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Osmotic dehydration of cubic pieces of melon: description through a three-dimensional diffusion model considering the resistance to mass flows on the surface

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Abstract

The objective of this article was to describe the osmotic dehydration of cubic pieces of melon immersed in solutions of water and sucrose, using a three-dimensional solution of the diffusion equation in Cartesian coordinates, considering the resistance to mass flows on the surface. Three experiments were conducted at room temperature, with no continuous stirring, at the concentrations of 25, 45 and 65 °Brix. A mathematical model that uses a strategy based on the optimal removal of experimental points (OREP) was proposed to determine the process parameters. The kinetics of each process was simulated using the first 8000 terms of the analytical solution with boundary condition of the third type (20 terms for each of the three sums). A comparison with literature results for the same experiments, using the boundary condition of the first type, indicates that although this latter model describes the process reasonably well, the statistical indicators of the model proposed in this article were superior for all experiments, suggesting the existence of resistance to mass flows on the surfaces of melon cubes.

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Abbreviations

A n, A m, A k :

Coefficients of the three-dimensional analytical solution for the local value of the dependent variable

B n, B m, B k :

Coefficients of the three-dimensional analytical solution for the average value of the dependent variable

Bi :

Biot number of mass transfer

D ef :

Effective mass diffusivity (m2 s−1)

h :

Convective mass transfer coefficient (m s−1)

L x, L y, L z :

Parallelepiped edge lengths in the axes x, y, z (m)

m i :

Initial mass of the samples (kg)

m w :

Mass of water at the instant t (kg)

m s :

Mass of solids at the instant t (kg)

N p :

Number of experimental points

S :

Percentage of sucrose (% of the initial mass of the sample)

t :

Time (s)

x, y, z :

Cartesian axes

V :

Volume (m3)

W :

Percentage of the amount of water (% of the initial mass of water in the sample)

μ n, μ m, μ k :

Roots of the characteristic equation for the boundary condition of the first type

\( 1/{\upsigma}_i^2 \) :

Statistical weight of the i-th experimental point

Φ:

Dependent variable of the diffusion equation (the dimension depends on the process studied)

\( {\overline{\varPhi}}^{\ast }(t) \) :

Average value of the variable Φ at an instant t

Φeq :

Equilibrium value of the dependent variable Φ.

\( {\Phi}_i^{sim} \) :

Simulated value of Φ corresponding to the i-th point

\( {\Phi}_i^{\mathrm{exp}} \) :

Experimental value of Φ corresponding to the i-th point

Φ0 :

Value of the variable Φ at the initial instant

χ 2 :

Chi-square and objective function

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Acknowledgments

The second author would like to thank CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) for the support given to this research and for his research grant (Process Number 301708/2019-3; PQ-1A).

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Authors and Affiliations

  1. Federal Institute of Education, Science and Technology of the Ceará State, Ceará, CE, Brazil

    Rubens Maciel Miranda Pinheiro & Denise Silva do Amaral Miranda

  2. Federal University of Campina Grande, Center of Science and Technology, Campina Grande, PB, Brazil

    Wilton Pereira da Silva, Cleide M. D. P. S. eSilva & Taciano Pessoa

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  1. Rubens Maciel Miranda Pinheiro
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  2. Wilton Pereira da Silva
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  3. Denise Silva do Amaral Miranda
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  4. Cleide M. D. P. S. eSilva
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Correspondence to Wilton Pereira da Silva.

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Pinheiro, R.M.M., da Silva, W.P., do Amaral Miranda, D.S. et al. Osmotic dehydration of cubic pieces of melon: description through a three-dimensional diffusion model considering the resistance to mass flows on the surface. Heat Mass Transfer 57, 405–415 (2021). https://doi.org/10.1007/s00231-020-02928-4

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