## 3 Results
### The Interactions of the Independent Variables on the Pressure Drop  
Based on the ANOVA analysis in Section 3.1, the _Mc-v\({}_{air}\)_, _Mc-L_, and _v\({}_{air}\)-L_, respectively, have significant influences on the \(\Delta p\). The response surface as well as its corresponding contour plots are depicted in the following Figures 4-6. As can be seen from Figure 4, the \(\Delta p\) increases with the increase of \(v_{air}\) under constant _Mc_, which might be due to the fact that the inertia resistance of the air increases with the increase of \(v_{air}\), just as reported by [PERSON] et al. [10]. On the other hand, the \(\Delta p\) increases with increase of _Mc_ under constant \(v_{air}\), which might be caused by the increased \(\varepsilon\) in high _Mc_, just as reported by [PERSON] et al. that the \(\varepsilon\) of paddy layer increases with increase of paddy moisture content [38]. Though the suitable \(\Delta p\) for the engineering application should be further investigated by comprehensively considering the power of the fan, the contours shown in Figure 4 can be the reference for the single factor analysis.  
Figure 4: The interaction of _Mc_ and _v\({}_{air}\)_ on the \(\Delta p\) (**a**) and the contour plots (**b**).  
Figure 3: The results of the Anderson–Darling normality test.  
Figure 5 depicts the interaction of \(Mc\) and \(L\) on the \(\Delta p\), similar with the trend shown in above Figure 4. \(\Delta p\) increases with increase of \(L\), which might be caused by the fact that the path of air flow through the paddy grain layer increases with the increase of \(L\) and further lead to the increase of \(\Delta p\); a similar finding has been reported by [PERSON] et al. for \(\Delta p\) of paddy rice layer [39]. On the other hand, the \(\Delta p\) increases with increase of \(Mc\); the same reason analyzed in Figure 4 can be also used to explain the trend. Interestingly, the \(\Delta p\) under different \(Mc\) with the \(L\) under 0.4 m almost remains constant, indicating that the \(\Delta p\) is slightly affected by the \(Mc\) when the \(L\) is small, which can be regarded as a design reference of the bed layer depth. Moreover, it can be seen from Figure 5 that the \(\Delta p\) linearly varies the single factor \(L\) or \(Mc\), while the \(\Delta p\) non-linearly varies with the interaction terms of \(Mc\)-\(L\), just as shown in the following Figure 5.  
The interaction of \(v_{air}\) and \(L\) on the \(\Delta p\) are shown in the following Figure 6. As can be seen from Figure 6 that the \(\Delta p\) varies from the minimum 17.11 Pa to the maximum 689.56 Pa, the variation range is much larger than that of the interaction terms of \(Mc\)-\(L\) and \(Mc\)-\(v_{air}\), indicating that the influence of term \(L\)-\(v_{air}\) on \(\Delta p\) is more significant than that of \(Mc\)-\(L\) and \(Mc\)-\(v_{air}\), just as analyzed in Section 3.1. Accordingly, in order to reach the objective of the efficient and energy-saving drying, efforts should be firstly made to optimize the drying parameters related to the \(L\) and \(v_{air}\) in the engineering drying application. Especially when the air with high \(v_{air}\) flow through the bed layer with large \(L\), the \(\Delta p\) rapidly increases  
Figure 5: The interaction of \(Mc\) and \(L\) on the \(\Delta p\) (**a**) and the contour plots (**b**).  
Figure 6: The interaction of \(v_{air}\) and \(L\) on the \(\Delta p\) (**a**) and the contour plots (**b**).  
with the interaction term of \(L\cdot v_{air}\) (as shown in Figure 5(b), in other words, the larger driven force for supplying the drying medium is needed when the \(L\cdot v_{air}\) is high.