694 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 20, NO. 3, MAY 2005

Embedded Solid State Heat Extraction in IntegratedPower Electronic Modules

Jaco Dirker, Wenduo Liu, Jacobus Daniel Van Wyk, Fellow, IEEE, Arnaud G. Malan, and Josua P. Meyer

Abstract—The use of embedded solid-state heat extractors toincrease the power densities in power electronic modules seemspromising. Cross-sectional geometric optimization was done onheat extraction insert and it was found that the most suitable heatextraction configuration for the dimensional range applicablein power electronics is the use of flat continuous heat extractionlayers aiding in conducting heat to externally mounted heatsinks. Theoretically expected thermal enhancement factors weredetermined and experimentally verified. The adverse influenceof interfacial thermal resistances on the effectiveness of heatextraction inserts was also evaluated.

Index Terms—Cross-sectional geometric optimization, em-bedded solid-state heat extractors, externally mounted heat sinks.

NOMENCLATURE

– view cross-sectional area m .– view aspect ratio [dimensionless].

Slenderness of heat-extraction layer in thedirection [dimensionless].Relative – view aspect ratio of coolinginsert [dimensionless].Magnetic flux density weber/m .

and Constants used in Steinmetz type equation.Thermal characterization coefficient ofdomain case m K/W .Volumetric heat generation density increasewhich could be supported [%].Frequency [Hz].Thermal conductivity [W/mK].Magnetic core loss W/m .Volumetric heat generation density W/m .Thermal interface resistance m K/W .Temperature [K or C].Cartesian coordinate.Cartesian coordinate.Cartesian coordinate.

Manuscript received April 13, 2004; revised December 7, 2004. This workwas supported in part by the Engineering Research Center Program, NationalScience Foundation, under Award EEC-9731677. This work was presented inpart at the IEEE Power Electronics Specialist Conference, Aachen, Germany,June 2004. Recommended by Associate Editor J. A. Ferreira.

J. Dirker is with the Department of Mechanical and Aeronautical Engi-neering, University of Pretoria, Pretoria, 0001, South Africa, and also withthe Department of Mechanical Engineering, Rand Afrikaans University,Johannesburg, South Africa (e-mail: jaco.dirker@up.ac.za).

W. Liu and J. D. Van Wyk are with the Center for Power Electronics Systems,Virginia Polytechnic Institute and State University, Blacksburg, VA 24061 USA.

A. G. Malan and J. P. Meyer are with the Department of Mechanical andAeronautical Engineering, University of Pretoria, Pretoria, South Africa.

Digital Object Identifier 10.1109/TPEL.2005.846532

Greek and Special SymbolsFraction of volume occupied by cooling inserts[dimensionless].Thermal conductivity ratio [dimensionless].Magnetic flux [weber].

A Half centre-to-centre -directional offset of neigh-boring cooling inserts [m].Half directional dimension of cooling insert [m].

B Half centre-to-centre directional offset of neigh-boring cooling inserts [m].Half directional dimension of cooling insert [m].Half directional dimension of structure [m].

SubscriptsCooling insert.Taking lost magnetic field bearing material volumeinto account.Whole domain.External (toward heat sink).Internal (between heat generating and heat extrac-tion materials).Heat generating medium.Maximum.Minimum.

0 Reference cooling insert temperature.

I. INTRODUCTION

COOLING techniques and thermal management has beena key aspect in the design of, and for the efficient oper-

ation of the majority of electronic components and equipment[1]. Many different cooling technologies have been developedfor use in this industry ranging from conductive heat transferto evaporative cooling to active heat removal such as thermo-electric cooling. As development in electronics accelerated, ad-vances in cooling techniques were necessary to accommodatemore efficient removal of heat at higher rates. Some innova-tive cooling technique approaches include the use of two-phaseheat spreaders with heat transfer augmentation on the evapo-rator surfaces [2], synthetic micro jet cooling [3], miniature andaugmented heat-pipes [4], [5] and embedded heat pipes to in-crease heat spreading [6], [7]. Most cooling techniques focus onincreasing heat transfer efficiency from the surface of heat-gen-erating components.

