Modeling Dielectric Heating: A First Principles Approach

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Modeling Dielectric Heating: A First Principles ApproachRoger W. Pryor, Ph.D.Pryor Knowledge Systems, Inc.4918 Malibu Drive, Bloomfield Hills, MI, 48302-2253, rwpryor@pksez1.comAbstract: Dielectric heating is an important,widely employed electromagnetic heatingtechnology utilized by consumers, smallbusinesses and industry. Specific frequencybands are currently allocated, by internationalagreement [1], for use in the exploration,development, and application in operatingdevices. For example, consider that the readilyavailable, commercial, consumer microwaveovens have been allocated an operatingfrequency of 2.45 GHz. In this paper, I present aFirst Principles Model of the applied dielectricheating process. This model is used to explorethe physical differences manifested whendifferent frequencies are utilized to execute theheat generation process on similar materials insimilar geometries.Keywords: dielectric, RF, microwave, complexrelative permittivity.1. IntroductionThere are basically two well-known electricalloss mechanisms in physical materials. In thiscase, Figure 1 shows an example of dielectricheating loss results that occur when energy at afrequency of 2.45 GHz is applied to whey gel[2]. The application of the 2.45 GHz energygenerates volumetric heat and raises thetemperature of the whey gel into thepasteurization temperature range (71.7 C for 15seconds).Dielectric heating typically occurs in the absenceof free carriers in nominally non-conductivematerials [3]. Dielectric heating occurs as aresult of the relative motion of bound electrons,ions, atoms, and molecules, in situ, resulting invibrational energy coupling to the bulk of thematerial (heat).The other electromagnetic loss mechanism is byJoule heating [4]. Joule heating involves chargedfree carrier flow through the particular material.The free carriers are usually electrons orelectrons and ions. Joule heating occurs when aconductive material is subjected to anelectromagnetic potential difference.Different types of materials, due to their internalstructure, are more or less sensitive to both therelative amplitude and the frequency of theapplied electromagnetic field. As a result, forcomputational purposes, the characteristics of thematerial’s electronic heating behavior is typicallymathematically represented as a lumped-constantparameter named the relative permittivity(dielectric constant) [5]. The relative permittivityof a material is measured by how much it differsfrom the permittivity of Free Space. Thepermittivity of Free Space (a perfect vacuum) isa fundamental constant whose value is:(1)where:and:and:The permittivity of a material is:(2)where:and:For very complicated materials that haveintrinsic phase delays and energy losses, therelative permittivity is represented by a complexnumber, such as:Figure 1. Dielectric Heating at 2.45 GHz.Excerpt from the Proceedings of the 2015 COMSOL Conference in Boston

(3)The formula for the real part Fit curve is:where:(5)and:and:where:where:The loss equation is:(4)where:Figure 3 shows both the whey gel imaginary partpermittivity component data measured at fourindividual frequencies and the power seriespolynomial curve created by me to fit that data.2. Dielectric Heating Model MaterialsAs a first approximation, whey gel ( gelledmilk) is essentially water, with added impurities( 10%), formed into a gelatinous mass. In thecase of this model, it is assumed that the basicphysical properties of liquid water, as availablein the COMSOL Multiphysics Materials Library,can be modified sufficiently, as a First PrinciplesApproximation, to ballpark the whey gelphysical characteristics, by adding the measuredcomplex permittivity values for whey gel [2] tothe basic physical properties of water.As shown in equation three (3), the complexpermittivities for all materials comprise twocomponents, the real component and theimaginary component. Figure 2 shows both themeasured whey gel real permittivity componentdata at four individual frequencies and the powerseries polynomial curve created by me to fit thatdata.Figure 3. Permittivity Imaginary Part Data (red) andPolynomial Expansion Fit Curve (blue).The formula for the imaginary part Fit curve is:(6)where:3. The COMSOL Multiphysics ModelFigure 4 shows the COMSOL MultiphysicsModel Builder tree, partially expanded. Thismodel utilizes the Electric Currents (ec) and theHeat transfer in Solids (ht) Modules.All of the model’s Parameters are defined in theGlobal Parameters file. They include: inputvoltage (V in), frequency (f0), temperature (T),and dimensionless frequency (f01).Figure 2. Permittivity Real Part Data (red) andPolynomial Expansion Fit Curve (blue).All of the model’s variables are included in theVariables 1 file. They include: the dielectricheating energy loss equation (Qd), dimensionlesstemperature (T1), total complex relativeExcerpt from the Proceedings of the 2015 COMSOL Conference in Boston

