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ABSTRACT
This article studied the use of diffusion models to describe variation of water quantity and sucrose quantity during osmotic dehydration of bananas cut into cylindrical slices. Bananas with radius of 1.7 cm and 18 °Brix (on average) were cut into 1.0 cm of thickness. A solution was proposed for the diffusion equation in cylindrical coordinates using the finite volume method, with fully implicit formulation. The diffusion equation was discretized assuming diffusivities and dimensions with variable values for the banana slices. Boundary conditions of the third kind have also been considered. The osmotic dehydration experiments were conducted in binary solutions (water and sucrose) under conditions of 40 and 60 °Brix and temperatures of 40 and 70°C. Mathematical modeling was proposed to describe the processes presented good results for water quantity and sucrose quantity, with good statistical indicators for all fits.
Nomenclature
| = | Coefficients of the discretized diffusion equation | |
| a, b | = | Fitting parameters |
| = | Local water quantity at the instant t (g/100 g) | |
| = | Local sucrose quantity at the instant t (g/100 g) | |
| = | Equilibrium water quantity (g/100 g) | |
| = | Equilibrium sucrose quantity (g/100 g) | |
| h | = | Convective mass transfer coefficient ( |
| L | = | Height of the finite cylinder ( |
| = | Initial height of the finite cylinder ( | |
| = | Dimensionless height | |
| = | Radius of the cylinder ( | |
| = | Initial radius of the cylinder ( | |
| = | Dimensionless radius | |
| = | Coefficient of determination (dimensionless) | |
| = | Thickness of a control volume ( | |
| = | Transport coefficient ( | |
| = | Dependent variable of the diffusion equation (g/L00g) | |
| = | Chi-square or objective function (dimensionless) |
Funding
Wilton Pereira da Silva would like to thank the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for the support given to this research and for his research grant (Processes Number 302480/2015-3 and 444053/2014-0).