In integration of power electronic converters, the technologyis moving toward three-dimensional integration of modules con-taining both active switching devices and integrated electromag-netic power passives [8]. This hybrid technology contains manylayers of materials of different thermal conductivity, with losses

0885-8993/$20.00 © 2005 IEEE

DIRKER et al.: EMBEDDED SOLID STATE HEAT EXTRACTION 695

being generated locally in these layers. For instance, embeddedpassives with switches brings together materials with differentthermal conductivities, but also layers with loss densities dif-fering by orders of magnitude [9]. Especially layers of ceramicmagnetics and ceramic dielectrics show a low thermal conduc-tivity, yet generate appreciable losses at high frequencies.

Since these modules are thermally limited in the first place,it is essential to improve the heat extraction. Furthermore, im-proved heat extraction could lead to an appreciable increase inpower density since the materials can be subjected to increasedelectrical stress (higher current densities and electromagneticfields) that translates in higher loss densities. A study was un-dertaken to evaluate the thermal and computational aspects ofembedding solid state heat extraction [10] indicating the feasi-bility of this approach.

This paper now evaluates this further for application to in-tegrated power electronic modules and also gives attention tosome consideration regarding practical implementation, such asactual thermal interface resistances.

Different possibilities exist for the material to be used in theheat extractors. The material should be electromagnetically in-active so as not to interfere with the operation of the modules,and should have a relatively high thermal conductivity. Suit-able materials include beryllium oxide, aluminum nitride, andsynthetic polycrystalline diamond with thermal conductivitiesin the regions of 270 W/mK, 170 W/mK, and 2300 W/mK, re-spectively. The latter was included since this will represent thecurrent absolute practical boundary of what can be achieved.Optimization and other analyses were conducted for these ma-terials as heat extractors embedded into ceramics such as ferritewith a thermal conductivity in the range of 4 to 6 W/mK.

II. OPTIMUM USE OF VOLUME

Consider Fig. 1 showing a distribution of identical parallelrunning solid-state embedded heat extractors with a rectangularcross section in a medium with uniform heat generation. Heatflows via the heat extractors to the surroundings in either thepositive or negative directions. Heat extraction inserts are dis-tributed evenly in the and directions. Offsets in the anddirections are not necessarily the same.

In order to design a heat extraction system that occupies aslittle as possible volume while adding sufficient thermal en-hancement, it is needed to first do geometric optimization of theheat extractor inserts.

By optimizing the cross-sectional geometry of a heat extrac-tion insert, the peak temperature, , within the heat-gener-ating medium may be reduced for a given heat-generation rate,or conversely the heat generation rate may be increased for agiven maximum operating temperature.

A numerical approach was followed to perform the opti-mization processes, as it would have been too time-consumingand costly to do it experimentally. An analytical approach alsoproved to be elusive due to mathematical discontinuities on theinterfaces between heat-generating and heat-extracting materialregions [11].

The numerical optimization process consisted of an auto-mated procedure where significant numbers of models were

Fig. 1. Generalized heat extraction distribution.

constructed by using wide ranges and combinations of mate-rial, geometric and thermal conditions. By solving for steadystate thermal conditions, geometrically related models couldbe compared in terms of their peak temperatures from whichoptimized heat extraction insert cross sectional trends could bedescribed. A finite difference numerical scheme were used todiscretize and solve for the energy equation in three dimensions

(1)

Here, [w/mK] refers to the thermal conductivity of the partic-ular solid-state medium under consideration while W/mrepresents uniform heat generation density where applicable.

At the interface between heat generating and heat extrac-tion mediums, the heat transfer rate W/m across the inter-face were described by means of the following one-dimensional(1-D) equation:

(2)

Here, [K or C] refers to the temperature difference acrossthe interface while internal interface thermal contact resistance,is represented by m K/W where applicable.

A uniform grid-structure in all three Cartesian directions wereused to divide the representative domain into smaller controlvolumes over which the energy equations could be solved. Itwas found that the numerical obtained temperature solution ex-hibited little mesh dependence for grid structures where morethan 10 divisions in each Cartesian direction were used. No gridpoints were defined on material interfaces as this often led toinstability during the solution procedure. In order to speed upsolution rates, a fully implicit solutions scheme was used whilealso employing numerical bandwidth reduction algorithms.

For the purposes of the optimization investigation, the worst-case thermal scenario was assumed, where heat could only es-cape to the surroundings through the exposed surfaces of theheat extractor inserts. All other exposed surfaces were assumedto be adiabatic. Further it was assumed that the surroundings areisothermal and that heat extractors have equal thermal connec-tivity to the surroundings.

