A geometrical fractal model for the porosity and thermal conductivity of insulating concrete

• An intermingled fractal units is presented to model porous microstructure and thermal properties.
• Even non fractal structures can be effectively modelled with an intermingled fractal units.
• Applying this model thermal conductivity values in line with experimental data has been obtained.

The analysis of the porous microstructure can be addressed through the use of fractal geometry. The translation of the experimental data into mathematical equations allows researchers to obtain a number of geometric representations for which it is possible to apply those relations which are suitable to measure physical magnitudes otherwise difficult to measure. In this research we concentrated on the study of different kinds of cement as follows: – clay – wood aggregates. The determination of the thermal conductivity of the materials which were chosen can be carried out using the well-known concept of electrical analogy. Their microstructures are simulated using fractal patterns. Using the value of the effective conductivity that has been calculated in the previous stage as the value of conductivity of the solid phase, it is possible to obtain a set of results that will be fully comparable with the experimental ones. A further circuit diagram has been created to simulate the different compositions of the mixtures of the samples we studied, and again, the values were very close to the experimental ones.