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



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.


Heat transfer Phase change Numerical modeling CFD 



Surface area (m2).


Specific heat (J kg−1 K−1).


Apparent specific heat (J kg−1 K−1).


Fluid specific heat (J kg−1 K−1).


Dimension (m).


Shape factor.


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


Ultrasound intensity (W m-2).


Thermal conductivity (Wm−1 K−1).


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


Latent heat of freezing (J kg−1).


Nusselt number.


Nusselt value when sonication is applied.


Prandtl number.


Radius (m).


Reynolds number.


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


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


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


Temperature (°C).


Time (s).


Initial freezing temperature of potato (°C).


Potato freezing temperature (°C).


Freezing temperature of water (°C).


Initial product temperature (°C).


Free stream temperature (°C).


Bulk velocity (m s−1).


Volume (m3).


Mass fraction (kg kg−1).


Ice fraction.


Total water fraction.


Bond water fraction.

x, y, z

Dimension (m).

X, Y, Z

Boundary coordinate (m).


Density (kg m−3).


Fluid density (kg m−3).


Viscosity (Pa.s).


Compliance with ethical standards

Conflict of interest

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


  1. 1.
    Dwivedi M, Ramaswamy H (2010) An empirical methodology for evaluating the fluid to particle heat transfer coefficient in bi-axially rotating cans using liquid temperature data. Food Bioprocess Technol 3:716–731. CrossRefGoogle Scholar
  2. 2.
    Koribilli N, Aravamudan K, Aditya Varadhan M (2011) Quantifying enhancement in heat transfer due to natural convection during canned food thermal sterilization in a still retort. Food Bioprocess Technol 4:429–450. CrossRefGoogle Scholar
  3. 3.
    Mujumdar A, Law C (2010) Drying technology: trends and applications in postharvest processing. Food Bioprocess Technol 3:843–852. CrossRefGoogle Scholar
  4. 4.
    Ramaswamy H, Dwivedi M (2011) Effect of process variables on heat-transfer rates to canned particulate newtonian fluids during free bi-axial rotary processing. Food Bioprocess Technol 4:61–78. CrossRefGoogle Scholar
  5. 5.
    Rosnes J, Skåra T, Skipnes D (2011) Recent advances in minimal heat processing of fish: effects on microbiological activity and safety. Food Bioprocess Technol 4:833–848. CrossRefGoogle Scholar
  6. 6.
    LeBail A, Chevalier D, Mussa DM, Ghoul M (2002) High pressure freezing and thawing of foods: a review. Int J Refrig 25:504–513CrossRefGoogle Scholar
  7. 7.
    Cai J, Huai X, Yan R, Cheng Y (2009) Numerical simulation on enhancement of natural convection heat transfer by acoustic cavitation in a square enclosure. Appl Therm Eng 29:1973–1982. CrossRefGoogle Scholar
  8. 8.
    Cai J, Huai X, Liang S, Li X (2010) Augmentation of natural convective heat transfer by acoustic cavitation. Front Energy Power Eng Chin 4:313–318CrossRefGoogle Scholar
  9. 9.
    Kim H-Y, Kim YG, Kang BH (2004) Enhancement of natural convection and pool boiling heat transfer via ultrasonic vibration. Int J Heat Mass Transf 47:2831–2840. CrossRefGoogle Scholar
  10. 10.
    Hyun S, Kleinstreuer C (2002) Acoustic streaming induced by ultrasonic flexural vibrations and associated enhancement of convective heat transfer. J Acoust Soc Am 111:875–883CrossRefGoogle Scholar
  11. 11.
    Hyun S, Lee D-R, Loh B-G (2005) Investigation of convective heat transfer augmentation using acoustic streaming generated by ultrasonic vibrations. Int J Heat Mass Transf 48:703–718. CrossRefGoogle Scholar
