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WADC TECHNICALJ, REPORT 53-1191 WCOSI-3

A METHOD OF PREDICTIHG SKIN, COMPARTMENT, ANDEQUIPMENT TEMPERATURES FO R AIRCRAFT

LAWRENCE SLOTEWILLIAM I). MURRAY

NEW YORK UNIVERSITY

JUlL iv5.v

* 1110 11I A MI M A\ | I '%•; ' F N • |

When Government drawings, speciflctwion, Or, te aaaeuefor any purposelother than in conneto withe aeiitl re ated Guumentprocrenisnt operation, the United defniel related Goere n-

curnoesonmaliy nv ormanwhatoever;~ and the fact thatth overmentmay ave ormuate furnished, or in any way supplied

bye da rw"4 pcfiainO te ta, Is not to be regardedby mplcaton r thewis asin nymanner licensing the holder orany other person or corporationor conveying any righs or permissionto manufacture, use, or sell any patented Invention that may in any waybe related thereto.

The Information furnished herewith Is made availble for studyupmtonteunderstandingta the Government's Prop""ietr nterests inand relating thereto shall not be Impaired. It In desired tha the judgeAdvocate (WCA) Wright Air Developmen Center, Wright-PattersonAir Force Base, Ohio, be promptly notified of aby apparent conflict be-tween the Government's Proprietary Interests and those of others.

WADC TECHNICAL REPORT 53-119 lily 1953

ERRATA - September 1954

The following corrections are applicable to WADC Technical Report

53-119, "A Method of Predicting Skin$ Compartment, and Equipment Temperaturefor Aircraft", dated July 1953:

Page vii

Change to read:

Pr Prandtl Number 3600 Cj) J` g dimensionlessK

Adds

F* Ambient Pressure FM atmospheres

Page viii

Change to read:

/denity of air o #98 2

Page 17

Change Equation (19) to read:

.f _R) (* 3600OCP /~--ý - 0.53 .KKf /qf

Change to read:

/1 fe

C, g 2A C p CD2

3600Ar' IR 2 Tf 2

ý;b-titutu F* for P in equations (20) and (21).

Wright Air Development CenterAir Rese~rch find Development Ccmmand

United -"totes Air ForceWright-Natternon Air Force Uinoe, Ohio

i I 6f.

ERRATA (Continued)

SEquations 23 and 25

Delete (p)1/2 insert (p*)1/2

Iff229 Steps 4 and 5Delete 1.8. insert 272.7

Page 30Phase IV - Step 2 change to reads

Ac2 Ac•_ -=2x 5--.x392

Ac + Aq 5.792 - .732 ft 2

Step 4: Delete P, insert p*

Delete 4 2insert

Step 5: Page 32

Delete p 2 insert

Page 3!.Phase II - Step 2 change to read:

C - 27,000

Phase II - Step 6 change to reads C - 27,000

Step 7 change to read: C - 27,000Step change to read: Ts - 425OR

. il- Stej 2 change to remd:

. (Ts-i -� 425)

.)J56 oh

2

p

ERRATA (Continued)

Page 36

Step 4 ehenge to read:Delete P, insertp*

Delete 4 insert

Step 6 cha•ge to read:

T - 468OR

Page 37

Step 9 change to read; , value of Tq - 46 R is correct."

Phase V -

Step 1 change to read: Tq 468*R

Step 5: Delete insert

Change to read: Tq - 4685R

Cae to fe Page 38

"where Tq h4680R and

Delete 4//E2 , insertp

Step 6 ehange to read: Tc d4 OR

Pages 58 and 59. Figures 15 and 16

Delete (,P) add1/4

3

'UADC TECHNICAL REPORT 53-119

A METHOD OF PREDICTING SKIN, COMPARTMENT, ANDEQUIPMENT TEMPERATURES FOR AlIRCRAFT

Lawrence SloteWilliam D. Mturray

New York University

July 1I5.?

EnMviromenlill Criteria! IiranchSystems~ Planning office?

W)r*'ctorateriln Air W~eapon Sy.sttmsContrairt N". Al: 33(610)-122

RD( No. 560O-76,

k\, ~(.igOlf Air~r I)(!Vtl .ull oiitiit (Xliuelu,

FORMEORD

This report was prepared by the Research

Division of the College of Engineering, New York

University under Contract AF 33(616)-122. It pre-

sents a method for the calculation of the equilibirum

surface temperature, compartment air temperature and

equipment temperature of bodies in high and low speed

flight and contains examples of the temperatures to be

expected in tpical aircraft section.

The contract was initiated under a project

identified by the Research and Development Order 560-76,

title unclassified, "Study - Design Temperature Require-

ments for Operation of USAF Aircraft and Equipment", and

was administered by the Environment.1 Criteria Branch,

Systems Planning Uffice, Directorate of Air Weapon

3ystems, Wright Air Development Center, with James G. Law

as Project Engineer.

,ii, j vu 'i 3 I];

ARSTRkCT

This report presents a method for the calculationof the equilibrium skin temperature of aerodynamic shapes insteady flight. Graphical methods are presented for the cal-culation of equipmnwt temperature and compartment air tompcra-ture, The numerical and graphical solutions are presentedfor aircraft flyirg at speeds to Mach number 5 and for alti-tudes from 0 to 100,000 feet in the proposed ITAF Hot andCold Atmospheres.

Tn this report an attempt is made townrd simpli-fication of the empirical formulae by graphic presentationof calculations upon typical aerodynamic shapes. Analysisis based upon consideration of a flat plate and the case ofan isothermal surface and constamt free stream velocity.Methods for applying the graphs to other surfaces arep resented.

PUBLICATION RFEVIEW

The publicat"on of this report does not con-stitute approval by the Air Force of thefindings or the conclusions containedtherein.It is published only for the exchange andstirmlation of ideas.

FOP TWE COIMANDER"

H . A.* T3OU7,1EAYColonel, 'TRAFfireetor nf Air Weapon Systems

"W•Abjr Th r..-)j19 :ii.'

TABLE OF CONTENTS

Page No.

List of Illustrations ....... . . . . . . . . . . . .. v

Nomenclature ...... . . . . •. =. . . o . . . . . . vi

Heat Balance Equation ...... 1

Adiabatic Surface Temperature, Te. . . . " . . . . . 2Temperature for Evaluating Air Properties, T' .... 3Prandtl's Number, Pr, and Thermal Conductivity, K.. 4Reynold's Number, Re ..... e .4....• • .Heat Transfer Coefficient, hs ............ 6Radiation Exchange .... . . . . . . 8Equip-ent Heat qe- .............. • 9Method of Solution ................ 9Sample Calculation. ........ ... ..... 11Graphical Solution of Heat Transfer Equation . . . . . 13Sample Calculation . . . . . . 15Inside Skin Temperature, Tsi ............ & 15Equipment Temperature, Tq . . . . . ... 16Compartment Air Temperature, Tc .... . . .. . • 19

Conclusions . . 9 .e 9 e. .* * * * * * . 19

Bibliography * . . . . . . .& . . . . . . . .* 24

Appendix I . ... . . ... . . .. . . . * ., • . .• 261. Example Comparing Te and T' . . . ...... . . 262. Example of Variation of Recovery Factor . . . . . 26

Appendi 11 ........... 271. Exa ple of i eth o ..et.... ...... 27

Appendix!I .................... . . 9 * 391. Table I - Total Normal Mean Emissivity

and Absorbtivity. ........... 39

2. Table 11 - Example Temperature Calculationsfor Typical Aircraft Sections ..... 42

WADC TR 53-119 iv

LIST OF ILLUSTRATIONS

FIGURE Pae

1. USAF Proposed Cold and Hot AtmospheresTemperature vs. Actual Altitude . . . . .•g4

2. USAF Proposed Cold and Hot AtmospheresPressure vs. Actual Altitude ...... J 5

3. Thermal Conductivity and Prandtl Numberas Functions of Temperature . .*. . . . . 46

4. Adiabatic Surface Temperature as aFunction of Temperature and Mach Number . 47

5. Reference Temperature as a Function ofTemperature and Mach Number . .. . . . . 8

6. Solar and Nocturnal Irradiation as aFunction of Altitude. . . . . . . . . . . 49

7. Critical Angle for Cones in SupersonicFlow .. . . ... .. ..a*e.**o . ... 50

8. Mach Numberat Surface of Cone as a

Function of Free Stream Mach Number . . . 51

9. Pressure at Surface of Cone. . . . . 52

10. Temperature at Surface of Cone , , , . 535

11. Modified Reynolds Modulus for Air . . 5

12. Heat Transfer in Laminar Flow ..... , 55

13. Heat Transfer in Turbulent Flow ..... 56

14. Chart for Calculation of EquilibriumSkin Temperature........,." " 57

15. Chart for Calculation ofEquipment Temperature . . . ... 8

16. Chart for Calculation of CompartmentAir Temperature . . * . . .s. . . * a * . 59

17. Station B Mx-NYU M=O.5 . . . ...... 60

le'. Station B Mx-NYU M=3.0 .. ... .. 61

19. Station B Mx-NYU M-5.0 ......... , 62

KADC TH 55-119 v

NOMNCLATURE

a pesd of sound ft/sec

A., tot.;l area (su'fac.) ft 2

Ab surface area of coMmparxtmet ft 2

A iurfar:e area of equipment ft 2

q

AO+Aq

A p jected area ft 2

C specitic heat of skin BTU/Ib *R

c spec-Ifi" heat of air at constant pressure BTU/Ib *RP

D ehaya(. Lb..isIG di:lension ft

g acceleration due to gravity 32.2 ft/sec 2

G nocturnal irradiation from above the 2a surface BTU/hr ft2

Snocturnal irradiation from below thesurface BTU/hr ft 2

G nocturnal ir2diation - 1/2(Ga%) BTJ/hr ft 2

G solav i r'radiation BTU/hr, f 2

h outer surfa.ce coefficient, of convec-S tive heat transfer: BTU/hr ft *R

hif convective (air film) coefficient ofheat transfer for single horizontal BTU/hr ft2

cylinders

1 q rjornve(:t1ve (air film) coefficient ofbq ea trarnsfer for single horizontal BTU/hr ft -Rr..yIrideciP3 r- 1/2 h.

