Abstract
A mathematical model is discussed in terms of moisture transfer during the drying process of Masson pine (Pinus massoniana) lumber in industrial practice. The model was validated by comparing the simulated result of moisture distribution with experimental data. In the model, the wood drying process was divided into two phases. The first one dealt with processes above fiber saturation point (FSP), that was driven by capillary flux of free water and conductive flux of vapor, and the second one dealt with those of below FSP, which was driven by diffusive flux of bound water and vapor. Moisture content distribution (MCD) inside wood is simulated by solving a parabolic partial differential equation under Dirichlet boundary conditions. The moisture content profile (MCP) was asymmetrical in experiments, and the simulation result agreed well with the experiments. An easy empirical formulation was also proposed to calculate real wood permeability, as it showed general characteristics of liquid and vapor permeability. This permeability model is verified as the cause of asymmetrical MCP in this paper.
This research was supported in part by a grant from ‘A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions’.
Appendix
Temperature variation (°C) as a function of drying time and position of the samples in the 1st set of experiment. Drying temperature was 105/85°C for dry-bulb/wet-bulb thermometer and air velocity was 2 m s-1.
| Temperature (°C) in various distances from the surface (mm) | |||||||
|---|---|---|---|---|---|---|---|
| 0 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | ||
| Drying time (h) | |||||||
| 0 | 21.0 | 21.0 | 21.0 | 21.0 | 21.0 | 21.0 | |
| 1 | 77.5 | 70.3 | 60.4 | 54.2 | 53.2 | 53.6 | |
| 2 | 81.1 | 79.1 | 77.9 | 77.1 | 77.1 | 77.1 | |
| 3 | 85.7 | 81.7 | 80.3 | 79.5 | 79.1 | 78.9 | |
| 4 | 85.1 | 81.3 | 81.5 | 81.7 | 81.7 | 81.7 | |
| 6 | 85.1 | 81.1 | 81.1 | 81.1 | 81.1 | 81.1 | |
| 12 | 89.5 | 86.1 | 84.7 | 84.3 | 84.3 | 84.1 | |
| 18 | 94.3 | 89.1 | 83.9 | 83.9 | 83.9 | 83.6 | |
| 24 | 94.6 | 90.7 | 89.1 | 87.7 | 87.4 | 87.1 | |
| 30 | 95.9 | 95.1 | 92.5 | 91.5 | 90.6 | 90.3 | |
| 36 | 97.7 | 96.5 | 94.3 | 93.5 | 93.1 | 92.7 | |
| 42 | 99.9 | 98.7 | 97.5 | 97.3 | 96.5 | 94.9 | |
| 48 | 102.5 | 101.9 | 101.9 | 101.9 | 101.9 | 101.9 | |
Moisture content (MC%) as a function of drying time and position of the samples in the 1st set of experiments.
| Moisture content (MC%) in various distances from the surface (mm) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2.78 | 8.33 | 13.89 | 19.44 | 25.00 | 30.56 | 36.12 | 41.67 | 47.22 | ||
| Drying time (h) | ||||||||||
| 0 | 140.00 | 140.00 | 140.00 | 140.00 | 140.00 | 140.00 | 140.00 | 140.00 | 140.00 | |
| 6 | 88.38 | 94.39 | 112.62 | 115.47 | 120.06 | 118.82 | 113.90 | 106.09 | 93.35 | |
| 12 | 37.37 | 60.47 | 81.52 | 90.80 | 95.44 | 92.01 | 80.43 | 73.64 | 55.05 | |
| 18 | 25.24 | 46.83 | 68.33 | 75.71 | 78.60 | 70.08 | 68.70 | 57.25 | 41.73 | |
| 24 | 13.86 | 30.44 | 49.68 | 57.38 | 59.84 | 58.11 | 52.65 | 42.66 | 22.84 | |
| 30 | 9.57 | 19.57 | 32.33 | 42.42 | 42.65 | 38.20 | 29.73 | 19.57 | 10.28 | |
| 36 | 8.59 | 12.84 | 17.91 | 24.27 | 28.53 | 26.48 | 22.57 | 13.90 | 9.57 | |
| 42 | 7.97 | 10.73 | 12.67 | 14.96 | 18.02 | 15.02 | 11.90 | 9.81 | 8.05 | |
| 48 | 5.87 | 6.27 | 6.36 | 6.79 | 6.72 | 6.64 | 6.36 | 6.06 | 6.00 | |
Temperature variation (°C) as function of drying time and position of the samples in the 2nd set of experiments. Drying temperature was 110/90°C for dry-bulb/wet-bulb thermometer and air velocity was 2 m s-1.
