## 2 Materials and Methods
### Rsm  
In this research, _RSM_ was used in the form of Historical data design as implemented in Design Expert 10 software to analyze the data and optimize the drying process of carrots with a microwave dryer under different pretreatments. The independent variables (input) of the Design Expert software in the microwave dryer included the _MP_ (at three levels of 100, 200, and 300 W) and the _ST_ (2, 4, and 6 mm). The experiments were performed in the form of factorial design on a completely random basis in 3 repetitions. The dependent variables are \(D_{t}\), \(D_{\textit{eff}}\), _SEC_, \(E_{\text{eff}}\), _GHG_ emissions (CO\({}_{2}\), NO\({}_{x}\)), color, and shrinkage. They were used to model the behavior of two-line operating systems and investigate their interaction effects [10]. \[y_{k}=\beta_{0}+\sum_{i=1}^{k}\beta_{i}x_{i}+\sum_{i=1}^{k}\beta_{ii}x_{i}^{2} +\sum_{i}\sum_{j=2}^{k}\beta_{ji}x_{j}x_{i} \tag{9}\]  
where \(y_{k}\) is the response variable, \(x_{i}\) shows the independent variable value, \(x_{j}\) is the actual value of each parameter, \(\beta_{0}\) and \(\beta_{i}\) denote the intercept and the coefficients of the variables, respectively, while \(\beta_{ji}\) is the coefficients of the interaction effects of the variables. Drying variables (independent) are shown in Table 1 with their coded levels. Three important steps in the process optimization with _RSM_ include a statistical design of experiments, a prediction of coefficients in a mathematical model, and an estimation \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Independent Variables**} & \multirow{2}{*}{**Coded Variables**} & \multicolumn{3}{c}{**Levels**} \\ \cline{3-5}  & & \(-\)**1** & **0** & **+1** \\ \hline Thickness (mm) & A & 2 & 4 & 6 \\ \hline Microwave power (W) & B & 100 & 200 & 300 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The coded levels of the independent variables studied and their levels. Changes in the \(D_{t}\) of sample slices for the control sample are depicted in Figure 2 for (a) controls, (b) ultrasonicated, and (c) blanched samples. The longest \(D_{t}\) (170 min) was observed for control samples with 6 mm thickness dried at the 100 W power, while the shortest \(D_{t}\) (42 min) was achieved at the \(MP\) of 300 W and 2 mm thickness in the samples pre-treated with blanching. According to Figure 2, the \(D_{t}\) has decreased linearly and significantly (\(p<0.0001\)) by reducing the \(ST\) and increasing the \(MP\). The microwave-induced power raises the temperature within the plant due to the collision of the ions placed in the electric field. The placement of water molecules along the field direction leads to friction, and hence, to heat production in the product. Subsequently, thermal energy is transferred to all different parts of the carrot through convection and conduction; therefore, the heat diffusion mechanism at higher \(MP_{\text{s}}\) will shorten the \(D_{t}\)[33]. Similar findings were published by other researchers for different products such as kiwi [34], dragon fruit [35], and mushrooms [36]. Moreover, thicker slices of carrot samples dried slower than thinner ones for all experimental treatments, indicating that thinner materials approached equilibrium \(MC\) in a shorter time. Compared to the thicker slices, the moisture can be easily removed from the surface of the thinner products [34]. A study on drying yarn slices under a hot air dryer stated that the \(D_{t}\) decreases by reducing the \(ST\)[26]. Comparison of the \(D_{t}\) of ultrasound pretreated carrot slices with control samples shows that ultrasound pretreatment can accelerate the drying process. Ultrasound waves  
Figure 2: Response surface plots showing the effect of slice thickness (A) and microwave power (B) on drying time: (a) control, (b) ultrasonicated, and (c) blanched samples. can open the micropores of carrot cells (due to the cavitation phenomenon), facilitating the moisture diffusion and significantly shortening the \(D_{t}\).