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


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.


Microwave Tempering Heating Modeling Dielectric Estimation 


Roman Letters

a, b

Dimensions of the waveguide, in meters


Magnetic induction, in newton seconds per coulomb meter


Velocity of light in a vacuum, in meters per second


Specific heat capacity, in joules per kilogram kelvin

C1 to C6

Constants for dielectric properties


Electric displacement, in coulombs per square meter


Local electric field strength, in volts per meter


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


Incident electric field, in volts per meter


Frequency of the electromagnetic wave, in hertz


Cutoff frequency, in hertz


Incident microwave power flux, in watts per square meter


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


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


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


Magnetic field intensity, in amperes per meter


Criterion to minimize


Thermal conductivity, in watts per meter per kelvin


Thickness of the sample, in meters


Number of experimental measurements for each temperature probe


Nusselt number


Number of elements within the vector p opt


Incident microwave power, in watts


Absorbed microwave power, in watts


Reflected microwave power, in watts


Transmitted microwave power, in watts


Vector of parameters to estimate


Volumetric heat generation term, in watts per cubic meter


Rayleigh number


Initial temperature of the product, in kelvin


External temperature, in kelvin

x, y, z

Spatial coordinates, in meters


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

Greek Letters


Free space wavelength, in meters


Cutoff wavelength, in meters


Guided wavelength, in meters


Propagation constant within air medium


Pulsation of the microwave radiation, in radians per second


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


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


Complex permittivity (dimensionless)


Relative dielectric constant (dimensionless)


Relative dielectric loss factor (dimensionless)



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


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

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

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