Processes 2021 , 9 , 1117
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energy loss, the energy provided by the drying system is only used for paper drying; (3) the absolute dry weight of the paper does not change during drying.
K · Δ t Δ W
1 Δ u / Δ t
K M dp ·
Δ H ≈
(6)
=
A relationship model between evaporation heat ( Δ H ) and the first derivative of paper moisture ( Δ u / Δ t ) has been established in Equation (7). That means the evaporation heat curve can be obtained as long as the drying curve (Figure 1b) was measured. K / M dp is the model parameter. Through theoretical analysis, it is found that it is feasible to theoretically estimate the heat of evaporation by measuring the drying curve, but there is still a key problem to be solved, which is to determine the constants K and M dp . The method for determination of the model parameter K / M dp is introduced in Figure 2. In the initial drying period, free water is preferentially evaporated. The thermodynamic and physical properties of free water are the same as that of bulk water. Its evaporation heat is just the latent heat of bulk water ( Δ H lat ). Therefore, Equation (7) can be obtained according to the law of energy conservation. u ∞ is the paper moisture in the initial drying period, mainly referring to the constant drying rate phase.
/ K 1 M u t ' '
dp
lat H '
u
u f
Figure2. Determination of model parameter K / M dp .
1
K M dp ·
Δ H ≈
= Δ H lat
(7)
du
dt
u = u ∞
The model parameter ( K / M dp ) can be calculated as following: K M dp = Δ H lat · du dt u = u ∞
(8)
At atmospheric pressure, Δ H lat is a single variable function of evaporation temperature that is approximately equal to paper temperature ( T p ). By inquiring the physical property data of water, the following fitting Equation (9) can be utilized to calculate the latent heat of water vaporization ( Δ H lat ), which is obtained by regressing the physical property data of water at atmospheric pressure. Δ H lat kJ/kg = 2504.7 − 2.4789 T p ◦ C (9)
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