J i ',,h•r,.• l. eq'xivaL•nt of heat '78 ft lb/BTU

" 'be..,'D_,,.cndcbi..-A.,y of skin BTU/hr ft> (Ol/ft)

WADC l'if ,-:.9vI

k thermal conductivity of air BTU/hr f-2(¶R/ft)

L total distance from leading edge ft

M Mach Number a dimensionless

Nu Nusselt Number -- dimensionless

k

P ambient pressure lb/ft 2

Pr Prmndtl Number dimensionless/k

qe equlipment heat release BTU/hr

qcv heat dissipated by convection BTU/hr

qr heat dissipated by radiation BTU/hr

r recovery factor dimensionless

R universal gas constant 1711 lb ft/slug OR

Re Reynold' s Number V/0 dimensionless

s slant length on cone ft

t time hours

T ambient temperature OR

Te adiabatic surface temperature &R

T compaz'tment air temperature OR

T equipment surface temperature ORq

Ts outer equilibrium skin temperature OR

Tsi inner equilibrium skin temperature OR

8T temperature difference OR

TI reference temperature OR

V velocity ft/sec

WADC TR 53--l9 vii

W weight lbs

w specific weight of skin material ib/ft 3

x local distance from leading edge ft

coefficient of thermal expansion 1TOR

7 ratio of specific heats = 1.4 dimensionless

oý5 nocturnal absorbtivity dimensionless

O(S solar absorbtivity dimensionless

6 mean emissivity, dimensionless

Semissivity of outer surface dimensionless

C• emissivity of hot surface dimensionless

C7. emissivity of cold surface dimensionless

-10 BUh 2 R40- Stefan-Boltzmann constant 17.3 x 10 BTU/hr ft

Sdensity of air lb/ft 3

Sskin thickness ft

2absolute viscosity lb sec/ft

9 1/2 vertex angle degrees

no subscript denotes local condition

o subscript denotes free strean condition

c0 subscript denotes sea level condition

x subscript denotes local or point value

m subscript denotes mean value

f subscript refers to air film

WADC TR 53-119 vll

INTRODUCTION

As actual and proposed speeds and altitudes offlight increase, the problem of maintaining a satisfactoryenvironment for airborne equipment becomes increasinglydifficult.

The skin and internal temperatures of an aircrafttravelling through the atmosphere at a high Mach number maybecome excessive unless a sufficient amount of cooling issupplied. Conversely, in low speed aircraft operating underextremely low temperature conditions it is essential thatartificially produced heat maintain the temperature above aminimum design value (presently -80OF non-operating, -65OFoperating). Calculations of skin and equipment temperaturesare therefore essential to the development of high altitudeaircraft and to the problem of controlling the actual tem-perature of airborne equipment to a value that will providesatisfactory life.

This report is the result of an investigation todetermine by literary search and computations those proper-ties of the atmosphere which affect the heating and coolingof a body in motion at various altitudes. This informationis used to determine stabilized skin temperatures, equipmenttemperatures, and typical compartment air temperatures.

This report examines the problem of aerodynamicheating of typical aerodynamic shapes in steady subsonicand supersonic flight to determine the value and signiff.-canoe of the pertinent parameters with the aim of usingthese parameters to calculate the temperatures that can beexpected as a function of altitude and speed. An attemptis made toward the simplification of empirical formulae bygraphic presentation of calculations. In our analysis weshall consider two basic shapes, planes and cones. Theseare of interest for aircraft for the following reasons.

Generally, much of the body of an aircraft iscylindrical. Since the body diameter is very large com-pared to the boundary layer thickness, conditions on thesurface of this cylinder are similar to those on a flatplane, except for the effects of the distrubance producedfarther upstream by the nose of the aircraft.

WPf)C TR 53-iL9 ix

The nose of the aircraft may be conical or ogival.In the latter case the nose may be considered a series oftruncated cones, so procedures used in dealing with conesare applicable to an ogival nose to a reasonable degree ofaccuracy.

The usual assumptions made in analyzing boundarylayers are applicable here. The system considered is onein which the temperature over any surface considered isassumed to be uniform over the entire surface. The boundarylayer thickness is negligible• compared to the length of thesurface. It is further assumed,that boundary layer conditionswhich exist with subsonic velocities are not affected by in-crease of speed to supersonic values, except for effects onboundary layer air which are considered in this report.Also, the system considered is one which has a boundary layerunder zero pressure gradient beginning from some known pointwith zero thickness.

With this concept in mind appropriate generalaerodynamic parameters may be established for the determin-ation of equilibrium skin temperatures. Although a deter-mination of the accuracy of temperatures obtained by methodspresented herein can only be made after checking the resultsof an experimental investigation, it is estimated that thefollowing maximum errors will result from the e graphical

.methods: Te . 5%, J(Ts - Te)* 10%,I(Tq - Tf)|-+ 20%,I(Tc - Tq)I ± 20%. Accuracy will be discussed in more detaillater in the report.

WADC TR 53-119 x

A TMTHOD OF PREDICTING SKIN, COMPARTMENT, ANDEQUI PMTT TP.1EM11PERATU RES FOR AIRCRAFT

Analysis

Heat Balance Equation

If the initial conditions and the specified flighttrajectory are known, skin temperature can be evaluated as afunction of time by means of the following differentialequation:

dTsa

AtIr 7- mh At(Te--Ts)÷ + Ge+ *ApaGs+q %" -CrAt (%)1 (()

The equilibrium skin temperature T., is the skin tem-perature which will be reached after a sufficient lapse of timeunder steady flight conditions at constant altitude, i/.Equation (1) defines the value of To, since in the liiit ast -ft oo, dTg .* . o and Equation (1) reduces to

dt

heAt (Te-Ts) + At I GAe(zs1 + qe - A (Ts)k 4 O (2)

or

.The thermal balance of a given area of the skin is theresultant of the following sources of heat flow:

1. Heat gained by the body due to aerodynamic heating,hs(Te - T )

2. Heat gained by the body due to solar mid atmosphericirradiation, ýcX G• + A sS

At

3. Heat release of the equipment, qe

WADC TB 53-119 2.

4. Heat lost by the body due to radiation to outer space,

- ~(Ts) 4

Adiabatic Surface Temperature, Te

In order to calculate equilibrium surface tempera-tures, adiabatic surface temperatures are first computed fromthe following equation:

r2

Te = T rV (4.)2gJc p

orTe W T (i Y- r •)(5)

2

If a fluid is brought from a state of motion to astate of rest by friction, as occurs at the surface of a flatplate oriented parallel to the air stream, the temperature ofthe fluid is raised to a value different from that obtainedby bringing the fluid to rest adiabatically. The ratio ofthe temperature rise due to friction to the temperature risedue to adiabatic compressure is known as the recovery factor.2/, 3/, 4/. The value of the recovery factor depends onihetger The flow is laminar or turbulent. For laminar flow,the recovery factor, r, can be taken as (Pr)i 1 2 and forturbulent flow, the recovery factor, r, can be taken as (Pr)-,/.

In this study, the value of the recovery factor, r, istaken to be 0.87 which is an average value obtained from exist-ing information on subtonic and supersonic flow, both laminarand turbulent, on flat plates and cones. Y , the ratio ofspecific heats for air, is 1.4. Equation (5) then becomes:

T e= T(l +O0.74MW) (5a)

Equation (5a) is presented in graphical form asFigure 4.

WADC TR 5j-lbL

Temperature for Evaluating Air Properties, T'

6/, 7/ The reference temperature T' is obtainedfrom Croccs olution of the boundary layer equations cover-ing Mach numbers 0 to 5. It is the temperature at which thephysical properties of the air are evaluated so as to elimi-nate the effect of small variations in the variables Pr, Mand Ts-

T - O.h2T (1 . .076 ) 0. 58 To (6)

Since Equation (6) contains the term T9 which isthe equilibrium surface temperature that we are eventuallytrying to determine, we will substitute in its place theadiabatic surface temperature Te in order to obtain a closeapproximation of T. When Te is substituted for Ts up to aMach number of 5, these values are close and therefore thissubstitution is acceptable. This is also the condition foran insulated plate. If qe in Equation (3) is small in com-parison with the other terms this then approaches the caseof an insulated plate.

Since varying the reference temperature causes theNusselt number and the Reynold's number to change in the samedirection, the effects of an improper choice of temperatureare greatly minimized Equation (6) then becomes:

T' -T (1 + 0.03192 M2 0.3.16 r ) (6a)

This simplification is also justified from the results ob-tained by Hantzsche and Wendt 8/ who have shown in theirexperiments on a flat plate thV effects of varying fluidproperties resulting from temperature variations in theboundary layer. Their results indicate that at a Mach num-ber of 5, the exact unit thermal conductance differs fromone for isothermal flow by less than 5% for ratios of surfaceto fluid absolute temperatures ranging from 1 to 8. Theeffect of variable properties should even be much less pro-nounced at low Mach numbers.

