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Heat and Mass Transfer

, 47:1671 | Cite as

Numerical simulation of mushrooms during freezing using the FEM and an enthalpy: Kirchhoff formulation

  • M. V. Santos
  • A. R. LespinardEmail author
Original

Abstract

The shelf life of mushrooms is very limited since they are susceptible to physical and microbial attack; therefore they are usually blanched and immediately frozen for commercial purposes. The aim of this work was to develop a numerical model using the finite element technique to predict freezing times of mushrooms considering the actual shape of the product. The original heat transfer equation was reformulated using a combined enthalpy-Kirchhoff formulation, therefore an own computational program using Matlab 6.5 (MathWorks, Natick, Massachusetts) was developed, considering the difficulties encountered when simulating this non-linear problem in commercial softwares. Digital images were used to generate the irregular contour and the domain discretization. The numerical predictions agreed with the experimental time–temperature curves during freezing of mushrooms (maximum absolute error <3.2°C) obtaining accurate results and minimum computer processing times. The codes were then applied to determine required processing times for different operating conditions (external fluid temperatures and surface heat transfer coefficients).

Keywords

Simulation Freezing Heat transfer Food processing 

List of symbols

CG

Global capacitance matrix

Cp

Specific heat J (kg °C)−1

Cpap

Apparent specific heat J (kg °C)−1

D

Button (cap) diameter (m)

e

Thickness (m)

E

Kirchhoff function (W m−1)

FG

Global force vector

h

Surface heat transfer coefficient (W (m2 °C)−1)

H

Volumetric enthalpy (J m−3)

k

Thermal conductivity (W (m °C)−1)

L

Length of mushrooms (m)

KG

Global conductance matrix

MG

Global convective matrix

N

Vector containing the shape functions

Nj

Shape function j

t

Time (s)

T

Temperature, vector of nodal temperatures (°C)

Text

External fluid temperature (°C)

Tf

Initial freezing temperature (°C)

Tref

Reference temperature (°C)

x

Mass fraction

v

Velocity (m s−1)

Greeks letters

Δt

Time increment (s)

δΩ

Surface of the domain

ε

Residual (Wm−3)

ρ

Density (kg m−3)

Ω

Domain

Gradient

Subscripts

0

Initial

1, 2

Domain

e

Element

e1

Border element

exp

Experimental

sim

Simulated

w

Water

Superscripts

t

Transpose

Notes

Acknowledgments

The authors acknowledge the financial support provided by the Consejo Nacional de Investigaciones Científicas y Tecnológicas (CONICET), Agencia Nacional de Promoción Científica y Tecnológica (ANPCYT), and Universidad Nacional de La Plata, Argentina. We also acknowledge the support given by Dr. R. Mascheroni, Dr. A. Califano and Dr. N. Zaritzky.

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Centro de Investigación y Desarrollo en Criotecnología de Alimentos (CIDCA), CONICET-La PlataFacultad de Ciencias Exactas, Universidad Nacional de La PlataLa PlataArgentina
  2. 2.Facultad de Ingeniería, Universidad Nacional de La PlataLa PlataArgentina
  3. 3.Facultad de Ciencias Agrarias y Forestales, Universidad Nacional de La PlataLa PlataArgentina

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