permittivity (rpw), the real part of the totalcomplex relative permittivity (epr) and theimaginary part of the total complex relativepermittivity (epi).applied to the top surface of the two whey gelstrips. Ground 1 is applied to the entire lowersurface of the model, including both whey strips(2) and all three air strips (3).Figure 5 shows the Dielectric Heating geometryemployed in this model. This geometrycomprises two whey gel strips, surrounded bytwo air strips and separated by a single air strip.The geometries and volumes of the two whey gelstrips are identical to each other. The geometriesand volumes of the three air strips are identical toeach other.Figure 7 shows the configuration of the HeatTransfer in Solids (ht) module. Heat is generatedvolumetrically in the two whey gel strips. Heat islost through all the external surfaces.Figure 6. Electric Current (ec) ConfigurationFigure 4. Dielectric Heating Model Builder TreeFigure 7. Heat Transfer in Solids (ht) Configuration4. Solving the Dielectric Heating ModelThe first step in solving the Dielectric HeatingModel is to mesh the model. Figure 8 shows themodels mesh.Figure 5. Geometry ConfigurationThe next step in the solution of the DielectricHeating Model is to configure the solvers.Solution of this model requires the use of a twostep process. This Model is solved first in theElectric Currents Module using the FrequencyDomain Solver. Next, it is solved in the HeatTransfer Module, using the Stationary Solver.Figure 9 shows the solver configuration.Figure 6 shows the configuration of the ElectricCurrent (ec) Module. The Electric Potential 1 isExcerpt from the Proceedings of the 2015 COMSOL Conference in Boston

Figure 8. Dielectric Heating Model MeshFigure 11. Model Calculation at 915 MHzFigure 9. Solver Configuration5. Dielectric Heating SolutionsFigure 10, Figure 11, Figure 12, and Figure 13show the calculated solutions for inputfrequencies of 2.45 GHz, 915 MHz, 40 MHz and27 MHz, respectively.Figure 12. Model Calculation at 40 MHzFigure 13. Model Calculation at 27 MHzFigure 10. Model Calculation at 2.45 GHzAs can readily be observed, Figures 10, 11, 12,and 13 are almost identical. The input voltagewas adjusted to achieve the same level of heatingindependent of frequency. Figure 14 shows thecalculated data points for each test frequency anda Fit curve for the input voltage as a function offrequency.Excerpt from the Proceedings of the 2015 COMSOL Conference in Boston

Figure 14. Input Voltage vs. Frequencyat a Constant Heating LevelThe equation for the Input Voltage curve is:(7)where:6. ConclusionsThe dielectric heating process is a powerful tool.It is available for use over a broad spectrum ofresearch and applications. The results of themodeling process are sensitive to the specificbehavior of the material being modeled andneeds to be explored thoroughly. In the case ofmaterials with a large volumetric fraction ofwater, the required input voltage decreases asfunction of frequency, for the allocated industrialfrequencies.7. References1. Radio Regulations, 2012, ITU-R2. Yifen Wang, et.al., J. Food Eng., 57 (2003), pp. 257-2683. https://en.wikipedia.org/wiki/Dielectric heating4. https://en.wikipedia.org/wiki/Joule heating5. https://en.wikipedia.org/wiki/PermittivityExcerpt from the Proceedings of the 2015 COMSOL Conference in Boston

at a Constant Heating Level . The equation for the Input Voltage curve is: (7) where: 6. Conclusions . The dielectric heating process is a powerful tool. It is available for use over a broad spectrum of research and applications. The results of the modeling process are sensitive to the specific behavior of the material being modeled and

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