Substituting the value of the recovery factor,r - 0.87 into Equation (6a), we obtains

WADC TR 53-119 3

T' - T (1.+0.1331M2) (6b)

Figure 5 shows the plot of Equation (6b). Someinvestigators use the adiabatic surface temperature T. as thetemperature to evaluate the fluid properties and their experi-mental findings are also in good agreement with data obtainedempirically. In order to illustrate the amount of variationdue to using Te and T' as the reference temperature, anexample is shown in the appendix.

Prandtl's Number, Pr, and Thermal Conductivity, K

Prandtlis number is defined as:

Pr , 3600 91 cP (7)k

It can be regarded as the ratio of momentum diffusivity tothermal diffusivity. As the temperature increases, the valueof Prandtl's number decreases as shown in Figure 3.Figure 3 also shows the variation of thermal conductivityof air, k, with temperature.

Reynold's Number, Re

Reynold's number is defined as:

Re -,,O x(8)

In this report we will use what we call a modifiedReynold'4 ,iumber, the Reynold's number without a distanceparameter, which is defined as:

Le- b (P)(T) 1/2(M) (8a)x (T')1.7

This expression is derived as follows:

Reynold's Number, Re =- X

From the perfect gas law, (3 -

WADC TR 53-119 4

Using the viscosity I1 , ( )

and Re V Px R. T;1ieoo (T'/Tc.)"7

VP

R/i*f0 (T,) 1 .7

Now V- where a is the speed of sound and is equal toa (T/To• V Then

OD O Then:

Re P a (T/Too)1/2 M SODx CT0,). (T,)1'7

(T00

a -(T(T') 1 .7

at aODa(T O).2

/10

Therefore, Re (P)(T)1/2(M)

7 (TeI)I( 7

In this form Re/x can be presented as a nomographas shown in Figure 11. By use of this modification of

WADX TR 53-119 5

Reynold's number a parameter, is found which remains constantwith x along a continaous suria:e.

Equation (8a) is a convenient way of expressingthe modified Reynold?s nuimber- as a function of a specificatmosphere (P & T), speed of Air,,raft (M), and the referencetemperature (T'). The magnitude of this modulus is an indi-cation of the rate of new fluid arriving in the thermalboundary layer to carry heat to or from the surface. Thecritical Reynold's number Is that value of Re at which theflow characteristics of the fluid change fr6m laminar toturbulent conditions. This value will be taken as 5 x 10ofor purposes of compatation in this report, that is,,,Re>S xlOwill be considered as turbulefnt flew and Re< 5 x 10> will beconsidered as laminar flow.

Other investigators have used other values of e fortransition. These values range from 1 x 105 to 2.5 x 100 .The value used herein has been found to agree with most experi-mental results available. It should be noted that many inves-tigators bave used frcc stream conditions for the evaluationof Reynold's number and thus have obtained values higher thanthose used in this report.

Heat Transfer Coefficient, hS

9/ It is now possible to introduce the Nusseltnumber, for the flat plate which combines the heat transfercoefficient, Prandtl number, and the Reynold's number into anextremely useful parameter defined by:

x h x - 0.33 (Re) (PE) (9)

and ( 11 kX 0.03 (Re).8 (Pr) "33 (10)(Nu). k .0

Equation (9) is applicable only to a laminar boun-dary layer while Equation (10) is applicable to a turbulentboundary layer. Equations (9) and (10) can be re-writtenas fol1 ows.

0. 13ýRe .5(Pr) 3

WJJC TPF >.• ,-

"I "0.03 (P) k

Equation.# (D_) ,d (Ia) are prese.'..Ad •. .uc.•'.grarn in figu~res12 and 13.

For a f]. plat.ý, free •:..'in. uonit.:icn• cf ve.ocit-yand pressure are used in t}.'e det?.ernijrat-i.on of the referenoetamperature T', and bdsed on this value of T' the propertleiof the fluid are evaluated. The.se properties are, thermal.conductivity, density, and viieosi ty. Prandtl's nuniber isalso deternined for this referenoe t~emperature T'.

For any other aerodynamic shape, the free streamconditions of velocity, pressure and tempeature are replacedby the local conditions just outside of the boundary larer atthat. point. These properties can be found once the pressuredistribution around the body in question is known. 13/, 34/This data can be determined from wind tunnel experimdents orfrom free flight, -ests and, in some cases, computed. Thechange in these properties for a cone at various speeds canbe found from Figures 7,8,9, and 10, which make use of thefact that velocity is constant along the surface of a cone.For ogives we can assume series of truncated cones or a conef aired into a cylinder.

In addition, it has been shown in reference 8 thatthe local heat transfer coeffic ent in laminar flow for thecone must be multiplied by (3)1/2 to account for curvature.For the case of turbulent flow on a cone, the heat transfercoefficient as obtained by Gazley, .6/ appears to be 1.15times larger ÷han the ]oca.4 heat, tr Per coefficient asobtained by the flat plate equations. This reasoning willalso be applied to .thrt-r bodies of rwvo•.tion.

It should he no .ed tba4. equations (9) through (12)are the local values of Nuvselt. nriber and heat transfercoefficient at. x. The mean value over any continuous flatsurface for Nusselt r'ner and the heat. tramsfer coefficientare given by the oj'].ow,'g ex-pr'esiors:

.. (9a)

wC 'MR '()- 1(9 'a

(h)m a o. 6 6 k ( (Pr).33 (U-a)

(h)m W 0.O375 2 (k). 3 3 (12a)

where L - the total distance from the leading edge to thepoint in question.

The relation between the local and mean heat transfercoefficient for a cone with laminar flow is shown to be:

(h)m = L (h)

and similarly for turbulent flow:

(h)m s -0 (h)x

Radiation Exchange

ll/ Another factor affecting surface temperature isradiation. A heated body emits radiant energy at a rate andof a quality dependent on the temperature of the body. Thisenergy relationship is shown by the following expression:

dq . T (Ts)~ (13)

dt

where the emissivity 6 , varies with wavelength (or tempera-ture of radiation), degree of roughness and, if a metal, withthe degree of oxidation. 10/ Table I gives the emissivitiesof various surfaces for various emission temperatures.Although the values in this table apply strictly to normalradiation from the surface, they may be used with negligibleerror for hemispherical emissivity except in the case of wellpolished metal surfaces, for which the hemispherical emissiv-ity is 15 to 20 per cent higher than the normal value.

WADC TH 53-],T'

Values in Table I also hold for absorbtivitty whichis dependent upon the nature of the incident rAdlation indshould be evaluated at. the color temperature of the irradiat-ing source. For purposes of computaticn, the valne of absorb-tivity due to nocturnal irr-adiation will be taken as that ofa source whose temperature is 1009F.

The radiation gained from the swn, space and earthis shown by the second and third tarms of Equation (3) where,

dt At

is the irradiation to the surface from the sun assumed to beat its zenith and from the earth and surrounding atmosphereand which is expressed as a function of altitude in Figure 6.Above 50,000 feet these values are assumed to be constant.During a night flight the only irradiation factor involvedis that due to the earth and the surrounding atmosphere.

Since all the terms of Equation (3) except, thosefor solar radiation use total. surfa-,e area and this term usesthe projected surface area or effective irradiation area tothe sun, the term Ar/At is introduced. The projected surfacearea Ap, for a horizontal flat plate (wing) is 1/2 the totalsurface area At. For a body of revolution A is 1/w times thethe total surface area, At.

Equipment Heat q,

A quantity of heat is dissipated from internal com-ponents (electronic tubes, resistors, motors, etc.) operatingat a given load. This value of heat, q,_, is the net heatreleased from all such components and is divided by At in orderto be expressed in terms of BTU per square foot of compartmentsurface. If such components are artificially cooled the valueof q. will be reduced and in the case where cooling exceedsheat output of equipment qe will have a negative value.

Method of Solution

All charts 'nd graphs necessary to achieve solutionr7f' Ue specified paranoters are contained in the appendix

WADC TR 53-1] J

of this report. The following steps are taken for solution

of the parameters to be used in the heat balance equation (3).

Step Fig. or Table Result

1. Altitude, Speed, Atmosphere Given Alt, MO

2. For given altitude and speeddetermine ambient pressureand temperature from atmosphereto be used for solution 1,2 Po, T0

3. Determine local conditionsadjacent to the boundazylayer

For a flat plate local con-litions are same as free strewn

--iblent) conditions 1,2 P,T,M

For a c4\ne in supersonic flowwhen tE-;"ihock wave is detacheduse free stream conditions asan approximation and when theshock wave is attached use thefollowing figures to determinelocal conditions 7,8,9,10 P,T,M

4. Determine adiabatic surfacetemperature for givpin speedand local temperature 4 Te

5. Determine reference temperaturefor property evaluation forgiven speed and local temperature 5 T'

6. Determine Modified Reynold's No. .1 Re/x

7. Multiply value of Re/x as foundin step 6 by the distance in ft.from the leading edge to thesection being investigated. Ifthe value is >,5 x 10 turbulentconditions exist and if the valuei's < 5 x 1. aminar conditions Re

WADC 7R 5_s-19.

