A hybrid approach for predicting the effective thermal conductivity of sintered porous materials

Estimating the effective conductivity of porous media has been widely based on homogenisation techniques with a limited number of discrete analyses. Though bulk estimates may be sufficient within prescribed bounds and applications, localised properties are not readily available. This work employs resistive network analytics in conjunction with 2D and 3D porous media modelling, to estimate the effective conductivity through local interrogation of porous sintered bronze disks. The resulting hybrid method uses rigid body simulations to generate the porous network and analytical mathematics to evaluate the effective conductivity. The analytics are herein verified and validated for both 2D and 3D cases. The 2D analysis used printed circuit boards to validate the analytics and produced an experimental mean and standard error of 308.7 ± 12.6 μΩ for networks having resistors ranging from 10 to 1000 Ω. A 3D analysis of sintered porous bronze disks was performed for both electrical and thermal conductivities. A set of simulated samples consistent with the physical specimens were generated using an open source 3D creation software and tested in manners consistent with experiments. The electrical tests across the diameter of the bronze samples yielded equivalent experimental and theoretical resistances of 1.93 ± 0.42 mΩ and 2.03 ± 0.17 mΩ respectively. A Xenon flash analysis across the thickness of the samples produced an experimental and theoretical Effective Thermal Conductivity (ETC) of 21.9 ± 3.4 W/mK and 18.1 ± 0.3 W/mK respectively. This method was able to successfully estimate the ETC within 17% of the measured mean, while traditional contact-based empirical correlations were found to underpredict the ETC by as much as 58%. The models align well with both experimental studies in both thickness and diametric analysis. Extension of the models to samples of differing particle sizes revealed the ETC to increase with particle size.