Vera Solange de Oliveira Farias

Diffusion Models to Describe the Drying Process of Peeled Bananas: Optimization and Simulation

This article aims to study the mass transient diffusion in solids with a cylindrical shape. To this end, the one-dimensional diffusion equation was discretized using the finite volume method with a fully implicit formulation. The solution can be used to simulate diffusive processes and to determine thermophysical parameters via optimization techniques. The computational package developed was applied to study the thin-layer drying of peeled bananas. Three models were used to describe the drying process: (1) the volume V and the effective mass diffusivity D are considered constant; (2) variable V and constant D; (3) V and D are considered variable. For all models, the convective mass transfer coefficient h is considered constant. The statistical indicators show that for the two cases analyzed (low and high temperature), model 3 describes the drying process better than the other models.

Three-Dimensional Diffusion in Arbitrary Domain Using Generalized Coordinates for the Boundary Condition of the First Kind: Application in Drying

This work presents a three-dimensional numerical solution for the diffusion equation in transient state, in an arbitrary domain. For this end, the diffusion equation was discretized using the finite volume method with a fully implicit formulation and generalized coordinates, for the equilibrium boundary condition. For each time step, the system of equations obtained for a given structured mesh was solved by the Gauss-Seidel method. The computational code was developed in FORTRAN, using the CFV 6.6.0 Studio, in a Windows platform. The proposed solution was validated using analytical and numerical solutions of the diffusion equation for different geometries (orthogonal and non-orthogonal meshes). The analysis and comparison of the results showed that the proposed solution provides correct results for the cases investigated. The developed computational code was applied in the simulation of the drying of ceramic roof tiles for the following temperature: 55.6 °C. The analysis of the results makes it possible to affirm that the developed numerical solution satisfactorily describes the drying processes in this temperature.

Effective diffusivity and convective mass transfer coefficient during the drying of bananas

Neste artigo, e usada uma metodologia para a determinacao simultânea da difusividade efetiva e do coeficiente de transferencia convectivo de massa em solidos porosos que possam ser considerados como um cilindro infinito, durante sua secagem. Dois modelos sao utilizados para a otimizacao e a simulacao do processo de secagem: o modelo 1 (volume e difusividade constantes, com condicao de contorno de equilibrio); e o modelo 2 (volume e difusividade constantes, com condicao de contorno convectiva). Algoritmos de otimizacao por varredura, baseados no metodo inverso, foram acoplados as solucoes analiticas referentes aos dois modelos utilizados, possibilitando ajustar tais solucoes aos dados experimentais da cinetica de secagem em camada fina de produtos com a forma cilindrica. Foi feita uma aplicacao da metodologia de otimizacao na descricao da cinetica de secagem de bananas inteiras, usando dados experimentais disponiveis na literatura. Os indicadores estatisticos relativos aos ajustes possibilitam afirmar que a solucao da equacao de difusao com condicao de contorno convectiva produz resultados significativamente melhores que aqueles considerando a condicao de contorno de equilibrio.In this article, a methodology is used for the simultaneous determination of the effective diffusivity and the convective mass transfer coefficient in porous solids, which can be considered as an infinite cylinder during drying. Two models are used for optimization and drying simulation: model 1 (constant volume and diffusivity, with equilibrium boundary condition), and model 2 (constant volume and diffusivity with convective boundary condition). Optimization algorithms based on the inverse method were coupled to the analytical solutions, and these solutions can be adjusted to experimental data of the drying kinetics. An application of optimization methodology was made to describe the drying kinetics of whole bananas, using experimental data available in the literature. The statistical indicators enable to affirm that the solution of diffusion equation with convective boundary condition generates results superior than those with the equilibrium boundary condition.

Transient Diffusion in Arbitrary Shape Porous Bodies: Numerical Analysis Using Boundary-Fitted Coordinates

This chapter provides information about the diffusion phenomenon (heat and mass transfer) in porous materials such as definition, classification, modeling and experiments, with particular reference to capillary-porous body with arbitrary shape. A transient three-dimensional mathematical formulation written in boundary-fitted coordinates and all numerical formalism to discretize the diffusion equation by using the finite-volume method, including grid generation and numerical analysis of the computational solution are presented. Applications to food and ceramic industries have been done with success. An optimization technique has been presented to estimation of transport properties by comparison between numerical and experimental data.

