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Evaluation of distributed parameters mathematical models applied to grain hydration with volume change

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Abstract

Several studies have taken into account the volume change of foods that undergo hydration or drying. However, the simplest boundary condition at the surface is usually considered to facilitate the solution of variable volume models. This paper presents a model of moisture diffusion in soybean grains that considers the volume change of these grains when absorbing water and also the dependence of diffusivity on moisture content. The boundary condition of equality of diffusive and convective flows on the surface was used and compared with two other approaches commonly found in the literature of grain hydration. This boundary condition was also applied to the case of constant volume of the grains and it was concluded that there are significant differences when the change in volume is taken into account. An analysis of the diffusion coefficients determined as functions of moisture content, temperature, and hydration time is presented for the best model.

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Abbreviations

D:

Diffusion coefficient (m2/s)

Deff :

Effective diffusion coefficient (m2/s)

\({\text{D}}_{\text{eff}}^{*}\) :

Effective diffusion coefficient with respect to radius and time (m2/s)

D0 :

Pre-exponential factor (m2/s)

DPFE:

Distributed parameters flux equality

DPXeq :

Distributed parameters Xeq

i:

Index of summation (dimensionless)

k1 :

Exponential factor (kgds/kgwater)

KC :

Mass transfer coefficient (kg/m2 s)

N:

Divisions in the radial coordinate (dimensionless)

a0–a8 :

Correlation coefficient

r:

Radial coordinate (m)

R:

Grain radius (m)

Rp :

Grain radius as a function of time (m)

t:

Time (s)

teq :

Equilibrium time (s)

T:

Temperature (°C)

X:

Moisture content (kgwater/kgds)

Xm :

Average moisture content calculated by the models (kgwater/kgds)

Xeq :

Equilibrium moisture content (kgwater/kgds)

Xexp :

Experimental moisture content (kgwater/kgds)

Xmax :

Maximum moisture content (kgwater/kgds)

X0 :

Initial moisture content (kgwater/kgds)

Xs :

Moisture content at the surface of the grain (kgwater/kgds)

β:

Saturation rate (s−1)

δr:

Radius increment (m)

ρDS :

Density of dry solid (kg/m3)

ϕ:

Squared residuals (kg 2water /kg 2ds )

ϕm :

Average squared residuals (kg 2water /kg 2ds )

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Acknowledgments

This work was supported by the Coordination for the Improvement of Higher Education Personnel—CAPES—Brazil.

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Authors and Affiliations

  1. Chemical Engineering Graduate Program, Chemical Engineering Department, State University of Maringá (UEM), Av. Colombo, 5790 Block E46-09, Maringá, PR, CEP 87020-900, Brazil

    Douglas J. Nicolin, Regina Maria M. Jorge & Luiz Mario M. Jorge

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  1. Douglas J. Nicolin
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  2. Regina Maria M. Jorge
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  3. Luiz Mario M. Jorge
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Correspondence to Douglas J. Nicolin.

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Nicolin, D.J., Jorge, R.M.M. & Jorge, L.M.M. Evaluation of distributed parameters mathematical models applied to grain hydration with volume change. Heat Mass Transfer 51, 107–116 (2015). https://doi.org/10.1007/s00231-014-1404-3

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