Advertisement

Food and Bioprocess Technology

, Volume 7, Issue 2, pp 371–384 | Cite as

Estimation of Dielectric Properties of Food Materials During Microwave Tempering and Heating

  • S. CuretEmail author
  • O. Rouaud
  • L. Boillereaux
Original Paper

Abstract

The present study concerns the estimation of the dielectric properties of both frozen and defrosted materials during a microwave tempering and heating process. A continuous wave at 2.45 GHz is fed into a rectangular waveguide and the sample, made of methylcellulose gel, fills the whole cross-section of the guide. Temperatures are detected within both frozen and defrosted samples during the heating treatment. The experimental temperatures are compared to the results obtained with a 2D finite element model, using the COMSOL® 4.2 software. The dielectric properties of the sample are estimated from the local temperature changes during the microwave tempering. For the defrosted zone, the estimation is compared to dielectric properties measurements with the open-ended coaxial probe. The results show good correspondence between experimental and simulated data. The uncertainties of the estimated permittivity and loss factors are also evaluated with a good accuracy for the frozen and defrosted phases. The estimation procedure is thus a promising tool in order to avoid complex experimental measurements of dielectric properties.

Keywords

Microwave Tempering Heating Modeling Dielectric Estimation 

Nomenclature

Roman Letters

a, b

Dimensions of the waveguide, in meters

B

Magnetic induction, in newton seconds per coulomb meter

C0

Velocity of light in a vacuum, in meters per second

Cp

Specific heat capacity, in joules per kilogram kelvin

C1 to C6

Constants for dielectric properties

D

Electric displacement, in coulombs per square meter

E

Local electric field strength, in volts per meter

E0

Maximum amplitude of the incident electric field, in volts per meter

Ein

Incident electric field, in volts per meter

f

Frequency of the electromagnetic wave, in hertz

fc

Cutoff frequency, in hertz

Fin

Incident microwave power flux, in watts per square meter

Ftrans

Microwave power flux transmitted to the water load, in watts per square meter

Fabs

Microwave power flux absorbed by the sample, in watts per square meter

h

Convective heat transfer coefficient, in watts per square meter per kelvin

H

Magnetic field intensity, in amperes per meter

J

Criterion to minimize

k

Thermal conductivity, in watts per meter per kelvin

L

Thickness of the sample, in meters

N

Number of experimental measurements for each temperature probe

Nu

Nusselt number

n

Number of elements within the vector p opt

Pin

Incident microwave power, in watts

Pabs

Absorbed microwave power, in watts

Pref

Reflected microwave power, in watts

Ptrans

Transmitted microwave power, in watts

p

Vector of parameters to estimate

Qabs

Volumetric heat generation term, in watts per cubic meter

Ra

Rayleigh number

T0

Initial temperature of the product, in kelvin

T

External temperature, in kelvin

x, y, z

Spatial coordinates, in meters

ZTE0

Impedance of the electromagnetic wave within air in the waveguide, in ohms

Greek Letters

λ0

Free space wavelength, in meters

λc

Cutoff wavelength, in meters

λg0

Guided wavelength, in meters

κair

Propagation constant within air medium

ω

Pulsation of the microwave radiation, in radians per second

μ0

Magnetic permeability of a vacuum (1.256 × 10−6 H m−1)

ε0

Permittivity of a vacuum (8.85 × 10−12 F m−1)

εr

Complex permittivity (dimensionless)

εr

Relative dielectric constant (dimensionless)

εr

Relative dielectric loss factor (dimensionless)

Notes

Acknowledgments

This work received financial support from the French ANR concerning the project CLPP (Plug & Play Software Sensors).

