Thermal conductivity of random media and regular fractals

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Abstract
The Laplace equation can be solved in any two‐ and three‐dimensional porous medium by means of a vectorized numerical code. It is applied to several structures such as random media derived from site percolation; close to the percolation threshold, the critical exponents are found to be very close to the ones corresponding to networks; the results are usefully compared to previous variational upper bounds and to the prediction of an approximate space renormalization. Media with double porosity such as catalyst pellets are also addressed. Finally the conductivity of most fractals is shown to follow an Archie’s law in the limit of large generation numbers; the exponents of the power laws can be retrieved by various renormalization arguments.