NASA ContractorReport 168322

! NASA-CR-16832219840010510

EngineeringCorrelationsof Varlable-PropertyEffectsonLaminarForced ConvectionMass Transfer for Dilute VaporSpecies and Small ParticlesIn Air

SfileymanA. G6ko_lu

Analex CorporationCleveland,Ohio

and

Daniel E. Rosner

Yale UniversityNew Haven, Connecticut

3anuary1984 ,_,,,_,,

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NATIONALAERONAUTICSAND SPACE ADMINISTRATIONLewisResearch CenterUnder ContractNAS3-23293and NAG3-201

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EngineeringCorrelationsof Varlable-Property

Effectson LaminarForced ConvectionMass Transferfor Dilute Vapor

Speclesand Small Particlesin Alr.

S_leymanA. G_ko_lu*

Analex Corporation•, Cleveland,Ohio 44135

and

Daniel E. Rosner**

Yale UniversityChemicalEngineeringDepartmentNew Haven, Connecticut06520

SUMMARY

A simple englneer_ngcorrelationscheme is developedto predictthe varl-able propertyeffectson dilute species laminarforcedconvectionmass transferapplicableto all vapor moleculesor Brownlandiffusingsmall particles,covering the surfaceto mainstreamtemperatureratio of 0.25 < Tw/Te _ 4.The accuracy of the correlationis checkedagainst rigorousnumericalforcedconvection laminarboundary layer calculationsof flat plate and stagnationpoint flows of air containingtrace speciesof Na, NaCl, NaOH, Na2SO4, K, KCI,KOH, or K2S04 vapor speciesor their clusters. For the cases reportedherethe correlationhad an averageabsoluteerror of only 2 percent(maximum13percent)as comparedto an averageabsoluteerror of 18 percent(maximum54percent) one would have made by using the "constant-property"results.

INTRODUCTION

Althoughconsiderabletemperaturevariationsare encounteredacross theboundary layer (BL) in many heat and mass transfersituations,no simple pro-cedure to accountfor variable (nonconstant)property(ncp) effectson masstransfer rate exists in the literature. For such cases, the applicationofthe constantproperty (cp) analytic solutions,or the experimentaldata, maylead to unacceptableerrors. Readilyavailablecorrectionsare urgentlyneededto improvethe accuracyof transferrate predictionsand to facilitateengi-neeringdesign.

T-Supportedby NASA Lewis ResearchCenter ContractNAS3-23293[Analex]andGrant NAG3-201 [Yale U.].

* Research scientist.**Professorof Chemical Engineering,Director,High TemperatureChemical

ReactionEngineeringLaboratory.

Most of the nonconstant property results for heat transfer predictionpurposes indicate that very simple corrections generally suffice over a moder-ate temperature range. A thorough review of the current literature as well asa detailed discussion of the subject Is given in reference 1 both for ltquidsand gases for laminar and turbulent flows. One of the commonschemesused tocorrect for variable properties ts the property ratio scheme. For gases, thetemperature-dependent-property effects for heat transfer can usually be ade-quately correlated by:

II

_ (-qw) Nuh Sth T_ _ aFncp,h

- - -- - --- - _ee) (1)i-qw)cp NUh,cp Sth,cp

where the constant-propertyquantitiesare evaluatedat free-streamtemperaturefor externalflows.

For mass transferacross boundarylayerswith steep temperaturegradients,however,a slmilarcorrelatlonscheme Is lacklng,and the conventionalheat andmass transferanalogy is usuallyand unjustifiablyemployed. Many engineeringflelds involvingmass transfer such as CVD, surfacecatalyzedcombustion,saltdepositionon gas turbineblades associatedwith hot corrosion,etc. deal wlthnonlsothermalBLs. A carefullyformulatedmass transfertheory, therefore,expllcltlynecessitatestractablevarlable-propertycorrelatlonsto facllltateefficientand accuratemass transfer rate predictions(2 and 3).

A correlationof variablepropertyeffectson mass transferforchemlcally-frozenlaminarBLs has been proposedIn reference4 using an equiv-alent "blowing(suction)parameter"for a number of vapor species. The presentpaper takes a much simplerapproach slmllarto the propertyratio scheme asexampllfledby equation1 and extendsthe applicabilityto larger particlesizes includingvapor species (10-3 _ le E I).

