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Application of a phase change numerical model to the simulation of freezing and thawing of wrapped foods

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Abstract

The process of heat transfer is one of the most important issues in the food industry and plays a crucial role in the storage of frozen foods. The main objective in this field is to extend the storage time, which can be achieved by limiting the heat transfer between the ambient air and the frozen food product. In this paper, the authors applied a numerical model of the phase change process to simulate the freezing and thawing process of a package wrapped with compressible multilayer polymer thermal insulation. The model was solved in COMSOL Multiphysics program and verified with experimental results with satisfactory agreement. Based on the performed simulations and experiments, it was proved that the freezing time of the tylose package is almost the same regardless of the applied film, while the thawing time of the package strongly depends on the type of film—transparent, opaque or metallized. The use of transparent film allows to extend the maximum thawing time of food products by 2 times, the use of opaque film—by about 3.7 times, and the use of metallized film—by about 4.1 times.

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Abbreviations

HPCM :

Enthalpy of the material at a given temperature, J·kg−1

hPCM :

Enthalpy, J·kg−1

ΔHPCM :

Heat capacity (difference of enthalpies), J·kg−1

href :

Standard enthalpy, J·kg−1

Tref :

Standard temperature, °C

\({{\text{C}}}_{{\text{p}}}\) :

Specific heat of the material at constant pressure, J·(kg−1·°C−1)

LPCM :

Latent heat of the material in liquid state, kJ/kg

\({\theta }_{L}\) :

Proportion of the liquid phase, %

\({{\text{T}}}_{{\text{l}}}\) :

Melting point, °C

Ts :

Solidification point, °C

\({\uprho }_{PCM}\) :

Density, kg·m−3

\({{\text{T}}}_{0}\) :

Set temperature, °C

\({\text{u}}\) :

Velocity, m·s−1

\({\uptheta }_{{\text{S}}}\) :

Fraction of the solid phase, %

\({{\text{C}}}_{{\text{p}},{\text{S}}}\) :

Specific heat of the solid material at constant pressure, J·(kg−1·°C−1)

\({{\text{C}}}_{{\text{p}},{\text{L}}}\) :

Specific heat of the liquid material at constant pressure, J·(kg−1·°C−1)

\({{\text{L}}}_{1\to 2}\) :

Phase change enthalpy, J·kg−1

\({{\text{k}}}_{{\text{S}}}\) :

Thermal conductivity of the solid material, W·(m−1·°C−1)

\({{\text{k}}}_{{\text{L}}}\) :

Thermal conductivity of the liquid material, W·(m−1·°C−1)

\({\uprho }_{0}\) :

Initial fluid density, kg·m−3,

\({\rho }_{PCM}\) :

PCM density, kg/m−3,

\({C}_{p,PCM}\) :

Specific heat of the PCM at constant pressure, J·(kg−1·°C−1),

\(\mathbf{u}\) :

Heat transfer vector, -

\({k}_{PCM}\) :

Thermal conductivity (W·(m−1·°C−1))

References

  1. Góral D, Kluza F, Spiess WEL, Kozłowicz K (2016) Review of Thawing Time Prediction Models Depending on Process Conditions and Product Characteristics, Food Technol. Biotechnol 54:3–12

    Google Scholar 

  2. Clark S, Jung S, Lamsal B (2014) Food Processing: Principles and Applications, 2nd edn. Wiley

    Book  Google Scholar 

  3. Coles R, McDowell D, Kirwan MJ (2009) Food Packaging Technology. Wiley-Blackwell

    Google Scholar 

  4. Poursartip A, Street K (1995) Proceedings of the Tenth International Conference on Composite Materials. Woodhead Publishing

    Google Scholar 

  5. Asdrubali F, Pisello AL, D’Alessandro F, Bianchi F, Cornicchia M, Fabiani C (2015) Innovative cardboard based panels with recycled materials from the packaging industry: thermal and acoustic performance analysis. Energy Procedia 78:321–326

