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Surface and Coatings Technology, 59 (1993) 59—66 59 Modelling of a microwave postdischarge nitriding reactor H. Malvosa,b A. Ricardc, J. SzekeIy~’, H. Michela, M. Gantoisa and D. Ablitzer” aLaboratoire de Science et Genie des Surfaces, URA CNRS 1402, and bLaboratoire de Science et Genie des Matériaux Metalliques, URA CNRS 159, Ecole des Mines, Parc de Saurupt, 54042 Nancy Cedex (France) cLaboratoire de Physique des Gaz et des Plasmas, URA CNRS, Bt 212, Université Paris-Sud, 91405 Orsay (France) dMJT Department ofMaterials Science and Engineering, Cambridge, MA 02139 (USA) Abstract In a postdischarge nitriding reactor, reactive species, which have a short lifetime, are created by means of a plasma and then sent by convection towards the sample which is to be treated. The aim of the model presented here is to optimize the gas flow characteristics (composition, flow rate, pressure etc.) in order to obtain a maximum reactivity around the sample. The experimental reactor used has a very simple geometry and works with low power (less than 200 W) microwave discharges (2450 MHz) in Ar—N 2 mixtures for a pressure in the 10—1000 hPa range. This reactor allowed us to point out the complexity of the different operating parameters, justifying the development of a predictive model. Such a model was developed with the code PHOENICS. It allowed us to determine the effect of the operating parameters on the velocity field, the temperature field and the atomic nitrogen (the nitriding species) mass fraction map. The standard operating conditions used for the treatment of iron samples were chosen as reference conditions. Then several sets of operating conditions were tested, pointing out the extremely important effect of pressure and gas velocity in the reactor on the atomic nitrogen mass fraction. 1. Introduction diffusion mechanisms. Thus, the gas velocity must be high enough so that the active species do not become Postdischarge nitriding treatments have been per- de-excited before they reach the sample. We notice here formed recently. In such treatments, nitrogen active that the higher the pressure is, the more frequent are the species are produced in flowing postdischarges and impacts between the particles and the shorter is the work-pieces are placed downstream inside a separate heating device [1]. The first metallurgic results obtained show that there is a strong correlation between the I Transport I I Active sp.c:e! of species Nitriding reactor superficial nitrogen composition of the treated iron generation i 5 mm a 30 mm I samples and the atomic nitrogen density of the flowing L 0.7 m L 1.2 gas inside the nitriding reactor [2, 3]. Experimental I I I studies allowed us to show the effect of the main I I I operating parameters on this density [4, 5] and to I propose an interpretation from simple kinetic models I I Vacuum [5, 6]. The complexity of the interactions between these pump parameters justifies the development of a predictive I model, which is presented now. _j_j[~amPl~~ 2. Postdischarge reactor —__________________ jj I ___ 2.1. Experimental set-up __________________ Plasma sourca The reactor we modelled uses a microwave discharge. surfaguide The experimental set-up is shown in Fig. 1. 2450 MHz Heating devic. The power generator (1200 W) sends microwaves Ar-NO Optic fiber (2450 MHz) along a waveguide. The plasma is created Pressure in a quartz tube and remains in this position. The neutral spectroscopic gauge excited species are transported by the gas flow towards L~UiPment the sample. Using an external heater, this sample is maintained at the correct temperature to activate the Fig. I. Experimental reactor. 0257—8972/93/$6.00 © 1993 Elsevier Sequoia. All rights reserved

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Page 1: Modelling of a microwave postdischarge nitriding reactor

Surfaceand CoatingsTechnology,59 (1993) 59—66 59

Modellingof a microwavepostdischargenitriding reactor

H. Malvosa,b A. Ricardc,J. SzekeIy~’,H. Michela,M. GantoisaandD. Ablitzer”aLaboratoiredeScienceet GeniedesSurfaces,URACNRS1402, andbLaboratoiredeScienceet GeniedesMatériauxMetalliques,URACNRS159,

EcoledesMines, ParcdeSaurupt,54042NancyCedex(France)cLaboratoiredePhysiquedesGazetdesPlasmas,URACNRS,Bt 212, UniversitéParis-Sud,91405Orsay (France)dMJT DepartmentofMaterialsScienceand Engineering,Cambridge,MA 02139 (USA)