For such a set of boundary assumptions, the temperature fieldaround each heat extractor is symmetric in al three Cartesian di-rections and can be represented by a domain shown in Fig. 2.

696 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 20, NO. 3, MAY 2005

Fig. 2. Schematic of the representative domain.

The half centre-to-centre distances between neighboring heatextractors in the and directions are given by A and B respec-tively, while the half dimensions of a heat extractor are and. is half the depth of the medium being cooled. In practice,

dimensions A and B might be restricted by external geometricfactors such as structure configurations and access restrictionsto a “cold” ambient.

A uniform heat flux was defined on the exposed surface of theheat extractor with a magnitude in accordance with the principleof conservation of energy during steady state conditions. Thetemperature at the centre of an exposed surface was defined tobe .

The – plane aspect ratios of the overall domain and thecooling structure can be defined, respectively, as

AB

(3)

(4)

The – plane cross-sectional area of the representative do-main and cooling structure can be written, respectively, as

(5)

(6)

The fraction of the volume used for heat extraction purposesis denoted by . These four variables in conjunction with thedepth, , define the geometry of the representative domain fully.Due to geometric constraints, the cooling structure aspect ratiohas maximum and minimum allowed values

(7)

(8)

The ratio between the thermal conductivities of the heat ex-traction and heat generation regions, respectively, and[W/mK], is defined as

(9)

Internal interface thermal contact resistance, m K/Wwas defined on the interface between the heat extractors and theheat-generating regions.

From conductive heat transfer theory it is known that thetemperature difference between two locations within the do-main is directly proportional to the uniform heat generation

Fig. 3. Merged heat extractor inserts.

density, W/m . This is also true for the temperature dif-ference , between the peak temperature, , and thetemperature on the exposed surface of the heat extractor. Thesecan be related to each other via a geometric factor

(10)

This means that neither nor has any influence on theoptimum heat extractor geometry.

III. GEOMETRIC OPTIMIZATION RESULTS

Only values greater than 1 was investigated, as mirrorbehavior for less than 1 is evident. For instance 2would give the same result set as 0.5. For greaterthan 1, it was found that the lowest peak temperature is alwaysassociated with a heat extracting structure aspect ratio, , inthe range of . A convenient way of normalizingis by defining a relative heat extractor aspect ratio,

(11)

When 1, it means that the insert is at its maximumaspect ratio as shown in Fig. 3 and inserts become so elongatedthat neighboring inserts merge into continuous flat layers. When

0 the cooling insert has the same – plane aspect ratioas the representative domain.

A. Results for 1

For a case where no internal thermal interface resistance ispresent, it was found that the optimum cross-sectional geom-etry of the insert is independent of physical – size, andthe depth, of the domain. The optimum geometry was depen-dent only on and irrespective of magnitudes of the thermalconductivities and . Fig. 4 gives the optimum relative as-pect ratios for a wide range of and conditions with

m K/W. Representation of the optimum geometry type is in-cluded on the vertical axis.

When however the interface thermal resistance is nonzero, itwas found that the optimum shape is no longer only dependenton and , but also on , , the magnitudes of and ,and .

The influence of can be seen in Fig. 5 for an examplewhere aluminum nitride is embedded into ferrite. The di-mensions used here fall within the scope of power electronicmodules.

DIRKER et al.: EMBEDDED SOLID STATE HEAT EXTRACTION 697

Fig. 4. Optimum a for R = 0 m K/W and a wide range of valuesfor a = 1.

Fig. 5. Influence of interfacial thermal resistance for an example with a =

1.

Significant deviation in the behavior of the optimum insertgeometry can be noted when internal interfacial thermal resis-tance is present.

In general for 1, it was found that for low valuesthe optimum heat extraction configuration resembles the setupshown in Fig. 3, while for very high values the inserts had thesame aspect ration as the representative domain in proportion tothe and directional heat extractor offsets.

B. Results for 2

Similar optimum geometric curves could be constructed forthe case where the directional offset between neighboring in-serts are twice that in the direction. As before for cases where

0, the optimum geometry is only dependent on and .For such conditions, optimum heat extractor insert aspect

ratio behavior is described by Fig. 6. It was found that the

Fig. 6. Optimum a for R = 0 m K/W and a wide range of valuesfor a = 2.

Fig. 7. Influence of interfacial thermal resistance for an example with a =

2.

optimum shape has a higher tendency to conform to continuousflat heat extraction layers than for 1.

