A novel fractal model for the prediction and analysis of the equivalent thermal conductivity in wood

Abstract

Abstract This study proposes a new fractal model to improve the accuracy of equivalent thermal conductivity (ETC) prediction for wood and determine how the wood’s pore structure influences ETC. Using fractal theory and mercury injection porosimetry data, a fractal model for the geometry of the wood’s pore structure was built. The geometric model was then transformed into an equivalent thermal resistance model to calculate ETC. The calculations produced an explicit expression for ETC derived from the wood’s structural parameters including the minimum and maximum pore apertures, aperture distribution, porosity, and fractal dimension. The model also includes a probability factor. The simulated ETC produced by the model was validated by experiments and it was found to be in good agreement with these. These simulation results will be used to study the influence of several factors on ETC. The proposed model has the potential to be able to predict and analyzing other wood properties such as its electrical conductivity, diffusivity, and permeability and the model can likely also be used to analyze other porous materials.