Heat Transfer via the Gaseous Phase

In general, the characteristic pore size within aerogels is well below the micron range which leads to the fact that the heat transfer via the gaseous phase within the aerogel 

The heat transfer in the gaseous phase is characterized by the Knudsen number Kn, which is the ratio of the mean free path /g of the gas molecules and the effective pore dimensirm D  

In principle, mie has to distinguish between three different cases  

Molecular heat transfer, Kn 1 The average pore size is significantly smaller than the mean free path of the gas molecules. The gas molecules collide predominantly with the solid backbone of the aerogel and the resulting thermal conductivity contribution is proportional to the number of gas molecules, i.e., the gas pressure. 

Diffusive heat transfer, Kn 1 The mean free path of the gas molecules is much smaller than the average pore size. The gas molecules collide predominantly with each other, which is the classical case of diffusive heat transfer [15]. The resulting thermal conductivity of the gaseous component equals the thermal conductivity of the free gas, which is independent of the gas pressure for ambient and moderate pressures. 

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