For an arbitrary case where aluminum nitride is embeddedinto ferrite, Fig. 7 shows the influence of internal interfacethermal resistance on optimum aspect ratios of the insert. Asbefore, the presence of nonzero , may have significantinfluence on the optimum insert shape.

C. Results for 5

For conditions with no internal thermal interface resistance,optimum heat extractor insert aspect ratio behavior is describedin Fig. 8. It should be noted that the relative optimum aspect ratiois significantly less influenced by the value and that there is aneven higher tendency to conform to a flat heat extraction layerconfiguration. It was also found that has a much smallerimpact on the optimum insert cross-sectional shape than before.

698 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 20, NO. 3, MAY 2005

Fig. 8. Optimum a for R = 0 m K/W and a wide range of valuesfor a = 5.

D. Summary of Results

In general, the optimum value tends toward 1 (rep-resenting continuous flat layered heat extraction) whendecreases, increases, decreases, decreases, or de-creases. Similar tendencies were found in a previous study [10].This result might seem intuitive, but depending on materialproperties, interfacial resistance, and geometric restrictions,better thermal performance might be attainable with the use ofdiscrete heat extraction rods rather than heat extraction layers.The optimum aspect ratio is most sensitive to changes in ,and . for cases where is nonzero. In case where iszero the optimum value is not influenced by eitheror . The individual influence of interfacial thermal resistanceis relatively complex and the description thereof falls outsidethe context of this paper.

IV. DIMENSIONAL SCALING

It is important to determine when it is advantageous to opti-mize the cross sectional aspect ratio to improve thermal perfor-mance. The maximum thermal performance improvement thatcan be achieved by optimising is shown in Fig. 9 for a widerange of physical dimensions for an example where no internalinterface thermal resistance is present.

It was found that the effectiveness of the heat extractor be-comes less dependent on its cross sectional shape as the ratiosof to decreases. For low ratios of to , where thedomain around a single insert becomes increasingly slender inthe -direction, the advantage of optimising the cross section inorder to increase the thermal performance of the setup becomesnegligible.

The advantage of inserting heat extractors however does notdiminish, but rather the effectiveness thereof for slender do-mains are more dependent on the fraction of the total volumeoccupied by the heat extraction system , rather than the crosssectional shape thereof.

In practice, this is of interest when heat extraction inserts canbe manufactured to have relatively small cross sectional areas,

Fig. 9. Maximum thermal performance increases due to geometricoptimization.

are relatively close to its neighbors and is relatively long in thez-direction such as fibers in a composite material. In such casesit would thus be sensible to use cross-sectional geometries thatare easier to manufacture or a geometry that would conformbetter to possible external restrictions placed on the configura-tion of a heat extraction system.

However, when internal interface thermal resistance ispresent, it was found the cross-sectional shape, , still has areduced but notable influence on the thermal performance of aheat extraction insert [11].

V. APPLICATION TO INTEGRATED POWER ELECTRONICS

Similar trends as shown in Fig. 9 were observed when alu-minum nitride, beryllium oxide, or synthetic diamond insertsare embedded into ferrite. In integrated power electronics, thegeneral dimensions of modules are of such an order that the in-fluence of the cross-sectional shape of the heat extraction insertson thermal performance is very small as discussed in Section IV.The proposed heat extraction setup for such modules is thus aconfiguration that is easily manufactured such as flat heat ex-traction layers as shown in Fig. 3.

It is useful to determine the steady-state performance of aparticular heat extraction system. For a geometric case with flatheat extraction layers, it is possible to predict the temperaturedistribution with a two-dimensional finite difference numericalmodel. The boundary conditions of the required representativedomain used for this purpose are shown in Fig. 10. Due toits symmetric nature, adiabatic boundaries are defined on allsides except one side exposed to the surroundings. Unlikethe boundary conditions assumed in the three-dimensionalnumerical model, the adiabatic conditions were relaxed tonot only allow heat transfer on the exposed face of the heatextractor insert, but also along the exposed face of the heatgenerating material.

Due to the common use of heat sinks in integrated power elec-tronic modules, the surroundings of the domain was modeled asan isothermal body at a temperature . A uniform external

DIRKER et al.: EMBEDDED SOLID STATE HEAT EXTRACTION 699

Fig. 10. Two-dimensional representative domains.

thermal interfacial resistance, , was defined on the in-terface to the heat sink from both the heat-generating andheat-extracting materials. As before, provision is also madefor internal interfacial resistance, , between the heat-gen-erating and heat extractor mediums.