NOMENCLATURE

a power of temperatureratio for variablepropertyeffectson heat transfer,equation (1)

b power of temperatureratio for variableproperty effectson mass transfer,equation (14)

Cp specificheat at constant pressureper unit mass of mixture

D Brownlan(Flck) diffusioncoefficient

Eu Euler number,d In ue/d In x

F functiondescribingvariablepropertyeffects,equations(1) and (7)

J" mass (diffusion)flux

Kn Knudsennumber based on particlediameter

k Boltzmannconstant

Le Lewis number (ratio of Brownlan(Fick) dlffuslvltyto carriergas thermaldlffuslvlty)

Nu Nusseltnumber

n power of temperaturefor Brownlan(Flck)diffusioncoefficient

Pr Prandtlnumber (ratioof carriergas kinematicviscosityto thermal-_ dlffuslvlty)

q" heat flux

Re Reynoldsnumber based on x

r power of temperaturefor thermalconductivity

Sc Schmldtnumber (ratioof gas kinematicviscosityto particleBrownlan(Fick) dlffuslvity)

St Stantonnumber

T absolute temperature

u velocityalong x

W dimensionlessmass fractionof particlesin prevailingmixture,equation (3)

x distancealong the surface

y distancenormal to surface

power of temperaturefor specificheat

B power of temperaturefor viscosity

€ Lennard-Jonesmolecular interactionenergy (well-depth)parameter

n dimensionlessBL coordinate,equation (4)

e d_menslonlesstemperature,equation(2)

thermalconductivityof carrier gas mixture

vlscosltyof carriergas mixture

p densityof carriergas mixture

mass fractionof particlesin the carriergas mixture

collisionintegral

3

Subscripts:

av averaged quantity

cp constant property

0 pertaining to Brownlan (Flck) diffusion coefficient

e outer edge of BL, mainstream conditions

h heat transfer --

1 species t

J species J

m mass transfer or outer edge of the mass transfer BL (e.g. Tm)

ncp nonconstant (variable) properties

w wall (surface) conditions

Superscripts:

' differentiation with respect to n

* pertaining to dimensionless temperature, kT/cav

R_scellaneous:

BL boundary layer

CVD chemical vapor deposition

CORRELATIONAPPROACH

Here we concentrate on chemically-frozen, gaseous, laminar BLs where thehost gas thermodynamic properties and the trace gaseous species transport prop-ertles are assumedto have simple power-law temperature dependencies g_ven by:

p ~ T-1, X ~ Tr, u ~ TB, Cp ~ T_, D ~ Tn

If one applies the conventional self-similarity transformation to the two-dimensional lamlnar BL equations and uses the nondlmenstonal variables definedby:

4

T-Tw

e(n) --T - T (2)e w

w(.)_-- w '(3)We - _w

where n is

n = y • ReI/2 (4)X W

equation (I) can then be reexpressedas:

B+Ir-

w

Fncp,h = • (5)w,cp

!

Tables of elgenvalues,eW, are presentedfor a family of wedge solutionsbyBrown and Donoughe (ref. 5) when air is used as the host gas (r = 0.85, B =0.70, _ = 0.19, Pr = 0.70). Based on these solutions,equation.(5)combinedwith equation (1) reducesto:

Fncp,h - e' _ (6)w,cp

where the best temperatureratio exponent,a, Is given In table l as obtainedfrom referenceI.

Similar to equation(I), the effect of variablepropertieson mass trans-fer, in the absence of thermaldiffusion("thermophoresls"for small parti-cles), can be describedas:

(-J_) Num StmF - - - (7)ncp,m - (-Jw)cp NUm,cp Stm,cp

Combiningwlth equations(3) and (4) we have:e

8+3

n--y- W'Fncp, m = • W,w (8)w,cp

which for air reducesto:

T( r_ n-1.85

Fncp'm = _Tee) • WWw (9)w,cp

The elgenvalues for mass transfer rate Including variable properties, W_,are obtained from the numerical solutions of the BL equations for any size ofdiffusing trace species, as outllned in reference 6 The elgenvalues for heattransfer rate, o_, generated as by-products by the calculatlons ofreference 6, agree excellently wlth the values reported tn reference 5, andconfirm the temperature ratio exponent given In table 1.

