A model of distributed parameters for non-Fickian diffusion in grain drying based on the fractional calculus approach

Matias, Gustavo S.; Lermen, Fernando Henrique; Matos, Camila; Nicolin, Douglas Júnior; Fischer, C.; Rossoni, Diogo Francisco; Jorge, Luis M.M.

doi:10.1016/j.biosystemseng.2022.12.004

Cited by 18 publications

(10 citation statements)

References 39 publications

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“…Scholars verify that these models are widely used to determine the kinetic model of drying for other types of seeds, such as soybeans, red lentils, maize, paddy, and mulatto beans (Asemu et al, 2020;Lisboa et al, 2019;Matias et al, 2023;Nicolin et al, 2018;Sitorus et al, 2021;Taheri et al, 2020).…”

Section: Resultsmentioning

confidence: 99%

“…However, despite having fewer parameters, both Page and the fractional order model showed good fitting to the experimental data, and the fractional order model was selected to develop an equation that generalizes the drying kinetics, involving all temperatures. Scholars verify that these models are widely used to determine the kinetic model of drying for other types of seeds, such as soybeans, red lentils, maize, paddy, and mulatto beans (Asemu et al, 2020; Lisboa et al, 2019; Matias et al, 2023; Nicolin et al, 2018; Sitorus et al, 2021; Taheri et al, 2020).…”

Section: Resultsmentioning

confidence: 99%

“…The distributed parameter (DP) provides more detailed and superior information about the seed drying process than the LP (Liu & Bakker-Arkema, 2001). Unlike the LP, the DP considers spatial variations (Matias et al, 2023).…”

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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%

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

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

Bissaro,

Defendi,

Aranha

et al. 2023

J Food Process Engineering

View full text Add to dashboard Cite

show abstract

“…Additionally, fractional calculus models can be used to optimize the drying process, leading to improved efficiency and control of the drying process. [11][12][13] Despite the potential benefits of fractional calculus in drying technology, it is not widely used because it is a relatively new field of research, and there is still limited knowledge and understanding of its applications. Additionally, the use of fractional calculus models in drying technology requires specialized knowledge and expertise in both drying technology and fractional calculus, which may be a barrier to its widespread adoption.…”

Section: Introductionmentioning

confidence: 99%

“…Additionally, the use of fractional calculus models in drying technology requires specialized knowledge and expertise in both drying technology and fractional calculus, which may be a barrier to its widespread adoption. [11][12][13] Moreover, there are still some technical challenges associated with the use of fractional calculus models in drying technology, such as the difficulty in obtaining accurate parameters for the models and the computational complexity of solving the models. These challenges require further research and development to overcome.…”

Section: Introductionmentioning

confidence: 99%

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

Aranha,

Ferrari,

Bissaro

et al. 2023

Can J Chem Eng

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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%.

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Mathematical modelling, energy consumption, and quality evaluation of wheat seeds subjected to intermittent drying

Aranha,

Defendi,

Suzuki

et al. 2024

Can J Chem Eng

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This work aims to evaluate the kinetic profile of intermittent drying of wheat seeds using traditional models from the literature and the fractional calculus technique. Furthermore, it aims to verify the application of the intermittent drying process on the amount of antioxidant compounds, protein, and lipid content of the grain, in addition to energy consumption to obtain the desired final moisture content of the wheat. It was verified that the prediction of drying kinetics by Page and fraction order models were similar (modelling efficiency varying between the range of 0.917–0.995, varying the drying condition and wheat cultivar). Regarding antioxidant compounds for the three wheat cultivars, it can be seen that the higher fraction of ethanol (74.0% and 90.36%) used for extraction had greater process efficiency. Regarding the protein content in the three wheat cultivars, lower drying temperatures and intermittency periods result in lower quality losses of material (12.3% for BRS‐Atobá wheat, 9.89% for BRS‐Jacana wheat, and 18.71% for BRS‐Sanhaço wheat). In terms of lipids, it was found that the influence of temperature was greater on the lipid content than on the protein content of the material (for the best drying condition, there were percentage decreases for the best condition of 36.16% for the BRS‐Atobá wheat, 34.9% for BRS‐Jacana, and 52.2% for BRS‐Sanhaço). Regarding energy consumption during the drying process, it can be seen that the conditions used for intermittency and drying time, in addition to the sample conditions, directly impact energy consumption.

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A model of distributed parameters for non-Fickian diffusion in grain drying based on the fractional calculus approach

Cited by 18 publications

References 39 publications

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

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

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

Mathematical modelling, energy consumption, and quality evaluation of wheat seeds subjected to intermittent drying

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