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# Effect of furnish and paper structure on thermal properties

The specific heat of paper is independent of paper structure. It is therefore given by the weighted average of the components

(1)

where ηi and cpi are the mass fraction and specific heat of constituent i, respectively. Figure 1 gives values for the specific heat of different oven-dry pulps.

Figure 1. Calculated values for the specific heat of different pulps as a function of temperature 1.

The most important parameters that affect thermal conduction in paper are moisture content, density, and filler content. Increasing filler content will increase the thermal diffusivity of paper because filler materials conduct heat better than fibres, as indicated in Table 1. Fillers also increase the density and decrease the heat capacity of paper.

Table 1. Thermal properties of some papermaking materials at room temperature. The values for fillers are for solid minerals. For clay, the values in parentheses are those of fireclay that has approximately 30% lower density than the mineral and a lower thermal conductivity.

 Material Density [g/cm3] Thermal conductivity [W/m·K] Specific heat [kJ/kg·K] Thermal diffusivity [10-7 m2/s] Fibre wall 1.2 0.157 1.45 0.90 Water 1.0 0.607 4.18 1.45 Dry air 0.0012 0.0263 1.00 218 Calcium carbonate 2.7 4.5–5.5 0.838 19.9–24.3 Talc 2.7 5–6 0.813 22.8–27.3 TiO2 (rutile) 4.2 9–13 0.714 30.0–43.4 Clay (fireclay at 400 °C) 2.6 (2.0) – (1.0) 0.939 – (5.32)

Figure 2(a) shows thermal diffusivities of different papers. Diffusivity is divided by density squared. This is a normalisation equivalent to changing thickness, z, to grammage (see Eq. 2 in Specific heat and thermal diffusivity). One can see that the normalised thermal diffusivity, α/ρ2, is almost a linear function of density. Assuming that the specific heat of the fibre furnish is constant at cp = 1.45 J/kg·K, the resulting thermal conductivity is rather insensitive to density, as shown in Figure 2(b). Only filler content causes deviations from the general trend.

Figure 2. Normalised thermal diffusivity, α/ρ2 (a), and thermal conductivity, λ (b) vs. density for different papers. The measurement was made with a thermoacoustic cell and thermal conductivity was calculated assuming a constant value cp = 1.45 J/kg·K for the fibre furnish 2.

Calendering or degree of inter-fibre bonding have no effect on the thermal conductivity of ordinary printing papers, as shown in 3 Figure 3. Direct inter-fibre bonding does not seem to be crucial, and heat can transfer quite effectively across small cavities. At elevated temperatures, thermal diffusivity can be substantially larger than at room temperature. The difference disappears at high densities. The effect may relate to effective convection in sheet pores at high temperatures.

Figure 3. Normalised thermal diffusivity, α/ρ2, of handsheets of different pulps vs. density at two different moisture and temperature levels 3.