Adv. Radio Sci., 12, 21–28, 2014www.adv-radio-sci.net/12/21/2014/doi:10.5194/ars-12-21-2014© Author(s) 2014. CC Attribution 3.0 License.

Local microwave heating of sand molds as a means to overcomedesign limitations in sand mold casting

O. Wiedenmann1, R. Ramakrishnan2, P. Saal2, E. Kılıç1, U. Siart1, T. F. Eibert1, and W. Volk2

1Technische Universität München, Lehrstuhl für Hochfrequenztechnik, Arcisstr. 21, 80333 Munich, Germany2Technische Universität München, Lehrstuhl für Umformtechnik und Gießereiwesen, Walther-Meißner-Straße 4,85747 Garching, Germany

Correspondence to:O. Wiedenmann (oliver.wiedenmann@tum.de)

Received: 20 December 2013 – Revised: 25 February 2014 – Accepted: 27 March 2014 – Published: 10 November 2014

Abstract. Microwave induced selective heating outmatchesconventional mold heating by convective heat transfer inmeans of energy efficiency and cycle time. Moreover, it pro-vides the opportunity of a local manipulation of solidificationand cooling processes within the sand casting mold. In thispaper, we investigate the suitability of different highly ab-sorbing materials to indirectly heat up the mostly microwavetransparent sand mold. The temperature-dependent permit-tivity of the involved materials is determined by resonatorexperiments and subsequently used to simulate the electro-magnetic field and the thermodynamic response of the sandmold prior to a metal casting process. Experimental resultsare presented and compared with the outcome of the cou-pled electromagnetic-thermodynamic simulations and the in-fluence of local microwave heating on the solidification andcooling of the cast is studied.

1 Introduction

Applying microwaves during the production and processingof industrial goods is a widely accepted and popular tech-nology. Especially in the food and ceramic industries dryingand heating by microwaves outmatches conventional heat-ing methods in many areas (Meredith, 1998). With regards tothe metal casting industry microwave technology is merelyused for drying and firing of ceramic mold materials (Robak,2005). Furthermore,Chandrasekaran et al.(2011) investi-gated the heating of different metals by microwave energy.This paper focuses on the generation of a custom tempera-ture field inside a sand mold by selective microwave heating.

In die casting processes temperature control by means ofheating and cooling channels is commonly used and neces-sary to assure a controlled solidification front and thus therequested mechanical properties of the cast part. In sandmold casting, however, the options for a temperature con-trol are limited. Only cooling elements, so called chills, orexothermic feeders are used frequently. Whereas convectiveheating of the mold is not reasonable, as the heat input cannot be locally defined, microwave heating offers a possibil-ity to generate an inhomogeneous temperature distribution.In this work, a custom temperature field in sand molds isachieved by positioning highly absorbing materials, so calledsusceptors, within the mold. Hence, we combine microwavetransparent bulk materials with susceptor materials in a sin-gle sand mold. This rigged sand mold is subjected to a mi-crowave field thus generating a locally heated sand moldprior to the casting process.

The first step is the selection of a suitable susceptor ma-terial, which fulfills all requirements for an application in asand casting process. All involved materials are dielectricallycharacterized by a resonator technique in a way that allows todetermine the permittivity of the material samples dependingon the temperature. This knowledge is used to develop a sim-ulation model to predict the electromagnetic and thermody-namic behavior of the experimental setup. Due to the strongtemperature dependency of the permittivity of the suscep-tor material, electrical and thermal phenomena are coupledto each other, so that electromagnetic and thermodynamicsimulations are no longer independent. Instead, a simulationmodel has to be derived that takes into account the couplingbetween the electromagnetic and the thermodynamic simu-lations. Finally, the results of the numerical methods and the

Published by Copernicus Publications on behalf of the URSI Landesausschuss in der Bundesrepublik Deutschland e.V.

22 O. Wiedenmann et al.: Local microwave heating in sand mold casting

casting experiments are compared and the effect of the localheating on the solidification and cooling process is investi-gated.

