  There are several models for the effective thermal conductivity of two-phase
composite materials in terms of the conductivity of the solid and the disperse
material. In this paper, we generalise three models of Maxwell type (namely,
the classical Maxwell model and two generalisations of it obtained from
effective medium theory and differential effective medium theory) so that the
resulting effective thermal conductivity accounts for radiative heat transfer
within gas voids. In the high-temperature regime, radiative transfer within
voids strongly influences the thermal conductivity of the bulk material.
Indeed, the utility of these models over classical Maxwell-type models is seen
in the high-temperature regime, where they predict that the effective thermal
conductivity of the composite material levels off to a constant value (as a
function of temperature) at very high temperatures, provided that the material
is not too porous, in agreement with experiments. This behaviour is in contrast
to models which neglect radiative transfer within the pores, or lumped
parameter models, as such models do not resolve the radiative transfer
independently from other physical phenomena. Our results may be of particular
use for industrial and scientific applications involving heat transfer within
porous composite materials taking place in the high-temperature regime.
