## 3 Results
### D\({}_{\text{eff}}\)  
The D\({}_{\text{eff}}\) of the carrot slices dried by different dryers was calculated by [PERSON] et al. [2] method as listed in Table 4. According to the previous studies, the D\({}_{\text{eff}}\) lies in the range of the 10\({}^{-12}\)-10\({}^{-7}\) m\({}^{2}\)/s. As can be seen in Table 4, the D\({}_{\text{eff}}\) of the carrot slices was in the same range for all applied dryers, reflecting a good consistency between this study and the previous ones. The highest D\({}_{\text{eff}}\) was observed in the samples treated by the fastest drying method (i.e., US+MW-HD), which is 2.78 \(\times\) 10\({}^{-8}\) m\({}^{2}\)/s; while the lowest value was for the slowest method (i.e., HD), which is 7.12 \(\times\) 10\({}^{-9}\) m\({}^{2}\)/s (\(p\)!0.05). The application of US pretreatment increased the D\({}_{\text{eff}}\) in all methods. US pretreatment opens capillary  
Figure 2: Drying rate of the carrot samples pretreated with ultrasound during different drying methods. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Process**} & \multicolumn{2}{c}{**Page**} & \multicolumn{2}{c}{**Logarithmic**} & \multicolumn{2}{c}{**Two-Term**} & \multicolumn{2}{c}{**[PERSON] et al.**} & \multicolumn{2}{c}{**Logistic**} \\ \cline{2-11}  & \(R^{2}\) & **RMSE** & \(R^{2}\) & **RMSE** & \(R^{2}\) & **RMSE** & \(R^{2}\) & **RMSE** & \(R^{2}\) & **RMSE** \\ \hline HD & 0.9975 & 0.0284 & 0.9969 & 0.0339 & 0.9958 & 0.0452 & 0.9997 & 0.0105 & 0.9988 & 0.0175 \\ INFD & 0.9964 & 0.0396 & 0.9972 & 0.0305 & 0.9949 & 0.0537 & 0.9995 & 0.0116 & 0.9992 & 0.0145 \\ MWD & 0.9949 & 0.054 & 0.9962 & 0.0415 & 0.9955 & 0.0477 & 0.9989 & 0.0164 & 0.9979 & 0.0251 \\ INF-HD & 0.9967 & 0.0361 & 0.9975 & 0.0279 & 0.9968 & 0.0355 & 0.9992 & 0.0144 & 0.9985 & 0.0203 \\ MW-HD & 0.9977 & 0.0266 & 0.9982 & 0.0228 & 0.9978 & 0.0259 & 0.9995 & 0.0111 & 0.9986 & 0.0192 \\ US+HD & 0.9937 & 0.0612 & 0.9955 & 0.0482 & 0.9945 & 0.0569 & 0.9991 & 0.0155 & 0.9977 & 0.0268 \\ US+INFD & 0.9969 & 0.0344 & 0.998 & 0.0237 & 0.997 & 0.0321 & 0.9997 & 0.0101 & 0.9991 & 0.0151 \\ US+MWD & 0.9952 & 0.0503 & 0.9964 & 0.0392 & 0.9958 & 0.0449 & 0.9993 & 0.0132 & 0.9986 & 0.0194 \\ US+INF–HD & 0.9969 & 0.0347 & 0.9982 & 0.0226 & 0.998 & 0.024 & 0.9995 & 0.0118 & 0.9992 & 0.0139 \\ US+MW–HD & 0.9981 & 0.0234 & 0.9988 & 0.0172 & 0.9982 & 0.0223 & 0.9997 & 0.0099 & 0.9994 & 0.0124 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of the non-linear regression analysis of different mathematical drying models. tubes due to the dispersion of the surface composition as well as the formation of the longer microscopic channels as the result of cellular deformations. Therefore, by deforming the cells and destroying the cell walls, US pretreatment can accelerate the moisture removal from the product [41]. Moreover, the application of the MW method can elevate D\({}_{\text{eff}}\), compared to the INFD and HD methods, because the MW power can increase the molecular movements of the water molecules and hence, enhance the D\({}_{\text{eff}}\). [PERSON] and [PERSON] [21] dried lemon using various dryers (MW-HD and INF-HD) with different pretreatments (osmotic, blanching, and US). According to their results, the D\({}_{\text{eff}}\) of the samples dried by INF-HD under various pretreatments varied from \(1.01\times 10^{-9}\) to \(8.44\times 10^{-9}\) m\({}^{2}\)/s, while this range was \(8.11\times 10^{-9}\)-\(4.05\times 10^{-8}\) m\({}^{2}\)/s for those dried by MW-HD under various pretreatments. In the work of [PERSON] et al. [36], the D\({}_{\text{eff}}\) of red beetroot ranged from \(3.42\times 10^{-9}\) to \(1.59\times 10^{-8}\) m\({}^{2}\)/s for various dryers (HD, MW-HD and US pretreatment). The D\({}_{\text{eff}}\) of apples dried by various dryers and US pretreatment ranged from \(1.77\) to \(2.77\times 10^{-9}\) m\({}^{2}\)/s [42].