Application of Analytical and Numerical Tools to Describe the Drying of Umbu Seeds (Spondias tuberosa)

Josefa Dayse Lima Silva; Aluizio Freire da Silva Júnior; Vanessa Bordin Viera; Maria Tereza Lucena Pereira; Amélia Ruth Nascimento Lima; Bruno Silva Dantas; Leidjane Matos de Souto; Célia Maria Rufino Franco; Jair Stefanini Pereira de Ataíde

doi:10.4028/p-mT9SzJ

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Application of Analytical and Numerical Tools to Describe the Drying of Umbu Seeds (Spondias tuberosa)
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HomeDefect and Diffusion ForumDefect and Diffusion Forum Vol. 445Application of Analytical and Numerical Tools to...

Application of Analytical and Numerical Tools to Describe the Drying of Umbu Seeds (Spondias tuberosa)

Abstract:

The umbu tree (Spondias tuberosa) belongs to the Anacardiaceae family and is part of the plant biodiversity of Brazilian biomes, such as the Caatinga. Some research related to the nutritional aspects of the pulp of this fruit is found in the literature. On the other hand, studies related to the drying of the seed of this fruit are still rare. Since drying is generally the first step before flour production, which will allow extraction of its nutrients, this work proposes a detailed description of this step. For this purpose, two solutions are proposed (analytical and numerical) for the diffusion equation in cylindrical coordinates, with boundary conditions of the third kind. For the analytical solution, three parameters were considered: the effective constant mass diffusivity (), the convective mass transfer coefficient for the north and south interfaces of the cylinder (), and the convective mass transfer coefficient for the east and west interfaces of the cylinder (). For the numerical solution, the effective diffusivity was considered as a function of the local moisture content (), the convective mass transfer coefficient was assumed to be equal for all interfaces (), and shrinkage was incorporated into the model. The convective mass transfer coefficients obtained through analytical solution show a greater convective effect at the top of the cylinder representing the seeds. Through the results obtained by the numerical solution it can be assumed that due to the heterogeneity of products such as umbu seeds, shrinkage can also be influenced by changes in sample porosity during processing.

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Periodical:

Defect and Diffusion Forum (Volume 445)

Pages:

279-292

DOI:

https://doi.org/10.4028/p-mT9SzJ

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Online since:

December 2025

Authors:

Josefa Dayse Lima Silva, Aluizio Freire da Silva Júnior*, Vanessa Bordin Viera, Maria Tereza Lucena Pereira, Amélia Ruth Nascimento Lima, Bruno Silva Dantas, Leidjane Matos de Souto, Célia Maria Rufino Franco, Jair Stefanini Pereira de Ataíde

Keywords:

Cylindrical Coordinates, Diffusive Model, Effective Mass Diffusivity, Fruit Residues, Shrinkage

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References

[1] M.A.C. LIMA, S.M. SILVA, V.R. OLIVEIRA, et al. Umbu—Spondias tuberosa. In: RODRIGUES, S.; SILVA, E. O.; BRITO, E. S. Exotic Fruits: Reference Guide, Elsevier, 2018, v. 1, pp.427-433.