Mathematical methodologies for calculating the mass diffusion coefficient of bananas during drying

Amendola, Mariângela; Queiroz, Marlene R. de

doi:10.1590/s1415-43662007000600011

Cited by 13 publications

(20 citation statements)

References 11 publications

(13 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Almeida et al (2009) o feijão vermelho, que apresentou valores entre 2,1 x 10 -10 a 10,4 x 10 -10 m 2 s -1 para temperaturas de secagem entre 25 e 55 °C . Amendola & Queiroz (2007) Como observado na Eq. 21, a energia de ativação para a difusão líquida no processo de secagem do crambe foi de 37,07 kJ mol -1 .…”

Section: Designação Do Modelo Modelounclassified

Coeficiente de difusão efetivo e modelagem matemática da secagem de sementes de crambe

Costa

Resende

Sousa

et al. 2011

Rev. bras. eng. agríc. ambient.

View full text Add to dashboard Cite

O mecanismo através do qual ocorre a difusão da água nos produtos agrícolas, é complexo devido à diversidade da composição química e estrutura física dos produtos. O objetivo no presente trabalho foi ajustar diversos modelos matemáticos ao processo de secagem das sementes de crambe (Crambe abyssinica), em diferentes condições de ar, determinar o coeficiente de difusão efetivo e obter a energia de ativação. As sementes de crambe utilizadas foram colhidas com teor de água de 0,26 (decimal b.s.) e secadas até o teor de 0,09 (decimal b.s.). A secagem do produto foi realizada sob variadas condições controladas nas temperatura de 30, 40, 50, 60 e 70 ºC e umidades relativas de 37,4; 22,3; 14,0; 8,3 e 5,1%, respectivamente. Dentre os modelos que apresentaram melhor ajuste aos dados experimentais, o de Wang e Singh foi o que melhor se ajustou aos dados nas diferentes condições de secagem. O coeficiente de difusão efetivo aumentou com a elevação da temperatura apresentando valores de 0,88 x 10-11; 1,99 x 10-11; 2,90 x 10-11; 3,48 x 10-11 e 5,85 x 10-11 m² s-1, para as temperaturas de 30, 40, 50, 60 e 70 ºC, respectivamente, durante a secagem do crambe. A relação entre o coeficiente de difusão efetivo e a temperatura de secagem pode ser descrita pela equação de Arrhenius, que apresenta uma energia de ativação para a difusão líquida na secagem de 37,07 kJ mol-1.

show abstract

Section: Designação Do Modelo Modelounclassified

Coeficiente de difusão efetivo e modelagem matemática da secagem de sementes de crambe

Costa

Resende

Sousa

et al. 2011

Rev. bras. eng. agríc. ambient.

View full text Add to dashboard Cite

show abstract

“…The computational implementation of this method is simple because the equation is solved in the differential form, with the numerical approximation of the operators. The following works may be cited as examples of using the finite difference method in the solution of the diffusion equation: Amendola and Queiroz (2007), Mariani et al (2008), Ismail et al (2008), andThuwapanichayanan et al (2011). Another method used in the solution of partial differential equations is the finite element method.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional numerical analysis of water transfer in wood: determination of an expression for the effective mass diffusivity

Silva

Farias

et al. 2013

Wood Sci Technol

View full text Add to dashboard Cite

The objective of this article is to determine an expression for the effective mass diffusivity related to the description of wood drying using a diffusion model and experimental data. With this objective, a three-dimensional numerical solution of diffusion equation for the parallelepiped, with convective boundary condition, was used to describe the drying process. For the adopted diffusion model, the convective mass transfer coefficient h was considered constant. The effective mass diffusivity D was considered as a function of the local moisture content, and several expressions were tested to describe the process. To this end, the numerical solution was coupled to an optimizer based on the inverse method, which determines the process parameters D and h using an experimental dataset. For both temperatures of the drying air studied in this article (40 and 80°C), the results obtained by considering the variable effective mass diffusivity are better than those obtained when considering such parameter with a value constant. In addition, with the results for D and h obtained by optimization, the drying kinetics was simulated with success. List of symbols A, BCoefficients of the discretized diffusion equation (dimensionless) DEffective mass diffusivity (m 2 s -1 ) hConvective mass transfer coefficient (m s -1 ) MLocal moisture content at instant t (db, kg kg -1 ) MAverage moisture content at instant t (db, kg kg -1 ) M 0 Initial moisture content (db, kg kg -1 ) M 1 Equilibrium moisture content (db, kg kg -1 )

show abstract

“…A discrete form can be found by using FDM. Betta G., et al [4], Amendola and Queiroz [3], Tabrizi and Hamdullahpur [12], Ahmet Kaya et. al.…”

Section: Mathematical Simulation Modelingmentioning

confidence: 99%

Some Numerical Methods for Temperature and Mass Transfer Simulation on the Dehydration of Herbs

Islam¹,

Alias²

2010

IJCEE

View full text Add to dashboard Cite

Abstract-Advances in herbs based products preservation and technologies are very significant in order to reduce post-harvest losses. The dynamic mathematical model of concurrent heat and moisture transfer are being established for the simulation of temperature and moisture distributions inside the herbs material during dehydration potential of herbs in a slab-shaped solid. Mathematical modeling presents the exchange of heat and mass transfer between material and drying air. Finite-difference method (FDM) based on Crank-Nicolson was used to discretise a parabolic type partial differential equations (PDE). The key purpose of this study is to illustrate the simulation of tropical herbs' dehydration through some numerical methods such as Jacobi, Gauss-Seidel and Red-Black Gauss-Seidel. This study focuses on the implementation of sequential algorithms on the simulation. 3D geometric visualization by COMSOL Multiphysics and graphical numerical results of FDM approximation in mass and heat transfer demonstrate the results of this study. The contribution of this study is a flourishing and modified mathematical simulation in representing the concrete process of dehydration in herbs product based industry. Most thermal and moisture models are empirical rather than theoretical. Therefore, the novelty of this paper is the best sources of thermal and moisture data for the commercial tropical herbs dehydration derived from the mathematical model in order to avoid high prototype costs and to improve inaccurate conditions and process parameters with the advancement of dryer technologies. The computational platform is based on Intel®Core™2Quad processors with MATLAB software. The performance analyses of Numerical methods are presented in terms of execution time, computational complexity, number of iterations, errors, accuracy, and convergence rate.

show abstract

Mathematical methodologies for calculating the mass diffusion coefficient of bananas during drying

Cited by 13 publications

References 11 publications

Coeficiente de difusão efetivo e modelagem matemática da secagem de sementes de crambe

Coeficiente de difusão efetivo e modelagem matemática da secagem de sementes de crambe

Three-dimensional numerical analysis of water transfer in wood: determination of an expression for the effective mass diffusivity

Some Numerical Methods for Temperature and Mass Transfer Simulation on the Dehydration of Herbs

Contact Info

Product

Resources

About