With this model the reduction in the peak temperature dueto the presence of the heat extractors could be estimated fordifferent geometric, thermal interfacial resistances and materialproperty conditions. The reduced peak temperature can be usedto determine the increase in power loss or heat generation den-sity that can be supported due to the presence of the heat ex-tractor system for a specified peak operating temperature.

The effective volumetric heat-generation density increase ata fixed peak temperature, [%], can be defined as thepercentage increase in the overall heat generation density in thecomposite volume consisting of both heat-generating and heatextracting materials above that of a homogeneous heat-gener-ating material

with heat extraction

no heat extraction

with heat extraction(12)

For a case where B 2.5 mm, 0.25 mm (thus,0.1), 31 mm, 170 W/mK, and 5 W/mK,

is shown in Fig. 11 for a wide range of interfacialthermal resistance values.

To obtain the local heat generation density increase (withinthe heat-generation medium only) that can be supported withinthe heat generation region, [%], the following equationshould be used:

(13)

It can be seen from these results that the performance ofa heat extraction system depends heavily on both the internaland external interfacial thermal resistances. Theoretically for

Fig. 11. Allowable increase in heat generation density.

Fig. 12. Schematic representation of experimental setup.

the currently described case, an value of 332% canbe achieved if negligible thermal interfacial resistances werepresent.

VI. EXPERIMENTAL VERIFICATION

An experimental study [12] was conducted to verify the the-oretical prediction of Fig. 11 for and values in theregion of m K/W and 2.0 10 m K/W, re-spectively. A schematic representation of the experimental setupused is shown in Fig. 12. A photograph of the setup is also givenin Fig. 13.

Experiments were done on magnetic loop structures that ei-ther consisted of ferrite 3F3 only, or ferrite with aluminum ni-tride heat extraction layers. When aluminum nitride layers wereincluded, it occupied 10% of the total volume of the structure( 0.1).

The ceramic heat extractors of aluminum nitride used for theexperimental work was of commercially finished grade. No ad-ditional polishing was done to the “as delivered” surfaces. Thesesurfaces were as produced after firing the ceramics in the com-mercial process. Furthermore, the ferrite surfaces were also as

700 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 20, NO. 3, MAY 2005

Fig. 13. Photograph of experimental setup.

commercially delivered by vendors, i.e. this also entailed no pol-ishing or further finishing. The interface resistance is naturally afunction of the interfacial pressure for unwetted surfaces, so theinfluence of pressure was investigated and it was found that apressure of only 500 kPa was sufficient. The advantage of usingas delivered surfaces is that no thermal interface stresses willaffect the long-term stability and performance of the system.

However, although the confines of this paper does not allowthe full discussion, the use of thermal adhesives has also beeninvestigated. Although this obviates the use of a small clampingforce to keep the stack together and enhances interface heattransfer, its use now introduces the problem of thermally gener-ated interface stresses due to mismatch in coefficients of thermalexpansion. This is a separate study, including the influences onphysics of failure and failure modes of the entire assembly.

In the experimental investigation, the setup consisted of amagnetic loop structure operated as the core of an inductor ata frequency of 1 MHz. One side of the magnetic loop, equippedwith 10 K-type thermocouples, was used as the test section ofthe setup. Thermocouples were located both on the surface ofthe ferrite as well as embedded within the ferrite core sectionsto monitor and obtain the temperature distribution within thetest-section. The thermocouple dimensions and insertion fre-quencies were chosen carefully, so as not to influence the mea-surements detrimentally.

On two sides the magnetic material loop structure wasclamped into contact with identical aluminum heat sinks.The temperatures of each heat sink were measured with twoembedded thermal couples.

Obtained steady state peak temperatures within the ferrite interms of the heat sink temperature for different experimental testruns with ferrite only, or ferrite with aluminum nitride layers areshown in Fig. 14 for a wide range of heat sink temperatures. Theheat sink temperature can be used as a measure of the heat beinggenerated within ferrite due to core losses.

By comparing the gradients, , of line fits through result setsfor each experimental setup condition, the relative thermal per-formance of setups with aluminum nitride layers against thosewithout aluminum nitride layers can be obtained

(14)

Fig. 14. Experimentally obtained linear relationships.

