The effective thermal conductivity of porous materials is determined by all details of their microstructure. Since lower bounds (both Wiener and Hashin-Shtrikman bounds) are not available for porous materials (with vacuous voids), all predictions based on the porosity alone are necessarily model-based and thus tentative. In this contribution we first recall the exact solution of the single-inclusion problem for spherical and spheroidal pores , give a comprehensive summary of admissible nonlinear model relations (Maxwell-Eucken relation, Coble-Kingery relation, power-law relation, our exponential relation)  and explicitly exclude those model relations that are either redundant (self-consistent / Landauer-Bruggemann model), non-admissible (Spriggs‘ exponential relation) or useless (minimum solid area models) . Further it is shown how the exact solution for spheroidal pores (oblate or prolate) is to be implemented into the admissible nonlinear effective medium approximations . In the second part of this contribution we show that the problem of characterizing microstructural details and implementing microstructural information beyond volume fractions can be circumvented via cross-property relations (CPRs). In particular, the knowledge of the relative tensile modulus (Young’s modulus) can be used to predict the relative thermal conductivity of porous materials. The CPRs currently available for this purpose are recalled, including the Sevostianov-Kováčik-Simančík CPR , our CPR for isometric pores  and the recently proposed generalized version of the latter for anisometric pores (spheroidal-prolate and spheroidal-oblate) . Using numerical modeling on a wide range of different computer-generated digital microstructures (convex pores, concave pores, spheroidal pores, foams) it is shown that our CPR provide the best thermal conductivity predictions currently available.
- Pabst W., Gregorová E.: Conductivity of porous materials with spheroidal pores, J. Eur. Ceram. Soc. 34 (11), 2757-2766 (2014).
- Pabst W., Gregorová E.: Elastic and thermal properties of porous materials – rigorous bounds and cross-property relations (Critical assessment 18), Mater. Sci. Technol. 31 (15), 1801-1808 (2015).
- Pabst W. Gregorová E.: Minimum solid area models for the effective properties of porous materials – a refutation, Ceram. Silik. 59 (3), 244-249 (2015).
- Sevostianov I., Kováčik J., Simančík F.: Correlation between elastic and electric properties for metal foams: Theory and experiment, Int. J. Fract. 114, L23L28 (2002).
- Pabst W., Gregorová E.: A cross-property relation between the tensile modulus and the thermal conductivity of porous materials, Ceram. Intern. 33 (1), 912 (2007).
- Pabst W., Gregorová E.: A generalized cross-property relation between the elastic moduli and conductivity of isotropic porous materials with spheroidal pores, Ceram. Silik. 61 (1), 74-80 (2017).
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