Modelling the Effective Mass and Heat Diffusivities of Pulp and Uncoated Paper

In the present study different paper structures are created by randomly distributing band-shaped fibres in the paper cross-section. By solving the diffusion equation and the heat conduction equation for such structures the effective mass diffusivity and the effective heat conductivity of the structure is calculated. The models for diffusion agree well with experimental data for water vapour diffusion through hand sheets and pulp sheets, when selecting a physically realistic aspect ratio of the fibre, α ≈ 5. When using a value of 0.33 W/m/K for the heat conductivity of the fibre wall the calculated heat conductivities agree well with measured heat conductivities for a number of paper qualities with porosities between 0.25 and 0.62. However, the comparison with experimental data is hampered by the uncertainty regarding the heat conductivity of the fibre wall.