Descrição da secagem de placas cerâmicas por meio de um modelo de difusão

This work aimed to study the water transfer in ceramic plates that can be used as coatings masonry by a liquid diffusion model, as well as to present an optimization algorithm based on the inverse method. The presented algorithm was coupled to the analytical solution of the diffusion equation, enabling to determine the process parameters from the experimental data of drying the plates. The boundary condition employed was of the third kind and the geometry considered was a parallelepiped. Once the process parameters were determined, the drying kinetics of ceramic plates was simulated for each temperature. The ceramic plates were molded with red clay, which is also used in making bricks and tiles. Samples of the product with initial moisture content (dry basis) of 0.110 kg were placed into a kiln at 50.0, 60.0, 70.0 and 90.0 oC and the data of the drying kinetics were obtained. The analysis of the obtained results (statistical indicators and graphics) makes it possible to affirm that the diffusive model adequately describe the drying kinetics. The values obtained for the convective mass transfer coefficient and for the effective water diffusivity were consistent with values reported.

Numerical Solution of the Three-Dimensional Diffusion Equation in Solids with Arbitrary Geometry for the Convective Boundary Condition: Application in Drying

In this work, a numerical solution for the diffusion equation applied to solids with arbitrary shape considering convective boundary condition is presented. To this end, the diffusion equation, written in generalized coordinates, was discretized by the finite-volume method with a fully implicit formulation. The transport parameters and the dimensions of the solids are considered constant during all process. For each time step, the system of equations obtained for a given non-orthogonal structured mesh was solved by the Gauss-Seidel method. One computational code was developed in FORTRAN, using the CFV 6.6.0 Studio, in a Windows platform. The proposed solution was validated using analytical and numerical solutions of the diffusion equation for different geometries (parallelepiped and finite cylinder). The analysis and comparison of the results showed that the proposed solution provides correct results for the cases investigated. In order to verify the potential of the proposed numerical solution, we used experimental data of the drying of ceramic roof tiles for the following temperature: T = 55.6 °C. The analysis of the results and the statistical indicators enables to affirm that the developed numerical solution satisfactorily describes the drying processes in this temperature for the convective boundary condition.

Description of Whole Banana Drying through a Diffusion Model Using Numerical Solution via Generalized Coordinates

Drying is a method of preservation widely used to prolong the post-harvest life of several agricultural products. In this work, experiments were accomplished involving drying of whole bananas, using hot air at temperature of 40.0 ºC and constant velocity of 1.5 m s-1. The mass loss in regular time intervals was measured using the gravimetric method. In order to describe the process, the liquid diffusion model was used, assuming variable volume and effective mass diffusivity [. Thus, the diffusion equation was numerically solved through the finite volume method, with a fully implicit formulation. Due to the geometry of the product, the diffusion equation was written in generalized coordinates, and then discretized, assuming boundary condition of the third kind [. To take advantage of the symmetry, bananas were considered as revolution solids, obtained by the rotation of an area in the plane (x,y) about the axis y. The area was obtained directly of the photography of a banana, which served to create a non-orthogonal structured grid with 32 x 40 control volumes. The thermo-physical parameters were obtained through an optimization algorithm, based on the inverse method. Once the thermo-physical parameters were known, the drying kinetics as well as the water distribution within the bananas in stipulated times were presented and analyzed. The statistical indicators enable to conclude the methodology proposed to describe whole banana drying presents good results.

Study of Diffusion and Water Vapor Permeability in Chitosan Films and Chitosan Emulsified Films

Chitosan is an abundant, natural polysaccaride obtained from fishing industry waste and films of chitosan also provide an efficient oxygen barrier. However, they are a poor water vapor barrier, which can be improved by incorporation of a hydrophobic compound, forming a emulsified film. Chitosan films were produced with the addition of palmitic acid lipid analysis and then the process in parallel with the diffusive permeability to water vapor. The objective of this work was to characterize the diffusion and water vapor permeability behavior of chitosan films and chitosan emulsified films.