006.12.014

[17] T. B. Lewis and L. E. Nielson, “Dynamic Mechanical Properties of Particulate-Filled Composites,” Journal of Applied Polymer Science, Vol. 14, No. 6, 1970, pp. 14491471. doi:10.1002/app.1970.070140604