Abstract

In a postdischargenitriding reactor,reactivespecies,which havea short lifetime, arecreatedby meansof a plasmaandthensentbyconvectiontowardsthesamplewhich is to betreated.Theaim of themodel presentedhereis to optimizethegasflow characteristics(composition,flow rate,pressureetc.)in orderto obtaina maximumreactivity aroundthesample.Theexperimentalreactorusedhasa very simplegeometryandworks with low power(less than 200 W) microwavedischarges(2450MHz) in Ar—N

2 mixturesfor apressurein the 10—1000hPa range.This reactorallowed us to point out the complexityof the different operatingparameters,justifying thedevelopmentof a predictivemodel.Sucha model wasdevelopedwith thecodePHOENICS. It allowed usto determinetheeffect of theoperatingparameterson the velocity field, the temperaturefield and theatomic nitrogen(the nitriding species)massfractionmap.Thestandardoperatingconditionsusedfor the treatmentof iron sampleswerechosenas referenceconditions.Thenseveralsetsof operatingconditionsweretested,pointingout theextremelyimportanteffect ofpressureandgasvelocity in thereactoron theatomicnitrogenmassfraction.

1. Introduction diffusion mechanisms.Thus, the gas velocity must be

high enoughso that the active speciesdo not becomePostdischargenitriding treatmentshave been per- de-excitedbeforethey reachthe sample.We noticehere

formed recently. In such treatments,nitrogen active that the higherthe pressureis, the morefrequentare thespecies are produced in flowing postdischargesand impacts between the particles and the shorter is thework-pieces are placed downstreaminside a separateheatingdevice [1]. The first metallurgicresultsobtainedshow that there is a strong correlation between the I Transport I I

Active sp.c:e! of species Nitriding reactorsuperficial nitrogen composition of the treated iron generation i 5 mm a 30 mm Isamplesand the atomicnitrogen densityof the flowing L 0.7 m L 1.2

gas inside the nitriding reactor [2, 3]. Experimental I I Istudies allowed us to show the effect of the main I I Ioperating parameterson this density [4, 5] and to Ipropose an interpretationfrom simple kinetic models I I Vacuum

[5, 6]. The complexity of the interactionsbetweenthese pump

parametersjustifies the developmentof a predictive Imodel,which is presentednow. _j_j[~amPl~~

2. Postdischargereactor —__________________ jj

I ___

2.1. Experimentalset-up __________________

Plasma sourcaThe reactorwe modelledusesa microwavedischarge. surfaguide

The experimentalset-upis shownin Fig. 1. 2450 MHz Heating devic.The power generator(1200 W) sends microwaves Ar-NO Optic fiber

(2450 MHz) along a waveguide.The plasmais created Pressure

in aquartztubeandremainsin thisposition.Theneutral spectroscopic gaugeexcitedspeciesare transportedby the gas flow towards L~UiPmentthe sample. Using an external heater,this sample ismaintainedat the correct temperatureto activate the Fig. I. Experimentalreactor.

0257—8972/93/$6.00 © 1993 — Elsevier Sequoia.All rights reserved

Page 2: Modelling of a microwave postdischarge nitriding reactor

60 H. Malvos et al. / Modellingof a microwavepostdischargenitriding reactor

lifetime of the active species.None the less, from an caneasily passthroughthe activationgap,thusformingindustrial point of view, it is interestingto work close in solution in the metal sample.to atmosphericpressure,becausethis allows convective Therefore,the only reactivespeciesthatwill beconsid-heatingof the reactorand,thus,naturalhomogenization ered here is atomic nitrogen: the dissociation, at thein the temperatureof the samplesto be treated. surfaceof the sample,of molecularnitrogenvibrationally

The model presentedrepresentsthe flowing postdis- excitedonly representsasmall percentageof the atomiccharge only. Therefore,the electromagneticproblems nitrogen which formsin solution in the metal sample.related to the dischargeitself are not involved and we Moreover,asthe densitiesof theexcitedspeciesin theconsideronly the cylindrical reactor and the external postdischargeare very low in comparisonwith theheaterwhosedimensionsare reportedin Fig. 2. densityof the moleculesin their fundamentalstate,we

will takethe physicalpropertiesof the molecularnitro-2.2. Reactivespeciesin theplasma gen (or of the Ar—N mixture used)in its fundamental

Our model takesinto accountall the transportphe- state (viscosity, thermaldiffusivity, specific heat)for thenomena in order to draw maps of reactive species study of the plasmaflow in the reactor.densitiesin the reactor. Therefore,we will first recallhere what are the main species responsiblefor thenitriding.

