Mathematical modeling of beans, corn and wheat drying by fractional calculus

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 applicationsFractional 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.