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The fractional calculus in studies on drying: A new kinetic semi‐empirical model for drying
Author(s) -
Souza Matias Gustavo,
Bissaro Camila Andressa,
Matos Jorge Luiz Mario,
Rossoni Diogo Francisco
Publication year - 2019
Publication title -
journal of food process engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.507
H-Index - 45
eISSN - 1745-4530
pISSN - 0145-8876
DOI - 10.1111/jfpe.12955
Subject(s) - fractional calculus , laplace transform , mathematics , differential equation , calculus (dental) , generalization , differential calculus , exponential function , mathematical model , process (computing) , order (exchange) , computer science , mathematical analysis , statistics , medicine , finance , economics , operating system , dentistry
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.