The average gradient for the case with heat extraction wasfound to be 3.101 while for the case without heat extraction theaverage gradient is 8.883. This gives a performance enhance-ment factor value of 2.87, which translates into an increase of187% in the local heat generation density that could be sup-ported due to the presence of the heat extraction action of thealuminum nitride.

This translates into an value of 168% for caseswith heat extraction layers. It corresponded well with the ex-pected value of between 173% and 186% obtained from Fig. 11for the relevant thermal interfacial resistances. Due to the pres-ence of the aluminum nitride heat extracting layers, the effec-tive volumetric power loss density in the ferrite 3F3 core couldthus be increased by 168% while maintaining the same oper-ating temperature as before for a case without heat extractionlayers.

VII. HEAT EXTRACTION USING DIFFERENT MATERIALS

The thermal enhancement that may be obtained with the useof heat extraction layers is very much dependent on the heatextraction material used and it is of interest to compare the per-formances of different materials.

It was found that when both and are zero,is influenced only by , and not by the physical

values of or . For such conditions it was also foundthat only the slenderness ratio, , are of interest, and not thephysical dimensions of B and . Here, is defined as

B(15)

When however, thermal contact resistance is present, theseare no longer valid and the values of , , B, and need tobe taken into consideration.

For cases where and 0.1, the influence ofand is indicated in Fig. 15. Two thermal interface resistanceconditions to the heat sink are illustrated here, namely an ex-ample with m K/W and a general case where

DIRKER et al.: EMBEDDED SOLID STATE HEAT EXTRACTION 701

m K/W. In a previous study the use of thermal padmaterials at the interface to the heat sink resulted in valuesof m K/W or less [12].

It was found that as increased, the maximum theoreticalthermal enhancement value increases dramatically. For the casewhere synthetic diamond is embedded into ferrite ( 450),with ideally zero internal and external thermal interfacial resis-tance, enhancements above a 1000% is expected, depending on

.Unfortunately, in practice thermal interfacial resistances are

present and can dramatically reduce as indicated inFig. 11. For 2 10 m K/W with the same dimensionsused before as in Fig. 11, the maximum thermal enhancementvalues for synthetic diamond is already reduced by a factor ofabout 6 to 553%. If, in addition internal thermal interface resis-tance is also present is further reduced.

In Fig. 16 the influence of and on for theidealised case with no interface thermal resistances where100 is shown. As could be noted before in Fig. 15, an increase in

has as a result an a nonlinear increase in . Whenis increased, a higher effective thermal enhancement is also

expected.

VIII. MAGNETIC FLUX DENSITY—THERMAL OPTIMISATION

The cooling action of heat extractors in magnetic materialstranslates into higher allowed operating magnetic flux densitiesbut reduced active cross sectional area. It is thus of interest to es-timate the optimum volume that should be occupied by the heatextractors in order to maximize the effective magnetic field den-sity for a specified operating peak temperature within the struc-ture. This peak temperature can be expressed as a temperaturerise, , above that of the controlled heat sink temperature.

If the magnetic field lines are assumed to be uniform, themagnetic core loss, , W/m responsible for heat generationcan be approximated by the Steinmetz equation [13]

(16)

Here, [Hz] represents the operating frequency,weber/m represents the magnetic flux density and

through are constants. It should however be stressed thatthis equation type is used for tendency approximation purposesonly.

By ignoring the magnetic flux, [Weber] through the heatextractors and setting equal to , the following expressiondescribing the dependence of the effective magnetic density fluxdensity on can be obtained for a unit depth

(17)

Here it should be noted that is a function of and thatit is possible to optimize in terms of .

Assuming a case where the saturation magnetic field density,have not been reached during the maximization of the mag-

netic flux density, Fig. 17 shows the dependence of the theo-retical optimum value on and for the experimentaltest case operated at 1 MHz ( 2.25). For a case where both

Fig. 15. Thermal performance improvements for R being zero.

Fig. 16. Influence of a and � onE forR andR being zero.

and is 2 10 m K/W, the optimum is thus about0.33. This means that 33% of the volume should be occupied byheat extraction layers for this particular case to yield the max-imum supportable , assuming that is not exceeded.It was found that optimum is reduced as either orincreases. Similar graphs can be constructed for different heatextraction materials and geometries.

Practically, if the saturation magnetic field density isbelow the thermally maximized magnetic field density, theadditional constraint of an upper limit on or is required toestimate the range of suitable for thermally allowing to beincreased to . Even though in such cases the presence of heatextraction contributes to a smaller effect in the increase in thesupportable magnetic flux density, it could be used to reduceoperating temperatures.