The plasmais generatedin a small volume by an 3. Transportof the reactivespecieselectrical field which createsion—electron pairs. Theelectronsare thenacceleratedby the electricalfield and 3.1. Studyofthemassbalancetheir collisions with the gas molecules create three 3.1.1. Massconservationequationdifferent kindsof transfer: The massbalancefor the atomicnitrogenis given by

transferof momentum;transferof kinetic energy~ V (P Ct) V — D p V CD) = Sconvection diffusion net creation

transferfromkinetic energyof theelectronto potentialenergyof the molecule. wherep representsthe densityof the plasma,co the mass

The first two transfersare negligible for the gas mole- fraction of the speciesN, V the barycentricvelocity, Dcules,becauseof the low massof the electroncompared the diffusion coefficient and S the sourceterm of thewith the mass of the nitrogen molecule.However, the speciesN (creationminusdestruction).third typeof transfercanleadto anexcitation(electronic, Herewe are in a steadystatehypothesis.This meansvibrational androtational)of the nitrogenmolecule, to that we do not considerthe problems inherent to thean ionization or to a split into atomicnitrogen, starting of the treatment.In fact, we should call this a

Different experiments,carriedout at the Laboratoire ‘quasi-steady state’, because,during the process, thede Physiquedes Gaz et des Plasmas,Orsay, showed sample surfaceis made up of the phasesFe(ot), Fe(y’)that the speciesmainly responsiblefor the nitriding is and Fe(s), one after another. However, each of thesethe atomic nitrogen [7]. Indeed, becauseof its high phasesremainsat the surfacelong enoughto apply thepotential energy (around 9.6eV), the atomic nitrogen quasi-steadystatehypothesis.

Exierii,ti I lealci

- 1 iron Sample

30 380 300 2t) 300 200-- ..

Fig. 2. Geometryof theflowing postdischargereactor.

Page 3: Modelling of a microwave postdischarge nitriding reactor

H. Malvoset a!. / Modellingof a microwavepostdischargenitriding reactor 61

-

-~ 50 rn/s.

(a) Velocity

330 330p __(b) 350 4~gj\\71io

~ 601) 700 3002. E-3 ., ~ TemperaturetK ) 600

1.

1¼O~~ ~ 2.SE.3 2.~3 N

I(c) Atomic Nitrogen MassFraction

Fig. 3. Computedresultsobtainedfor thefollowing parameters:pressure,l0~Pa; massflux, 0.53 kg s m2 of N

2.

3.1.2. Sourceterm S Unfortunately,this mechanismis not quantifiedat thisThe increasein volume of the atomic nitrogenoccurs time.

entirelyin the discharge,In the postdischarge,theatomic However, Yamashita [9] proposed the followingnitrogen only recombinesitself by the mechanism mechanismsfor the destructionof atomic nitrogen on

Pyrexwalls:N+N+N2—+N~+N2

N+wall—~N~+wallas shown by Partridgeet a!. [8] and Yamashita [9]. k

Moreover, the variation of k with temperaturewas N + N +wall —* N~+walldeterminedexperimentally[10]. k

In fact, Yamashitashowedthat only the first mechanism3.1.3. Boundarycondition is significant.The atomic nitrogenconcentrationat the entranceof

the reactor is known. It is determinedby the NO 3.2. Studyofthe momentumbalancetitration method [3]. 3.2.1. Natureoftheflow

On the surfaceof the sample, the atomic nitrogen To determinethe natureof the flow, we calculatethedisappearsas it goes into solution in the metal sample. Reynoldsnumber:

Page 4: Modelling of a microwave postdischarge nitriding reactor

62 H. Malvoset a!. / Modellingof a microwavepostdischargenitriding reactor

-- I

--

50 rn/s.