2 Selection of susceptor materials

The microwave experiments for the selection of susceptormaterials are carried out in a laboratory microwave furnaceMKE – 0.8/2.45 – 0.6/5.8 manufactured by Linn High ThermGmbH. Microwaves are applied to the cylindrical chamberwith a frequency of 2.45 GHz which has proven to be suit-able for most needs (Clark, 2005). The inner chamber diam-eter is 330 mm with a depth of 260 mm. The packing spacefor the microwave furnace is specified by the manufacturerwith a volume of 100× 100× 100 mm3 in the center of thecylinder.

The key to accomplish selective sand mold heating bymicrowave energy is the right choice of materials. The mi-crowave energy is used to heat the susceptors, which con-sist of a material that shows a high microwave absorptionrate. For the investigations of appropriate susceptor materi-als a simple two-part sand block is used, hereinafter calledsusceptor carrier. The bulk of the susceptor carrier, whereno heating is desired, should be as microwave transparent aspossible in order to convey the microwave field to the sus-ceptors which lie within the sand. Commonly used mold-ing sands on quartz basis meet this requirement, since thesematerials do not heat up significantly in a microwave field.For our experiments we manufactured the susceptor carri-ers from laser croning sand Resital® QLS 50 CG (Hüttenes-Albertus Chemische Werke GmbH) by selective laser sinter-ing (SLS) in an EOSINT S700 (EOS GmbH) laser sinteringmachine. The susceptor carrier consists of a bottom blockwith a pocket for the susceptor material and a top block forcovering the susceptor. Each bottom and top block has a sizeof 80 mm× 80 mm× 50 mm. In the bottom part of a suscep-tor carrier one susceptor specimen can be positioned. Fig-ure1 schematically shows an example of the susceptor car-rier with a susceptor specimen.

Inside the cylindrical microwave chamber a supportingsurface out of aluminum oxide is positioned, which can beassumed as microwave transparent. On top of the plate thesusceptor carrier including the susceptor is positioned. Thepresence of a metallic thermocouple inside a microwave fieldhas a great influence on the field distribution inside the mi-crowave chamber. Arcing and microwave interference withtemperature measurement are common problems (Grellingerand Janney, 1993; Chandrasekaran et al., 2011). Therefore,thermocouples have to be inserted shortly after the mi-crowave is turned off. The prepared susceptor carrier withone susceptor is positioned in the designated packing spaceof the microwave furnace. After a microwave irradiation thetemperature is measured in a distance of 4 mm from the sus-ceptor surface. This is the designated distance – and mini-

Figure 1. Scheme of the microwave chamber with susceptor carrierand susceptor positioned inside. For temperature measurements athermocouple can be inserted when the magnetron is turned off.

mum mold wall thickness – between the susceptor and themelt in the later casting process.

As the desired microwave heat treatment of a sand moldtakes place before casting, the mold stability required for asatisfying casting result has to be kept up during the irradia-tion. Binders in molding sands lose their stability by mechan-ical or thermal stress. With rising susceptor temperatures thedesired effect on the casting process will be more significant.However, high susceptor temperatures increase the probabil-ity of erosion within the mold due to binder degradation.Exothermic reactions excited in susceptor materials by themicrowave process can also reduce the stability of the sus-ceptor itself or surrounding molding sand. Therefore, highreactivity of the susceptor materials has to be avoided gener-ally, regardless of whether the susceptors are in direct contactto the casting cavity, thus shape the cast part, or surroundedby molding material.

Further demands on susceptor materials are an easy fab-rication of variably shaped susceptors and that they do notrepresent a danger for health during fabrication, irradiationor casting. Based on a literature review the following mate-rials are investigated as possible susceptor materials. (Rhee,2002; Lukasz, 2005; Lühken, 2005; Bott, 1991; Gerdes et al.,1998):

– Silicon carbide (SiC)

– Tungsten carbide (WC)

– Copper oxide (CuO)

Adv. Radio Sci., 12, 21–28, 2014 www.adv-radio-sci.net/12/21/2014/

O. Wiedenmann et al.: Local microwave heating in sand mold casting 23

0

100

200

300

400

500

600

700

800

900

1000

1100

0 1 2 3 4 5 6 7 8 9 10

tem

pera

ture

in °C

mold stability criterion

technical CuO powder

medical activated carbon

carbon powder

CuO powder

granular CuO

SiC

Figure 2.Maximum temperatures in 4 mm distance to the susceptor(pure materials) after an irradiation time of 300 s plotted over themold stability.