Step Fig. or Table Result

8. Determine value of thermalA conductivity and Prandtl

number for the determinedvalue cf T' 3 k, Pr.

9. Knowing k, Pr, x, Re/xdetermine value of heattransier coefficient for properflow conditions 12,13 bs

10. Determine absorbtivity ofmaterial for solar and noc-turnal irradiaticn Table I OýS o4(

11. Determine emissivity ofsurface Table I $

12. Determine irradiation on sur-face at t6e given altitude.At night only nocturnal irradi-ation is present and during theday both nocturnal and solar 6 G sGirradiation are present. Forsymmetrical bodies 1 /2(Ga%

13. Determine net heat exchanged fromequipment per square foot of corn- epartment surface A,

From the above thirteen steps, the various parametersnecessary to solve Equation (3) have been obtained. We can nowsolve Equation (3):

" "T ) G ++ l

Sample Calculation

An example is presented to illustrate the applicationof th- method of solution of the various parameters requiredfor bolution of Eqwation (3). The example is for an aluminum('USr) fltt plats (i.e. wing) with sero angle of attack, flying

WADc TR 5-19 1..

at Mach numbe 2 at a constant altitude of 4o,000 feet inth 12/ proposed USAF Cold Atmosphere during the day. Theprobr'em is to detemnine the parameters necessary to solveEquation (3) for the steady state equilibrium temperature Ts.

Step 1 40,000 feet, Mach No. 2, Cold Atmosphere

Stop 2 From Figs. 1 & 2, P. - 334. b/ft 2 To - 375 OR

Step 3 M - 2 P - 334 Ib/ft2 T - 375 "R

Step 4 From Fig. 4, Te = 6 50o R

Step 5 From Fig. 5, T' - 570 "R

Step 6 From Fig. ll, Re/x - 2.5 x 106

Step 7 for x a I ft, Re - 2.5 x 106 Since this value isgreater than 5 x I0 , turbulent conditions exist

Step 8 From Fig. 3, k .0158 BTU/hr ft 2 ('F/ft), Pr - .71

Step 9 From Fig. 13, hs - 65 BTU/hr ft2 OF

Stop 10 From Table I, a<4- .53 - 2

Step 11 From Table I, u - .30

Step 12 From Fig. 6, ( -36 BTU/hr ft 2

G4- 1410 BTU/hr ft

Step 13 No equipment heat dissipation q. 0

The previous example was for a wing (flat plate)but it can also be applied to aircraft body (cone) by usingthe corrections of charts, Figures 7,8,9, and 10, as shownin the following example for a 30* cone under the sam fly-ing conditions.

Step 1 40,000 feet, Mach No. 2, Cold Atmosphere

Step 2 From Figs. 1 & 2 Po - 334 ib/ft2, To -375 OR

WADC TR 53-119 12

Step 3' From Figs. 7,8,9,10 30" cone shock wave is at-

tached M - 1.75 P 501 lb/ft 2 T - 420 OR

Step4 FromFig. 4 T - 660 OR

Step 5 From Fig. 5 T' - 600 "R

Step 6 From Fig. 11 Re/X - 3.2 x 106

Step 7 For x - I ft Re ,3.2 x 106 Since this value isgreater than 5 x 10 turbulent conditions exist

Step 8 From Fig. 3, k .016 BTU/hr ft2 (OF/ft) Pr - .695

Step 9 From Fig. 13, h 77 BTU/hr ft2 "FFor a cone in terbulent flow multiply this valueby 1.15 or h =89 BTU/hr ft2 F

Step 10 From Table 1, - .53 - .26

Step i. From Table I, • - .30

Stepl12 From Fig.6, G. .36 BTU/hr ft' 1 G B TU/hrft 2

Step 13 No equipment heat dissipation q. " 0

Graphical Solution of Heat Transfer Equation

Up to this point existing information on aerodynamicheating was reviewed and the parameters involved in the heattransfer Equation (3) were analyzed and set up in such a waythat they are amenable to simple graphical determination.It is believed that this type of presentation will reduce thegreat amount of work required of those having need for thisinformation. Likewise, it is logical that having presentedthe graphical solution for the parameters involved in theheat transfer Equation (3), the solution of this equation forthe equilibrium skin temperature should also be presented asa graphical determination.

Rearranging Equation (3) as follows:

(A (t•) + 50 (15)

WS

WADO TR 53-119 1

and performing the following substitutions:

Bm h

Equation (15) becomeas

AT.4 + B T. - 0- (16)

This form of fourth degree equation can be readilysolved by graphical methods. This graph is constructed inFigure 1h of the appendix.

The manner in which this graph is used to determinethe equilibrium skin temperature T3 is as follows:

1. For the given flight conditions, compute values of B & C.

2. On scale B, mark off the computed value of B (note scalefactors on graph).

3. Draw a straight line from the origin 0-0 to value of Bpreviously determined in step 2.

4. On scale C, mark off the computed value of C (notescale factors on graph).

5. Through this value of C draw a straight line parallelto the line dram in step 3.

6. where the straight line from step 5 intersects theprop Mer curve, drop a line perpendicular to thetemperature axis and where this perpendicular inter-sects the temperature ads is the value of Te, theequilibrium skin temperature.

a a figure 14 in the appendix of this report shows theactual detail working graph for the solution of the equilib-rium skin temperature Ts. An exmple is presented to illus-trate the use of this figure in the solution of Equation (3)

WADC TR 53-UL9

for the equilibrium skin temperature, Ts.

Sample Calculation

Using the data obtained from the example for thewing on page 12 we obtain the followingi

B - .- " 216.74 .3

G [I~ . o( a o) +± + h*C At Ab ÷8 To

(.26 x 36 + 1/2 x .53 x 4o) + 0 , 6' x 650

.3

c -• 11,4oo

Noting the scale factors on Figure l4, draw a linefrom origin 0 -0 to B - 216.7. Then through value ofC - ]Ji4,hO draw a line parallel t. the line dran from ori-gin to B. Where this line intersects curve (1) drop a per-pendicular to the temperature axis and read the value of theequilibrium skin temperature T* . 650 OR.

Now, having determined the equilibrium skin tem-perature T , we are in a position to compute the value ofthe equip~int temperature and the compartment air temperature.

Inside Skin Temperature. Tei

When the walls are poor conductors there exists atemperature gradient within the wall. If this gradientexists then the inside skin surface temperature Tgi must bedetermined so that it can be used in the determination ofeipment temperature and compartment air temperature, To.The following is the expression for determining the insideskin equilibrium surface temperature, (Tel).

WADO TR 53-39 15

_% k-- (Tel T 3) (17)

Ac~

qe heat dissipated by equipment, BTU/hr ft of compart-Am ment surfacec

k - thermal conductivity of skin, BT/hr fýt 2 (F/ft)

- skin thickness, feet

To outside equilibrium skin temperature, OF

Tsi - inside equilibrium skin temperature, OF

Squipnent Temperature, Tq

To determine the temperature of components buriedwithin the interior of electronic equipment located within acompartment is a very complicated matter becmase of the com-plex nature of the heat transfer. ,In this analysis, forreasons of simplification, it is convenient to assess anaverage temperature of the equipment by considering it as asmooth heat generating package separated from the skin by aconsiderable blanket of air across which the equipment ismounted by vibration mounts which offer good thermal insul-ation to the compartment wall. The heat lost from the equip-ment by conduction through the vibration mounts will thus beassumed to be a very small factor.

The following is the equation for a heat balanceon an assumed piece of equipment.

% - %v * r (18)

In this analysis, the chassis and the componentsenclosed are considered at identical temperature and beecmseof the complex mass of the equipment, it will be treated asa simple smooth package such as a small boiler tube hundlesin a box for which data mq be obtained from references 17and 18.

WADM TR 53-119 16

From Mckdams 17/ the heat transfer coefficientby convection from singIe horizontal cylinders is given bythe following expression:

hf D iAD f t 3, 2 1/4

Jf Z (19)kf 0.53 2 (1kf

Let PO

R Tf

2

kfIc. R 2Tf2f f

Equation (19) becomes-

h - 0.53 kf (p).1/2 (0)/ (,&r)l . (20)

DI "

The coefficient of heat transfer hf is for the airfilm to which all the terms with subscript f refer, and theconstant is the shape factor.

Equation (20) gives the ýPalue of the heat transfercoefficient hf for single horizontal cylinders which approxi-mate the heat transfer coefficient for small rectangularboxes, flat plates, etc.

The suppression of convection by proximity of theshell to the component bundle may be neglected if the con-vection is handled in the manner suggested in reference 18/where AT is the difference between hot and cold surfaces-andconvective transfer is 50% of normal convection to free air.Equation (20) becomes:

h 0.27 kf (P) (oV2 ) 'C*& (AT)l( / (21)

D 1/4

WADC Ta 13-119

AS a means of simplification all terms having thesubscript f are evaluated at the temperature Tf which will betaken as the average between the equipment temperature andthe equilibrium inside skin surface temperature.

The heat transferred by convection is 17/1

%v W hq Ae A T (22)

orq oW0.27 kI A (P) 32 ( )0 0A9 (Tq - T)0/ (2)

qc- = 1T/(

Here effective area, As, accounts for the difference in areaof the equipment and inside wall.

