Several researchers have developed studies to obtain a mathematical model able to describe grain drying kinetics. However, most of these studies neglect the effect of grain initial moisture content on drying curves. In this study, we assessed the dependence of drying curves and mass transfer coefficients on this initial moisture, on air temperature and its velocity by measuring grain mass losses within time on a tray dryer. Mathematical models were adjusted and results indicated that initial grain moisture content has significant influence on drying curves and mass transfer coefficients.

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.

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Variable diffusivity and volume of the grains are taken into account in the diffusion model that describes mass transfer in soybean hydration. The variable space grid method (VSGM) was used to consider the increase in grain size, and the diffusivity was considered an exponential function of the moisture content. An equation for the behavior of the grain radius as a function of time was obtained by global mass balance over the soybean grain and the differential equation considered that the increase in radius happens due to the influence of the convective and diffusive fluxes at the surface of the grains. The model was solved by an explicit numerical scheme which presented satisfactory results. The results showed the behavior of moisture profiles obtained as a function of time and radial position and also showed how the grain radius increased with time and changed the solution domain of the diffusion equation.

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