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

Ferrari, Andressa Lopes; Aranha, Ana Caroline Raimundini; Nascimento, Flavio Mosella; Romansina, Bruna Clara; Jorge, Luíz Mário de Matos; Nicolin, Douglas Júnior; Gomes, Maria Carolina Sérgi; Defendi, Rafael Oliveira

doi:10.1111/jfpe.14390

Cited by 4 publications

(2 citation statements)

References 37 publications

(51 reference statements)

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“…To carry out the generalized model, a constant average value of α can be assumed according to studies carried out with wheat, bean, and corn (Ferrari et al, 2023) and the parameter k can be described as a function of only one variable (temperature). For black soybeans, the α average value used was 0.801 and the fitted polynomials considered were first second and third degree.…”

Section: Resultsmentioning

confidence: 99%

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

Bissaro,

Defendi,

Aranha

et al. 2023

J Food Process Engineering

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The main objective of the present work was to assess the temperature and the initial moisture content using models of lumped and distributed parameters, in the description of the drying kinetics in the thin layer of the new Brazilian black soybean cultivar. Lumped models (Page, Newton, Approximation of Diffusion, Hii, Law and Cloke, and Midilli) were fitted based on experimental moisture content data for drying experiments carried out in different temperatures. Fractional order model was also performed and it was generalized as a function of temperature. Distributed parameter models were also fitted to evaluate the influence of initial moisture content on drying kinetics, in addition to estimating the moisture profile along the position inside the black soybean seed. Results indicated that the best kinetic fitting of drying by the lumped parameter technique was obtained for models with a greater number of parameters.Practical applicationsResults indicated that the best kinetic fitting of drying by the lumped parameter technique was obtained for models with a greater number of parameters. The generalized model showed with first degree function, and the maximum global deviation was 15%, and distributed parameters were predicted with a maximum overall deviation of 10%. This result portrays that the fractional order model can be applied to describe the continuous drying process.

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Section: Resultsmentioning

confidence: 99%

“…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).…”

Section: Moisture Determinationmentioning

confidence: 99%

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

Bissaro,

Defendi,

Aranha

et al. 2023

J Food Process Engineering

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

Raimundini Aranha,

Oliveira Defendi,

Sérgi Gomes

et al. 2024

J of Chemical Tech & Biotech

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BACKGROUNDThis article aims to fit kinetic models of the passion fruit seed drying process, in addition to mathematical modeling using traditional models and fractional calculus of the extraction of lipids from the seeds.RESULTSRegarding the drying process, it was found that the model that best suited the two drying temperatures employed was the fractional order one.CONCLUSIONAnalysis showed that for both drying conditions the value of parameter α was greater than 1, indicating that the profile that occurs for the seeds is superdiffusion. Regarding the mathematical fits of oil extraction, it was found that the two models that presented the best fits for the lipid extraction kinetics were hyperbolic and fractional order. Regarding the fractional order model, as the value of parameter α was lower than 1, it can be seen that the process again does not follow Fick's law, and in this case a subdiffusion process occurs. © 2024 Society of Chemical Industry (SCI).

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Heat consumption and modeling of corn seeds intermittent drying

Raimundini Aranha,

Lopes Ferrari,

Paschoal

et al. 2023

JSFA Reports

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BACKGROUNDCorn seed is produced on a large scale, and as production is carried out seasonally, the storage is needed to supply uninterrupted demand. To carry out the storage, as the material from the harvest has a high initial moisture content, it is necessary to carry out the drying process. In order to reduce energy consumption, an alternative is intermittent drying. The purpose of this article is to fit mathematical model of intermittent drying by distributed parameters, based on experimental data of temperature and moisture content of corn seeds submitted to intermittent drying, to determine the diffusivity value and to assess heat consumption.RESULTSFor samples dried to the final moisture content of 16.0 % in dry basis (d.b.), the condition of intermittent drying at a temperature of 40 °C and 10 minutes of tempering period led to the lowest heat consumption, in comparison to conventional drying and to intermittent drying under higher temperatures. In addition, to obtain a final moisture content of 14.0 % (d.b.), the conventional drying condition at 55 °C resulted in the lowest heat consumption, compared to the other drying conditions. The distributed parameter model can predict the experimental data with a global deviation lower than 10.0 %CONCLUSIONAnalyzing the moisture distribution profiles for the corn seeds, it was verified that there was a difference in the moisture content along the position inside the material, being necessary to evaluate the influence of moisture distribution along the position inside the material in kinetic drying models.This article is protected by copyright. All rights reserved.

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

Cited by 4 publications

References 37 publications

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

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

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

Heat consumption and modeling of corn seeds intermittent drying

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