# Mathematical Description of Changes of Dried Apple Characteristics during Their Rehydration
## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c} \hline
**Model No.** & **Model Name** & **Parameter Equations** \\ \hline (1) & Peleg & \(A_{1}=0.087419-2.2\times 10^{-5}.T_{r}{{}^{2}}+0.02319.L^{2}-18.10^{-5}.T_{r}{{}^{2}}+0.0042 2.T_{r}v_{d}-0.08602\)\(\cdot\)\(v_{d}\) \\  & \(A_{2}=0.329564+2.97\times 10^{-5}.T_{r}{{}^{2}}-0.00178.T_{r}{{}^{2}}+0.00024 2.T_{d}+0.0339644\cdot\)\(v_{d}\)\(\cdot\)\(L\) - \(0.00125\)\(\cdot\)\(L\)\(T_{r}\) \\ \hline (2) & Pilosof–Bouquet–Batholomai & \(A_{3}=3.045997-0.00028.T_{r}{{}^{2}}+0.014144.T_{r}{{}^{2}}-0.00385.T_{r}{{}^{2} }-0.31729.v_{d}\)\(\cdot\)\(L\) + \(0.01189\)\(\cdot\)\(L\)\(T_{r}\) \\  & \(A_{4}=0.280897+0.04096.L^{2}-5.5\times 10^{-5}.T_{r}{{}^{2}}\) \\ \hline (3) & [PERSON] and [PERSON] & \(A_{5}=2.252442+0.021388.T_{d}-0.00031.T_{r}{{}^{2}}-0.00693.T_{d}\)\(\cdot\)\(L\) - \(0.0265\)\(\cdot\)\(v_{d}\)\(\cdot\)\(L\) + \(0.013017\)\(\cdot\)\(L\)\(T_{r}\) \\  & \(A_{6}=4.083154\)\(\times\)\(0.001954.T_{r}{{}^{2}}-0.04949.L\)\(\cdot\)\(T_{r}\) \\ \hline (4) & [PERSON] ([PERSON]) & \(k=2.327949+0.001058.T_{r}{{}^{2}}-0.02735\)\(\cdot\)\(L\)\(T_{r}\) \\ \hline (5) & [PERSON]–[PERSON] & \(k=1.940489+0.000939.T_{r}{{}^{2}}-0.02355\)\(\cdot\)\(L\)\(T_{r}\) \\  & \(a=0.895178+7.94\times 10^{-6}.T_{r}{{}^{2}}\) \\ \hline (6) & [PERSON] & \(k=0.72067+0.00015\)\(\cdot\)\(T_{r}{{}^{2}}\) \\  & \(n=0.612353-9.7\times 10^{-6}.T_{r}{{}^{2}}\) \\ \hline \end{tabular}
\end{table} 
Table 3: Parameter equations for the models applied to mass gain during rehydration of dried apples. into consideration, and the [PERSON], Pilosof-Bouquet-Batholomai, or Singh and Kulshrestha models are the better choice. If, however, air drying velocity is not so very important for prediction, the best fit is the modified Page model. According to Table 4, only parameters \(A_{5}\) and \(A_{6}\) for the Singh and Kulshrestha model applied to volume increase depended in a statistically significant manner on all considered drying and rehydration conditions, namely, characteristic dimension, drying air temperature, drying air velocity, and rehydration temperature. As far as the other models are concerned, the following parameters depend statistically significantly on \(L\) and \(T_{r}\): \(A_{1}\) for the Peleg model; \(A_{3}\) and \(A_{4}\) for the Pilosof-Bouquet-Batholomai model; and \(k\) for the [PERSON] (Newton), Henderson and Pabis, Page, and modified Page models. It turned out from the investigation that parameter \(A_{2}\) for the [PERSON] model depended in a statistically significant manner on \(L\), \(v_{d}\), and \(T_{r}\), whereas parameter \(k\) (Page and modified Page models) depended only on \(T_{r}\), and the dependence of parameter \(a\) for the Handerson and Pabis model on the all considered drying and rehydration conditions was statistically insignificant. Taking into account the results shown in Tables 2 and 4, it can be concluded that the application of the Singh and Kulshrestha model for the prediction of the volume increase during rehydration of dried apples enabled the taking into consideration of the influence of \(L\), \(T_{d}\), \(v_{d}\), and \(T_{r}\). If, however, drying conditions are not so very important for the process prediction, the Page and modified Page models seem to be the most appropriate. It can be noticed (Table 5) that parameters \(A_{1}\) and \(A_{2}\) for the Peleg model and parameters \(A_{3}\) and \(A_{4}\) for the Pilosof-Bouquet-Batholomai model used to characterise the dry matter loss during rehydration of dried apples depended in a statistically significant manner on all considered drying and rehydration conditions (\(L\), \(T_{d}\), \(v_{d}\), \(T_{r}\)). Parameter \(A_{5}\) dependence (for the [PERSON] and [PERSON] model) on rehydration temperature was statistically insignificant, whereas for \(A_{6}\), the influence of drying air velocity was statistically insignificant. The situation for the models 4-7 appeared as follows.