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Mathematical modeling of soybean drying by a fractional‐order kinetic model
Author(s) -
Nicolin Douglas Junior,
Defendi Rafael Oliveira,
Rossoni Diogo Francisco,
de Matos Jorge Luiz Mario
Publication year - 2018
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.12655
Subject(s) - fractional calculus , generalization , mathematics , series (stratigraphy) , mathematical model , kinetic energy , order (exchange) , calculus (dental) , computer science , statistics , mathematical analysis , physics , finance , economics , biology , medicine , paleontology , dentistry , quantum mechanics
In this article, a mathematical model based on the generalization of first‐order kinetic model, to model soybean drying kinetic, is proposed by taking into account that the humidity variation rate is given by a derivative of arbitrary order. The Bootstrap technique was used to study the minimum required number of terms of the analytic solution to fit the parameters with stable variability. Results were highly successful for the estimated moisture curves. These results were compared with the first‐order kinetic model and with the classic Page model. Series solution minimum number of terms varied both with respect to the model parameters and temperature. Practical applications The modeling procedure presented in this article presents the use of fractional calculus as a potential tool to generalize mathematical models based on differential equations. The proposed model proved to be statistically better than its version which was based on conventional calculus. Thus, the model proposed is suitable for modeling kinetic processes in general and can be used to project drying equipment. Due to the fact that drying of food could present nonexponential behavior, the fractional model proposed would be an adequate option to capture the characteristics of the kinetic curve which the conventional calculus cannot. In addition, this article presents a statistical approach to evaluate the correct number of terms to be used in an equation based on an infinite series in order to result the least variability possible. Such approach provides more reliable results when the model is applied to experimental data.