Fractional calculus is a way to describe mathematically a process, and the foundation of this technique is the replacement of the integer‐order differential with fractional order. The approach used in this study was the Caputo derivative and the process analyzed was the drying of beans, corn, and wheat. The fractional order model was compared with Page and first‐order models. For beans, all the conditions analyzed demonstrated an adequate fit, some divergences were found for corn and wheat. The analysis of variance allowed the generalization of parameter k present in the fractional order model as a function of temperature and the results were a first‐degree equation, for beans and wheat, with and without humidification, and for corn, the equation was a second‐degree one; these were successful results for drying of beans, corn, and wheat in the proposed conditions. Practical applications Fractional order model can predict the drying of beans, corn, and wheat grains with higher accuracy in comparison to traditional models applied to drying studies, indicating that the process does not follow a derivative of integer order as usually considered. According to the efficiency values obtained for the generalized model, it was verified that this model can be applied to equipment design and drying process optimization.
The purpose of this study is to assess the drying temperature and initial moisture content on beans and corn seeds drying kinetics and transport properties. It was verified that the best empirical lumped models fitting whereas obtained by Approximation of Diffusion and Hii, Law and Cloke models. This was expected because the fitting tends to improve as the model has more parameters. However, despite having only two parameters, the Page model showed good fitting in all conditions analyzed, therefore, this generalized model could predict experimental data with a maximum global deviation of around 10.0 %. The distributed parameter model assessed moisture content distribution inside the grain, which could predict experimental data with an overall deviation of around 10.0 %. Results indicated that both drying temperature and initial moisture have a significant influence on drying rates and mass transfer coefficients and verified that it is not advisable to neglect the influence of the initial moisture content and its distribution along the position inside the material for beans and corn seeds drying studies.
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