Non-Linear Effect of Volume Fraction of Inclusions on The Effective Thermal Conductivity of Composite Materials: A Modified Maxwell Model

ABSTRACT

In this paper, non-linear dependence of volume fraction of inclusions on the effective thermal conductivity of composite materials is investigated. Proposed approximation formula is based on the Maxwell’s equation,**in that a** non-linear term dependent on the volume fraction of the inclusions and the ratio of the thermal conductivities of the polymer continuum and inclusions is introduced in place of the volume fraction of inclusions. The modified Maxwell’s equation is used to calculate effective thermal conductivity of several composite materials and **agreed** well with the earlier experimental results. A comparison of the proposed relation with different models has also been made.

In this paper, non-linear dependence of volume fraction of inclusions on the effective thermal conductivity of composite materials is investigated. Proposed approximation formula is based on the Maxwell’s equation,

Cite this paper

nullS. Kumar, R. Bhoopal, P. Sharma, R. Beniwal and R. Singh, "Non-Linear Effect of Volume Fraction of Inclusions on The Effective Thermal Conductivity of Composite Materials: A Modified Maxwell Model,"*Open Journal of Composite Materials*, Vol. 1 No. 1, 2011, pp. 10-18. doi: 10.4236/ojcm.2011.11002.

nullS. Kumar, R. Bhoopal, P. Sharma, R. Beniwal and R. Singh, "Non-Linear Effect of Volume Fraction of Inclusions on The Effective Thermal Conductivity of Composite Materials: A Modified Maxwell Model,"

References

[1] J. C. Maxwell, “A Treatise on electricity and magnetism,” (Clarendon Press, Oxford), 3rd Ed (1), 1904, 440.

[2] T. Lewis and L. Nielsen, “Dynamic mechanical properties of particulate-filled composite,” J. Appl. Polymer Science 14, 1970, 1449.

[3] M. E. Cunningham and K. L. Peddicord, “Heat conduction in spheres packed in an infinite regular cubical array,” Int. J. Heat & Mass Transfer, 24 1981, 1088.

[4] S. Torquato, “Effective electrical conductivity of two-phase disordered composite media,” J. Appl. Phys., 58, 1985, 3790-3797.

[5] G. R. Hadley, “Thermal conductivity of packed metal powers,” Int. J. Heat & Mass Transfer, 29, 1986, 909-920.

[6] Y. Agari and T. Uno, “Estimation on thermal conductivities of filled polymers,” J. Appl. Polym. Sci., 32, 1986, 5705-5712.

[7] K. Misra, A. K Shrotriya, R. Singh and D. R. Chaudhary, “Porosity correction for thermal conduction in real two-phase systems,” J. Phys. D. Appl. Phys., 27, 1994, 732-735.

[8] R. Singh and H. S. Kasana, “Computational aspects of effective thermal conductivity of highly porous metal foams,” Appl. Thermal Engg., 24, 2004, 1841-1849.

[9] L. S. Verma, A. K. Shrotriya, R. Singh and D. R. Chaudhary, “Thermal conduction in two-phase materials with spherical and non-spherical inclusion,” J. Phys. D: Appl. Phys., 24, 1991, 1729-1737.

[10] V.V. Calmidi and R. L Mahajan, “The effective thermal conductivity of high porosity fibrous metal foam,” ASME J. Heat Transfer, 121, 1999, 466-471.

[11] A. Bhattacharya, V. V. Calmidi and R. L. Mahajan, “Thermoplastic properties of high porosity metal foam,” Int. J. Heat & Mass Transfer, 45, 2002, 1017-1031.

[12] W. Pabst and E. Gregorova, “A new percolation-threshold relation for the porosity dependence of thermal conductivity,” Ceramics International, 32, 2006, 89-91.

[13] N. M. Sofian, M. Rusu, R. Neagu and E. Neagu, “Metal Powder-filled Polyethylene Composites V. Thermal Properties,” J. Thermoplastic Composite Materials, 14, 2001, 20-33.

[14] A. Boudenne, L. Ibos, M.Fois, E. Gehin and J. C. Majeste, “Thermophysical Properties of Polypropylene/Aluminum Composites,” J. Polymer Science: Part B: Polymer Physics, 42, 2004, 722-732.

