## 4 Results and Discussion
### Influence of Ultrasound Pre-Treatment on Drying Kinetics of Conveyor-Belt Dryer  
Based on the numerical results, the parameters of the characteristic drying-curve model are established. As can be seen in Figure 8, the numerical drying kinetic curve can be divided into two periods. In the first drying period, the drying rate remains more or less constant with a high value. When the moisture content is lower than the critical moisture content, the drying rate drops quickly, and the second drying period commences. This drying behavior has been observed in the experimental data as well. The critical moisture content \(X_{\text{cr}}\) is determined from the numerical drying curve at the transition point between these two periods. The impact of drying temperature and US pre-treatment on the critical moisture content is plotted in Figure 9. As can be seen, the critical moisture content reduces when the drying temperature increases. It can be reasoned that at high temperatures, a large value of the effective moisture diffusivity (Figure 5) can help to sustain the sample surface sufficiently wetted for a longer period. Additionally, the effective moisture diffusivity is enhanced by the US pre-treatment; therefore, a lower critical moisture content can be observed compared to the non-pre-treatment drying process. Afterwards, the drying rate retardation coefficient \(f\) of the second drying period is computed as the ratio between the temporal drying rate and the drying rate at the transition point. The numerical drying rate retardation coefficient \(f\) is correlated as a function of the normalized moisture content \(X_{n}\) using Equation (28). The result indicates that at high temperatures, the relationship between \(X_{n}\) and \(f\) approaches linearity. However, for the sake of model simplicity, the data obtained from different temperatures are all  
Figure 8: An exemplary drying kinetic curve obtained from numerical and experimental data. Figure 9: Impact of drying temperature on the critical moisture content. fitted together. Values of \(p=0.718\) and \(p=0.746\) are used to represent the drying rate retardation coefficient \(f\) for the non-pre-treatment and US pre-treatment drying processes, respectively. The discrepancy between the correlated characteristics drying curve and the numerical drying curve obtained from the diffusion model is presented in Figure 10. As can be seen, the correlation using Equation (28) fairly reflects the numerical drying behavior. Thus, Equation (28) with \(p\) values of 0.718 and 0.746 can be readily integrated into the conveyor-belt-drying model. The conveyor-belt-drying model simulation is performed on both non-pre-treated and US pre-treated carrot slices, with the operational conditions outlined in Table 3. The simulation results are plotted in Figure 11. The results indicate that US pre-treatment accelerates the drying process in the belt dryer. The solid temperature remains at the adiabatic saturated temperature for a longer time in the dryer compared to the non-pre-treated product. This implies that the first drying period is extended. As a result, the moisture content decreases more rapidly in the US pre-treated carrot slices. To compare the drying effectiveness, the final moisture content of 1 kg water/kg dried solid, 0.75 kg water/kg dried solid, and 0.5 kg water/kg dried solid are chosen to determine the required belt length. The results are presented in Table 4, revealing that US pre-treatment significantly reduces the belt length needed, by approximately 12.9% to 14.7%. The influence of US pre-treatment on the required belt length becomes even more pronounced at lower final moisture content.