# Heat transfer in porous media

In a previous post, I already have shown the following graph. I got interested why the evacuation of mineral wool has a thermal conductivity decrease larger than the one of the gas.

The author of the graph has sent me two papers and a presentation.

• A presentation showing that the larger decrease of the thermal conductivity is not only the gas thermal conduction but also a coupling term.
• A paper about the evacuation of different thermal insulations.
• Another paper about the equipment to measure thermal conductivity under vacuum in a large temperature range.

It is already mentioned that the decrease can be 6 times the thermal conductivity of the gas in case a bed of glass spheres is used. This is indeed already reported in another paper where the thermal conductivity under vacuum is measured with a hot wire method.

In the last paper, convection is mentioned but a clear explanation of the large decrease is not given.

Further, in a nice master thesis of Matthias Demharter, Technical University Munchen, the evacuation of expanded perlite is described. Also in this work, the decrease is described as the sum of gas conduction and a coupling term, which is given in the following graph.

In my opinion, the large decrease is simply free convection. I have the following gedanken experiment:

• Assume the measuring system is filled with only air and that we are in a space ship around earth without any gravity and so without any free convection. We will measure 0.026 W/mK.
• We add mineral wool or expanded perlite. In that case, the solid replaces some air and contributes to an extra thermal conductivity path. The total thermal conductivity must be smaller than the sum of the one of air and the one of the solid in an evacuated state. However, in the case of mineral wool, expanded perlite or glass spheres, the sum is still smaller than the measured one on earth under gravity.
• As a consequence, free convection is present and in the case of the highly permeable bed of glass spheres, the effect is very large.

Although free convection is standard in the world of porous media, the concept is not popular in the world of mineral thermal insulation. And indeed, when the material contains free convection, it is also sensitive to forced convection like on attic in a windy environment. The only way to eliminate the free convection is to decrease the permeability by increasing the density. But in a lot of cases, it makes more sense to work with cellular glass at a lower density and closed cell structure like GLAPOR.