    Article  Google Scholar 

  6. Asdrubali F, Pisello AL, D’Alessandro F, Bianchi F, Fabiani C, Rotili M, Cornicchia A (2016) Experimental and numerical characterization of innovative cardboard based panels: thermal and acoustic performance analysis and life cycle assessment. Build Environ 95:145–159

    Article  Google Scholar 

  7. Kasperski J, Grabowska B (2016) Optimizing the thermal effectiveness of an insulation wrap with internal folded polypropylene film for the transportation of frozen food. Int J Refrig 67:42–53

    Article  Google Scholar 

  8. Grabowska B, Kasperski J (2018) Modeling of thermal properties of thermal insulation layered with transparent, opaque and reflective film. J Therm Sci 27(5):463–469

    Article  Google Scholar 

  9. Kasperski J, Grabowska B (2018) The effect of plastic film transmittance on heat transfer in a multilayer insulation structure of rectangular air cells for frozen food wrapping. Int J Refrig 92:94–105

    Article  Google Scholar 

  10. Grabowska B (2006) Influence of Thermal Insulation Properties on Temperature Characteristic during Freezing and Defrosting of Food Products, (Ph.D. thesis). Faculty of Mechanical and Power Engineering, Wroclaw University of Science and Technology, SPR report 28:112

  11. Grabowska B, Królicki Z, Poliński J (2012) Method of manufacturing flexible channel structure material, apparatus for manufacturing flexible channel structure material, and flexible channel structure material. Patent PL 211660:14

  12. Parandi E, Pero M, Hossein K (2022) Phase change and crystallization behavior of water in biological systems and innovative freezing processes and methods for evaluating crystallization. Discover Food 2:6. https://doi.org/10.1007/s44187-021-00004-2

    Article  Google Scholar 

  13. Kiani H, Sun D-W (2018) Numerical simulation of heat transfer and phase change during freezing of potatoes with different shapes at the presence or absence of ultrasound irradiation. Heat Mass Transf 54:885–894. https://doi.org/10.1007/s00231-017-2190-5

    Article  Google Scholar 

  14. Santos MV, Lespinard AR (2011) Numerical simulation of mushrooms during freezing using the FEM and an enthalpy: Kirchhoff formulation. Heat Mass Transf 47:1671–1683

    Article  Google Scholar 

  15. Delgado AE, Sun DW (2001) Heat and mass transfer models for predicting freezing processes – a review. J Food Eng 47:157–174

    Article  Google Scholar 

  16. Buceta JP, Passot S, Scutella B, Bourl’es E, Fonseca F, Trelea IC (2022) Use of 3D mathematical modelling to understand the heat transfer mechanisms during freeze-drying using high-throughput vials. Appl Therm Eng 207:118099

    Article  Google Scholar 

  17. Pham QT (2006) Modeling heat and mass transfer in frozen foods: review article. Int J Refrig 29:876–888

    Article  Google Scholar 

  18. Pham QT, Thermal properties of unsalted MH1000 Tylose gel.

  19. Rouaud O, Pham QT (2012) Heat and mass transfer modelling during freezing of foodstuffs, COMSOL Conferencethe, Milan, Agricultural and Food Sciences, Engineering Corpus ID: 201919598:6

  20. Fadiji T, Ashtiani SHM, Onwude DI, Li Z, Linus UL (2021) Finite Element Method for Freezing and Thawing Industrial Food Processes. Foods 10(4):869. DOI: 10.3390/foods10040869

    Article  Google Scholar 

  21. Sorensen LB (2002) Frozen food legislation, Bulletin de I’Institut International du Froid

  22. Bourdillon AC, Verdin PG, Thompson CP (2015) Numerical simulations of water freezing processes in cavities and cylindrical enclosures. Appl Therm Eng 75:839–855. https://doi.org/10.1016/j.applthermaleng.2014.10.021

    Article  Google Scholar 

  23. Resende ED, Kieckbusch TG, Toledo ECV, Maciel MRW (2007) Discretization of the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements. Braz J Chem Eng 24:399–409

