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Simulation of mass transfer during osmotic dehydration of apple: a power law approximation method

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Abstract

In this study, unsteady one-dimensional mass transfer during osmotic dehydration of apple was modeled using an approximate mathematical model. The mathematical model has been developed based on a power law profile approximation for moisture and solute concentrations in the spatial direction. The proposed model was validated by the experimental water loss and solute gain data, obtained from osmotic dehydration of infinite slab and cylindrical shape samples of apple in sucrose solutions (30, 40 and 50 % w/w), at different temperatures (30, 40 and 50 °C). The proposed model’s predictions were also compared with the exact analytical and also a parabolic approximation model’s predictions. The values of mean relative errors respect to the experimental data were estimated between 4.5 and 8.1 %, 6.5 and 10.2 %, and 15.0 and 19.1 %, for exact analytical, power law and parabolic approximation methods, respectively. Although the parabolic approximation leads to simpler relations, the power law approximation method results in higher accuracy of average concentrations over the whole domain of dehydration time. Considering both simplicity and precision of the mathematical models, the power law model for short dehydration times and the simplified exact analytical model for long dehydration times could be used for explanation of the variations of the average water loss and solute gain in the whole domain of dimensionless times.

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Abbreviations

C:

Concentration (g/100 g of fresh fruit)

De :

Effective diffusivity (m2/s)

Des :

Effective sucrose diffusivity (m2/s)

Dew :

Effective moisture diffusivity (m2/s)

Jn :

Bessel function of the first kind

l:

Half height of apple samples (mm)

L:

Slab thickness (mm)

P. A.:

Polynomial approximation method

r:

Radius (mm)

R:

Cylinder radius (mm)

S:

Weight of solids in the fruit (g)

S1 :

A constant related with water loss (h−1)

S2 :

A constant related with solid gain (h−1)

SG:

Solid gain (g/100 g fresh fruit)

t:

Time (s)

T:

Temperature (°C)

W:

Weight of fruit (g)

WL:

Water loss (g/100 g fresh fruit)

X:

Dimensionless coordinate

0:

Initial

e:

Equilibrium

Exp:

Experimental

s:

Sucrose

t:

At the time t

w:

Water

φ:

Dimensionless concentration

µn :

Roots of the Bessel function of the first kind

τ:

Dimensionless time (=Det/R2)

∞:

At time ∞ (equilibrium)

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Authors and Affiliations

  1. Chemical Engineering Department, Faculty of Engineering, University of Guilan, Rasht, Iran

    B. Abbasi Souraki, H. Tondro & M. Ghavami

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  1. B. Abbasi Souraki
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  2. H. Tondro
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  3. M. Ghavami
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Correspondence to B. Abbasi Souraki.

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Abbasi Souraki, B., Tondro, H. & Ghavami, M. Simulation of mass transfer during osmotic dehydration of apple: a power law approximation method. Heat Mass Transfer 50, 1443–1453 (2014). https://doi.org/10.1007/s00231-014-1351-z

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  • DOI: https://doi.org/10.1007/s00231-014-1351-z

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