Mathematical modelling of wheat drying by fractional order and assessment of transport properties

Abstract

The purpose of this study is to evaluate both the temperature and the initial moisture content of the material in mathematical models of drying. For this, empirical lumped parameter models were fitted based on experimental data of moisture over time. Furthermore, a new semi‐empirical drying kinetics model was applied. This model was developed using the generalization of arbitrary order of the Lewis equation obtained through the Laplace transform. After performing the fit, the fractional order model for drying wheat seeds as a temperature function was generalized. Distributed parameter models were also fitted to evaluate the influence of initial moisture content on drying kinetics and to estimate the moisture profile along the position inside the seed. It was verified that the fractional order model presented statistical results similar to models with a higher number of constants, being used to generalize the kinetic drying model for the three wheat cultivars. Generalized models showed better fits for the 3 cultivars with first‐degree function, and the maximum global deviation was 10%, 15%, and 20% for the cultivars BRS–Atobá, BRS–Jacana, and BRS–Sanhaço, respectively. In addition, the distribution of moisture content inside the seed was verified by the distributed parameter model, which predicted the experimental data with an overall deviation of around 10%.

Mathematical modeling of the drying and oil extraction processes of passion fruit seeds using fractional calculus

“…samples of these seeds remained in the oven at a temperature of 105 °C for 24 h to determine their moisture content. 7,12 Lumped parameter models for drying To carry out mathematical modeling of the passion fruit seed drying process, five traditional models were applied (Eqns (1)-( 5)), described in Table 1.…”

“…However, for this to happen, the seed needs to have a lower moisture content than when it arrives from the industries, making the drying process necessary. 7 During drying, both heat and mass transfer occur. The main factor to be evaluated during this process is how the water inside the material migrates to the surface.…”

“…Typically, this transport occurs through liquid diffusion, which is considered the main flow mechanism. [7][8][9] To predict the behavior of the drying process, mathematical models are used. These models aim to optimize drying, explain the variability of process data and reduce experimental errors, in addition to studying heat and mass transfer processes.…”

“…These models aim to optimize drying, explain the variability of process data and reduce experimental errors, in addition to studying heat and mass transfer processes. 7,10,11 Mathematical models in the study of drying can be theoretical (based on the laws of conservation of mass, energy and the process), empirical (experimental data and correlations of input and output variables) or semi-theoretical. Furthermore, these models can be represented in differential form (mainly first order), or fractional models, in which the order of the derivative is an arbitrary non-integer number.…”

Mathematical modeling of Brazilian black soybean: Lumped and distributed parameter models

“…After the drying process, aliquots of the black soybean seeds submitted to drying were removed and placed in crucibles, which remained in the oven at a temperature of 105 C and for a period of 24 h to determine the total moisture content (Aranha, Ferrari, et al, 2023;Ferrari et al, 2023).…”