# Mathematical Description of Changes of Dried Apple Characteristics during Their Rehydration
## 3 Results and Discussion
** & **Model Name** & **Variable** & **SSE** & **R\({}^{2}\)** & **Adjusted R\({}^{2}\)** & **RMSE** \\ \hline \multirow{3}{*}{(1)} & \multirow{3}{*}{Peleg} & mass gain & 0.0488–0.6590 & 0.9597–0.9966 & 0.9578–0.9964 & 0.0570–0.1910 \\  & & volume increase & 0.0203–0.4924 & 0.8622–0.9950 & 0.8631–0.9946 & 0.0430–0.1496 \\  & & dry matter loss & 0.0018–0.0385 & 0.9329–0.9976 & 0.9299–0.9974 & 0.0116–0.0454 \\ \hline \multirow{3}{*}{(2)} & Pilosof-Bouquet-Batholomai & mass gain & 0.0488–0.6590 & 0.9597–0.9966 & 0.9578–0.9963 & 0.0570–0.1910 \\  & & volume increase & 0.0203–0.4924 & 0.8622–0.9950 & 0.8531–0.9946 & 0.0430–0.1496 \\  & & dry matter loss & 0.0018–0.0385 & 0.9329–0.9976 & 0.9299–0.9974 & 0.011  
The results of investigation of the effects of characteristic dimension \(L\), drying air temperature \(T_{d}\), drying air velocity \(v_{d}\), and rehydration temperature \(T_{r}\) on the model constants are shown in Table 3 for the models applied to mass gain during rehydration of dried apples, in Table 4 for the models applied to volume increase, and in Table 5 for the models applied to dry matter loss. It is shown in Table 3 that parameters \(A_{1}\), \(A_{2}\), \(A_{3}\), and \(A_{5}\) for models such as Peleg, Pilosof-Bouquet-Batholomai, and Singh and Kulshrestha applied to describe the grain depended in a statistically significant manner on \(L\), \(T_{d}\), \(v_{d}\), and \(T_{r}\), whereas parameters \(A_{4}\) and \(A_{6}\) depended in a statistically significant way on characteristic dimension and rehydration temperature. As far as models 4-7 were concerned, the rehydration rate constant \(k\) depended statistically significantly on characteristic dimension and rehydration temperature for the [PERSON] (Newton), Henderson and Pabis, and modified Page models, whereas for the Page model, it depends only on \(T_{r}\). Parameter \(a\) for the Henderson and Pabis model depends in a statistically significant manner on \(T_{d}\) and \(T_{r}\); parameter \(n\) for the Page model depends on \(T_{r}\); and parameter \(n\) for the modified Page model depends on \(L\), \(T_{d}\), and \(T_{r}\). It turned out from the discussion that the dependence of the parameters of models 4-7 on drying air velocity was statistically insignificant. Taking into account the results presented in Tables 2 and 3, it can be stated that in the process of the prediction of the course of mass gain during the dried apple rehydration, \(L\), \(T_{d}\), \(v_{d}\), and \(T_{r}\) should be taken \begin{table}
\begin{tabular}{c c c} \hline
**Model No.** & **Model Name** & **Parameter Equations** \\ \hline (1) & [PERSON] & \(A_{1}=0.432052+0.0144.L^{2}-5.7\times 10^{-5}.T_{r}{{}^{2}}\) \\  & \(A_{2}=0.064866+0.003357.v{{}^{2}}\)\(+0.042058.L^{2}-3.6\times 10^{-5}.T_{r}{{}^{2}}\) \\ \hline (2) & Pilosof–Bouquet–Batholomai & \(A_{3}=1.797968-0.00243.L\)\(T_{r}\) \\  & \(A_{4}=0.33569+0.043488.L^{2}-6.2\times 10^{-5}.T_{r}{{}^{2}}\) \\ \hline (3) & Singh and Kulshrestha & \(A_{5}=1.351868-0.00028.T_{r}{{}^{2}}-0.00101.T_{r}{{}^{2}}v_{d}+0.000959.T_{d} T_{r}-0.01163.L\)\(T_{r}\) \\  & \(A_{6}=3.563119+0.001701.T_{r}{{}^{2}}+0.058523.T_{d}{{}^{2}}v_{d}-0.00208.T_{d} T_{r}-1.22396.v_{d}\)\(\cdot\)\(L\) \\ \hline (4) & [PERSON] (Newton) & \(k=1.968387+0.000829.T_{r}{{}^{2}}-0.02088.L\)\(T_{r}\) \\ \hline (5) & Henderson-Pabis & \(k=1.622107+0.000699.T_{r}{{}^{2}}-0.01724.L\)\(T_{r}\) \\  & \(a=0.914742\) \\ \hline (6) & Page & \(k=1.367971+0.0004.T_{r}{{}^{2}}-0.01023.L\)\(T_{r}\) \\  & \(n=0.623547-7.1\times 10^{-6}.T_{r}{{}^{2}}\) \\ \hline (7) & Modified Page & \(k=1.797016+0.000814.T_{r}{{}^{2}}-0.01995.L\)\(T_{r}\) \\  & \(n=0.623556-7.1\times 10^{-6}.T_{r}{{}^{2}}\) \\ \hline \end{tabular}
\end{table} 
Table 4: Parameter equations for the models applied to volume increase during rehydration of dried apples.