  12. 12.
    Dhanalakshmi NP, Nagarajan R, Sivagaminathan N Prasad BVSSS Acoustic enhancement of heat transfer in furnace tubes. Chem Eng Process Process Intensif.
  13. 13.
    Rahimi M, Dehbani M, Abolhasani M Experimental study on the effects of acoustic streaming of high frequency ultrasonic waves on convective heat transfer: Effects of transducer position and wave interference. Int Commun Heat and Mass Transfer.
  14. 14.
    Kiani H, Sun D-W, Zhang Z (2012) The effect of ultrasound irradiation on the convective heat transfer rate during immersion cooling of a stationary sphere. Ultrason Sonochem 19:1238–1245. CrossRefGoogle Scholar
  15. 15.
    Li B, Sun D-W (2002) Effect of power ultrasound on freezing rate during immersion freezing of potatoes. J Food Eng 55:277–282CrossRefGoogle Scholar
  16. 16.
    Loh BG, Hyun S, Ro PI, Kleinstreuer C (2002) Acoustic streaming induced by ultrasonic flexural vibrations and associated enhancement of convective heat transfer. J Acoust Soc Am 111:875–883CrossRefGoogle Scholar
  17. 17.
    Kiani H, Sun D-W, Delgado A, Zhang Z (2012) Investigation of the effect of power ultrasound on the nucleation of water during freezing of agar gel samples in tubing vials. Ultrason Sonochem 19:576–581. CrossRefGoogle Scholar
  18. 18.
    Kiani H, Sun D-W, Zhang Z (2013) Effects of processing parameters on the convective heat transfer rate during ultrasound assisted low temperature immersion treatment of a stationary sphere. J Food Eng 115:384–390. CrossRefGoogle Scholar
  19. 19.
    Fikiin KA (1996) Generalized numerical modelling of unsteady heat transfer during cooling and freezing using an improved enthalpy method and quasi-one-dimensional formulation. Int J Refrig 19:132–140. CrossRefGoogle Scholar
  20. 20.
    Pham QT (2006) Modelling heat and mass transfer in frozen foods: a review. Int J Refrig 29:876–888. CrossRefGoogle Scholar
  21. 21.
    Otero L, Ousegui A, Guignon B, Le Bail A, Sanz PD (2006) Evaluation of the thermophysical properties of tylose gel under pressure in the phase change domain. Food Hydrocoll 20:449–460. CrossRefGoogle Scholar
  22. 22.
    Pham Q (1995) Comparison of general-purpose finite-element methods for the Stefan problem. Numer Heat Transfer 27:417–435CrossRefGoogle Scholar
  23. 23.
    Hamdami N, Monteau J-Y, Le Bail A (2004) Heat and mass transfer in par-baked bread during freezing. Food Res Int 37:477–488. CrossRefGoogle Scholar
  24. 24.
    Hamdami N, Monteau J-Y, Le Bail A (2004) Simulation of coupled heat and mass transfer during freezing of a porous humid matrix. Int J Refrig 27:595–603. CrossRefGoogle Scholar
  25. 25.
    Hamdami N, Monteau JY, Le Bail A (2003) Effective Thermal Conductivity Evolution as a Function of Temperature and Humidity, During Freezing of a High-Porosity Model Food. Chem Eng Res Des 81:1123–1128. CrossRefGoogle Scholar
  26. 26.
    Hamdami N, Monteau J-Y, Le Bail A (2004) Transport properties of a high porosity model food at above and sub-freezing temperatures. Part 2: Evaluation of the effective moisture diffusivity from drying data. J Food Eng 62:385–392. CrossRefGoogle Scholar
  27. 27.
    Hamdami N, Monteau J-Y, Le Bail A (2004) Transport properties of a high porosity model food at above and sub-freezing temperatures. Part 1: Thermophysical properties and water activity. J Food Eng 62:373–383. CrossRefGoogle Scholar
  28. 28.
    Hamdami N, Monteau J-Y, Le Bail A (2004) Thermophysical properties evolution of French partly baked bread during freezing. Food Res Int 37:703–713. CrossRefGoogle Scholar
