Diffusion models for the description of seedless grape drying using analytical and numerical solutions

Wilton Pereira da Silva^*, Cleide Maria Diniz Pereira da Silva e Silva, Jürgen Wolfgang Precker, Josivanda Palmeira Gomes, Pedro Luiz Nascimento, Laerson Duarte da Silva

Federal University of Campina Grande, Campina Grande, PB, Brazil.

DOI: 10.4236/as.2012.34065                

Abstract

This article compares diffusion models used to describe seedless grape drying at low temperature. The models were analyzed, assuming the following characteristics of the drying process: boundary conditions of the first and the third kind; constant and variable volume, V; constant and variable effective mass diffusivity, D; constant convective mass transfer coefficient, h. Solutions of the diffusion equation (analytical and numerical) were used to determine D and h for experimental data of seedless grape drying. Comparison of simulations of drying kinetics indicates that the best model should consider: 1) shrinkage; 2) convective boundary condition; 3) variable effective mass diffusivity. For the analyzed experimental dataset, the best function to represent the effective mass diffusivity is a hyperbolic cosine. In this case, the statistical indicators of the simulation can be considered excellent (the determination coefficient is R² = 0.9999 and the chi-square is χ² = 3.241 × 10^–4).

Keywords

Optimization; Convective Boundary Condition; Diffusion Model; Finite Volume Method

Conflicts of Interest

The authors declare no conflicts of interest.

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