[15] D. Kumlutas and I. H. Tavman, “A numerical and experimental study on thermal conductivity of particle filled polymer composite,” J. Thermoplastic Composite Materials, 19, 2006, 441-455.

[16] S. W. Kim, B. Choi, S. H. Lee and K. H. Kang, “Measurement of Thermophysical properties of articulate-filled polymer composites,” High Temperature–High Pressures, 37, 2008, 21-30.

[17] W. Woodside and J. H. Messmer, “Thermal conductivity of porous media II Consolidated rocks,” J. Appl. Phys., 32, 1961, 1699-1706.

[18] T.K. Dey and M. Tripathi, “Thermal properties of silicon powder filled high-density polyethylene composites,” Thermochimica Acta, 502, 2010, 35-42.

[1] J. C. Maxwell, “A Treatise on electricity and magnetism,” (Clarendon Press, Oxford), 3rd Ed (1), 1904, 440.

[2] T. Lewis and L. Nielsen, “Dynamic mechanical properties of particulate-filled composite,” J. Appl. Polymer Science 14, 1970, 1449.

[3] M. E. Cunningham and K. L. Peddicord, “Heat conduction in spheres packed in an infinite regular cubical array,” Int. J. Heat & Mass Transfer, 24 1981, 1088.

[4] S. Torquato, “Effective electrical conductivity of two-phase disordered composite media,” J. Appl. Phys., 58, 1985, 3790-3797.

[5] G. R. Hadley, “Thermal conductivity of packed metal powers,” Int. J. Heat & Mass Transfer, 29, 1986, 909-920.

[6] Y. Agari and T. Uno, “Estimation on thermal conductivities of filled polymers,” J. Appl. Polym. Sci., 32, 1986, 5705-5712.

[7] K. Misra, A. K Shrotriya, R. Singh and D. R. Chaudhary, “Porosity correction for thermal conduction in real two-phase systems,” J. Phys. D. Appl. Phys., 27, 1994, 732-735.

[8] R. Singh and H. S. Kasana, “Computational aspects of effective thermal conductivity of highly porous metal foams,” Appl. Thermal Engg., 24, 2004, 1841-1849.

[9] L. S. Verma, A. K. Shrotriya, R. Singh and D. R. Chaudhary, “Thermal conduction in two-phase materials with spherical and non-spherical inclusion,” J. Phys. D: Appl. Phys., 24, 1991, 1729-1737.

[10] V.V. Calmidi and R. L Mahajan, “The effective thermal conductivity of high porosity fibrous metal foam,” ASME J. Heat Transfer, 121, 1999, 466-471.

[11] A. Bhattacharya, V. V. Calmidi and R. L. Mahajan, “Thermoplastic properties of high porosity metal foam,” Int. J. Heat & Mass Transfer, 45, 2002, 1017-1031.

[12] W. Pabst and E. Gregorova, “A new percolation-threshold relation for the porosity dependence of thermal conductivity,” Ceramics International, 32, 2006, 89-91.

[13] N. M. Sofian, M. Rusu, R. Neagu and E. Neagu, “Metal Powder-filled Polyethylene Composites V. Thermal Properties,” J. Thermoplastic Composite Materials, 14, 2001, 20-33.

[14] A. Boudenne, L. Ibos, M.Fois, E. Gehin and J. C. Majeste, “Thermophysical Properties of Polypropylene/Aluminum Composites,” J. Polymer Science: Part B: Polymer Physics, 42, 2004, 722-732.

[15] D. Kumlutas and I. H. Tavman, “A numerical and experimental study on thermal conductivity of particle filled polymer composite,” J. Thermoplastic Composite Materials, 19, 2006, 441-455.

[16] S. W. Kim, B. Choi, S. H. Lee and K. H. Kang, “Measurement of Thermophysical properties of articulate-filled polymer composites,” High Temperature–High Pressures, 37, 2008, 21-30.

[17] W. Woodside and J. H. Messmer, “Thermal conductivity of porous media II Consolidated rocks,” J. Appl. Phys., 32, 1961, 1699-1706.

[18] T.K. Dey and M. Tripathi, “Thermal properties of silicon powder filled high-density polyethylene composites,” Thermochimica Acta, 502, 2010, 35-42.