Abstract
This study deals with the effective thermal conductivity of porous and ultra-porous unconnected solid phase media composed of α-alumina in air at low temperature (<500K), and at ambient pressure. A multi-scale model is developed, starting from the quantum scale, to describe the conductivity of the single crystal, passing through a microscopic scale to describe the particles (grain size), a mesoscopic scale to take into account the intraparticle porosity and a macroscopic scale with the interparticle porosity. The model is based on percolation theory to describe the strong decrease in conductivity with porosity in this type of medium. This translates into the breaking of contacts between particles past a certain porosity, the critical porosity pc. This original approach makes it possible to consider this microstructural factor, which accounts for the thermal contacts between particles. These parameters are theoretically deduced or measured for certain samples using an X-ray micro-tomograph (µCT). Combining all these parameters, our model is able to predict 99.7% of the thermal conductivity decay from the pure crystal to the particle bed. Our model proves to be more consistent than current existing models on the same subject. Its validation range extends over the entire porosity range from 0 to 1.
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