– Graphite modifications (C)

These materials are investigated in different modificationsaccording to the reached temperature during a definedmicrowave irradiation and their reactivity, which goes alongwith mold stability.

First the mentioned susceptor materials are used in pow-der form with different grain sizes. The powders are filled inthe susceptor carrier pocket and irradiated for 300 s. For thefirst experiments a reduced susceptor volume is used. Thepocket volume filled with susceptor powder is 1000 mm3 forgraphite and 2000 mm3 for other materials, preventing ex-pected reactions of graphite.

The results of the experiments are summed up in Fig.2. Itshows the maximum temperatures measured in a distance of4 mm to the susceptor materials after an irradiation time of300 s over a mold stability criterion. This criterion was de-fined by visually evaluating (pairwise comparison) the dam-age inflicted on the sand mold in the susceptor’s vicinity. Lowmold stability criterion values indicate severe binder degra-dation and therefore strong mold disruption. To affect thesolidification and cooling behavior of the cast metal signifi-cantly, an increase in temperature of 300◦C is defined as thedesired lower limit. The target area, defined by the desiredminimal temperature rise of 300◦C and the acceptable moldstability criterion of 5 or higher, is highlighted.

The powder materials used in the stage 1 experiments(Fig. 2) did either not achieve the desired temperature riseof 300◦C or heated up so much, that the stability of suscep-tor and surrounding molding sand was destroyed and thusa defined temperature measurement in a distance of 4 mmwas not possible. The temperatures reached in these suscep-tors amount to approximately 1000◦C. One reason for thesehigh temperatures is an overlay of microwave heating andexothermal reaction. In the case of graphite, microwave ir-radiation induces combustion of graphite powder with sur-rounding air, which destroys the mold stability. In order tocombine the good heating conditions reached with some ma-terials and the required inert characteristics of others, the ini-

0

100

200

300

400

500

600

700

800

900

1000

1100

0 1 2 3 4 5 6 7 8 9 10

tem

pera

ture

in °C

mold stability criterion

49% grained SiC + 49% H32 sand73% H32 sand + 25% WC powder98% grained SiC49% grained SiC + 49% WC powder83% grained SiC + 15% WC powder88% grained SiC + 6% graphite spray79% grained SiC + 13% graphite powder94% grained SiC + 3% graphite powder94% grained SiC + 3% activated carbon80% grained SiC + 15% green SiC powder57% grained SiC + 29% SiC powder63% grained SiC + 32% techn. CuO powder47% grained SiC + 47% WC powder63% SiC powder + 32% carbon powder60% grained SiC + 30% carbon powder93% WC powder73% SiC powder80% green SiC powder

Figure 3. Maximum temperatures in 4 mm distance to the suscep-tor (compressed and bound mixtures, weight balance equals binderamount) after an irradiation time of 300 s plotted over the mold sta-bility.

tial materials extended by tungsten carbide are mixed in dif-ferent portions and bound with varied amounts of INOTEC®binder and compressed using a hand press. Silicon carbideand quartz sand (H32) were used as carrier materials, asthey show low reactivity and good wettability characteris-tics for the INOTEC® binder. Using these mixtures, the sus-ceptor volume could be increased to 8000 mm3 to induce ahigher amount of energy without losing mold stability. Fig-ure 3 shows the results of the corresponding experimentssummarized. Considerable improvements could be reachedin terms of mold stability. However silicon carbide (SiC) alsoshowed an unexpected high maximum temperature which weattribute to the compression of the susceptor. Having one ofthe lowest temperatures without compression, the SiC sus-ceptor reached the highest temperature in the stage 2 experi-ments. Based on this result, SiC bound with INOTEC® andcompressed was selected as the most suitable material forsusceptor applications.