In Equation (18) the radiative heat transfer qr isgiven by the following expressions

6 A*(T4- - T 14 (24)

Substituting Equations (23) and (24) in Equation (18)the following expression is obtained:

0.27 ICf As 1/2 (O('A (T5T)AE.A 4_~T 4, 2%% ~ ~ ~ ~ ~ s e- D4 () V( T Te oqATq Tsi) (5

Equation (25) can be solved by a trial and errormethod but this requires a great deal of laborious procedure.The computations are reduced to a minimum by resorting tographs. The first step in the graphical solution to Equa-tion (25) is to plot Equations (23) and (24) as functions ofTq and Tsi. In this way we will have two graphs, one forconvective heat transfer as a function of T and T i and onefor radiative heat transfer as a function of Tq and Tai.

By making an estimate of the equipment temperatureTq, we can obtain from these graphs the values of qr and qcv.93.nce we know qe, the total heat dissipated by the equipment,the sum of the computed qr and qcv should equal qe. If they

WADC TR 53-119 18

do not, the initially assumed value of T was in error.After a few trials we should be able to obtain a veryclose value of equipment temperature Tq which sat.isfieaRquation (25). This graph is shown as-Figure 15 in theappendix of this report. Examples showing the use of thisgraph are also contained in the appendix.

After having determined the equipment temperatureT we know the value of the convective heat transfer, qcv.Since it is this heat transfer that is heating up the com-partment air, we can solve for the compartment air tempera-ture, T..

Compartment Air Temperature, Tc

The compartment air is heated by the convectiveheat from the equipment since radiation from the equipmentpasses through the air to the outer skin:

%v" hf A AT (22)

The heat transfer coefficient hf is determined by

Equation (19) where AT is equal to (Tq- T) and Tf , Tq4Tc

2

Equation (20) can be solved by graphical means. A graph isconstructed of qcV as a function of T and To. 'Since Tq andqcVare known, the point at which thede two values intersecton the graph is the value of Tc that satisfies Equation (7).Figure 16 and an illustrative example of its use are con-tained in the appendix.

Conclusions

The continuously increasing airplane performanceand the recent achievements in the design of miniaturizedelectronic equipment has created the broad problem of aero-dynamic heating uhich has come into focus comparativelyrecently. This inevitable merging of miniaturised designswith sonic region environments necessitates evaluation ofthe combined effects upon not only the aircraft structure

WADC T 53-319 ..

but also on the mechanical and electronic components.Becmase of the complexity of the modern aircraft which macontain many distinct systems, it becomes self evident thatthese systems must operate satisfactorily when exposed tothe ever increasing problems of aerodynamic heating and ofcooling at high altitudes.

In view of the above, an attempt has been madeto present a concise simplified graphical solution of theaerodynamic heating problem as it applies to the solutionof the equilibrium skin temperature, equipment temperatureand compartment air temperature. It is believed that themethods presented in this report will aid electronicdesigners and applications engineers in determining andevaluating electronic equipment for amy value of air tem-peratnre, altitude, and installation environment.

Aside from the internal heat dissipation, themost important factor in establishing component tempera-ture is frequently the temperature of the surroundingsurfaces such as the aircraft,structure. This one factalone allows a test set-up to be made where the walls ofthe test cell can be maintained at the equilibrium skintemperature as determined by the methods of this reportand conditions of altitude can also be simulated. Thepiece of equipment under question can then be insertedinto this simulated environmental aircraft compartment.and its operation and performance studied. From thesetests which- simulate actual compartment environments inhigh performance aircraft, specifications for equipmentto be installed in aircraft can be based on the conditionsto be expected and not on conditions which exist in rela-tively low performance aircraft of the past. This testset-up is more realistic and practical than any hypotheticalanalysis presented for determination of equipment temperature.

The example of equipment temperature has been res-tricted to a single, rather elementary unit in a relativelyuniform environment under ideal conditions, and unfortunatelymost practical problems encountered we not nearly thissimple. .The surface temperature of the equipment is dis-tinctly non-uniform, and it must be considered that thehottest point on the equipment is the one that determinesits useful life.

Aside from the thermal environment and its effecton electronic equipment, there are two main considerations

WADO TR 53-19 20

pertaining to the influence of elevated temperatures uponthe mechanicul performance of high speed aircraft and Eds-

jiles; that isn, the effects upon the structure (strength andrigidity),, and upon fuel and interior equipment. The struco-tural design problem involves the selection of materials ofsatisfactory elevated temperature strength and rigidity.A secondary and just as important, structural 4,esign problemis the deteruination of thermally induced str~ses. Similarlythe graphical. solution of the aerodynamic heating problem ofequlbrium skin temperatare as presented in this report will,,aid the aircraft and missile designer in evaluat~ing structures,,ordinance and mechanical equipment for any value of air temn-perature, altitude and installation -environmaent.

Am can be semen in the final ezuiples of a typi.calfUselag compartnent (Figure. 17 # 38 8, 19 )a at the highervelooitie ste difference between component,, compartment, sod

eqiirium skn temperatures in negligible, eacpt when2equipment heating per unit area is extremely large (qJA3.5000 BTU/hr ft2

Omerse3,, 'at the"sespeed& a great deal. of cooling iIfreqredto si~otieamn zi *e the equipamet temperature. It Isinteresting to set, that at, the lower altitudes,, again exceptuhom equipunt'hsa.Ung or cooling we of a very high magnitude,the valae of sqd.2faium skin temipeature Is equal to thevidiabski. owfe" t~era ,reAs altitudes Increase above40$000 feets, then i ea, deparbore trw the, adiabatic surfaseetemer~atume, Wth eqdpa heat being prodaoe4, asIn theexampe, shs=4 at lo: *As nei thIy e skin temerature isMbU Ow the mfte swf ase temperatwe, due to thisequipem" heatt. A te hsigh Nash ~mabe however, the skin- - _ -at Is loww than the adiabatic surface temperature,,

due to heat low fromi the skim by radation,.

2US e.mle ~iil sewn to Indieate the roge oftaqwerms to be minso~ustaed by aircraft and aircraftequipment fl,11ag IV to U10,000 feet at speeds fream N a 0 toN a 5,. Three sa'ves for skin and equipmet temperature for atntsal fuselage section we shown at ecah of tbu'ee speeds.A N a 5v thiýe .mtsl curve indlte temppaerae for littlebeat being pyeomdScd the 2ow taqpera@ecup Indicates theeffect of seeling (qA -- 500 DTIJr Aft)j and the higher,temerature. curve sblwsmpewatume to be attained withgiven myct of eqtdipmet heating, OA 500 'A~r ft).

An idea of the pyboblemas of kceeping aircraft skinscool. at the high Mach numbers is shown by a calculation of

WADC TR 53-119 21

cooling reqdtred for the surface of this typical compartmentto be maintained below 100DR under steady flight conditions.In this section at. M - 5, approx~imtely'90,000 BTU/hr of cool-ing aLre required per square foot of surface area. Whon a valueof this order is multiplied by the total. araritt surface areathe magrfftude of cooling is shown Wo be fantastically large.The most applicable method of maintaining internal equipemntbelow reasonable temperature linits at these speeds, even athigh altitudes, is to use a layer of good thermal insulation inconunction with an efficient cooling system. For example, atwo inch layer of insulation with a conductivity of .15 BTtJ/hrft 2 OF, would require that only 250 B1¶/br fft of cooling besupplied to maintain internal equipment at approximately 6100R(l-50F) at M-5, 60,000 ft, with the sample section investigated.Although this does not solve the problem of excessive skin tem-perature and the associ ated decrease in strength, equipment inthe aircraft c an be held at reasonable temperatures with thissystem.

Although it is possible to show an example of rangesto be expected of skin and equipment temperature, it is impos-sible at the present time to make recommendations regardingequipment temperature specifications. This is due to the widerange of temperatures to be encountered depending on speeds,part of aircraft, type, size and shape of components, andrelationship to other components. It can be stated, however,that equipment should operate down to temperatures of theatmosphere encountered in the altitude range of the aircraft.This is especially important, as can be seen in Figure 17with low speed ai rcraft where equipment temperatures are veryclose to free air temperatures,

With increase in aircraft velocities high tempera-ture difficulties become pronounced. Acdse of the methodspresented in this report will serve to offer a range of tem-peratures to be encountered by specd fie equipment systemsoperating in specific parts of specific aircraft, or of thecooling requirements to maintain temperature below some limitunder such conditions. In general, it is recommended that t.hesystem of using a test chamber of- -the same size and oonfigu-ration as the ai reraft compartment and with walls at temperao-tures determined in this report be used to nperimentallydetermir.e equipment temperatures and to evaluate high tmpera-ture I. fe of equipment. It is also recomumended that equipmentbe designed to operate at as high temperatures as possible in

sp-.pee aircraft in order to reduce the requirements for

WADC TR 53-1,15

cooling and the excessive weight ipposed by large capacitycooling systms.

A rough evaluation of accuracy to be obtaLned usingthe methods of this report ha been carried out. The widerange of tmperatures encountered prohibits statement of anexpeoted accuracy for the total mothod. However, mean accur-may of portions of the system can be estimated as foflows:

To - accurate to,,! 5%. This is based on variationof recovery factor experienced under actual conditions withthe average recovery factor of this report. Under most con-ditions the value of To wil1 be ,curate to within this value.

I~eTsTo cclurste to '~O.The accuracy of thisdifference is estimated from a kn*1edge of errors generallyassociated with a method of solution of the type presented.

ITs - TqI I1q - Tol - accurate to 120%. Hereaccuracy is esti;eUd from general accuraoy obtainable withsolutions of problem of natural convective heating.

