Analytical Fractal Model for Calculating Effective Thermal Conductivity of the Fibrous Porous Materials

Accurately predicting the effective thermal conductivity of the fibrous materials is highly desirable but remains to be a challenging work. In this paper, the microstructure of the porous fiber materials is analyzed, approximated and modeled on basis of the statistical self-similarity of fractal theory. A fractal model is presented to accurately calculate the effective thermal conductivity of fibrous porous materials. Taking the two-phase heat transfer effect into account, the existing statistical microscopic geometrical characteristics are analyzed and the Hertzian Contact solution is introduced to calculate the thermal resistance of contact points. Using the fractal method, the impacts of various factors, including the porosity, fiber orientation, fractal diameter and dimension, rarified air pressure, bulk thermal conductivity coefficient, thickness and environment condition, on the effective thermal conductivity, are analyzed. The calculation results show that the fiber orientation angle caused the material effective thermal conductivity to be anisotropic, and normal distribution is introduced into the mathematic function. The effective thermal conductivity of fibrous material increases with the fiber fractal diameter, fractal dimension and rarefied air pressure within the materials, but decreases with the increase of vacancy porosity.