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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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
References
L. Liebenberg, J.P. Meyer, Appl. Therm. Eng. 27, 2713 (2007)
S.L. Suárez-Gómez, M.L. Sánchez, F. Blanco, J. Ayala, F.J. de CosJuez, J. Hazard. Mater. 336, 168 (2017)
R.M. George, Trends Food Sci. Technol. 4, 134 (1993)
L.E. Jeremiah, Freezing Effects on Food Quality, 1st edn. (CRC Press, Boca Raton, 1996)
M. Zhang, Z.H. Duan, J.F. Zhang, J. Peng, J. Food Eng. 61, 393 (2004)
S. Songsaeng, P. Sophanodora, J. Kaewsrithong, T. Ohshima, Food Chem. 123, 286 (2010)
A.C. Cleland, S. Özilgen, Int. J. Refrig. 21, 359 (1998)
Z. Wang, H. Wu, G. Zhao, X. Liao, F. Chen, J. Wu, X. Hu, J. Food Eng. 79, 502 (2007)
Q.T. Pham, J. Food Eng. 127, 85 (2014)
A.C. Cleland, R.L. Earle, J. Food Sci. 49, 1034 (1984)
A. Biglia, L. Comba, E. Fabrizio, P. Gay, D.R. Aimonino, Energy Procedia 101, 305 (2016)
F. Sepahvandi, H.M. Heravi, S.R. Saleh, Int. J. Heat Technol. 35, 75 (2017)
J.B. Dima, M.V. Santos, P.J. Baron, A. Califano, N.E. Zaritzky, Food Bioprod. Process. 92, 54 (2014)
E. Mokheimer, N.A. El-Aziz, H.E. Amin, M. Salem, Int. J. Energy Res. 27, 1117 (2003)
P.D. Sanz, M. Ramos, J. Aguirre-Puente, J. Food Eng. 40, 233 (1999)
G.L. Lei, W. Dong, M. Zheng, Z.Q. Guo, Y.Z. Liu, Int. J. Heat Mass Transf. 107, 934 (2017)
A.G. Ivanova, V.M. Fuksov, S.F. Gerasimov, A.I. Pokhodun, Int. J. Thermophys. 38, 31 (2017)
S.K. Singh, T.N. Mishra, K.N. Rai, Comput. Therm. Sci. 7, 327 (2015)
A. Chabarov, M. Aider, Innov. Food Sci. Emerg. Technol. 21, 151 (2014)
M. Farid, R. Kizilel, Chem. Eng. Process. 48, 217 (2009)
M. Leung, K.Y. Chan, J. Zhejiang Univ. Sci. A 10, 1 (2009)
L. Bronfenbrener, Chem. Eng. Process. 48, 476 (2009)
L. Bronfenbrener, R. Bronfenbrener, Cold Reg. Sci. Technol. 64, 19 (2010)
M. Leung, W.H. Ching, D.Y.C. Leung, G.C.K. Lam, J. Phys. D Appl. Phys. 38, 477 (2005)
S. Ho, J. Food Sci. 69, E224 (2006)
M. Farid, Chem. Eng. Process. 41, 1 (2002)
R. Basu, JOM 68, 1679 (2016)
H. Yuan, Z. Lu, J. Lu, Food Processing and Preservation Technology (Chemical Industry Press, Beijing, 2000)
Z. Zhong, Research on the intrinsic relationship between the thermophysical parameters of fruits and vegetables and their physiological and biochemical indexes and the neural network prediction model. Ph.D. Thesis, Shanghai Ocean University (2010)
G.C.J. Bart, Int. J. Refrig. 21, 55 (1998)
Funding
This project was funded by the National Natural Science Foundation of China (No. 51706154).
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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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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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DOI: https://doi.org/10.1007/s10765-021-02826-9