    Article  Google Scholar 

  24. Benkaddour A, Mustapha F, Hamza F (2020) Numerical study of the thermal energy storage behaviour of a novel composite PCM/Concrete wall integrated solar collector. Mater Today: Proc 30:905–908. https://doi.org/10.1016/j.matpr.2020.04.348

    Article  Google Scholar 

  25. Faraji H, El Alami M, Arshad A, Hariti Y (2021) Numerical Survey on Performance of Hybrid NePCM for Cooling of Electronics: Effect of Heat Source Position and Heat Sink Inclination. J Thermal Sci Eng Appl 13(5):051010. https://doi.org/10.1115/1.4049431

    Article  Google Scholar 

  26. Arshad A, Jabbal M, Faraji H, Talebizadehsardari P, Bashir MA, Yan Y (2021) Numerical study of nanocomposite phase change material-based heat sink for the passive cooling of electronic components. Heat and Mass Transfer https://doi.org/10.1007/s00231-021-03065-2

  27. Mehling H (2023) Use of Phase Change Materials for Food Applications—State of the Art in 2022. Appl Sci 13(5):3354. https://doi.org/10.3390/app13053354

    Article  Google Scholar 

  28. Birwal P, Goyal MR, Sharma M, Zhang X, Shi Q, Luo L, Fan Y (n.d) Handbook of Research on Food Processing and Preservation Technologies

  29. Zhang X, Shi Q, Luo L, Fan Y, Wang Q, Jia, G (2021) Research Progress on the Phase Change Materials for Cold Thermal Energy Storage. Energies 14(24):8233. https://doi.org/10.3390/en14248233

    Article  Google Scholar 

  30. Singh S, Gaikwad KK, Lee YS (2018) Phase change materials for advanced cooling packaging. Environ Chem Lett 16:845–859. https://doi.org/10.1007/s10311-018-0726-7

    Article  Google Scholar 

  31. Gin B, Farid MM (2010) The use of PCM panels to improve storage condition of frozen food. J Food Eng 100:372–376. https://doi.org/10.1016/j.jfoodeng.2010.04.016

    Article  Google Scholar 

  32. Flick D, Hoang HM, Duret S, Delahaye A, Laguerre O (2022) Insulated box and refrigerated equipment with PCM for food preservation: State of the art Tanathep Leungtongkum. J Food Eng 317:110874

    Article  Google Scholar 

  33. Cuesta F, Sanchez-Alonso I, Navas A, Careche M (2021) Calculation of full process freezing time in minced fish muscle. MethodsX 8:101292. https://doi.org/10.1016/j.mex.2021.101292

    Article  Google Scholar 

  34. Ilicali C, Icier F (2010) Freezing time prediction for partially dried papaya puree with infinite cylinder geometry. J Food Eng 100:696–704. https://doi.org/10.1016/j.jfoodeng.2010.05.022

    Article  Google Scholar 

  35. Sharma MK, Pratihar AK (2021) Study of Heat Transfer and Freezing TimeTemperature Behavior of Individual Pea Grains by Numerical and Experimental Methods. J Therm Sci Eng Appl 13:021002. https://doi.org/10.1115/1.4047277

    Article  Google Scholar 

  36. Hoang DK, Lovatt SJ, Olatunji JR, Carson JK (2020) Validated numerical model of heat transfer in the forced air freezing of bulk packed whole chickens. Int J Refrig 118:93–103. https://doi.org/10.1016/j.ijrefrig.2020.06.015

    Article  Google Scholar 

  37. Sadot M, Curet S, Le-Bail A, Rouaud O, Havet M (2020) Microwave assisted freezing part 1: Experimental investigation and numerical modeling. Innov Food Sci Emerg Technol 62:102360

    Article  Google Scholar 

  38. Xu C-C, Liu D-K, Guo C-X, Wu Y-Q (2020) Effect of cooling rate and super-chilling temperature on ice crystal characteristic, cell structure, and physicochemical quality of super-chilled fresh-cut celery. Int J Refrig 113:249–255