Although the accuracy of the methods of solving for-teieratuwe differences does not appe good, a review of themapituds of thes differences oopared to the value ofseiiheo sufaoe temperature, To, show that errors intro-dnoed we of mafler mognitude thin those in T., mpd thus the5% scuraW in determination of To is the major factor in de-terLaIng accurmay of the ovearall mthod of solution.

VADC TR 53-119 23

BIBLIOGRAPHY

1. Huston, W. B. A 8tudx of Skin Temperatures of CoricalBodies in Supersonic Flight NACA TN 1724 Oct. 1.948

2. &-kert,E. and DrewitzO. The Heat, Transfer to a Pl~dPin Flow at High Speeds NACA TM 1045 1943

3. Squire,H.B. Heat Transfer Calculation for Aer:.-fcile

R & A 1986 Ncveber 1942

4. Frankl, F. Heat Transfer in the Turbulent BoundaryLayer of a Comoressible Gas at High Speeds NACA TM1032 1942

5. Tribus,M. and Boelter,L.MX. An Investigation of Air-craft Heaters Pt. II - Properties of Gases NACA AR

(WR - V - 9) October 1942..

6. Crocco, L. Transmission of Heat from a Plate to a FluidFlowing at a High Velocity N•A TM 690 February 1932

7. Crocco, L. Bounday Layer of Gases along a Flat PlateRend. Mat. Univ. Roma V Vol. 2 p 138 394.l

8. Hanztsche,V. and Wendt,H. The Ladnar Boundary Laer ofthe Flat with and without Heat Transfer Considering Com-pressibility Jdufoch 1942 der deutachen Luftfahrt-forschung Part I pp 4O-50

9. Kare,J. and Keenan,J. Report of Progress and Measure-

ments of Friction Coefficients, Recovery Factors, andHeat Traisfer Coefficients for Sups'sonic nlow of Airin a Pive Fluid Mechanics and Heat Transfer Inst.,

Berkeley, California June 1949

10. Dyste, N. L. and Seb"a, Re A, Cemting Surface Temper-atures at Hie Sp!2jv AF Technical Report 6177, AircraftLaboratory,, WADC, Wrght-Fattoreon Air Force Base, Ohio

11. Boelter, L.M.K. An Investigation of Aircraft HeatersXXX Nocturnal Irradiation aa a Function of Altitude andIts Use in Determination of Heat Requirements of AircraftNCA TM 1454 January 1949

WADC TR 53-329 24

12. Technical Memorandum Report CSE - 141 Proposed Stan-dard Cold an Hot Atmospheres for Arnatical DeuizhWADC, Wright Patterson Air Force Base, Ohio, June 20,1952

13. Taj1or,G.I. and Macoll-,J.W. Air Pressure on a Cone Movingat Rith Speeds Proc. Roy. Soo. 1933 Series A Vol. 139

14. Kopal, Z. Supersonic Flow of Air Around ConesTechnical Report 11 M.I.T. 1947

15. B0olter,L.M.K. JA Investization of Aircraft HeatersXVIVI - A Design Manual for Exhanst G0s and Air Heat3cchaers NACA Am 5Aw6 August 1945

16. Gauley, C. Theoretical Evaluation of the TarbulentFriction and Heat Trasfer on a Cone in Suersonic FlightGeneral Electric Company Rapt. R49AD524 November 1949

17. Mcodam, W.H. Heat Trmimdsion Second Edition, McGraw-Hill Book Co. New York 1912

18. King, W. The Basic Lws and Data of Heat TransmissionMechanical Engineering Vol. 54 1932

A. AAF Technical Report 5632 A IDmian Manual for Detenun-ing the Thermal Characteristics of Hiah Sxeed AircraftAircraft Laboratoryq WADC, Wright-Patterson Air ForceBase, Ohio September 19%7

WADc TR 53-119 25

Appeni

1. Example Comparing Te and TOO

An example comparing the values of heat transfercoefficient using T' and Te as the reference temperatures toevaluate the properties of air is as follows:

P-l10 lb/f 2 T Wo OR M m

From Figures I4 md 5:

To -221 OR T' 1730 OR

Reference Temperature Te = 2io OR TO - 1730 OR

Re/x (Fig. 11) 1.8 x 105 2.4 x 105

k (Fig. 3) .o83 .0o14

Pr'(Fig. 3) .64 6

(h) (Zulo ft Fig. 13)(turbulent) 14.o 14.0

(h) (x-1 ft Fig. 12)(laminar) 6.5 6.0

It can be seen from the above example that ourchoice of referene temperature T' as defined in this reportprodaces results in the determination of the heat transfercoefficient comparable to the results of some other investi-gators when uing the reference temperature T It inbelieved that use of T' is, however, more realistic and villoffer betterS~accuracy at the higher speeds.

2. Example of Variation of Recovery Factor

Based on the fidings of various investigators,the results of their experi-ments on flat plates end ogiveshave shoýv recovery factor to have values from .82 to .96.These values were obtained for conditions of subsonic andsupersonic flow both laminar and turbulent. Based on these

WADC TR 53-119 26

findings for flat plates, cones, and ogives, we have assumedfor purposes of the development, of the method presented herein,that the value of the recovery factor was equal to the averageof 0.87. Many values of recovery factors have appeared in theliterature and 0.87 was determined as an average from review-ing the results of the various investigators. Although it isknown that this assumption reduces the accuracy of the results,its effects are shown to be small.

"m 5 Po 100 l/ft To - 400o R

r .82 .87 .96 r .82 .87 .96Te 204~0 2140O 2320 T' 1L67'0 1728 1833

%a -4.5~8% - 1184%%Ah -3. d% - +551

Should further accuracy be required, a more exactvalue of recovery factor can be used in a second solution forTe and T I. The error will be reduced considerably for lowervalues of Mach number.

1. Examples of Methods Presented

a. The following example will show the use of all thefigures and charts in this report.

Data

(1) 40,000 feet Cold Atmosphere Daytime

(2) Mach Number 2

(3) Conical nose compartment,. thin wall, Ic - .091"

D - .6" S " 31"

WADO TR 53-1].9 :7

Surface Irea of oompartnt w .r -w x 8 x 31 -778 in 2

1.4) Material of compatment aluminum (248T)(5) Eletronic Wdupment

horizontal cylinder 3" diameter, 6" longsurface painted black, surface area w .392 ft

(6) Heat dissipated by electronic equipomnt-540 STU/hr w 100 BTU/hr ft2 of compwtment surface.

Phase I - Determination of Heat Transfer Parmeter-

Step 1 40.,000 feet Mach No. 2, Cold Atiosphere, daytimeStop2 FromFig. l&2 P0 -334 Ib/ft 2 To -375R.Step 3 From Figs. 7,8,9,10 30 Cone Shook wave attached

Mm1.75 u)~/t T - 20.0 ORStep 4 FromFig. 4 To 660 -R

Step5 FromFig. 5 T' -600 "R

Step 6 From Fig.U 62R/ , 0s~p6 n•.n Re/i- .'3.2 O1

Step ? For x - L - 31"- 2.58 ft Re -8.26 x O6

Since this value is greater than 5 x l0 turbu-lent conditions =dot.

Step 8 From Fig. 3 k w .016 BTU/hr ft (IF/ft)Pr - .695

Step 9 From Fig. 13 (h) 64! BTU/hr ft 2 .•for a cone in turbulet flow, multiply this valueby 1.15 or (h) - 73.6 OTJ/hr ft 2 V. In thisparticular caui, we will use the mean heat transfercoefficient (hi 3 which in 3.0 (h), or 1i x 73.681.8 BTI/hr ft, *- T 9

Step 10 From Table I O - .53 0 - .26

Step 11 From Table I 464 - .3Step 12 From Fig. 6 36 BTU/hr ft2

Gan 41l0 BTU/hrft

Step 13 Equipment heat dissipation 2 2

- . 1.00 B3-/hr ft

WADO TR 53-119 28

Phase II - Determination of Equillbrium Skin Temperature,.T

Stpi B~h 81.8Step 1 B .h£•8._83 - •o* °_

S(.26 x 36 x 1x .53 x 410) + 100 + 81.0 x 660

.3

C -180,730Step 3 Using Figure 14 and computed values of B and C

Step 4 On Scale B, mark off the computed value of B - 81.8(note scale factor on graph)

Stop 5 Draw a straight line fro~r:.the origin 0 - 0 to valueof B 0 81.8

Step 6 On scale ', mark off the computed value of C - 180,0(note scale factor on graph)

Step 7 Through this value of C - 180,730 draw a straightline parallel to the line dran in Step 5

Step 8 Where the straight line from Step 7 intersects theproper curve (curve 3, note scale factor on graph)drop a line perpendicular to the temperature msand where this perpendicular intersects the tempera-ture esai is the value of T , the equflibrium skintemperature - 660 -R

Phase III - Inside Skin Temperature

Since the wall. of the compnarwent is very thin, theinside skin temperature Tsi is the same as the outside equilib-rium skin temperature Ta Tsi To 660 -R

St#p 1 q kW0 - Ts 51 im 2)Ac '

wADc TR 53-119 22

lk 14 BTU/hr ft2 (O*Wft) (alumdlnwn)

- .091". - 0075 ft

Stop 2 100 660).0075 "Di

".71. ( -660)

Step 3 To, 660R

Phase IV - Eqpipment Tenmerature

Step 1 q% - 40 BTU/hr

Stop 2 As - . .732fb 2

AC +Aq 5.9

effective area A. - .732 ft 2

Step 3 Using Figure 15 and knowingqe " q 0v +

As Ae Ae

• q 1,• ..732 An A.,

1738 + _ *_As Ae

Step 4 P - .1559 a1upher,.

