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Effects of Asymmetric Boundary Conditions on Freezing Process of Raw Potatoes with Variable Thermophysical Properties

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Abstract

In this paper, the effects of asymmetric boundary conditions encountered in refrigerators on the freezing process of raw potatoes were investigated in order to improve their preservation and extend their shelf life. A 2D numerical model, based on experimentally determined temperature-dependent thermophysical properties of potatoes, was first developed using COMSOL Multiphysics software in order to thermally characterize a potato during freezing process. This potato, having a square cross-section of various edge lengths (40 mm and 50 mm), was placed on a meshed surface and subjected to a coolant (air) flow of temperature −40 \(^{\circ }\)C and different velocities (ranging between 0 m\(\cdot\)s\(^{-1}\) and 8 m\(\cdot\)s\(^{-1}\)) from its top, left, and right sides. The evolutions over time of the temperature distribution and the soft–solid interface position in the potato were determined and analyzed. The developed model was then validated thanks to experiments carried out in the same conditions considered in the numerical simulations. An analytical model of the literature was finally established and the obtained results showed an acceptable agreement with the experimental data.

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Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

b :

Distance between interface y-direction and edge on top side, m

Bi :

Biot number

\(c_p\) :

Specific heat capacity, J\(\cdot\)kg\(^{-1}\) \(\cdot\)K\(^{-1}\)

Fo :

Fourier number

g :

Gravitational acceleration, m\(\cdot\)s\(^{-2}\)

Gr :

Grashof number

h :

Heat transfer coefficient, W\(\cdot\)m\(^{-2}\)\(\cdot\)K\(^{-1}\)

H :

Enthalpy, J\(\cdot\)g\(^{-1}\)

K :

Proportion of state change per temperature unit, K\(^{-1}\)

L :

Potato edge length, m

Nu :

Nusselt number

Pr :

Prandtl number

Q :

Ratio of extracted heat power to total heat power needed to be extracted

Re :

Reynolds number

Ste :

Stefan number

t :

Time, s

T :

Temperature, \(^{\circ }\)C

v :

Velocity, m\(\cdot\)s\(^{-1}\)

x :

Abscissa, m

y :

Ordinate, m

\(\beta\) :

Thermal expansion coefficient, K\(^{-1}\)

\(\Delta\) :

Difference

\(\lambda\) :

Thermal conductivity, W\(\cdot\)m\(^{-1}\)\(\cdot\)K\(^{-1}\)

\(\mu\) :

Dynamic viscosity, Pa\(\cdot\)s

\(\varphi\) :

Volumetric heat source, W\(\cdot\)m\(^{-3}\)

\(\rho\) :

Density, kg\(\cdot\)m\(^{-3}\)

\(\theta\) :

Moisture content, %

a :

Air

amb :

Ambient

cd :

Conduction

fc :

Forced convection

fr :

Freezing

ls :

Liquid–solid

nc :

Natural convection

p :

Potatoes

w :

Wall

\(*\) :

Equivalent

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Funding

This project was funded by the National Natural Science Foundation of China (No. 51706154).

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Authors and Affiliations

  1. Tianjin University of Commerce, Guangrong Rd 409, Beichen District, Tianjin, 300134, China

    Georges El Achkar & Bin Liu

  2. Paris-Saclay University, 61 Avenue du Président Wilson, 94235, Cachan, France

    Rachid Bennacer

Authors
  1. Georges El Achkar
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  2. Bin Liu
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  3. Rachid Bennacer
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Contributions

All authors contributed to this study conception and design. The numerical model development, material preparation, experiments achievement, data collection, and analysis were performed by Georges El Achkar and Rachid Bennacer. The first draft of the manuscript was written by Georges El Achkar and all authors commented on the previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Georges El Achkar.

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El Achkar, G., Liu, B. & Bennacer, R. Effects of Asymmetric Boundary Conditions on Freezing Process of Raw Potatoes with Variable Thermophysical Properties. Int J Thermophys 42, 71 (2021). https://doi.org/10.1007/s10765-021-02826-9

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