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

## TL;DR

This paper extends Maxwell-type models to include radiative heat transfer in gas voids, accurately predicting the thermal conductivity of porous materials at high temperatures, aligning with experimental observations.

## Contribution

It generalizes classical Maxwell models to account for radiative transfer within voids, improving high-temperature thermal conductivity predictions for porous composites.

## Key findings

- Models predict thermal conductivity levels off at high temperatures.
- Radiative transfer significantly influences heat conduction in porous materials.
- Models align with experimental data at high temperatures.

## Abstract

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.