References

  1. Akkari, E., Chevallier, S., & Boillereaux, L. (2005). A 2D non-linear “grey-box” model dedicated to microwave thawing: Theoretical and experimental investigation. Computers and Chemical Engineering, 30(2), 321–328.CrossRefGoogle Scholar
  2. Azarpazhooh, E., & Ramaswamy, H. S. (2012). Modeling and optimization of microwave osmotic dehydration of apple cylinders under continuous-flow spray mode processing conditions. Food And Bioprocess Technology, 5(5), 1486–1501.CrossRefGoogle Scholar
  3. Bairi, A. (2008). Nusselt–Rayleigh correlations for design of industrial elements: Experimental and numerical investigation of natural convection in tilted square air filled enclosures. Energy Conversion and Management, 49(4), 771–782.CrossRefGoogle Scholar
  4. Bengtsson, N. E., & Risman, P. O. (1971). Dielectric properties of food at 3 GHz as determined by a cavity perturbation technique. II. Measurements on food materials. The Journal of Microwave Power, 6(2), 107–123.Google Scholar
  5. Campañone, L., Paola, C., & Mascheroni, R. (2010). Modeling and simulation of microwave heating of foods under different process schedules. Food and Bioprocess Technology, 5(2), 738–749.CrossRefGoogle Scholar
  6. Chamchong, M. (1997). Microwave thawing of foods: Effects of power levels, dielectric properties and sample geometry. Ph.D. thesis, Faculty of the Graduate School of Cornell University, Ithaca.Google Scholar
  7. Curet, S., Rouaud, O., & Boillereaux, L. (2008). Microwave tempering and heating in a single-mode cavity: Numerical and experimental investigations. Chemical Engineering And Processing, 47(9–10), 1656–1665.CrossRefGoogle Scholar
  8. Curet, S., Rouaud, O., & Boillereaux, L. (2009). Effect of sample size on microwave power absorption within dielectric materials: 2D numerical results vs. closed-form expressions. AICHE Journal, 55(6), 1569–1583.CrossRefGoogle Scholar
  9. Farag, K. W., Lyng, J. G., Morgan, D. J., & Cronin, D. A. (2008). Dielectric and thermophysical properties of different beef meat blends over a temperature range of −18 to +10 °C. Meat Science, 79(4), 740.CrossRefGoogle Scholar
  10. Hemis, M., Choudhary, R., & Watson, D. G. (2012). A coupled mathematical model for simultaneous microwave and convective drying of wheat seeds. Biosystems Engineering, 112(3), 202–209.CrossRefGoogle Scholar
  11. Herve, A. G., Tang, J., Luedecke, L., & Feng, H. (1998). Dielectric properties of cottage cheese and surface treatment using microwaves. Journal of Food Engineering, 37(4), 389–410.CrossRefGoogle Scholar
  12. Hu, X. P., & Mallikarjunan, P. (2005). Thermal and dielectric properties of shucked oysters. Lwt-Food Science And Technology, 38(5), 489–494.CrossRefGoogle Scholar
  13. Jacob, R., Basak, T., & Das, S. K. (2012). Experimental and numerical study on microwave heating of nanofluids. International Journal Of Thermal Sciences, 59, 45–57.CrossRefGoogle Scholar
  14. Lanz, J. E. (1998). A numerical model of thermal effects in a microwave irradiated catalyst bed. Ph.D. thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia.Google Scholar
  15. Liu, C. M., Wang, Q. Z., & Sakai, N. (2005). Power and temperature distribution during microwave thawing, simulated by using Maxwell’s equations and Lambert’s law. International Journal of Food Science and Technology, 40, 9–21.CrossRefGoogle Scholar
  16. Malafronte, L., Lamberti, G., Barba, A. A., Raaholt, B., Holtz, E., & Ahrne, L. (2012). Combined convective and microwave assisted drying: Experiments and modeling. Journal Of Food Engineering, 112(4), 304–312.CrossRefGoogle Scholar
  17. Mao, W. J., Watanabe, M., & Sakai, N. (2003). Dielectric properties of frozen surimi at 915 MHz and 2450 MHz. Food Science And Technology Research, 9(4), 361–363.CrossRefGoogle Scholar
  18. Marquardt, D. W. (1963). An algorithm for least squares estimation of nonlinear parameters. Journal of the Society for Industrial and Applied Mathematics, 11(2), 431–441.CrossRefGoogle Scholar