Based on equation 8, attention ls directed toward correlating the massI I

transfer elgenvalue ratlo, Ww/Ww It Is known that tn the limltlng caseof Sc >> 1 for small partlcles,'_e mass transfer BL is very thin compared tothe momentum(or heat) transfer BL. Therefore, constant-property resultsObtained by evaluating the properties at the wall temperature wtll glve correctanswers. It is also known from asymptotic laminar BL theory for Sc >> 1 that,tn the absence of thermophoresls, W_ Is proportional to Scl/3 (ref. 7).Hence, for Sc >> 1:

, W' - I/3 B+l-n

WW . w,cp,T=Tw _cw T(__2_ 3 (lO)W-T----_ W' - _ I/3 =w,cp w,cp,T=Te bce Ve/

whlch for air reducesto:

,Ww__ _ 3 (11)Ww,cp

Equation (ll) is confirmedalso by the calculationsof reference6.

In the limitingcase where Le _ l, however,it is expectedthat Fncp,mcomes close to Fncn h, the dlfference.belngdue primarilyto the temperaturedependenceof the d_fuslon coefficientof the species(D ~ Tn). Note thatIn the case of alr as the host gas, the temperaturedependenceof the Prandtlnumber is:

Pr ~ TB+_-r = TO.04 (12)

and the temperaturedependenceof the.Schmldtnumber Is:

Sc - Tr_+l-n= T1.70-n (13)

6

Hence, for Le = 1, Fncp,m = Focp,h only If n = 1.66. Thls should becomparedwtth n = 1.652 used rot the vapor spectes considered in reference 4.In fact, n = 1.66 ts a good approximation for species diffusing In a gas wlthT* = kT/cav greater than about 4, where Cav = (etch) 1/2 (see also the"DISCUSSION" section). Based on the arguments given above, we propose thefollowing stmple correlatlon:

_,1 -n b-n

W-_-_ _ • (14)w,cp

which for atr reduces to:

1.70-n

w-T--- =- • (15)w,cp

where b Is a constant and Tm ts the temperature at the outer edge of themass transfer BL. In the absence of thermophorests Tm ts well approximatedby:

1/3Tm _ Tw + Lear (Te - Tw) (16)

where Leav Is evaluated at Tar = (Tw + Tm)/2. In equations (14) and(15) the first term tn the parentheses accounts for the temperature dependenceof Sc, and the second term In the parentheses accounts for the property vari-ation across the mass transfer BL. Note that for Le = 1, equation (8)becomes:

B+3 b-n b-'_"

Fncp,m z • = (17)

which ls independent of n, and, for atr, reduces to:

T/_ef/b-1.85Fncp,m _ (18)

, If one assumes that FncD,_ = Fncp h for Le = 1, then the value of bis fixed and ts given by- a . 1.85, as tabulated tn table 2. The accuracyof equation (15) with the values of b given In table 2 ts checked againstrigorous numerical calculations as shown In figure 1, where air ls the carriergas. Indeed, our suggested correlation ts found to be generally applicableand successful for many different vapor species ltke Na, NaC1, NaOH, Na2S04,K, KC1, KOH, K2SO4 and clusters made of these molecules. The cases consideredcovered the ranges 0.25 _ Tw/Te _ 4 and 10-3 _<Le _<1 for both the flat plate(Eu = O) and two-dimensional stagnation point (Eu = 1) flows. Our correlationgave a meanabsolute error of only 2 percent (maximum13 percent) as opposed

to a mean absolute error of 18 percent (maximum54 percent) tf the "constant-property" results were used.

DISCUSSION

The generalityof the correlationsuggestedabove is accomplishedbycondensingthe temperaturedependenceof the individualtransportcharacteris-tics of differentspeciesInto a single parametern. Therefore,In order toutilizethe correlationone needs to be able to readilyobtain the temperaturedependenceof the diffusioncoefficientfor any speciesIn question. For vapormoleculesthe temperaturedependenceof the diffusioncoefficientIs given bythe Chapman-Enskogtheory as:

T3/2 TnD _D(T,) - (19)

where _D is the collisionintegralwhich Is a functionof the dimensionlesstemperature T* = kTav/cavevaluatedat the averagemass transfer BL

l + . From equation (Ig) one obtainsthat:temperature Tar = _ (Tm Tw)

3 d In _On = _- d In T* (20)

The calculatlonof the collisionintegralis cumbersomeand Is given inreference8. In order to facilitatethe calculationof n, the tabulateddatagiven In reference7 Is numericallydifferentiatedto get an approximationtod In _D/d In T*. A curve, based on the _ expressiongiven In reference8, Isfitted through these points as shown in figure 2. The analyticalexpressiondescrlblngthls curve-fltIs given by:

d In _Dd In T* - 0.150 . 0.385 exp_ (1.637 loglOT*+ 0.340)] (21)

As can be seen from figure 2, for h_gh temperaturesituationswlth air as thecarriergas where T* is usuallygreaterthan about 4, n = 1.66 Is a goodapproximationfor many vapor species. This supportsthe assumptionmade ear-lier that Fncp,m = Fncp,h for Le = I.

