Alger has touched upon a problem ofmajor importance. With the growing em-phasis in college curriculums on electroniccircuits, field theory, information theory,and many other recent developments, thetime available for study of machinery is be-ing severely limited, and in some collegesthere is even thought of eliminating thesystematic study of machinery altogether.With the important part that machinesplay in the applications of electrical engi-neering today, this would appear to be a

grievous mistake. However, it is evidentthat the methods of presenting machinery,basically unchanged in most curriculumsfor decades, must be radically overhauled.In such an overhaul it seems highly desir-able to make better use of equivalent cir-cuits as a unifying concept, to show thebasic similarities of various types of ma-chines. Field theory may be called uponto establish the validity of the circuit con-cepts, but there is strong evidence thatcircuit methods are simpler and easier to

apply than field methods in obtainingnumerical results, and therefore should befully utilized.The author would again like to thank

Alger for his encouragement which has beetione of the important motivations in thepreparation of the present paper.

REFERENCE

1. DEFINITIONS OF ELECTRICAL TBRMS: ROTAT-ING MACHINERY. ASA C42.10-1957, AmericanStandards Association, New York, N. Y., 1957.

THE CALCULATION of the tempera-ture rise of dry-type transformers

differs from that of liquid-filled trans-formers because radiation from the coreand coil plays a considerable part in theheat transmission and because the tem-perature of the cooling air is not as uni-form as that of liquids. Very little, ifanything has been published about cal-culation of temperature rise of dry-typetransformers for design purposes. Thispaper presents a method for such acalculation.

Limitations

This paper deals only with the tempera-ture rise of the coils of dry-type trans-formers.Only the steady state of the coils is

considered. This is the temperature atwhich they stay at unchanged load, volt-age, and ambient temperature. Tran-sient phenomena, like temperature risedue to short circuits, are not discussed;neither is forced air cooling. Air is men-tioned as coolant throughout the text.The results are applicable to other gasesby changing the constants accordingly.

High- and low-voltage (and tertiary,if any) parts of a coil are considered asseparate units, because different amountsof heat are generated in those parts per-

Paper 58-155, recommended by the AIEE'Trans-formers Committee and approved by the AIEETechnical Operations Department for presentationat the AIEE Winter General Meeting, New York,N. Y., February 2-7, 1958. Manuscript submittedOctober 11, 1957; made available for printingNovember 26, 1957.

A. A. HALACSY is with the H. K. Porter Company,Philadelphia, Pa.

unit volume of copper and per-unit heat-transfer area. Experience has shown thatthe high- and low-voltage parts of a coilfrequently have quite different tempera-tures.

Proposed Procedure

In sumnmary, this paper proposes cal-culating the temperature rise by the fol-lowing method:

1. Calculating the total watts WI whichcan be dissipated at a series of coil tem-peratures T, where T= Tamb+ Trie, anddrawing a curve

WI=f(T) (1)

in Cartesian co-ordinates.2. Calculating the total watts W2 generatedin the coil at the same series of temperaturesT, and drawing another curve

(2)in the same Cartesian co-ordinates.

3. Reading the coil temperature rise Tcoil,where Tc0 = (T- Tamb), at the intersectionof the two curves, WI and W2.

Heat Dissipation

Heat is transferred by radiation, con-vection, and conduction. Radiation fol-lows the Stefan-Boltzmann law in a some-what modified form

Wr-S.4 F e(T4 -TB4) (3)

Convection follows Newton's law

wc=hA (T-TA) (4)

Conduction follows Fourier's law

Aw5= k -(T-TB)

x(5)

These mathematical expressions are forthe steady state, where w is the heatenergy leaving the area A of the surfaceper-unit time; T is the temperature ofthe surface; TA is the bulk temperature ofthe surrounding fluid; TB is the tem-perature of an opposite surface; F is theview factor, a function of the geometryof the two opposite surfaces; e is theemissivity; x is the length of the pathwith the cross section A through whichthe heat streams; and S, h, and k areconstants.