3 Material characterization by resonator experiments

For the electromagnetic simulation, the dielectric propertiesof all involved materials have to be determined. Therefore, aresonator technique is employed which is based on a cylin-drical cavity resonator as illustrated in Fig.4. A sample ofthe material to be analyzed can be inserted into the center ofthe resonator. By measuring the resonance frequency and thequality factor of the detuned resonator, real and imaginarypart of the permittivity of the sample material can be com-puted by an inversion algorithm. This approach also takesinto account the effects of lossy walls and of the filling holeby imposing inhomogeneous surface impedance boundaryconditions (Kılıç et al., 2013).

The method starts by converting the vector wave equa-tion for the magnetic field into a variational form. The finiteconductivity of the resonator walls is accounted for by en-forcing an impedance boundary condition along the metallicsurface. The filling hole, through which dielectric material

www.adv-radio-sci.net/12/21/2014/ Adv. Radio Sci., 12, 21–28, 2014

24 O. Wiedenmann et al.: Local microwave heating in sand mold casting

Figure 4. Cylindrical cavity resonator with an opening for the in-sertion of material samples.

samples can be plunged into the cavity, is modeled as a cir-cular hollow waveguide. Therefore, the surface impedance inthe cross section of the filling hole can be approximated bythe scalar wave impedance of evanescent waveguide modes.

The variational expression for the magnetic field can beexpanded by the natural modes of the lossless empty cav-ity, which form a complete set. This reduces the problem toa generalized eigenvalue problem for the unknown materialparameters in matrix form. In contrast to the direct problem,in which the wave number is determined from the permittiv-ity, the problem at hand is the other way around. Hence, itis an inverse problem, where the known quantity is the com-plex wave number which is determined by the measured res-onance frequency and the quality factor. The inverse problemis solved by a generalized Schur decomposition. This proce-dure provides an accurate way to obtain the permittivity of amaterial sample.

The described configuration allows heating up the materialsample prior to measurement, so that the temperature depen-dency of the permittivity can be accounted for. Thus, the tem-perature of the heated sample was recorded with an infraredcamera during the cooling process, while the scattering pa-rameters were measured in parallel with a vector networkanalyzer. The setup for the measurement of temperature andelectrical scattering parameters is illustrated in Fig.5.

Since the usage of an infrared camera only returns thetemperature on the material surface, the samples have beenheated up a second time, but this time the core temperaturehas been measured as well by inserting a thermocouple intoa tiny drilled hole. This offers the possibility to assign thesurface temperature measured during the resonator experi-ment to the corresponding core temperature. Measuring thetemperature with the thermocouple during the network ana-lyzer measurements is not feasible, because the metallic ther-

Figure 5.Measurement setup for the simultaneous determination oftemperature and electrical scattering parameters comprising a net-work analyzer and an infrared camera.

mocouple disturbs the fields and, thus, renders the measuredelectric data useless.

The results for the complex relative permittivityε′r − jε′′

rof silicon carbide are illustrated in Fig.6. It can be discernedthat there is a distinctive dependency on the temperature,which has to be taken into account in the numerical sim-ulation. A rational function is used to interpolate betweenthe measurement points, thereby creating a functional de-pendency between temperature and permittivity, which is re-quired as input to simulate the electric field distribution.

4 Numerical simulation of electric field and heatdistribution

In order to compute the expected temperature distributioninside the sand mold after microwave heating, an electro-magnetic full-wave simulation is necessary. The calculatedelectric field serves as input for a subsequent thermody-namic simulation which computes the heat flow betweenthe susceptors and the sand mold. For the computation ofthe electromagnetic field distribution, the software pack-age COMSOL Multiphysics is employed to solve Maxwell’s

Adv. Radio Sci., 12, 21–28, 2014 www.adv-radio-sci.net/12/21/2014/

O. Wiedenmann et al.: Local microwave heating in sand mold casting 25

Figure 6. Results for the temperature-dependent, complex permittivity of the susceptor material silicon carbide obtained through resonatorexperiments.

equations (Maxwell, 1873), which are given by

∇ ×H = J +∂D

∂t(Ampère-Maxwell law) (1)

∇ ×E = −∂B

∂t(Faraday’s law) (2)

