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Heat and Mass Transfer

, Volume 54, Issue 3, pp 885–894 | Cite as

Numerical simulation of heat transfer and phase change during freezing of potatoes with different shapes at the presence or absence of ultrasound irradiation

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Abstract

As novel processes such as ultrasound assisted heat transfer are emerged, new models and simulations are needed to describe these processes. In this paper, a numerical model was developed to study the freezing process of potatoes. Different thermal conductivity models were investigated, and the effect of sonication was evaluated on the convective heat transfer in a fluid to the particle heat transfer system. Potato spheres and sticks were the geometries researched, and the effect of different processing parameters on the results were studied. The numerical model successfully predicted the ultrasound assisted freezing of various shapes in comparison with experimental data of the process. The model was sensitive to processing parameters variation (sound intensity, duty cycle, shape, etc.) and could accurately simulate the freezing process. Among the thermal conductivity correlations studied, de Vries and Maxwell models gave closer estimations. The maximum temperature difference was obtained for the series equation that underestimated the thermal conductivity. Both numerical and experimental data confirmed that an optimum condition of intensity and duty cycle is needed for reducing the freezing time, as increasing the intensity, increased the heat transfer rate and sonically heating rate, simultaneously, that acted against each other.

Keywords

Heat transfer Phase change Numerical modeling CFD 

Nomenclature

A

Surface area (m2).

cp

Specific heat (J kg−1 K−1).

cp,app

Apparent specific heat (J kg−1 K−1).

cpf

Fluid specific heat (J kg−1 K−1).

D

Dimension (m).

F

Shape factor.

h

Convective heat transfer coefficient (W m−2 k−1).

IUS

Ultrasound intensity (W m-2).

k

Thermal conductivity (Wm−1 K−1).

kf

Fluid thermal conductivity (Wm−1 K−1).

L

Latent heat of freezing (J kg−1).

Nu

Nusselt number.

NuUS

Nusselt value when sonication is applied.

Pr

Prandtl number.

R

Radius (m).

Re

Reynolds number.

Sp

Source term caused by phase change (J m−3 s−1).

SUS

Source term caused by ultrasound irradiation (J m−3 s−1).

QUS

Heat generation rate caused by ultrasound irradiation (W kg−1).

T

Temperature (°C).

t

Time (s).

Tf0

Initial freezing temperature of potato (°C).

Tfm

Potato freezing temperature (°C).

Tfw

Freezing temperature of water (°C).

Ti

Initial product temperature (°C).

T

Free stream temperature (°C).

U

Bulk velocity (m s−1).

V

Volume (m3).

xx

Mass fraction (kg kg−1).

xice

Ice fraction.

xwtot

Total water fraction.

xwb

Bond water fraction.

x, y, z

Dimension (m).

X, Y, Z

Boundary coordinate (m).

ρ

Density (kg m−3).

ρf

Fluid density (kg m−3).

μ

Viscosity (Pa.s).

Notes

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Bioprocessing and Biodetection Lab (BBL), Department of Food Science, Technology and EngineeringUniversity of TehranKarajIran
  2. 2.FRCFT, School of Biosystems Engineering, Agriculture and Food Science Centre, University College DublinNational University of IrelandBelfieldIreland

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