(a) Velocity

841)

350 ~ ‘700 8o0~”~/\ \ ‘400400 10 700\5o0(b) Temperature(K.) 600

1.4 E-3

I.2E-3 1.6E-3

l.E.3\\t/~ I.8E~3

~ if! ~ 1.6 E-3 .4 E-3 .2 E-3

I’ ~LE.3\~

3. E-3 Atomic NitrogenMassFraction(c)

Fig. 4. Computedresultsobtainedfor thefollowing parameters:pressure,iO~Pa; massflux, 0.70kg s m2 of Ar—20%N

2.

— Vd 3.2.3. MomentumconservationequationRe_p (pVV)V=—VT—VP+pg

— where t representsthe stress tensor,VP the pressurewhered representsthe diameterof the reactor(3 cm), V gradientand g the gravity acceleration.the meanvelocity (around5 m s~)and v the kinematic We havea newtonianfluid, so the stresstensoris aviscosity (4 x l0~m

2 s~at 380 K, 5.8 x iO~Pa for a simpleexpressionof the viscosityandthe velocity.mixtureof Ar—li %N

2).The Reynoldsnumber is around 400, which means 3.2.4. Boundaryconditions

that the flow can be considered as being laminar At the entranceto the reactor, the radial velocity(Re.cz2100). valueis zero.On the walls, the velocity valueis zero. At

the exit from the reactor,the meanvelocity is calculatedfrom the massflow conservation.

3.2.2. Fluid continuity equationSince we are in a steadystate, the continuity equa- 3.3. Studyoftheheatbalance

tion is: 3.3.1. Energyconservationequation

V (p V)=0 V (p C~TV—k V T) =

Page 5: Modelling of a microwave postdischarge nitriding reactor

H. Malvos eta!. / Modellingof a microwavepostdischargenitriding reactor 63

—~ : 50 rn/s.

(a) Velocity

330____________________________ \ 350

8 1) KtX)~/ /(b) TemperaturetK.) 7(X)

1.E-5 5.E-5

I _ 3.E.4~ \____ ___ 2.E.4

(c) Atomic NitrogenMassFraction

Fig. 5. Computedresultsobtainedfor thefollowing parameters:pressure,5.8 x l0~Pa;massflux, 4.62 kg s - m 2 of Ar— 11%N2.

TABLE 1. Experimentaldata usedasboundaryconditionsfor themodel

Fig.3 Fig.4 Fig.5 Fig.6 Fig.7

Massflow rate(kg s - m 2) 0.53 0.70 4.62 4.62 7.97Gasmixturecomposition N2 Ar—20%N2 Ar—ll%N2 Ar—11%N2 Ar—ll%N2Pressure(Pa) I0~ l0~ 5.8 x l0~ l0~ l0~Temperatureof theexternalheater(K) 843 843 900 900 900Temperatureof thegasat theentranceto the 450 350 400 400 400reactor(K)Atomic nitrogenmassfractionat theentranceto 5.0 x l0~ 3.0 x iO~ 1.3 x I0~ 1.3 x I0~~ 1.3 x l0~thereactor

where T representsthe gas temperature,C~,the specific by gas moleculesand immediately reach the reactorheatat constantpressure,k the thermaldiffusion coeffi- walls. In this case,radiationdoesnot participatein thecient andST the sourceterm. heating of the gas. For higher pressures,experiments

In thecaseof low pressures,photonsarenotabsorbed have showed that the temperaturevariation is also

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64 H. Malvoset a!. / Modellingof a microwavepostdischargenitriding reactor

-* 50 mIs.

(a) Velocity

__ 330\~

1140 8tX///’

(b) TemperaturetK.) 7(X)

5. E.6 LE.5

l.E-3 5. E.4 2!E.4

(c) Atomic NitrogenMassFraction

Fig. 6. Effect of pressurewith a constantmassflow rate.Computedresultsobtained for the following parameters:pressure,l0~Pa; massflux,4.62 kg s

1 m2 of Ar—1l%N2.

negligible. In the same way, the contribution of the betweenthe sampleandtheexternalheaterto determine‘vibration—translation’collisions betweenthe gas mole- the equilibrium temperatureof the sample.cules is negligible. Finally, the valueof the sourcetermST is consideredto be zeroandthe energyconservation 3.4. Physicalpropertiesofthegasequationis written Density. Since the pressureis quite low (less thanV ( C TV — k V T) = 0 atmosphericpressure),we usethe perfectgaslaw.

p Diffusion coefficientof atomicnitrogenin argonor inmolecularnitrogen. We use the empirical relationship

3.3.2. Boundaryconditions developedby Cussler [11] and Fuller et al. [12]. ThisThe gas temperatureat theentranceto the reactoris relationshiptakes accountof the effect of temperature

measuredby spectroscopicanalysis.The heat flow at andpressure.thereactorandsamplewalls is estimatedby the calcula- Heat capacity. Since the heatcapacityof argonor ni-tion of the correspondingheattransfercoefficients.With trogenshowslittle sensitivity to pressureor temperaturethis aim, we had to considerthe radiativeexchanges in our experimentalrange,we usea constantvalue[13].