∇ ·B = 0 (Gauss’s law for magn. fields) (3)

∇ ·D = ρe, (Gauss’s law) (4)

whereE is the electric field,H the magnetic field,D theelectric displacement current,B the magnetic flux density,ρe the electric charge density andJ the electric current den-sity. This set of equations is solved numerically by the finiteelement method (Jin, 2002). The resulting electromagneticloss distribution acts as thermal heat source in a subsequentthermodynamic simulation. The solution of the heat conduc-tion equation

ρmc∂T

∂t= ∇ (k∇T ) + q (5)

provides the temperature distribution after a specified timet .Here,ρm denotes the mass density,T the temperature,k thethermal conductivity,c the specific heat capacity andq theabsorbed power in a unit volume. The absorbed power canbe written as

q = 2πf ε0ε′′r |Eeff|

2 (6)

and depends on the frequencyf , the permittivity of freespaceε0, the imaginary part of the relative permittivityε′′

rand the square of the effective value of the electric fieldEeff.

In order to take into account the temperature dependencyof the permittivity, electromagnetic and thermodynamic sim-ulation have to be coupled. This means that after every timestep of the transient thermal simulation, it has to be verifiedthat the material parameters have not changed significantlydue to the propagating heat. Each time the material parame-ters have altered to a certain degree, a new electromagneticsimulation has to be performed with updated material param-eters according to the actual temperature distribution. The

Figure 7. Simulation setup of a sand mold with susceptors insidethe microwave chamber.

refreshed heat sources are then used for the next time stepsof the transient thermal simulation, until the electromagneticproblem part has to be recomputed again.

This simulation setup is used to compute the expectedtemperature distribution inside a sand mold after a certainamount of time. In Fig.7, a model of the experimental setupis shown which includes a sand mold with two susceptors in-side a microwave chamber. The temperature distribution after210 s of heating is illustrated in Fig.8. It should be denotedthat the sand mold absorbs almost no electromagnetic energy,whereas the susceptors heat up significantly. Moreover, it canbe discerned that the heat is propagating well inside the sandmold, so that a potential influence on the solidification pro-cess of the cast metal is expected. The different temperature

www.adv-radio-sci.net/12/21/2014/ Adv. Radio Sci., 12, 21–28, 2014

26 O. Wiedenmann et al.: Local microwave heating in sand mold casting

Figure 8. Temperature distribution inside sand mold after heating.

of the two susceptors is due to the inhomogeneous electricfield. This issue can be addressed in future applications byembedding a mode stirring component (Wiedenmann et al.,2012).

5 Experimental results

5.1 Comparison with simulation results

To validate the simulation setup, numerical results are com-pared to results obtained from experimental measurements.For this purpose, the setup illustrated in Fig.1 is adapted.Instead of a thermocouple, an infrared camera is used tomeasure the susceptor temperature during the heating phase.Here a SiC susceptor is embedded in a sand block whichserves as susceptor carrier. Line of sight for the infrared cam-era is achieved by a cylindrical hole in the top part of thesusceptor carrier. Microwave heating is applied for 90 s andthe temperature is recorded using an infrared camera dur-ing heating and the subsequent cooling process. The mea-surement results are compared with the numerical results ob-tained from a simulation model with COMSOL Multiphysicsin Fig. 9. Since the thermal conductivity of SiC and sandcould not be measured, reference values obtained from lit-erature were used instead. Silicon carbide shows rather highthermal conductivity, so that a possible error influences theresults only negligibly. The considerably lower thermal con-ductivity of the sand effectively limits the heat transport awayfrom the susceptor. Therefore, small variations in this param-eter have a strong influence on the temperature characteris-tics. Whereas the thermal conductivity of the considered sandshould be around 0.8 W m−1 K−1, a better agreement withthe measurement curve can be observed if the thermal con-

ductivity is decreased by 25 %. If the thermal conductivitywas increased instead, the heat flow in the sand would be im-proved so that the surface temperature of the susceptor wouldbe lowered.

For a closer matching of experimental results and numer-ical simulation, a more accurate knowledge of the thermo-physical parameters such as thermal conductivity and spe-cific heat capacity would be required.