In the use of ferrites for high frequency operation, as inthese integrated electromagnetic power passives (at 1 MHz, forexample), the magnetic flux density is derated to a fraction of itssaturation density to keep losses within acceptable boundaries

702 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 20, NO. 3, MAY 2005

Fig. 17. Optimum � for the experimental test case geometry using aluminumnitride heat extractors.

(for example to less than 20% of ). This derating is due tothe low thermal conductivity of the ferrite, which allows onlymoderate loss generation within the medium. The consequenceof this low flux density operation is therefore that, if by theinsertion of heat extractors, the loss density can be increasedappreciably, substantiable improvement in the power densitycan be achieved by increasing the magnetic flux level to levelsapproaching saturation. Consequently, magnetic saturation isnot the primary consideration for these high frequency operatedferrite cores, enabling an optimization approach that is thermallydriven.

IX. CONCLUSION

Theoretically it was found that the presence of embedded heatextractors in heat generating mediums can reduce the operatingtemperatures for a particular heat generating density or con-versely increase the allowed heat generation density for a par-ticular operating temperature.

Cross-sectional geometric optimization was conducted and itwas found that the most suitable heat extraction configurationfor application in power electronics is the use of flat heat ex-traction layers aiding in conducting heat to externally mountedheat sinks.

Graphs were constructed describing the thermal enhancementthat could be achieved by employing heat extraction layers ofdifferent material properties at various geometric and thermalconditions. In an experimental investigation these theoretic pre-dictions were verified.

An effective increase of 168% in the heat generation densitythat could be supported were achieved by replacing 10% of thevolume of an inductor core with aluminum nitride heat extrac-tion layers.

It was found that the presence of interfacial resistancescould dramatically reduce the effectiveness of embedded heatextractor layers. By reducing the thermal interfacial resistancesassociated with a heat extraction system it should be possible

to decrease the peak temperatures within the heat generationmedium even further, and thus increase the sustainable volu-metric power density.

Optimum volume fractions occupied by the heat extractionsystem exist for which in the case of magnetic core materialthe magnetic field density has a theoretical maximum value as-suming that saturation in the magnetic material has not beenreached.

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[12] J. Dirker, W. Liu, J. D. Van Wyk, and J. P. Meyer, “Evaluation of em-bedded heat extraction for high power density integrated electromag-netic power passives,” in Proc. 35th IEEE Power Electronics SpecialistConf., Aachen, Germany, Jun. 21–25, 2004.

[13] J. Li, T. Abdallah, and C. R. Sullivan, “Improved calculation of core losswith nonsinusoidal waferforms,” in Proc. 36th IEEE Industry Applica-tions Conf., vol. 4, Sep. 30–Oct. 4 2001, pp. 2203–2210.

Jaco Dirker received the B.Eng degree (with honors)in mechanical engineering, the B.Sc. degree (withhonors) in mathematics and applied mathematics,the M.Eng degree (with honors) in mechanicalengineering, and the Ph.D. degree in mechanicalengineering from the Rand Afrikaans University,Johannesburg, South Africa, in 2000, 2002, and2004, respectively.

In 2004, he joined the Department of Mechan-ical and Aeronautical Engineering, University ofPretoria, South Africa, as a Lecturer. His research

interests include conductive and convective heat transfer, and cooling ofelectronics.

DIRKER et al.: EMBEDDED SOLID STATE HEAT EXTRACTION 703

Wenduo Liu received the B.S and M.S. degrees inmechanical engineering from Tsinghua University,Beijing, China, in 1998 and 2001, respectively, andis currently pursuing Ph.D. degree in the BradleyDepartment of Electrical and Computer Engineering,Virginia Polytechnic Institute and State University,Blacksburg.

His research interests include design and modelingof integrated passive modules, thermal performancecontrol, integrated packaging technology, and powerelectronics.

Jacobus Daniel van Wyk (F’90) received theM.Sc.Eng. degree from the University of Pretoria,Pretoria, South Africa, in 1966, the Dr.Sc.Tech.degree from the Technical University of Eindhoven,Eindhoven, The Netherlands, in 1969, and the D.Sc.degree (with high honors) in engineering from theUniversity of Natal, Natal, South Africa, in 1996.