    Article  Google Scholar 

  39. Alinovi M, Mucchetti G (2020) A coupled photogrammetric–finite element method approach to model irregular shape product freezing: Mozzarella cheese case. Food Bioprod Process 122:98–110

    Article  Google Scholar 

  40. Nguyen TTT, Do QK, Vo CC (2020) A numerical approach for fish fillet modeling during freezing process—Case study fromVietnamese catfish fillets. J Physics Conf Ser 1457:012018

    Article  Google Scholar 

  41. PN–EN 62552–1:2021–01 - Household refrigerating appliances - Characteristics and test methods - Part 3: Energy consumption and volume

  42. Ferreira SR, Rojas LOA, Souza DFS, Oliveira JA (2016) Freezing time of an infinite cylinder and sphere using the method of lines. Int J Refrig 68:37–49. https://doi.org/10.1016/j.ijrefrig.2016.01.021

    Article  Google Scholar 

  43. Cleland DJ, Cleland AC, Earle RL (1987) Prediction of freezing and thawing times for multi-dimensional shapes by simple formulae Part 1: regular shapes. Int J Refrig 10:156–164. https://doi.org/10.1016/0140-7007(87)90006-5

    Article  Google Scholar 

  44. Anderson BA, Singh RP (2005) Moisture Diffusivity in Tylose Gel (Karlsruhe Test Material). J Food Sci 70:E331–E337. https://doi.org/10.1111/j.1365-2621.2005.tb09973.x

    Article  Google Scholar 

  45. Mirahmad A, Sadrameli SM (2018) A comparative study on the modeling of a latent heat energy storage system and evaluating its thermal performance in a greenhouse. Heat Mass Transf 54:2871–2884. https://doi.org/10.1007/s00231-018-2316-4

    Article  Google Scholar 

  46. Arkar C, Medved S (2005) Influence of accuracy of thermal property data of a phase change material on the result of a numerical model of a packed bed latent heat storage with spheres. Thermochim Acta 438(1–2):192–201

    Article  Google Scholar 

  47. Zeneli M, Nikolopoulos A, Karellas S, Nikolopoulos N (2021) Numerical methods for solid-liquid phase-change problems Ultra-High Temperature Thermal Energy Storage, Transfer and Conversion, CHAPTER 7. Elsevier Ltd. https://doi.org/10.1016/B978-0-12-819955-8.00007-7

    Article  Google Scholar 

  48. Allen T (2019) Simulation of Solidification and Cooling of a Casting Product Using Comsol Muliphysics. Master’s Thesis, Science in Engineering, Faculty od Engineering, Lund University, Lund, Sweden

  49. Aadmi M, Karkri M, Hammouti ME (2014) Heat transfer characteristics of thermal energy storage of a composite phase change materials: Numerical and experimental investigations. Energy 72:381–392. https://doi.org/10.1016/j.energy.2014.05.050

    Article  Google Scholar 

  50. Pytlik B, Smykowski D, Szulc P (2022) The Impact of Baffle Geometry in the PCM Heat Storage Unit on the Charging Process with High and Low Water Streams. Energies 15:9349

    Article  Google Scholar 

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Funding

This research was funded by Wroclaw University of Science and Technology, Poland, project number 8211104160/2022, 8211104160/2023.

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Authors and Affiliations

  1. Faculty of Mechanical and Power Engineering, Wroclaw University of Science and Technology, Wybrzeze Wyspianskiego 27, 50-370, Wroclaw, Poland

    Beata Anwajler, Daniel Smykowski & Jacek Kasperski

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  1. Beata Anwajler
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Correspondence to Beata Anwajler.

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Anwajler, B., Smykowski, D. & Kasperski, J. Application of a phase change numerical model to the simulation of freezing and thawing of wrapped foods. Heat Mass Transfer 60, 701–724 (2024). https://doi.org/10.1007/s00231-024-03452-5

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