D - 3" - ,/4 ft

"T2 4JE57 -5.5.8

WADC TR 53-rL9 30

\,

step 6 - .5

.81 .8184+4f%-d6103 1.8 - .81

Step 6 Assume value of Tq aid compute

q~ q_

Ae Ile

T -1000 OR

Step 7 L 1 20

A6

Step 8 --

Ae

S t e p 9 -- - 3 .1 7 0 w h i c h i g r e a t e r t h a __

A*lA A8

therefore, assumed value of Tq is too large

Step 1O Assume T. f 940 OR

Step 11 %C, 83

Ae

stepl12 qr- -. 655Ae

Step 13 q- -v 83 + 655 738

Ae Ae

which is equal to q 2 738A

Tq - 94o OR

WADC TR 53-119 31

Phase V - Compartment *Ar Temperature

stop T - 914 .*R ad---v - 83q As

Step 2 As =2 Ab Aq m..732ft

Step 3 q6 = 83 x .732 a 60.7 BTU/hr

step 4 %ov 60.7 . 55 BI¶J/hr ftA .392q

Step 5 Using Figure 16

Ta,,. 195Aq

where Tq - 9 4O 9R 41

at ,_.5.--- 387A

intersect is the value of Ta

Stop 6 -Tc -680 -R

Another example for a wing section is as follow.

Data(1) 4O,000 feet, Cold Atmosphere, Dsrtime

WADC TR 53-119 32

(2) Mach Number 0.8

(3) Wing compwrtaent, skin-alumln= (2•IST), .091" thick-1/2" insulation ihose thermal conductivity in.025 BTU/hx' ft2 (.7/f 0

Dimensions of Compartmentz Length - 18"Width - 12"Depth -7.50

Surface Area of Compartment - 2 x (18" x 12-) 3 ft2

(4) Electronic Equipment - horizontal cylinder3" diameter, 6" long,, surface painted blackSurface area - .392 ft 2

(5) Heat dissipated by electronic equipment- 20 BTU/hr - 6.7 BTU/hr ft 2 of copawt-ment surface

Phase I - Determination of Heat Transfer Parmeters

Step 1 40,,000 feet Mach No. w 0.8 Cold Atmosphere

Daytime

Stop 2 From Fig. 1 & 2 Po - 334 lb/ft2 To I 375 OR

Step 3 M - 0.8 P - 334 lb/ft2 T - 375 "R

Step 1 From Fig. 4 To w 42o -R

WADC TR 53-119 33

Step 5 FromFig. 5 T' -415 °R

stp6 From ig. l Re/x -1.2x10

Step 7 Take x as the id point of the compartmentas measured fom the leadingix - 3.25 ftRe a 3.9 x9 Since this value is greaterthan 5 x 17 turbulent conditions exist.

Step 8 From Fig. 3 k - .012 BTU/hr ft,2 (OF/ft)Pr - .735

Step 9 From Fig. 13 h. - 19 BTU/hr ft 2 OF

Step 10 From Table I As a .53 C .26

Stp 11 From Table I Cs = .3Step

Stp 12 From Fig. 6 OSP A36 BTU/hr ft2Go w IlO BTU/hr ft 2

Step 13 Heat dissipated by equipment - 6.7 BTU/hr ft 2

of compartment surface.

Phase II - Determination of Equilibrium Skin Temperature, T

Step 1 B- -- 63.3

d G, • •~ ) + %+ heStop 2 C

(.26X 36 Tx: .53 z,4lO) ÷6.7 ÷ 19 x )20

.3

0 - 30,797

Step 3 Using Fig. 14 and computed values of B and C

WADC TR 53-119 3A

Step 4 On scale B, mark off the computed value of B 63*3(note scale factor on graph)

Step 5 Draw a straight line from the origin 0 - 0 to valueof B = 63.3

step 6 On scale C, mark off the computed value ofC - 30,797 (note scale factor on graph)

Step 7 Through this value of C = 30,797 draw a straightline parallel to the line drawn in Step 5

Step 8 Where the straight line from Step1 ? intersectsthe proper curve (curve 3, note sale factor on,graph) drop a line perpendicular to the tempera-ture aas and where this perpendicular intersectsthe temperature axis is the value of Tg, theequilibrium skin temperature T. a 49o eR

Phase III - Inside Skin Temperature

Step I % k

ks - 114 BTU/hr ft' (.F/ft) aluminum

-. .0911 = .0075 ft

ks = .025 BTU/br ft 2 ('F/ft) insulation

'C-.5*0 .0425 ft

Step 2 6.7 - (Te 6 "49o)

245 .0o42

Tai - 01 OR

Phase IV - Equipment Temperature

Step i Re " 20 BTU/hr

WADC TR 53-119 35

Ste 2AO.A 3.392

Effective area A. - .7 94 ft 2

Step 3 Using Fig. 15 and knowing

20 _ clV +

.794~ A, Ab

- a 28.8Ae A5

Step 4 P - *159 atmospheres

D w 30 = 1A ft

stop • .. 9 .9

L- .81 a.818

+ 4 - ,el, '-.8 - .81Step 6 Assume value of Tq and compute

AS Ae

Tq - 530 -R

WADC TR 53-119 36

Step 7 = -13

A6

stop 8 qr- 1 5.Ao

step 9 %gv -%+ . 1,3 + 15.8 -28.8

A*A

ihich is equal to % 28.8A 2

therefore, assumed value of Tq 5 30 OR is correct.

Phase V - Compartment Air Temewature

Step 1 know Tq m 530 R and q _. . 3qoAs

Stop 2 A - 2 POA -79 f

Step 3 qo- 13 x .794 -1o.3 MU/hr

Step 4 -%v w 10.3 = 26.3 BTV/hr fx 2

Aq .392

Step 5 Using Fig. 16

eTD = .558

Tq m 530 -R

c__v. -26.3Aq

WADC TR 53-119 37

where Tq ,30 OR and 2V - 26.3 intersect at

P .558 is the value of To

Step 6 To 505oR

WADc TR 53-119 38

1.

TABLE I

Total Normal Mean Emissivity and Absorbtivity

Description Mean Effective • and 0(

Metals 1000F 000F Solar

AluminumPolished .04 .08 .10Oxidiz ed . ii .18

Chromium .08 .26 .49

CopperPolished .04 .18 .26Oxidized .18 .18Oxidized & Corroded .38

IronPolished .06 .13 .45Oxidized .74 .78

NickelPolished .04 .10 .40Oxidized .39 .67

ZincPolished .02 .04 .4Oxidized .11

Alloys

Aluminum3 SO .24 .2453 SO, Weathered .73 .5524 ST .052 .5324 ST, Weathered .26 .3075 ST, Polished .07 .1575 ST, Anodized .56 .3275 ST, Unpolished .04 .08

InconelCloan and smooth .14Dull .21

WADC TR 53-119 39

TABLE I

Total Normal Mean Emissivity and Alsorbtivity

Description Mean Effective E and

048 64 0<3Alloy (Contd) 1006F 1000OF Solar

MagnesiumJ.H.Magnesium alloy

(Weathered) .58 .55M.H. 42 Magnesium alloy .70 .40F.S.A. Dowmetal .38 .38

NickelMonel, Clean .12 .10 .43Monel, Oxidized .46Chromenike el.64

Steel18-8 Stainless, Polished .12 .2718-8 Stainless,Unpolished .14 .3218-8 Stainless,Weathered .62 .6218-8 Stainless, Sand

Blasted .84 .8418-8 Stainless, Oxidized .85 .85Rolled Sheet .66Rough Sheet .94 .97

TinSpeculum Metal .08 .13 .39

Miscellaneous Surfaces

Shiny Bakelite, Clean .89Plexiglass .89Glas .85

Painted Surfaces

Aluminum painted withBlack Decoret .89

Bakelite painted withBlack Decoret .94

WADC TR 53-119 40

TABLE I

Total Normal Mean Emissivity and Absorbtivity

Description Mean Effective O and

43Painted Surfaces (Conttd) 100_ F 10007 Solar

External air drying enamelW.P.Fuller, D-70-6342 .85 .84

Aluminized Lacquer1234 over 75 ST Alclad .65

Clear Lacquer 1234 over75 ST Alclad .53

Pigments 125_ 750*F Solar

Lampblack paint .96 .97 .97Camphor Soot .98 .99 .99Acetylene Soot .99 .99 .99Platinum black .91 .95 .98

Lampblack .94 .94Flat Black Lacquer .96 .98Black Lacquer .80 .95Blue (G0203) .87 .86 .97Black (CuO) .85Red (Fe 2 03 ) .96 .70 .74

Green (Cu203 ) .95 .67 .73

Yellow (PbO) .74 .49 .48Yellow (bCrO4) .95 .59 .30

White (Al203 ) .98 .79 .16" (Y203 ) .89 .66 .26

" (ZnO) .97 .91 .18. (CnO) .96 .78 .15

" (MYgO3 ) .96 .89 .15" (ZrO2 ) .95 .77 .14" (ThO2 ) .93 .53 .14

" (MgO) .97 .8A .14" (PbCO3) .89 .71 .12

White Enamel .92Dark Glossy Varnish .89Spirit Varnish .83

WADC TR 53-n-9 4i

oeratlegof understues attained .. typicajl aircraft sections

operating under steady condl

8ons at a fixed a1titde.~C~tlp~eTABLE

II:XaMP~e Tem/persture GIculro r TABLE A

Flight Condition .. 010a , A jrcr q!t SectionsAlt. 40, ooo feet )o - 3 Po - 449 lb/ft 2 2o - gUSAI Hot Atmosphere, Dartim,-.26 ytm To 415