He has worked with the S.A. Iron and Steel Corpo-ration, the University of Pretoria, and was a memberof the Technical and Scientific Staff, University ofEindhoven, from 1961 to 1971. From 1971 to 1995,

he was a Chaired Professor of electrical and electronic engineering at the RandAfrikaans University, Johannesburg, South Africa, holding Chairs in electronicsand in power electronics until 1992. He founded the Industrial Electronics Tech-nology Research Group, Faculty of Engineering, in 1978 and directed this unituntil 1999. Since July 1995, he has held a special University Council ResearchChair in industrial electronics at the Rand Afrikaans University. He joined TheBradley Department of Electrical and Computer Engineering, Virginia Poly-technic Institute and State University, Blacksburg, in January 2000, where he isthe J. Byron Maupin Professor of Engineering, working in the National ScienceFoundation Engineering Research Center for Power Electronics Systems.

Dr. van Wyk received 20 prize paper awards including 11 IEEE prize paperawards, the prestigious IEEE William E. Newell Power Electronics Award in1995, an IEEE Third Millennium Medal in 2000, and a range of other awardsfrom IEEE Societies as well as from the South African Institute of ElectricalEngineers. He is a Fellow of the South African Institute of Electrical Engineers.He is active in several capacities within the IEEE and its Societies.

Arnaud G. Malan received the B.Eng and M.Eng.degrees in mechanical engineering from the Univer-sity of Pretoria, Pretoria, South Africa, in 1994 and1996, respectively, and the Ph.D. degree in computa-tional fluid dynamics from the University of Wales,Swansea, U.K., in 2003.

Prior to embarking on Ph.D. studies, he workedin industry from 1995 to 1999, starting in the finalyear of his M.S. studies. During the first year he wasa Consulting Engineering designing air-conditioningsystems, followed by finite element based structural

analysis and design work at BKS Advantech (Pty), Ltd. He has been a SeniorLecturer with the Department of Mechanical and Aeronautical Engineering,University of Pretoria since 2003.

Dr. Malan received the Commonwealth Scholarship for Research in Mechan-ical Engineering from the Association of Commonwealth Universities in 1999,the “Best Ph.D. Thesis for 2002 Award” from the Association of Computa-tional Mechanics in Engineering (United Kingdom), in 2003, and the YoungResearcher Fellowship for Exemplary Research in Computational Mechanicsfrom the Second Massachusetts Institute of Technology Conference on Compu-tational Fluid and Solid Mechanics in 2003. He is a Member of the EngineeringCouncil of South Africa and an Executive Committee Member of the SouthAfrican Association for Theoretical and Applied Mechanics. He is a RegisteredProfessional Engineer.

Josua P. Meyer received the B.Eng. degree (withhonors), the M.Eng. degree (with honors), andthe Ph.D. degree from the University of Pretoria,Pretoria, South Africa, in 1984, 1986, and 1988,respectively, all in mechanical engineering.

He completed his military service at the Faculty ofMilitary Science, University of Stellenbosch, SouthAfrica, where he lectured on aerodynamics for pilotsin the South African Air Force. After his military ser-vice (1988 to 1989), he accepted a position as As-sociate Professor in the Department of Mechanical

Engineering, Potchefstroom University, South Africa, in 1990. He was ActingHead and Professor in Mechanical Engineering before accepting a position asProfessor in the Department of Mechanical and Manufacturing Engineering,Rand Afrikaans University, in 1994. He was the Chairman of Mechanical En-gineering from 1999 until the end of June 2002 after which he was appointedas Professor and Head of the Department of Mechanical and Aeronautical En-gineering, University of Pretoria, in 2002. He has been Chairman of the Schoolof Engineering since 2004. The School consists of eight departments totallingmore than 4000 students. He specializes in heat transfer, fluid mechanics andthermodynamic aspects of heating, ventilation and air-conditioning. He is theauthor and co-author of more than 200 articles, conference papers , and patents.

Dr. Meyer received the Lecturer of the Year Award from the PotchefstroomUniversity and Rand Afrikaans University, as well as the Exceptional AcademicAchievers Award by the University of Pretoria. He is a Member of the SouthAfrican Institute for Mechanical Engineers, the South African Institute for Re-frigeration and Air Conditioning, the American Society for Mechanical Engi-neers, and the American Society for Air-Conditioning, Refrigeration and Air-Conditioning. He is a Registered Professional Engineer.