  29. 29.
    Pham QT (1989) Prediction of thermal conductivity of meats and other animal products from composition dataGoogle Scholar
  30. 30.
    McKellar A, Paterson J, Pham QT (2009) A comparison of two models for stresses and strains during food freezing. J Food Eng 95:142–150. CrossRefGoogle Scholar
  31. 31.
    Kiani H, Zhang Z, Sun D-W (2015) Experimental analysis and modeling of ultrasound assisted freezing of potato spheres. Ultrason Sonochem 26:321–331. CrossRefGoogle Scholar
  32. 32.
    Voller VR, Prakash C (1987) A fixed grid numerical modelling methodology for convection-diffusion mushy region phase-change problems. Int J Heat Mass Transf 30:1709–1719. CrossRefGoogle Scholar
  33. 33.
    Voller V, Swaminathan C, Thomas B (1990) Fixed grid techniques for phase change problems: A review. Int J Numer Methods Eng 30:875–898CrossRefMATHGoogle Scholar
  34. 34.
    Whitaker S (1972) Forced convection heat transfer correlations for flow in pipes, past flat plates, single cylinders, and flow in packed beds and tube bundles. AICHE J 18:361–371CrossRefGoogle Scholar
  35. 35.
    ASHRAE (2009) ASHRAE Fundamentals Handbook (SI) American Society of Heating Refrigerating and Air-conditioning Engineers Inc.Google Scholar
  36. 36.
    Heldman DR, Lund DB (2006) Handbook of food engineering CRCGoogle Scholar
  37. 37.
    Rahman S (2008) Food Properties Handbook, Second edn. Taylor & Francis, LondonGoogle Scholar
  38. 38.
    Sakai N, Hosokawa A (1984) Comparison of several methods for calculating the ice content of foods. J Food Eng 3:13–26. CrossRefGoogle Scholar
  39. 39.
    Tarnawski VR, Cleland DJ, Corasaniti S, Gori F, Mascheroni RH (2005) Extension of soil thermal conductivity models to frozen meats with low and high fat content. Int J Refrig 28:840–850. CrossRefGoogle Scholar
  40. 40.
    Boonsupthip W, Heldman DR (2007) Prediction of frozen food properties during freezing using product composition. J Food Sci 72:254–263. CrossRefGoogle Scholar
  41. 41.
    Cogné C, Andrieu J, Laurent P, Besson A, Nocquet J (2003) Experimental data and modelling of thermal properties of ice creams. J Food Eng 58:331–341. CrossRefGoogle Scholar
  42. 42.
    Flick EW (1998) Industrial solvents handbook William Andrew, New JersyGoogle Scholar
  43. 43.
    Kiani H, Sun D-W, Zhang Z (2012) The effect of ultrasound irradiation on the convective heat transfer rate during immersion cooling of a stationary sphere. Ultrason Sonochem 19:1238–1245. CrossRefGoogle Scholar
  44. 44.
    Li B, Sun D-W (2002) Effect of Power Ultrasound during Immersion Freezing of potatoes. J Food Eng 55:277–282CrossRefGoogle Scholar
  45. 45.
    Kiani H, Sun D-W, Zhang Z (2012) Effect of ultrasound irradiation on the convective heat transfer rate during immersion cooling of a stationary sphereInternational Conference of Agricultural Engineering, CIGR-Ageng 2012, Valencia, SpainGoogle Scholar
  46. 46.
    Sastry S, Shen G, Blaisdell J (1989) Effect of Ultrasonic Vibration on Fluid-to-Particle Convective Heat Transfer Coefficients. J Food Sci 54:229–230CrossRefGoogle Scholar
  47. 47.
    Delgado AE, Sun DW (2001) Heat and mass transfer models for predicting freezing processes - a review. J Food Eng 47:157–174CrossRefGoogle Scholar
  48. 48.
    Delgado A, Zheng L, Sun D-W (2009) Influence of ultrasound on freezing rate of immersion-frozen apples. Food Bioprocess Technol 2:263–270. CrossRefGoogle Scholar

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

Personalised recommendations