-36B Br/hr ft2

Pa- .023 /BT 2 *"?/rt) Pr . 67

Patrejr,.Station A B 1)

1Ar .a Atft 2 60 18o 2 20 2Co 10o 21ox or L ft L,5 x=17.5 x-32.20 2450 zo-STU/b , 200 o 3000 200, 0-f2 10 000 , 000 -3

A3 _, f ,2 6 o2 0 0 1 O0 1 2 0D,ft 2 10 220 240 8K 2 44T

2.70 2.70 2.70 2.70 3

P, -'Rft 469 L69 469 2.70 3 3P, lb/ft 2 697 697 697 697 4159 1T, P 10% 06 1065 1065

1067 697 44T R925 925 925 165 9106 3D65or Re 2T " .5 x i o 6 h . 5 x l O 6 4 g 6 4, 5 x iO6 3 r 1 0 6 3 9 1 0 O

c r 3-195'6,D6

42,

station A B c D N

(h) or (h), (328), (92)X (S1) (72)x (88) " 0),.re,~~ .p.x•l~ xo~ moo

To R1050 1060 1060 1080 1060 1055

Tq, G5 105% 3065 3265 2 - "

To, -R 1052 1062 2060 1120 1060 1055

WM I- 53-U9

10 ---0

95 USAF PROPOSED COLD AND HOT

ATMOSPHERES. TEMPERATURE90 VS. ACTUAL ALTITUDE.

85 BASED ON REFERENCE 12so

75 -COLD

70

HOTIi. 6 5

-55",, " -O_"

050

j FIG. I<40

440 __ -- _ -

35-

I020

\ Is_-

10 -

0 de5 A 1 h 5TEMPERATURE '

~ 1414

10 . . . . . . ... . ... . ..... ..... .....- - - - - - - - - - - - - - - - - . ...... ...... ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...- - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - . . . . . . . . . .. . . . . . . . . . . . . -- - - - - - - - - - - - - - . . I . - . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . .

. . .. . . .. . ... . .. . . .. . ..

=t7-

2 if I- I

LL

CD- - - .. . ....

cc

-----------------............... . .. . . . ....

t7

7 77- 7777ý 1-zooz

M-l-- - - - - - - - - -

7i-

20 40 60 3 80 100ALTITUDE IN 10 FT.

Jd UI39ImfN 1±OGNV~d

_ 0I0

z - 0

)LL- 0

CA 0

w~ Wm - -- -

0 W-am z w

a W 0 - _

0

0I

-I0

0

-- 0

0

0_ _ _ _ _ _ _ _ _ _ _

0 1 L.AA )f-4 H/n e IAlllloawo lV~J30

lit0

I 0000 1 T I J I9

ADIABATIC SURFACE TEMPERATURE AS A

FUNCTION OF TEMPERATURE AND

6 MACH NUMBER

5 Tess T(I+.174M 2) M

Mz4

2 "04 .

SM : 21.5

1000 ,_.0M_ 0.8

9 _0_

4 z A

.o~oFIG. 4

1.5

I I tI 1.5 2 2.5 3 4 5 6 7 8 9 10

T 0 R 1602

.u, ,: . i' I1

1 0009

REFERENCE TEMPERATURE AS A FUNCTIONOF TEMPERATURE AND MACH NUMB3ER

5 - T TCI#.133M 2

M:5

4 - ' 0 0 _ _ _ - -

2.5

~ I0000

Ma7aa

7 z7 RI zIALI ori 55-1

I - . _

zza0FP

0 CC6

00

0 -'0 h

0 A2

4 -

4 0 eF

04

F~ a0 w

0M

4~000

~~FadAG T u -j 4

0 Id0

Oj W .

81 z

Fww

all2 31'NV 3183

50aaADC T 53-11

00

A- AZ-

0 49

U. 0

_ 0 00 - - hi

0 ILz z -U ILIz z a - - II

0 _0

~~ z

I FI - -

42lei

-' V3 -M - B

-AD 0R53195

0so CJ

cm.

4.

CA

ca

IIa

16

Ud w

3002.m Rvs4WI god

4AD TR 5311 5

_________ ____ 0

0 00

10

cr

0

11 0woUUdq w

wz z

w L

0

w cm

4m 3. w8L 3. 03uiOUU3oin

WD wH5-195

10

Si.o .(I)

• ~(2)

9a

8 ~101-6T

TI

400

450

500

550

600

650

700

7506- 00

6 - 50

900950

1000

1100 731200-

1300

1400

1500

1 6

3

1 42

210 10

9 9

a

7 7

6

5 T 5

- 4 34

3 3

'.5

I0MODIFIED REYNQL.D1

T 5J-119

4 4

'" I062

64 - 2

2

4 010

S2 8

5

4

54

2

- I 0 -I,.

REYNOLDS MODULUS F OR AIR|I

* v*

17?00

18001900200021002200230024002500

TA

L, SL OTE

-PROCEDUREa FOrR A GIVEN P AND T FIND INTERSECTION ON (I)

b ALIGN INTERSECTION ON (I) WITH GIVEN M AND

FIND INTERSECTION ON (2)

C ALIGN INTERSECTION ON (2) WITH T' TO DETERMINE Re

x

FIG. II

/

Re

aX"

1 0

•8

"6

77

4

(I) -3

S 2

S1.5

a

_ I0

4

S• 2

•' k 1.5

a -•8

6

Re .

8 -86

4 - 1

33

22

1.55

60512100

8a

46~ (2)h41m:5

S" - 4

3

6 2

2.5 1.5

fPi 5 4

-8

6

, - 3.5

3-. 3

2.5 1.5

3I0

2=

- 1.5

--2- I0

HEAT TRANSFE"

,,u 'r~t 53-219 ,

4 2 10

15 1.53 _00 2

8 2.56 3

4 4

15 34 • 2 6

S1.5 8

1 - -30Z=6

S433

22L• 1"52

'.5

I0

EAT TRANSFER IN LAMINAR FLOW

cv

.1 j-J

Pr.8

6

(2)h

Pr

L .SLOTE

PROCEDUREa FOR A GIVEN k AND Re FIND INTERSECTION ON (1)

x

b ALIGN INTERSECTION ONI(I) WITH GIVEN Pr

AND FIND INTERSECTION ON (2)

c ALIGN INTERSECTION ON (2) WITH x TO

DETERMINE h

FIG. 12

,i4

ii

I!

/' ~(I)

io-I I

1 .5

I. 4I.

~1 10,

3.5

2ý5 1.5

10

15

2.5 1.5

2EA -T A SF R I

ii-li; Ti 53-19 5

3 -- 4 ;..4

, 8 1.510 6

2a 4 2.5

33

6 4

5 ~0 610 a

1.5 2

S 103 6

S6 1 .54

0 3

NISFER IN TU.RBULENT FLOW

2o

I 0:•

PrS.

1.5

3

4

a Av""6

102

(It

PROCQEDURE,*FOR A $IV EN It AND No- FIND INTERSECTION ON (1)

x

'b ALIGN INTERSECTION ON (1) WITH GIVEN Pr

AN4D FIND INTERSECTION ON (2)

o ALIGN INTERSECTION ON (2) WIT.H X TO

DETERMINE h

Fa 1

4-4 11 It, 1147' , Ai"iif E m If F: 4 4-,

3-i Hj i 11 'TTiW :1, 1 -1 1IT

411

1! IN i-TLFi4 i 1 1 1:1m I i

.41

If I WIN jpý7 '77

7 q,; it I i i I " +: ji i ,

i al I

141 H" ýil t f

1V

4

Ei LT7 71-! !1z I'!4

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:117

aijý

If it

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44; 1 41-

-7 T7ji:

117

'00

If

FI k1111 111

I lii~~4i I Li~~-t*t~

T Ii .i .' .F .i ~

.'' ... F..... ..

14I

1f F, ii'iI 1 fit.

iii H 2 ii *

-. 1' 4WIL'4*,14 1 "1

*------.---~--I MlI

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TTiii~ I , I 17

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WAI IT 11 4LI

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711

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T'.' 4 I, T i.

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MR, ý-1- ýfl - --- -m---] tt

90 L L-1+

t I I t ++ + I I

I L-1 I -:HLE4:FR

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70--

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60-- I I N i l I I I

4-ý

----- ------

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------- ----4C.-

k.- ýiH II I -TA

30

20

0 6004oo 500 TZW. oR

fW)" Til "JI-1 1-9 60

100 rl.... ...... ....

-- ----------- H

thi

ttt-90

I A I I I I I IA+

------- - - - - - - -

80

4# - --H+ -

41

70- I t I --I.-I1+ -#44i 4+14++

60 E E

11 T

-4 44

5004

IT-740

+

30-.-

20 --------- a

11111 it

io:, -

-- --------

0120D 1300 1400 1500

TEMP. -R

dAY, 'fit (A

900

80 ~ 11

40 41 'j

I I j si

. 1 ! ; 1 1

34 R - I L

16 18 20 22 274 26 28 30 32 34~