A Universal Model for the Overall Thermal Conductivity of Porous Media

Abstract

A general field theory is developed in this work to estimate the overall degradation of the thermal conductivity of the solid due to the presence of internal cavities. In addition to the volume fraction of cavities in the matrix material, the effect of internal heat transfer across the pore surface on the overall thermal conductivity is absorbed in an added tensor. Based on the field theory thus formulated, application is made to investigate the effects of pore geometry and internal heat transfer on the overall thermal conductivity. In the aspect of pore geometry, the overall thermal conductivity of the porous medium is obtained for insulated spherical cavities and penny-shaped cracks. In the aspect of internal heat transfer, on the other hand, the effect of heat conduction and convection across the pore surface is analyzed. All the cases under consideration are compared with the experimental results and the dominant physical modulus in the overall thermal conductivity is identified for each case.