International Scientific Journal


In this article, the collocated parameter models are used to estimate the effective thermal conductivity of the two-phase materials including the effect of various inclusions in the unit cell. The algebraic equations are derived using unit cell based isotherm approach for two dimensional spatially periodic medium. The geometry of the medium is considered as a matrix of touching and non-touching in-line octagon and hexagon cylinders. The models are used to predict the thermal conductivity of numerous two-phase materials (maximum conductivity ratio of 1000 and concentration ranging between 0 and 1). The estimated thermal conductivity data is in good agreement with the experimental data within ±15.84%, ±18.14% maximum deviation, respectively, from octagon and hexagon cylinders for various two-phase systems. The obtained results are compared with a wide range of experimental data for various geometrical configurations to estimate the effective thermal conductivity of two-phase materials.
PAPER REVISED: 2009-07-29
PAPER ACCEPTED: 2009-07-22
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2010, VOLUME 14, ISSUE Issue 2, PAGES [393 - 407]
  1. Maxwell, J. C., A Treatise on Electricity and Magnetism, Clarendon Press, Oxford, UK, 1873
  2. Hashin, Z., Shtrikman, S., A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials, Journal of Applied Physics, 33 (1962), 19, pp. 3125- 3131
  3. Wiener, O., Lamellare Doppelbrechung, Phys. Z., 5 (1904), pp. 332-338
  4. Zehner, P., Schlunder, E. U., On the Effective Heat Conductivity in Packed Beds with Flowing Fluid at Medium and High Temperatures, Chemical Engineering Technology, 42 (1970), pp. 933-941
  5. Hsu, C. T., Cheng, P., Wang, K. W., A Lumped Parameter Model for Stagnant Thermal Conductivity of Spatially Periodic Porous Media, ASME-Journal of Heat Transfer, 117 (1995), 2, pp. 264-269
  6. Crane, R. A., Vachon, R. I., A Prediction of the Bounds on the Effective Thermal Conductivity of Granular Materials, International Journal of Heat Mass Transfer, 20 (1977), 7, pp. 711-723
  7. Tsotsas, E., Martin, H., Thermal Conductivity of Packed Beds: A Review, Chemical Engineering Process, 22 (1987), pp. 19 -37
  8. Bruggeman, D. A. G., Dielectric Constant and Conductivity of Mixtures of Isotropic Materials, Ann. Phys. (Leipzig), 24 (1935), pp. 636 -679
  9. Raghavan, V. R., Martin, H., Modeling of Two-Phase Thermal Conductivity, Chemical Engineering and Processing, 34 (1995), 5, pp. 439- 446
  10. Krupiczka, R., Analysis of Thermal Conductivity in Granular Materials, International Chemical Engineering, 7 (1967), 1, pp.122-144
  11. Krischer, O., The Scientific Fundamentals of Drying Technology (in German), 1st ed., Springer-Verlag, Heidelberg, Germany, 1956
  12. Meredith, R. E., Tobias, C. W., Resistance to Potential Flow through a Cubical Array of Spheres, Journal of Applied Physics, 31 (1960), 7, pp. 1270-1273
  13. Rayleigh, L., On the Influence of Obstacles Arranged in Rectangular Order upon the Properties of a Medium, Phil. Mag. J .Sci., 34 (1892), 5, pp. 481-502
  14. Bauer, T. H., A General Analytical Approach toward the Thermal Conductivity of Porous Media, International Journal of Heat and Mass Transfer, 36 (1993), 17, pp. 4181-4191
  15. Dietz, P. W., Effective Thermal Conductivity of Packed Beds, Ind. Eng. Chem. Fundam., 18 (1979), pp. 283-286
  16. Progelhof, R. C., Throne, J. L., Reutsch, R. R., Methods for Predicting the Thermal Conductivity of Composite Systems: A Review, Polymer Engineering Science, 16 (1976), 9, pp. 615-25
  17. Deisser, R. G., Boregli, J. S., An Investigation of Effective Thermal Conductivities of Powders in Various Gases, ASME Transactions, 80 (1958), pp.1417-1425
  18. Kunii, D., Smith, J. M., Heat Transfer Characteristics in Porous Rocks, American Institute of Chemical Engineering Journal, 6 (1960), pp.71-78
  19. Landauer, R. The Electrical Resistance of Binary Metallic Mixtures, Journal of Applied Physics, 23 (1952), pp.779-784
