Prediction of effective stagnant thermal conductivities of porous materials at high temperature by the generalized self-consistent method

The generalized self-consistent method is developed to deal with porous materials at high temperature, accounting for thermal radiation. An exact closed form formula of the local effective thermal conductivity is obtained by solving Laplace's equation, and a good approximate formula with uncoupled conductive and radiative effects is given. A comparison with available experimental data and theoretical predictions demonstrates the accuracy and efficiency of the present formula. Numerical examples provide a better understanding of interesting interaction phenomena of pores in heat transfer. It is found that the local effective thermal conductivity divides into two parts. One, attributed to conduction, is independent of pore radius for a fixed porosity and, furthermore, is independent of temperature (actually, it is approximately independent of the temperature) if it is non-dimensionalized by the thermal conductivity of the matrix. The other is due to thermal radiation in pores and strongly depends on the temperature and pore radius. The radiation effect can not be neglected at high temperature and in the case of relatively large pores.