In the extreme limit where the diffusingparticlesare large enough to betreated as if they were in a continuum(Sc >> l, Kn << l), the temperaturedependenceof the diffusioncoefficientis given by the Stokes-Einstentheoryas:

D ~ T_~ TI-B(22)

and therefore, n = 1 - 13. In thls case we have from equations (8) and (I0):

Fncp,m =_(TWeW)1-13-B_3._i) 13.1-1.133= _Ti) -3.5136 (23)

whlch for alr reducesto:

T(____)-I.08Fncp,m _ (24)

For Intermedlateslze particleswhlch are not In the continuumregimethere Is no straightforwardmethod to obtain n. For such cases, the diffusioncoefficientcan be calculatedas outlined In reference9, and then n can beobtainedfrom:

In [D(Tm)/D(Tw)]

n = in(Tm/Tw) (25)

One shouldbear In mlnd, however,that whenever Sc Is large enough to vall-date the Sc >> l asymptotictheory obtalnedfor constantproperties,the mass

transferBL becomesextremelythln compared to the momentum (or heat) transferBL. For such cases we suggestthat Ww be exactlyobtainedfrom theasymptotictheory only wlth propertiesevaluatedat the "wall"conditions,insteadof using the variablepropertycorrectionrecommendedabove.

The effect of variablepropertieson mass transfernaturallydepends on(1) the magnltudeof the differencebetween the mainstreamtemperature,Te,and some averagetemperaturethat the mass transferBL experiences,and (2)the sensltlvltyof the speciesdiffusioncoefficientto temperature(namely,n). Therefore,similarto the argumentgiven for Sc >> l (Le << l) cases,for Sc << l (Le >> l) most of the mass transferBL experiencesa constanttemperatureprofileequal to the mainstreamtemperature,Te. Consideringthe fact that n Is almost the same for most vapor species,we expect,there-fore, that the effect of variablepropertleson vapor specieswlth Le > lwlll be even smallerthan the effect observedfor vapor specieswlth Le < I.Table 3 lists the exact numericalresultsobtalnedfor two vapor species,namely K2SO4 and Na. At 1500 K K2SO4 has Le = 0.344 (smallestamongthe vapor speciestried)and Na has Le = 0.807 (largestamong the vaporspeciestried). As expected,the effect of variablepropertiesfor the Na

, case wlth the larger Le Is less than for the K2SO4 case. For the othervapor speciestried, wlth intermediate Le, It is confirmedthat the effectofvariablepropertiesranks accordlngto the magnltudeof Le. Based on theabove argumentand given the fact that variablepropertyeffectsfor Na are

already negligiblysmall,we proposethat Fncp,m for vapor specieswlthLe > l should be taken as unity.

lhe followlngIs an outllneof the recommendedprocedurethat one should

follow to obtain the correctionfactor,Fncp,m,for any glven nonlsothermallaminarforcedconvectiontrace speciesmass transferapplication. It Is

assumedthat conventional BL procedures have already been fully exploited todetermine the mass transfer rate for constant properties, i.e., -Jw,cp orNUm,cpor Stm,cp are accurately known. Whenair ts the carrier (host) gas:

Step 1: Calculate the Le of the trace species. If Le > 1, then takeFncp.m = 1 If Le < 10-3 , then use the constant-propertysolutions with properties evaluated at TW.

Step 2: If the trace species is a vapor molecule, determined In _D /d In T* from equation (21) (or ftg. 2) and calculate nfrom equation (20).

Step 3: If the trace species is a small parttcle (cluster), determine nfrom equation (25).

Step 4: Calculate Tm from equation (16).

Step 5: Obtain the proper value of b from table 2. If tt ts not a flatplate or a stagnation point flow (e.g., wedge flow, etc.) use someaverage value of b from table 2.

Step 6: Use equation (15) to obtain W_/k_,cp.

Step 7: Use equation (9) to obtain Fncp,m.

Step 8: Use equation (7) to obtain the mass flux J_, Num or Stmcorrected for vartable property effects.