  20. Samantray, P. K, Karthikeyan, P., Reddy, K. S. Estimating Effective Thermal Conductivity of Two-Phase Materials, International Journal of Heat and Mass Transfer, 49 (2006), 21-22, pp. 4209-4219
  21. Karthikeyan, P., Reddy, K. S., Effective Conductivity Estimation of Binary Metallic Mixtures, International Journal of Thermal Sciences, 46 (2007), pp. 419-425
  22. Reddy, K. S., Karthikeyan, P., Estimation of Effective Thermal Conductivity of Two-Phase Materials Using Collocated Parameter Model, Heat Transfer Engineering, 30 (2009), pp. 998-1011
  23. Sugawara, A., Yoshizawa.Y., An Investigation on the Thermal Conductivity of Porous Materials and Its Application in Porous Rocks, Australian Journal of Physics, 14 (1961), 4, pp. 469-480
  24. Woodside, W., Messmer, J. H., Thermal Conductivity of Porous Media - Unconsolidated Sands, Journal of Applied Physics, 32 (1961), pp. 1688-1706
  25. Smith, W. O., The Thermal Conductivity of Dry Soil, Soil Science, 53 (1942), pp. 435-459
  26. Schumann, T. E.,W., Voss, V., Heat Flow through Granulated Material, Fuel Science Practice, 13 (1934), pp. 249-256
  27. Preston, F. W., Mechanism of Heat Transfer in Unconsolidated Porous Media at Low Flow Rates, Ph. D. Dissertation, Pennsylvania State University, Pennsylvania, Penn., USA, 1957
  28. Waddams, A., The Flow of Heat through Granular Materials. J. Soc. Chem. Ind, 63 (1944), pp. 336-340
  29. Goring, R. L., Churchill, S. W., Thermal Conductivity of Heterogeneous Materials, Chemical Engineering Progress, 57 (1961), 7, pp. 53-59
  30. Mischke, R. A., Smith, J. M., Thermal Conductivity of Alumina Catalyst Pellets, Ind. Eng.Chem. Fundam., 1 (1962), pp. 288-292
  31. Godbee, H. W., Zeigler, T. W., Thermal Conductivities of MgO, Al2O3 and ZrO2 Powders to 850 °C II - Theoretical, Journal of Applied Physics, 37 (1966), pp. 56-65
  32. Verschoor, H., Schuit, G. C. A., Heat Transfer to Fluid Flowing through Beds of Granular Solid, Applied Science Research, 2 (1951), 1, pp. 97-119
  33. Fountain, J. A., West, E. A., Thermal Conductivity of Particulate Basalt as a Function of Density in Simulated Lunar and Martian Environments, Journal of Geophysics Research,75 (1970), 20, pp. 4063-4069
  34. Tavman, I. H., Effective Thermal Conductivity of Granular Porous Materials, International Communication of Heat and Mass Transfer, 23 (1996), 2, pp. 169-176
  35. Messmer, J. H., Thermal Conductivity of Porous Media-Packing of Particles, 4th Conference on Thermal Conductivity, Proceedings, Part C., San Francisco, Cal., USA, 1964, pp. 111-115
  36. Shashkov, A. G., et al., Thermo-Physical Properties of Thermally Insulating Materials in the Cryogenic Temperature Region, International Journal of Heat and Mass Transfer, 15 (1972), pp. 2385-2390
  37. Baxley, A. L, Couper, J. R., Thermal Conductivity of Two-Phase Systems. Part-IV (Thermal Conductivity of Suspensions): Research report series No. 8, University of Arkansas, Eng. Exp. Station, Little Rock, Ark., USA, 1966
  38. Sugawara, A., Hamada, A., Thermal Conductivity of Dispersed Systems, Proceedings, 10th Thermal Conductivity Conference, Boston, Mass., USA, 1970, Vol. 3 pp. 7
  39. Nahas, N. C., Couper, J. R., Thermal Conductivity of Two-Phase Systems: Thermal Conductivity of Emulsions, Part- III, Research Reports Series, No. 7, University of Arkansas, Eng. Exp. Station, Little Rock, Ark., USA, 1966
  40. Knudsen, J. G., Ward, R. H., Thermal Conductivity of Liquid-Liquid Emulsions, Ind. Engi. Chem., 50 (1958), pp. 1667-1675.
  41. Cheng, S. C., Vachon, R. I., The Prediction of the Thermal Conductivity of Two and Three Phase Solid Heterogeneous Mixtures, International Journal of Heat and Mass Transfer, 12 (1969), pp. 249-264
  42. Ratcliffe, E. H., Thermal Conduction on Porous Media: Methodology, Results, Estimations, Proceedings , 18th Thermal Conductivity Conference, Lafayette, Ind., USA, Plenum press, New York, 1969, pp. 1141-1147

© 2022 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence