# Mathematical Models for Effective Thermal Conductivity

• Lis Marcussen
Chapter

## Abstract

Different mathematical models for effective thermal conductivity are described and discussed in view of experimental results for porous materials.

Models which apply the porosity of the solid as the only structural information are found not to be satisfactory. The degree of continuity in the phases is identified as an important structural parameter. Consequently, such a parameter is included in the models.

Model I: A solid lattice is assumed.

Model II: No specific structure of the solid is assumed, but a distribution in space is anticipated for the porosity.

Model III: An extended use of the EMA-model (Effective Medium Approximation for calculation of dielectric constants) to predict effective thermal conductivity leads to a model which involves a factor interpreted as a measure of the degree of continuity in the solid phase.

It is concluded that models II and III are the most promising models.

## Keywords

Thermal Conductivity Effective Thermal Conductivity Solid Lattice Equal Volume Fraction Heat Conduction Path
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.

## Literature

1. 1.
Dul’nev, G.N., and Novikov, V.V. “Conductivity of Nonuniform Systems,” J.Eng.Phys. 36 (5), 601 (1979).
2. 2.
Luikov, A.V., Shashkov, A.G., Vasiliev, L.L., and Fraiman, Yu.E. “Thermal Conductivity of Porous Systems”, Int.J.Heat Mass Trans. 11, 117 (1968).
3. 3.
Bruggeman, D.A.G. “Berechnung verschiedene physikalischer Konstanten von Heterogenen Substanzen,” Annalen der Physic 5. Folge 24, 636 (1935).Google Scholar
4. 4.
Niesei, W. “Die Dielektrizitätskonstanten heterogener Mischkorper aus isotropen und anisotropen Substanzen”, Annalen der Physik 6. Folge 10, 336 (1952).Google Scholar
5. 5.
Reynolds, J.A. and Hough, J.M. Phys.Soc.Proc. B 70, 769 (1957).