Effective Thermal Conductivity of Granular Materials in Cylindrical Beds

  • M. S. Khader
  • R. I. Vachon
  • J. S. Goodling


Measurements of porosity in cylindrical packed beds have been made over a wide range of parameters. It is found that porosity is not constant over the bed, but ranges from 1 to approximately 0.4. The spatial distribution of porosity comes from the influence of the enclosing wall and varies in a regular manner when particle size and container size are taken into account. It appears that the porosity function can be adequately described by a two-parameter equation.

A model for the effective thermal conductivity of granular material is chosen and modified by the spatial dependency of porosity. The purpose of the paper is to show how the porosity function influences the local effective thermal conductivity in packed cylindrical beds. The concept of “particle boundary layer” is introduced. Results are presented for different values of particle-size diameter to container diameter ratio for spherical and irregular particles over a range of particle size distributions.


Thermal Conductivity Granular Material Effective Thermal Conductivity Irregular Particle Porosity Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



constant in equation (2)


packed bed diameter (m)


particle diameter (m)


particles average diameter (m)


Young’s modulus (N/m2)


force (N)


indicates function of (equation 5)


height of the packing (m)


local effective thermal conductivity (W/m C)


thermal conductivity of continuous phase (W/m C)


effective thermal conductivity of continuous phase (W/m C)


thermal conductivity of discontinuous phase (W/m C)


Knudsen number


radial coordinate measured from the wall (m)




radiation number, shown in equation (6), defined in [3]


shape factor


axial coordinate measured from the bed surface (m)


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    R. A. Crane, R. I. Vachon, and M. S. Khader, Thermal Conductivity of Granular Materials - A Review, in: “Proceedings of the Seventh Symposium Thermophysical Properties”. NBS, Gaithersburg, MD (1977).Google Scholar
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    S. S. Kwong and J. M. Smith, Radial Heat Transfer in Packed Beds, Ind. Eng. Chem., 49: 894 (1957).Google Scholar

Copyright information

© Purdue Research Foundation 1983

Authors and Affiliations

  • M. S. Khader
    • 1
  • R. I. Vachon
    • 2
  • J. S. Goodling
    • 3
  1. 1.Mechanical EngineeringCairo UniversityEgypt
  2. 2.Mechanical EngineeringAuburn UniversityAuburnUSA
  3. 3.Mechanical Engineering Dept.Auburn UniversityAuburnUSA

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