If the carrier gas is not air, the formulation in the paper is kept gen- eralto allow Steps 1 to 8 (except Step 5) to be repeated with the proper values of a,B and r corresponding to the temperature dependencies of carrier gas properties.However, the values of b as ltsted in table 2 (Step 5) are only for air and haveto be determined for other gases.

CONCLUDINGREMARKS

Interfaclalmass transportrate formulationsincludingthermal (Sorer)diffusion("thermophoresls"for small particles)effectsrequireexplicitknowledgeof both Fgcp_h and Fncn m as shown in references2 and 3.Toward this end, a slmple correlati_ scheme is developedto predict the vari-able propertyeffectson mass transfer. The applicabilityrange of the cor-relationcovers 0.25 < Tw/Te < 4 and lO-3 < Le < I. When checkedagainstrigorousnumericalcaTculatlonsfor (1) dITute _apor speciesNa, NaCl, NaOH,Na2SO4, K, KCl, KOH, K2S04, (2) their clusters,and for (I) laminarflatplate flows and (2) laminarstagnationpoint flows, it is found that thecorrelationhad an averageabsoluteerror of only 2 percent (maximum13 per-cent) as opposedto an average absoluteerror of 18 percent (maximum54 per-cent) one would have made by using "constant-property"results. We proposethat constantproperty solutionsevaluatedat the "wall"temperaturebe usedfor larger particlesthan those wlth Le = lO-3 and expect the variableproperty effect to be negligiblysmall for cases where Le > I.

lO

REFERENCES

I. Kays, William M., and Crawford,MichaelE.: ConvectiveHeat and MassTransfer.Second ed., McGraw Hill, 1980.

2. Rosner, D. E.; and et al.: ChemicallyFrozen MultlcomponentBoundary LayerTheory of Salt/Ash Depos%tlonRates from CombustionGases. Combust.Sci.Technol.,vol. 20, no. 3-4, 1979, pp. 87-106.

3. Rosner, D. E.: Thermal (Soret)DiffusionEffectson InterfaclalMassTransportRates. PCH, PhysicoChemlcalHydrodyn.,vol. l, no. 2-3, 1980,pp. 159-185.

4. Sr%vastava,R.; and Rosner,D. E.: A New Approach to the CorrelationofBoundaryLayer Mass Transfer Rates with Thermal Diffusionand/or VariableProperties. Int. J. Heat Mass Transfer,vol. 22, Sept. 1979, pp. 1281-1294.

5. Brown,W. Byron; and Donoughe,PatrickL.: Tables of Exact LaminarBoundaryLayer SolutionsWhen the Wall is Porousand Fluid PropertiesareVariable. NACA TN-2479,1951.

6. G6ko_lu, S_leymanA.: ThermophoreticallyEnhancedDepositionofParticulateMatter Across NonlsothermalBoundary Layers. Ph.D.Dissertation,Yale Univ., 1982.

7. Bird, Robert B.; Stewart,Warren E.; and Lightfoot,Edwin N.: TransportPhenomena. Wiley, 1960.

8. Hirschfelder,Joseph, P.; Curtlss, CharlesF.; and Bird, Robert B.:MolecularTheory of Gases and Liquids. Wiley, 1954.

9. Rosner,D. E.; Israel,R.; Zydney,A.: Effect of Thermophoreslson theMinimum AerosolDiffuslonalDepositionRate Before the Onset of InertialImpaction. Presentedat the ACS/IEC-SIWinter Symposiumon AerosolSystems, (Tucson,AZ.), Jan. 26-28, 19Bl.

II

TABLE I. - EXPONENTOF TEMPERATURERATIO FOR VARIABLE

PROPERTYEFFECTSON HEAT TRANSFER,a

< TW Te >Te Tw

Flat plate (Eu = O) -0.01 0Two-dlmenslonalstagnationpoint (Eu = l) .lO .07

TABLE II. - EXPONENTOF TEMPERATURERATIO FOR VARIABLE

PROPERTYEFFECTSON MASS TRANSFER,b

< T Te > TwTe w

Flat plate (Eu = O) 1.84 1.85Two-dlmenslonalstagnationpoint (Eu = l) l.g5 1.92

TABLE III.- EXACT CALCULATIONSOF VARIABLE PROPERTYEFFECTS

FOR K2SO4 AND Na IN AIR

Na: Le (1500 K) = 0.807 K2S04: Le (1500 K) = 0.344

Tw/Te Fncp,m Tw/Te Fncp,m

0.25 0.985 0.25 0.905.40 .992 .40 .950.50 .994 .50 .967.60 .997 .60 .980.80 l.O00 .80 .994

l.O0 l.O l.O0 l.O1.50 1.046 1.50 1.0642.00 1.060 2.00 1.0883.00 1.054 3.00 1.0864.00 1.034 4.00 1.061