5.2 Casting experiments

The described process of heating sand molds selectively bymicrowave energy gives us the possibility to generate a tem-perature distribution inside the mold prior to casting. Herebywe are able to influence the solidification characteristics ofthe aluminum alloy AlSi12 for example. For the casting ex-periments we manufactured molds from H32 and SLS sandwith compressed SiC bound with INOTEC® as susceptormaterial. Figure10shows an opened sand mold with the sus-ceptors inside.

This mold is closed and placed into the microwave furnacefor heating (see also Fig.7). After that the aluminum alloy iscast into the mold’s inlet at a temperature of approx. 750◦Cand fills the specimen cavities from bottom to top. This wayturbulent filling of the mold can be avoided. By casting intoa series of these molds we could produce specimens whichcooled naturally on the one side and were heated due to thelocalized susceptors on the other side of the mold. The castspecimens were cut in the center and analyzed with respectto their dendrite arm spacing (DAS). During solidificationthe primary aluminum phase forms tree-shaped arms, the socalled dendrites. The DAS is defined as the distance betweentwo dendrite arms and is a common metallographic param-eter. Short solidification times result in small DAS and viceversa. Hereby we found, that specimens which cooled slower– since they were heated by the susceptors – had a larger DASthan naturally cooled ones. The results for different mold ma-terials and heating times are shown in Fig.11.

Although there is a relatively large deviation among themeasurements of the DAS we could observe a clear trend thatspecimens which solidified and cooled near a susceptor hada considerable higher DAS. This effect could be shown withboth mold materials and also with different heating times.Here longer heating times lead to a larger difference in DASwhich is a consequence of the stronger heating in the sus-ceptor area. These results correspond with the well-knownlink between solidification time and dendrite arm spacingand show that the solidification time of the aluminum alloyAlSi12 can be influenced by localized microwave heating. Itshould be noticed that DAS in this context is a measure forsolidification time only. The connection of DAS and mechan-ical properties is not of interest in this case as the scope of thepresented work is to overcome design limitations by locallymanipulating solidification times.

Adv. Radio Sci., 12, 21–28, 2014 www.adv-radio-sci.net/12/21/2014/

O. Wiedenmann et al.: Local microwave heating in sand mold casting 27

0 20 40 60 80 100 120 140 160 1800

100

200

300

400

500

600

Time [s]

Tem

pera

ture

[°C

]

measurement

simulation λλλλ=0.6

simulation λλλλ=0.8

simulation λλλλ=1.0

Figure 9. Comparison between experimental and simulation resultsfor the setup shown in Fig.1. The influence of the thermal con-ductivity of the sand is illustrated by considering the effect of anincrease/decrease of the thermal conductivity by 25 % on the tem-perature on the susceptor surface.

50 mm cavities for specimens

susceptors susceptor cavities sprue

Figure 10.Opened sand mold with two inserted susceptors (black)for casting of two round specimens.

6 Conclusions and outlook

In this paper we presented a method for selectively heat-ing a sand mold prior to a casting process. By using sucha selectively heated sand mold it is possible to influencethe thermal properties during the casting process and, hence,achieve desirable casing properties. The temperature field in-side the sand mold is generated by a microwave process.The sand mold – which is mostly microwave transparent –is locally equipped with susceptors, which strongly absorbthe microwave energy and function as a heat source. Basedon a selection of microwave absorbing materials we foundcompressed and chemically bound silicon carbide to be themost suitable material with respect to heating performanceand mold stability. The susceptors were dielectrically char-acterized using a resonator technique and the temperaturedependency was taken into account by parallel temperature

0

10

20

30

40

50

DA

S [

µm

]

210 s* 90 s 210 s 300 s

radiation time

Mit Suszeptor

Ohne Suszeptor

with susceptor

without susceptor

Figure 11. Dendrite Arm Spacing of specimens cast with (darkgrey) and without (light grey) the heating influence of a suscep-tor for different radiation times. The column marked with * rep-resents the only available experiment series with SLS molds. Thethree other displayed series were performed in H32 molds.

measurements with an infrared camera. A coupled electro-thermal simulation model was created so that the temper-ature distribution inside a sand mold can be predicted andoptimized. Comparisons between microwave heating exper-iments and numerical results showed fairly good agreementand first casting experiments confirmed the effect of localheating on the cooling process.

