Cleide M. D. P. S. e Silva

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.

Optimization and simulation of drying processes using diffusion models: application to wood drying using forced air at low temperature

This paper discusses the suitability of four diffusion models to describe the drying of wood. The first model refers to the analytical solution of an infinite slab with boundary condition of the first kind. In the last three models, the boundary condition is of the third kind and the analytical solutions refer to the following geometries: infinite slab, rectangle, and parallelepiped. The analytical solutions were coupled to an optimizer based on inverse method, which enables to calculate process parameters for an experimental data set. Once the process parameters were determined, the drying kinetics of wood was simulated through each model proposed. The obtained results lead to the conclusion that the first model does not represent the drying kinetics properly. The last three models adequately describe the drying kinetics, but statistical indicators enable to affirm that the best of them is the three-dimensional model.

Numerical Simulation of the Water Diffusion in Cylindrical Solids

In this article, a mathematical model was developed for the numerical simulation of the water diffusion in an infinite cylinder. A solver for the diffusion equation was created using the finite volume method, with a fully implicit formulation. In order to create such solver, it was assumed that the boundary condition of the first type is adequate to simulate the physical problem. The solver presupposes variable thermophysical properties and radius in the domain. In order to determine the parameters of the expression between the diffusivity and the moisture content, an optimizer was created, based on the inverse method. The developed mathematical model was applied to simulate the drying of banana and rough rice, using experimental data obtained from the literature. The results obtained in this article, considering the variable diffusivity, are better than the results obtained originally in the literature, where the water diffusivity was considered constant.

''LAB Fit ajuste de curvas'': um software em português para tratamento de dados experimentais

This paper aims to communicate the development of a software for treatment of experimental data called LAB Fit (curve fitting, 2D and 3D graphs, basic statistics, error propagation and mathematical tools). The english version was released two years ago and, due to the achieved success, verified by the great number of downloads, it is also being released a portuguese version. Typical examples of using of the LAB Fit show part of the potentialities of the program in the experimental teaching and research. The performance of the software has been verified with the Statistical Reference Datasets Project (SRDP) of the National Institute of Standards and Technology (NIST), which presents 27 datasets (and functions) with certified values for the parameters. All the 27 LAB Fit results are statistically identical to the certified values.

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.

Description of osmotic dehydration of apple using two-dimensional diffusion models considering shrinkage and variations in process parameters

ABSTRACT The main purpose of this paper is to study osmotic dehydration of apple in water and sucrose solutions. The kinetics of water quantity and solid gain are described by two mathematical models using numerical solutions of the two-dimensional diffusion equation in Cartesian coordinates with boundary condition of third kind. For the first model, both the process parameters and the product dimensions have been considered constant. For the second model these quantities have been taken as variable. The numerical solutions have been obtained via the finite volume method with fully implicit formulation. Process parameter estimation, using experimental data, was obtained by an optimizer based on the inverse method. The third-kind boundary condition was shown to be appropriate in view of the fact that the resistances to mass flows on the product surface are not at all negligible. The temperature and concentration of the osmotic solution used in the experiments influenced significantly the kinetics of solid uptake and water quantity as well as the values of estimated parameters. Mathematical model which considers the variations in the process parameters and the product shrinkage presents good physical consistency and well describes the mass migrations.

A Numerical Approach to Determine Some Properties of Cylindrical Pieces of Bananas During Drying

Abstract This article uses several liquid diffusion models to describe convective drying of bananas cut into cylindrical pieces. A two-dimensional numerical solution of the diffusion equation with boundary condition of the third kind, obtained through the finite volume method, was used to describe the process. The cylindrical pieces were cut into the following dimensions: length of about 21 mm and average radius of 15 mm. Drying air temperatures were 40°C, 50°C, 60°C and 70°C. In order to determine the process parameters, an optimizer was coupled with the numerical solution. A model that considers the shrinkage and variable effective moisture diffusivity well describes drying for all the experimental conditions, and enables to predict the moisture distributions at any given time. For this model, the determination coefficient has varied from 0.99937 (70°C) to 0.99995 (40°C), while the chi-square ranged from 3.41 × 10−4 (40°C) to 4.15 × 10−3 (70°C).

Calculation of the convective heat transfer coefficient and thermal diffusivity of cucumbers using numerical simulation and the inverse method

Cooling of fruits and vegetables, immediately after the harvest, has been a widely used method for maximizing post-harvest life. In this paper, an optimization algorithm and a numerical solution are used to determine simultaneously the convective heat transfer coefficient, hH, and the thermal diffusivity, α, for an individual solid with cylindrical shape, using experimental data obtained during its cooling. To this end, the one-dimensional diffusion equation in cylindrical coordinates is discretized and numerically solved through the finite volume method, with a fully implicit formulation. This solution is coupled to an optimizer based on the inverse method, in which the chi-square referring to the fit of the numerical simulation to the experimental data is used as objective function. The optimizer coupled to the numerical solution was applied to experimental data relative to the cooling of a cucumber. The obtained results for α and hH were coherent with the values available in the literature. With the results obtained in the optimization process, the cooling kinetics of cucumbers was described in details.

Numerical approach to describe continuous and intermittent drying including the tempering period: Kinetics and spatial distribution of moisture

ABSTRACT Continuous and intermittent drying experiments were performed with whole bananas, using hot air at 70°C. The intermittent drying experiments were performed with intermittency ratio equal to 1/2 and tempering times of 0.5, 1.0, and 2.0 h. The conditions imposed to the experiments permitted to investigate the influence of these tempering times on the processes. A one-dimensional numerical solution of the diffusion equation coupled with an optimizer was used to determine the process parameters for four experiments. To describe the processes, a model was proposed. Model includes shrinkage, variable effective mass diffusivity, and two values for convective mass transfer coefficient (within and outside the dryer), enabling to consider moisture loss during the tempering period. For all experiments, the simulation of the drying kinetics has resulted in good statistical indicators. Proposed model also made it possible to predict moisture distributions during the entire processes, including the migration of moisture from the central part to the peripheral region of the cross section of the bananas, during the tempering period. The results indicated that, for the same effective operation time and intermittency ratio, increasing the tempering time implied moderate decrease in the final average moisture content.

Comparison of boundary conditions to describe drying of turmeric ( Curcuma longa ) rhizomes using diffusion models

Turmeric is harvested with high moisture content and should be dried before the storage. It is observed that drying is quickest when the rhizomes are peeled and cut in small cylindrical pieces. In order to describe the process, normally a diffusive model is used, considering boundary condition of the first kind for the diffusion equation. This article uses analytical solutions considering boundaries conditions of the first (model 1) and third (model 2) kinds coupled to an optimizer to describe the drying process. It is shown that, for model 1, the fit of the analytical solution to the experimental data is biased, despite the good statistical indicators (chi-square χ2 equal to 1.7095 × 10−3 and coefficient of correlation R2 of 0.9988). For model 2, the errors of the experimental points about the simulated curve can be considered randomly distributed, and the statistical indicators are much better than those obtained for model 1: χ2 = 3.5596 × 10−4 and R2 = 0.9996.