Estimating thermal conductivity of lightweight nanoporous cement pastes using a hybrid fractal model

Nanoporous cement paste (NCP) has been successfully prepared by adding nanopore-forming agent into cement paste, and the measured effective thermal conductivity (lambda(e)) of NCP shows that it has excellent thermal insulation performance. To promote NCP design and application, lambda(e) estimation is essential. In this paper, a hybrid fractal model (HFM) was developed based on fractal theory and related iterative algorithm using Sierpinski carpets, and electrical equivalent theory. Subsequently, this model was validated with published data and then used to predict the lambda(e) of the NCPs prepared. The results indicated that the multi-scale pore structure of NCPs was well simulated by the HFM with randomly generated Sierpinski carpet combinations. Having considered Knudsen effect of nanoporous structure, the lambda(e) of the NCPs could be well estimated using iterative algorithm, and the mean relative deviation was low to 4.2%, giving confidence in the application of the HFM method to nanoporous materials.