Computation of the conducto-radiative effective heat conductivity of porous media defined by Triply Periodic Minimal Surfaces

Abstract

Triply Periodic Minimal Surfaces are attractive porous media for the design of volumetric solar energy receivers; their design involves the evaluation of their heat transfer capabilities in the mixed conductive/radiative mode. We present image-based computations of effective thermal conductivities (ETC) for different radiation/conduction ratios in twenty distinct TPMS structures, using a Hybrid Random Walk numerical method, considering Opaque/Transparent media. Results are cast in simple analytical correlations : the ETC is the sum of a purely conductive contribution proportional to the relative density and of a radiative contribution proportional to the radiation/conduction ratio; the coefficient of proportionality contains an emissivity-independent contribution and another contribution proportional to the emissivity which fades out above a critical ratio. This critical ratio is linearly proportional to the solid/void volume ratio of the media. These results are compared to similar ones obtained on open-cell foams. Application of these dimensionless laws to two realistic cases are presented as illustrative examples.