Food and Bioprocess Technology

, Volume 1, Issue 2, pp 161–170 | Cite as

Modelling Thermal Conductivity in Heterogeneous Media with the Finite Element Method

  • Juliane Floury
  • James Carson
  • Q. Tuan Pham


Three-dimensional finite element simulations were developed to predict the effective thermal conductivity of theoretical composite materials having complex structures. The models simulated a steady-state thermal conductivity measurement device performing measurements on theoretical materials with varying structures. The structure of a composite was considered to be composed of some simplified basic models. When the geometry, orientation type and number of dispersion are specified, the computer randomly generated the position and orientation for each dispersion and created the geometrical model and finite element mesh. The effective thermal conductivity of the theoretical composite was calculated using this method and compared to the values obtained by simple effective thermal conductivity models methods. The influence of some factors such as the volume fraction and the ratio of the thermal conductivities of the heterogeneities and the surrounding material on the effective thermal conductivity is discussed.


Finite element method Composite material Heterogeneous materials Effective thermal conductivity 



cross-section area of the cube


percentage error


effective thermal conductivity


thermal conductivity of the phase


length of the cube side


heat flux

\({\mathop {Q_{1} }\limits^ \cdot }\)

overall heat flux into the unit cell



x, y, z

spatial Cartesian coordinates

Greek symbols

ϕ, θ

spatial spherical coordinates


relative volume of the phase i



continuous phase


dispersed phase


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.UMR-1253 INRA Agrocampus-RennesRennes cedexFrance
  2. 2.Department of EngineeringUniversity of WaikatoHamiltonNew Zealand
  3. 3.Department of Chemical Sciences and EngineeringUniversity of New South WalesSydneyAustralia
  4. 4.UMR-1253 INRA Agrocampus-Rennes, Milk and Egg Science & Technology—Technological Process TeamRennesFrance

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