Page 7: Modelling of a microwave postdischarge nitriding reactor

H. Malvoset al. / Modellingof a microwavepostdischargenitriding reactor 65

- _________

—~ : 5(1 m/s.

(a) Velocity

330____________________ \ 350

8(X) ‘IX)

(b) Temperature(K.)

5.E-6 l.E.5

~ ~ 2.5 E.4 I. E.4

5. E.4

(c) Atomic Nitrogen MassFraction

Fig. 7. Effect of pressurewith a constantvolume flow rate.Computedresultsobtainedfor thefollowing parameters:pressure,l0~Pa;massflux,7.97kg s-~m

2 of Ar—ll%N2.

Thermalconductivity.Sincethe thermalconductivityis SIMPLE algorithm of Patankarand Spalding [21]. Thepressureindependentin our experimentalrange[14], we grid usedhereis uniform (56 x 250). To makethefiguressimply have to take account of the temperatureeffect easier to read, we use a scale factor of 25 in the y[15]. direction. Moreover,since the problem is symmetrical,

Dynamic viscosity.Sincethe dynamicviscosity is also we representhalf a cross-sectionpassingthrough the zpressureindependentin our experimentalrange [16], axis. In eachset of figures,we represent(a) the velocitywe only considerthe temperatureeffect [17]. of the gas in the reactor,(b) the temperaturemapand

The propertieswe havejust consideredcorrespondto (c) the massfractionmap of atomic nitrogen.puregases;forgasmixtures,weusedseveralcombination Figure 3 correspondsto a pressureof iO~Pa and arelationships proposed in refs. 18, 19, 14 and 20 massflow rateof 0.53kg s~m

2 of N2 Fig.4 represents

respectively, a pressureof io~Pa anda massflow rateof 0.70 kg s~

m2 of an Ar—20%N

2 gas mixture, and Fig. 5 corres-4. Computed results ponds to a pressureof 5.8 x l0~Pa anda massflow rate

The linked hydrodynamicequationsweresolvedwith of 4.62kg ~ m -2 of an Ar—11 %N2 gasmixture. Forthe PHOENICS code, which embodiesa variant of the thesethreesets of conditions, the gas temperatureand

Page 8: Modelling of a microwave postdischarge nitriding reactor

66 H. Malvos et a!. / Modellingof a microwavepostdischargenitriding reactor

theatomicnitrogendensityat the entranceto thereactor Acknowledgmentweredeterminedexperimentallyby spectroscopicanaly-sis andNO titration respectively.Theseparameters,and We are grateful to the Ministère de la Rechercheetthe temperatureof the externalheaterrequiredto main- de la Technologieand Electricité de France for thetam the iron sampleat around 843 K, are reproduced supportof this work.in Table 1. Figure 5 correspondsto the experimentalconditionschosento perform the nitriding of cylindricaliron samples.

From theselast experimentalconditions,we tried to Referencesincreasethe pressureto l0~Pa to studythe effect of thison the atomic nitrogendensity in the reactor. For this 1 A. Ricard, A. Pilorget, H. Michel and M. Gantois, Fr. Patent

treatment,we kept constantall the experimentalvalues App!., 87 10698 (1987); Eur. PatentApp!., 88 4019 506 (1988).

usedpreviously (especiallythe gas temperatureand the 2 A. Ricard,J. E. Oseguera-Pena,H. Michel and M. Gantois,Proc.1st mt. Conf on Plasma Surface Engineering, Garmish-

atomic nitrogen densityat the entranceto the reactor), Partenkirchen,September1988, Vol. 1, DeutscheGesellschaftfür

except the mass flow rate and,of course,the pressure MetallkundeInformationsGesellschaft,Oberursel,1989, p. 83.

