The fractional calculus in studies on drying: A new kinetic semi‐empirical model for drying

Abstract

In this article is introduced a new kinetic semi‐empirical model for drying. The model was developed by arbitrary‐order generalization of Lewis's kinetic equation that was obtained using the Laplace transform and Laplace's Inverse Transform. Kinetic data on soybean drying at 50, 60, 70, and 80 °C were retrieved to test the model which was compared to first‐order Lewis's model and to Page's model by quantitative criteria. Results show that the process is best described by the fractional‐order model and that arbitrary‐order equation may be employed to adjust experimental data on drying, with better results among other models analyzed. Practical applications Drying is one of the most complex and energy‐consuming chemical unit operations. The modeling of drying kinetics can be applied in the project of drying equipment and to reduce costs of energy consumption. In general, the approach used in drying kinetics modeling is based on differential balances to represent the temporal variability of moisture content. In some cases, the Mathematical models cannot fit good the experimental data by to the fact that the models obtained by differential balances are exponential and the experimental data nonexponential. The fractional calculus can be an alternative to generalize the order of differential equations and fit process. The modeling procedure presented in this article presents the use of fractional calculus to generalize the order of a classic differential model. The model obtained by the fractional calculus approach provides best fits and more reliable adjusts than the classic model, the results indicate an anomalous diffusion.

Kinetic Model for Drying in Frame of Generalized Fractional Derivatives

“…In this section, we analyze drying kinetics for soybean in 50 • C, 60 • C, 70 • C, and 80 • C. Matias et al [41] considered real data for the drying kinetics of soybean and managed to fit the data to the results obtained within Caputo fractional sense. From this point of view, we compared the generalized fractional derivative with Caputo, classical Lewis model, and Page model.…”

“…From this point of view, we compared the generalized fractional derivative with Caputo, classical Lewis model, and Page model. We used all parameters, like α order and k, Y e , n constants from [41], during our study. We adapted the k parameter in the Caputo-Lewis model as k α for preserving physical quantities and hence the value of k will change for each α parameters.…”

“…We adapted the k parameter in the Caputo-Lewis model as k α for preserving physical quantities and hence the value of k will change for each α parameters. We study to match generalized fractional results to the Caputo fractional results of [41]. Tables 1-4 show the parameters used in Figures 1-4 respectively.…”

“…Y e 0.10 0.12 0.09 0.01 α 0.57478 0.9 ρ 0.8 n 0.52 Table 2. Parameter values of models [41]. Table 1.…”

“…Recently, Matias et al [41] have studied fractional counterpart of Lewis model (2) within Caputo fractional derivative and they have achieved fitting experimental data with Caputo fractional version of Lewis model (2). Nicolin et al studied the empirical drying model with fractional order [42].…”