Is there a way to estimate sufficiently the thermal conductivity of building materials matrix? E.g. matrix of bricks, concretes, air aerated concretes (porosity is in a large range in case of these materials - about 5-85%).
It is not a problem to measure the effective thermal conductivity of the dry two-phase system (matrix, air), but the matrix values are problematic to estimate. When some models are used for the matrix property calculation by using the known values of air and measured effective properties, results are very different.
To determine the thermal conductivity from the composition of matrix knowledge is also problematic, due to the complex structure and non tabulated values of components.
Is there any source where to get some useful information?
See he following article. So, you can changed the solid phase by the matrix phase, when consider that the material is composed of tow phases:(e.g matrix, void or air )
Usually, the material parameters (local conductivities) of constituents are considered to be known, and the main problem is to properly describe geometry. In your case, as I assume, the following method could be used. You could measure the effective conductivity of your porous materials, when the matrix is filled with air and with various liquids with known conductivities (probably, the wettability problem should be taken into account when choosing the liquids). If so, then geometry remains the same and you could use Bergman-Milton spectral representation to obtain a set of equations, which includes an unknown spectral density function and the sought conductivity. As I suppose, the matrix conductivity could be extracted from the effective conductivity measurements under some assumptions concerning the spectral density function. Techniques developed by Elena Cherkaev (in particular, the use of Stieltjes representation) could be useful to do that.
you can use directly some correlations to predict effective conductivity, for exemple Kim's or calmidi's correlations.
I developed a very simple matlab script to approximate the homogenized thermal conductivity of a composite based in the RVE concept (2 dimensions), based on this paper http://link.springer.com/article/10.1007%2Fs10659-013-9445-2 . If you are interested, contact me and i will send you by email
Hello Lukas. In your nextdoor institute (UCT Prague), Willi Pabst has done a lot thinking on 2 phase mixture problems and effective properties for porous ceramics. You should talk to him. Otherwise, we have made good predictions for upto 65% porosity using Landauer's relation. You can solve it to predict the conductivity of the matrix phase. The choice of a relation depends on the type of porosity (open/closed).
Hi David. Thank You for the contact! We are (also) going this way: measurements of the thermal conductivity of specimens with the same matrix, but a different porosity and then extrapolation of measured data or homogenization techniques utilization.
Ktested=M*Kmatr*(1-P)^1.5+P^0.25*Kair
Here P is porosity. M is empirical parameter which takes into account (for ceramics and refractories ) influence of contact heat resistances between particles. For ceramics and refractories in the range up to 1200K M=0.56, with accuracy about 10-20%. At higher temperatures M increases up to 1 at temperature of materials sintering. If you know microstructure and composition of your materials, M can be calculated. See my papers in the JACS and others.
Those interested at this discussion may want to check also the following related discussion at this forum: https://www.researchgate.net/post/How_porosity_could_affect_thermal_conductivity_and_coefficient_of_thermal_expansion_in_carbon_fiber_reinforced_Aluminium_matrix_composite
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