(seeTable1). Then, Fig. 6 representsa pressureof 1 o~Pa 3 A. Ricard,J. E.Oseguera-Pena,L. Falk,H. MichelandM. Gantois,

with the samemassflow rate(4.62kg s~’m 2) of the IEEE Trans.Plasma Sci., 18 (1990) 940.Ar—1l%N2 mixture.This meansthat the meanvelocity 4 A. Ricard, J. Deschamps,J. L. Godard,L. Falk and H. Michel,

Mater. Sci. Eng., A139(1991) 9—14.at the entranceto the reactoris nearlyhalf of that in 5 L. Falk, J.E. Oseguera-Pena,A. Ricard,H. MichelandM. Gantois,

the precedingcase. In contrast,in Fig. 7, we kept the Mater. Sci. Eng., A139(1991) 132—36.samemeanvelocity and,thus, the pressureis 1 0~Paand 6 C. Chave,C. Boisse-Laporte,J. Marec and Ph. Leprince,Mater.

the massflow rate7.97kg s’ m2. Sci. Eng.,A140 (1991) 494—98.

7 A. Ricard,Topical Invited Lecture,XVII ICPIG, Budapest,1985.8 H. Partridge, S. R. Langhoff, C. W. Bauschlicherand D. W.

Schwenke,J. Chem.Phys.,88 (5) (1988) 3 180—83.5. Conclusions 9 T. Yamashita,J. Chem.Phys.,70 (9) (1979) 4248—53.

10 J. E. Oseguera-Pena,Dip!ômedeThese,INPL, Nancy, 1990, p. 99.

The resultswe presentedshow the extremelyimpor- 11 E. L. Cussler,Diffusion,MassTransferin Fluid Systems,Cambridge

tant effect of pressureandgasvelocity in the reactoron University Press,Cambridge,1984, pp. 112—13.12 E. N. Fuller, P. D. SchettlerandJ. C. Giddings,md. Eng. Chem.,

the atomic nitrogendensity.Indeed,the atomicnitrogen 58 (1966) 19.

massfractionaroundthesampledecreasesfrom4 X l0~ 13 W. M. Rohsenowand J. P. Hartnett, Handbookof Heat Transfer,

to 1.5 x iO~ when we increase the pressure from McGraw-Hill, New York, pp.2—90.

5.8 x io~to l0~Pa, keepingthe samemass flow rate 14 J. H. Perry, ChemicalEngineers’ Handbook, McGraw-Hill, New

(Figs. 5 and6). Sincethe meanvelocity is smallerin the York, 4th edn., pp. 3—225, 3—226.15 W. M. Rohsenowand J. P. Hartnett,Handbookof Heat Transfer,

secondcase,wecanassumethat thisis inpartresponsible McGraw-Hill, New York, Table35, pp. 2-82—2-85.for the decreasein the atomic nitrogen concentration. 16 W. M. Rohsenowand J. P. Hartnett,Handbookof Heat Transfer,

Moreover,the comparisonof Fig. 5 with Fig. 7 (where McGraw-Hill, New York, pp. 1-5.

we kept the samemeanvelocity) pointsout themarked 17 W. M. Rohsenowand J. P. Hartnett,Handbookof Heat Transfer,

effect of pressureitself on the atomic nitrogen concen- McGraw-Hill, New York, Table31, pp.2-72,2-73.18 J. H. Perry, Chemical Engineers’ Handbook, McGraw-Hill, New

tration, sincethe atomicnitrogen massfraction around York, 4th edn.,Chap. 14, p. 13.

the sampledecreasesfrom 4 x l0~to 2.5 x i0~when 19 J. H. Perry, Chemical Engineers’ Handbook, McGraw-Hill, New

pressureincreasesfrom 5.8 x io~to iO~Pa. This result York, 4th edn.,pp. 3-220.was expected,since the atomic nitrogen recombination 20 J. H. Perry, Chemical Engineers’Handbook, McGraw-Hill, New

is a three-bodymechanism. York, 4th edn.,pp. 3-230.21 S. V. Patankarand D. B. Spalding, Ire. J. Heat MassTransfer, 15

The model usedhere for a two-dimensiongeometry (1972) 1787—1806.

could be developedto describethree-dimensionalflowsencounteredin laboratory experimentsor in an indus-trial set-up.