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There are several models for the effective thermal conductivity of two-phasecomposite materials in terms of the conductivity of the solid and the dispersematerial. In this paper, we generalise three models of Maxwell type (namely,the classical Maxwell model and two generalisations of it obtained fromeffective medium theory and differential effective medium theory) so that theresulting effective thermal conductivity accounts for radiative heat transferwithin gas voids. In the high-temperature regime, radiative transfer withinvoids strongly influences the thermal conductivity of the bulk material.Indeed, the utility of these models over classical Maxwell-type models is seenin the high-temperature regime, where they predict that the effective thermalconductivity of the composite material levels off to a constant value (as afunction of temperature) at very high temperatures, provided that the materialis not too porous, in agreement with experiments. This behaviour is in contrastto models which neglect radiative transfer within the pores, or lumpedparameter models, as such models do not resolve the radiative transferindependently from other physical phenomena. Our results may be of particularuse for industrial and scientific applications involving heat transfer withinporous composite materials taking place in the high-temperature regime.

Maxwell-type models for the effective thermal conductivity of a porous material with radiative transfer in the voids