# The Effect of Pine Wood Thickness on the Freezing and Heating Process in Warm-Air Drying
## 3 Results and Discussion
There was a notable difference in the third zone, where thicker samples had a noticeable temperature differential between the surface and the centre, and the temperature increase was slower. The 30 mm thick samples reached the required temperature after approximately 2:45 h, and the 50 mm thick samples after 5:30 h. Different heating times were not affected by different freezing times but only by the thickness of the samples. Other research [8] also found that a rapid freezing rate of \(-10\)\({}^{\circ}\)C/h did not negatively impact the wood's strength. In contrast, slow freezing at a rate of \(-1\)\({}^{\circ}\)C/h significantly compromised its mechanical properties. Specifically, the study observed reductions in the modulus of rupture (MOR) and modulus of elasticity (MOE) by 20-30%, a decrease in Janka hardness by 18%, and a reduction in tensile strength by 10%. These findings highlight the critical role of the freezing rate in preserving or diminishing the structural integrity of wood during freezing treatments. During the heating process, the temperature differential across the cross-section of the samples was more significant for the 50 mm thickness, which corresponded to the larger measured values of the moisture gradient (Figure 2). Based on the measured temperature data in the samples and the ambient temperature, the time required for defrosting and heating of the 30 and 50 mm thick samples was calculated. The calculated values measured and the heating times determined according to STN EN 49 0651 [17] are given in Table 2.  
The times required for defrosting and heating were theoretically calculated and were longer than the experimentally measured times. The difference was less for a sample thickness of 50 mm. The prescribed times for heating frozen wood during drying according to ON 49 0651 [17] for 50 mm thick samples were almost identical to the calculated times (difference of 0:38 h). For a thickness of 30 mm, the difference was greater by 1:23 h. The larger difference for the thinner thickness may be since the thicker the timber is, the smaller the effect of the heat transfer coefficient on the heating time. The heating time increases faster with increasing sample thickness than the line of proportionality with thickness. Several studies [4; 7; 8] that focused on heating samples of different thicknesses back up this claim. Another reason is that with a thinner sample thickness, there is more moisture evaporation from the wood than with the theoretical predictions. The theoretical models for calculating the heating time are based on assumptions and simplifications that do not accurately describe the heating process. For example, they assume that the wood is orthotropic, that the thermal conductivity is constant during heating, etc. Therefore, there are deviations \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Thickness of Samples**} & \multicolumn{2}{c}{**30 mm**} & \multicolumn{2}{c}{**50 mm**} \\ \hline Initial temperature & \(t_{0}\) & (\({}^{\circ}\)C) & \(-20\) & \(-20\) \\ \hline Required temperature & \(t_{x}\) & (\({}^{\circ}\)C) & 65 & 65 \\ \hline Non-dimensional temperature & \(J\) & (-) & 0.056 & 0.056 \\ \hline Heat transfer coefficient & \(a\) & (W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-1}\)) & 8.883 & 7.241 \\ \hline Coefficient of thermal conductivity & \(l\) & (W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\)) & 0.430 & 0.430 \\ \hline Biot’s criterion & \(Bi\) & (-) & 0.310 & 0.421 \\ \hline Fourier criterion & \(F_{o}\) & (-) & 11.100 & 8.108 \\ \hline Heating time calculated & \(\tau\) & (hh:min) & 4:37 & 9:22 \\ \hline Heating time measured & \(\tau\) & (hh:min) & 2:45 & 5:30 \\ \hline Heating time according to ON 49 0651 & \(\tau\) & (hh:min) & 6:00 & 10:00 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Input parameters, criterion values, and times required for defrosting and heating of samples. between the calculated and measured values of the heating time.