12

LEGEND

m Eu-Io Eu-O

FirstNo. TwITe1 0.252 .403 .50

1.6 -- 4 .60

5 .80 _e 56 1.50 9147 2.O0 • /¢o916

1.5 -- 8 3.009 &O0 /

SecondNo. Lo /

L4 -- I 10-1<Le< 10o 814 /8152 I0-_<Le< 10-I O_l 63 I0-3< Le< i0-2 /

/L3 -- ThirdNo. Species

I Na /5

2 NaCI

- 3 NaOH 71;4;9151.2 -- 4 Na2SO4 / 716

5 K - - 912_/°9176 KCI 914 _ o_i:;

"_ 1.1- 2 4 812.J817'_'_616_-_ . 6171711f 715

_414- II #r -

1.0 -- 31(_'_',_,514._J,_____.615

__ 211o.'",_, 5"2Z"114

.9 234._-Z,._4__214• 134-,4-14_424'334

•8 -- 31_/"ye3241240

214_ o224

.l -- / I_4

OlZ4

.6" I I I I I I I I I I.6 .7 .8 .9 1.0 1.I 1.2 1.3 1.4 1.5 1.6

/w'w/w'w,cp)correlation

Figure1. - Accuracyofcorrelationsforfiat plateandtwo-dimensionalstagnationpointflowsin the range0.25".<TwITe.<4 and10-3.<Le.<1.

.60--

.50 -- _ _ Curve-fit, eq. (21)ferenUatlon,ref. (7)

,_0

=ILI

•20 --

.10

I I I10-1 100 T_, 101 102

Figure2. - d In _ .....t3D/dIn T asa functJonof1""obtainedbynumericaldifferentiationoftabulated_D versusT_

valuesofref. 7.-A curvefit throughthepointsisgivenbyeq. (21).

1. Report No 2. Government Accession No. 3. Recipient's Catalog No

NASACR-1683224. Title and Subtitle 5. Report Date

Engineering Correlations of Variable-Property Effects January 1984on Laminar ForcedConvectionMass Transfer for Dilute 6.PerformingOrganizationCodeVapor Species and Small Particles in Air

7. Author(s) 8. Performing Organization Report No.

Si_leymanA. Gbko_lu and Daniel E. Rosner None10. Work Unit No.

9. Performing Organization Name and Address

Analex Corporation and Yale University 11. Contract or Grant No.

21000 Brookpark Rd. Chemical Engineering Dept. NAS3-23293 and NAG3-201Cleveland, Ohio New Haven, Connecticut44135 06520 13. Type of Report and Period Covered

12. Sponsoring Agency Name and Address

Contractor ReportNational Aeronauticsand Space Administration 14SponsoringAgency CodeWashington,D.C. 20546

533-04-IA (E-l95915. Supplementary Notes

Final report. ProjectManager,Carl A. Stearns,MaterialsDivision,NASA LewisResearch Center,Cleveland,Ohio 44135.

16. Abstract

A simple engineering correlation scheme is developed to predict the variableproperty effects on dilute species laminar forced convection mass transferapplicable to all vapor molecules or Brownian diffusing small particles, coveringthe surface to mainstream temperature ratio of 0.25 < Tv/T e < 4. The accuracyof the correlation is checked against rigorous numerTcai for_ed convection laminarboundary layer calculations of flat plate and stagnation point flows of air con-taining trace species of Na, NaCI, NaOH, Na2S04, K, KCI, KOH, or K2SO4 vaporspecies or their clusters. For the cases reported here the correlation had anaverage absolute error of only 2 percent (maximum 13 percent) as compared to anaverage absolute error of 18 percent (maximum54 percent) one would have made byusing the "constant-property" results.

17. Key Wordl (Suggested by Author(s)) 18. Distribution StatementHeat and mass transferVariable properties Unclassified - unlimitedBoundary layers STARCategory 34CorrelationsDeposition

fg. Security C!=__=_!f.(of this report) 20. Secudty Cllmalf. (of this page) !21. No. of pages 22. Price"

Unclassifled Unclassified

*For sale by the NationalTechnical InformationService, Springfield,Virginia 22161

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