  19. Metaxas, A. C., & Meridith, R. J. (1983). Industrial microwave heating. London: Peter Peregrinus Ltd.Google Scholar
  20. Motavali, A., Najafi, G., Abbasi, S., Minaei, S., & Ghaderi, A. (2011). Microwave–vacuum drying of sour cherry: Comparison of mathematical models and artificial neural networks. Journal of Food Science and Technology. doi: 10.1007/s13197-011-0393-1.
  21. Motwani, T., Seetharaman, K., & Anantheswaran, R. C. (2007). Dielectric properties of starch slurries as influenced by starch concentration and gelatinization. Carbohydrate Polymers, 67(1), 73–79.CrossRefGoogle Scholar
  22. Nelson, S. O., & Bartley, P. G. (2000). Measuring frequency- and temperature-dependent dielectric properties of food materials. Transactions of ASAE, 43(6), 1733–1736.CrossRefGoogle Scholar
  23. Okiror, G. P., & Jones, C. L. (2012). Effect of temperature on the dielectric properties of low acyl gellan gel. Journal Of Food Engineering, 113(1), 151–155.CrossRefGoogle Scholar
  24. Raithby, G. D., & Hollands, K. G. T. (1998). Natural convection, chapter 4. Handbook of heat transfer (3rd ed.). New York: McGraw-Hill.Google Scholar
  25. Rattanadecho, P. (2006). The simulation of microwave heating of wood using a rectangular wave guide: Influence of frequency and sample size. Chemical Engineering Science, 61(14), 4798–4811.CrossRefGoogle Scholar
  26. Rattanadecho, P., Aoki, K., & Akahori, M. (2002). A numerical and experimental investigation of the modelling of microwave heating for liquid layers using a rectangular wave guide (effects of natural convection and dielectric properties). Applied Mathematical Modelling, 26(3), 449–472.CrossRefGoogle Scholar
  27. Romano, V. R., Marra, F., & Tammaro, U. (2005). Modelling of microwave heating of foodstuff: Study on the influence of sample dimensions with a FEM approach. Journal of Food Engineering, 71(3), 233–241.CrossRefGoogle Scholar
  28. Salazar-González, C., San Martín-González, M., López-Malo, A., & Sosa-Morales, M. (2012). Recent studies related to microwave processing of fluid foods. Food and Bioprocess Technology, 5(1), 31–46.CrossRefGoogle Scholar
  29. Taher, B. J., & Farid, M. M. (2001). Cyclic microwave thawing of frozen meat: Experimental and theoretical investigation. Chemical Engineering and Processing, 40(4), 379–389.CrossRefGoogle Scholar
  30. Vadivambal, R., & Jayas, D. S. (2010). Non-uniform temperature distribution during microwave heating of food materials—A review. Food and Bioprocess Technology, 3(2), 161–171.CrossRefGoogle Scholar
  31. Xin, Y., Vasquez, V. R., & Whiting, W. B. (2000). Effect of regression approach in the estimation of nonlinear model parameters on process design and simulation: Applications to kinetic and thermodynamic models. Computers and Chemical Engineering, 24(2–7), 1269–1274.CrossRefGoogle Scholar
  32. Zeng, X., & Faghri, A. (1994). Experimental and numerical study of microwave thawing heat transfer of food materials. ASME Trans J Heat Transfer, 116, 446–455.CrossRefGoogle Scholar
  33. Zhang, H., & Datta, A. K. (2005). Heating concentrations of microwaves in spherical and cylindrical foods: Part two: In a cavity. Food and Bioproducts Processing, Trans IChemE, Part C, 83(C1), 14–24.CrossRefGoogle Scholar
  34. Zhang, L., Lyng, J. G., Brunton, N., Morgan, D., & McKenna, B. (2004). Dielectric and thermophysical properties of meat batters over a temperature range of 5–85 °C. Meat Science, 68(2), 173–184.CrossRefGoogle Scholar
  35. Zhu, J., Kuznetsov, A. V., & Sandeep, K. P. (2007). Mathematical modeling of continuous flow microwave heating of liquids (effects of dielectric properties and design parameters). International Journal of Thermal Sciences, 46(4), 328–341.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.L’UNAM UniversitéONIRIS, CNRS, GEPEA, UMR 6144NantesFrance

Personalised recommendations