On the modelling of heat and fluid transport in fibrous porous media: Analytical fractal models for permeability and thermal conductivity

Building upon fractal theory and relying exclusively on analytical models, we develop models for predicting the permeability and effective thermal conductivity of two-directional (2-D) fibrous porous materials. In contrast to previous permeability and conductivity models, two hypothetical parameters (beta and zeta) with physical meaning are introduced to consider the contact thermal resistance at the fiber interfaces, and analytical models for both inplane and out-of-plane directions are developed. Relevant geometrical and physical parameters, including porosity, average tortuosity, and thermal resistance, are obtained by modeling the representative structure (RS) of the fibrous porous material. Good agreement with existing experimental data for fibrous materials over a wide range of porosity (from 0.50 to 0.99) validates the developed models, for both the permeability and effective thermal conductivity. It is demonstrated that, compared with previous models based on simplified geometries relying on periodic distribution assumptions, the current fractal model can better characterize the randomness of pore size and distribution commonly found in commercial fibrous materials.