In future works, the electro-thermal simulation shall be di-rectly coupled to a casting simulation, so that the whole pro-cess chain can be modeled and optimized.

Acknowledgements.The authors thank “Deutsche Forschungs-gemeinschaft” (DFG) for partially funding this work under grantEI 352/9-2 and HO 2165/38-2.

Edited by: U. van RienenReviewed by: M. H. Awida, T. Galek, and one anonymous referee

References

Bott, P.-M.: Untersuchungen zur Mikrowellenabsorption und zumReduktionsverhalten oxidischer Systeme, Ph.D. thesis, Univer-sität Tübingen, 1991.

Chandrasekaran, S., Basak, T., and Ramanathan, S.: Experimentaland theoretical investigation on microwave melting of metals, J.Mater. Process. Tech., 211, 482–487, 2011.

Clark, D. E. and Folz, D. C.: Microwave Solutions for Ceramic En-gineers, The American Ceramic Society, Westerville, 2005.

Gerdes, T., Willert-Porada, M., and Roediger, K.: Mikrowellensin-tern elektrisch leitfähiger Werkstoffe, Mikrowelleneinsatz in denMaterialwissenschaften, der chemischen Verfahrenstechnik undin der Festkörperchemie, Shaker Verlag, Aachen, 1998.

Grellinger, D. J. and Janney, M. A.: Temperature measurementin a 2.45 GHz microwave furnace, Ceramic Transactions Mi-

www.adv-radio-sci.net/12/21/2014/ Adv. Radio Sci., 12, 21–28, 2014

28 O. Wiedenmann et al.: Local microwave heating in sand mold casting

crowaves: theory and applications in materials processing, Am.Ceram. Soc. Bull., 36, 529–538, Westerville, 1993.

Jin, J.: The Finite Element Method in Electromagnetics, John Wiley& Sons, New York, NY, 2002.

Kılıç, E., Siart, U., Wiedenmann, O., Faz, U., Ramakrish-nan, R., Saal, P., and Eibert, T. F.: Cavity resonator mea-surement of dielectric materials accounting for wall lossesand a filling hole, IEEE T. Instrum. Meas., 62, 401–407,doi:10.1109/TIM.2012.2215072, 2013.

Lühken, A.: Ultraschall und Mikrowellenstrahlung im Chemieun-terricht – Entwicklung und Erprobung einfacher Experimentezum nichtklassischen Energieeintrag, Ph.D. thesis, Johann W.Goethe-Universität Frankfurt a. Main, 2005.

Lukasz, R.: Mikrowellenunterstützte Wärme- und Stoffübertragungbeim Trocknen und Entbindern technischer Keramik, Ph.D. the-sis, TU Bergakademie Freiberg, 2005.

Maxwell, J. C.: A Treatise on Electricity and Magnetism, OxfordUniversity Press, London, UK, 1873.

Meredith, R.: Engineers Handbook of Industrial Microwave Heat-ing, The Institution of Electrical Engineers, London, England,1998.

Rhee, S.: Mikrowellenprozesstechnik für keramische Werkstoffeder Mikrosystemtechnik, Ph.D. thesis, ForschungszentrumKarlsruhe GmbH, 2002.

Robak, L.: Mikrowellenunterstützte Wärme- und Stoffübertragungbeim Trocknen und Entbindern technischer Keramik, Ph.D. the-sis, Technische Universität Bergakademie Freiberg, Germany,2005.

Wiedenmann, O., Ramakrishnan, R., Kılıç, E., Saal, P., Siart, U.,and Eibert, T. F.: A multi-physics model for microwave heating inmetal casting applications embedding a mode stirrer, MicrowaveConference (GeMiC), 2012 The 7th German, Ilmenau, Germany,12–14 March 2012, 1–4, 2012.

Adv. Radio Sci., 12, 21–28, 2014 www.adv-radio-sci.net/12/21/2014/