| Temperature (°C) in various distances from the surface (mm) | |||||||
|---|---|---|---|---|---|---|---|
| 0 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | ||
| Drying time (h) | |||||||
| 0 | 19.0 | 19.0 | 19.0 | 19.0 | 19.0 | 19.0 | |
| 1 | 63.9 | 51.6 | 49.6 | 46.3 | 45.7 | 37.3 | |
| 2 | 87.3 | 86.1 | 85.9 | 85.3 | 84.9 | 84.5 | |
| 3 | 88.6 | 87.1 | 87.5 | 87.5 | 87.5 | 87.5 | |
| 4 | 91.8 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | |
| 6 | 92.8 | 91.0 | 88.8 | 88.6 | 88.6 | 88.4 | |
| 12 | 92.5 | 90.2 | 90.8 | 89.8 | 89.5 | 89.0 | |
| 18 | 96.4 | 94.7 | 92.0 | 91.2 | 90.4 | 89.8 | |
| 24 | 100.7 | 98.9 | 95.7 | 93.9 | 93.3 | 92.5 | |
| 30 | 102.0 | 100.8 | 99.2 | 96.8 | 94.5 | 95.7 | |
| 36 | 103.3 | 102.1 | 101.1 | 100.5 | 97.8 | 96.8 | |
| 42 | 105.6 | 105.0 | 104.6 | 103.7 | 102.9 | 102.1 | |
Moisture content (MC%) variation as fucntion of drying time and position of the samples in the 2nd set of experiments.
| Moisture content (MC%) in various distances from the surface (mm) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2.78 | 8.33 | 13.89 | 19.44 | 25.00 | 30.56 | 36.12 | 41.67 | 47.22 | ||
| Drying time (h) | ||||||||||
| 0 | 155.47 | 155.47 | 155.47 | 155.47 | 155.47 | 155.47 | 155.47 | 155.47 | 155.47 | |
| 6 | 131.87 | 124.07 | 129.70 | 116.24 | 111.51 | 98.73 | 91.19 | 85.81 | 90.88 | |
| 12 | 86.14 | 92.60 | 90.96 | 92.13 | 87.18 | 86.16 | 78.08 | 66.18 | 45.00 | |
| 18 | 69.86 | 73.95 | 71.56 | 67.75 | 64.96 | 64.64 | 57.57 | 41.98 | 38.50 | |
| 24 | 23.41 | 39.52 | 51.01 | 50.65 | 57.08 | 52.54 | 55.70 | 45.89 | 34.13 | |
| 30 | 13.61 | 14.51 | 32.25 | 41.4 | 43.75 | 43.58 | 39.37 | 25.81 | 11.70 | |
| 36 | 10.87 | 17.90 | 25.42 | 30.18 | 29.94 | 27.54 | 19.41 | 12.00 | 9.06 | |
| 42 | 8.56 | 10.72 | 15.03 | 19.87 | 21.31 | 17.20 | 12.68 | 9.72 | 8.12 | |
| 48 | 6.06 | 6.27 | 6.93 | 7.50 | 7.66 | 7.30 | 6.55 | 6.00 | 5.85 | |
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