All the heat from the surface of a solidis transferred to a fluid by radiation andconvection. In the case of a dry-typetransformer, the fluid is air. Conductionis mentioned only because an additionaltemperature drop across a solid insulatinglayer covering the copper is caused byconvection.

Radiation

Only a negligible error is introduced ifthe temperature of the enclosure is con-sidered to be equal to that of the coolantin equation 1, in cases where the enclosureforms the opposite surface to radiation ina conventional dry transformer.

TB = TA (6)

Calculation is simplified if equation 3is made similar to equation 4. Such aform is quite arbitrarily written in thecenter of equation 7

w,=qAF=SAFe(T4 -TA4) (7)

This equation, being arbitrary, holdsonly if qr is defined as follows

qr = Se(T4-TAI) (8)

The numerical value of the Stefan-Boltzmann constant is properly convertedto watts,/sq in (square inch) X (degreesKelvin)4

S=36.8X10-12 (9)

The relative emissivity of the surfaceis

e =0.9 (10)

Ilal,acsy-Temperature Rise of Dry-Type Transformers

Temperature Rise of Dry-TypeTransformersA. A. HALACSY

MEMBER AIEE

W2 =f2( T)

456) AUGUST 1 958

Table 1. Constants for Temperature Calculations

qc, Watts/Sq In q=qr +qo, Watts/Sq Inq, Watts/ - (234. S+T)

T* TA* T-TA* SqIn Lt=0.5 L=1 L=1.5 L=2 L=2.5 L=3 L=0.5 L=1 L1.S L=2 L=2.5 L=3 254.5

75....30.... 45...0.203... .0.170....0.143....0.130....0. 121 ... .0.114 ....0.109....0.373....0.346....0.333....0.324....0.317.. .0.312.... 1.2185....30.... 55...0.264....0.219.... 0.184.... 0.166 ....0.154.... 0 146 ....0.140.... 0.481.... 0.448.... 0.431.... 0.419.... 0.411.... 0.404....1.25

110.... 30.... 80...0.433.... 0.351... .0.295....0.267.... 0.248.... 0.235 .... 0.224.... 0.781.... 0.729.... 0.701.... 0.679....0.666.... 0.657.... 1.35140 .... 30 .... 110 ... 0.690.... 0. 523....0.439....0.396 ... 0. 369 ... 0. 349 .... 0.333 ... 1. 209 .... 1.125 .... 1.085....1.057 .... 1.040....1.020 .... 1.47180.... 30.... 150... 1.14 .... 0.776 ... 0. 652 .... 0.590 .... 0.548....0.518 .... 0.495 .... 1.906 .... 1.782 .... 1.722 .... 1.680.... 1. 653....1.630....1.63210 .... 30.... 180...1.525 .... 0.962 .... 0.810 .... 0.731 .... 0.678 .... 0.6458....0.616 .... 2.487....2.335 .....2.259 .....2.203 .... 2.171 .... 2.141 ... 1.75

* All temperatures measured in C. t All L measured in feet.

for materials used on the surface ofdry transformer coils. Pooling all thisinformation results in",2

q,=33.2 X 10-1( T4T-TA4) watts/sq in (11)

if T's are in degrees Kelvin; and thus theheat in watts wr, transferred by radiationthrough an A-sq-in surface at (T- TA)degrees centigrade (C) temperature differ-ence between surface and ambient, maycomputed by equation 7.

wr=qrAF (12)

Typical values of qr are listed in TableI.

Convection

While the Stefan-Boltzmann constantS is a purely dimensional constant, theheat-convection coefficient h in equation4 is a function of the geometry of the par-ticular device and of the properties andcondition of the cooling air. A film ofair is heated by conduction from the ver-tical surface of the dry transformer coiland begins to rise as it becomes lighterthan its surroundings. Thus a flow ofthe air is started.

Indeed the best correlation3 of test

SO.N57=4_+__4 __HI,_5 ,. r

4 z _ li r -1~3 _ 06 l_T tX

2>l_T-

20 5>> ls7+ T

FT.

0.3

02

0.1ILT;w3C

T: a

*.C

NI I--;

I!51 It I0*

7585 110 140 180210 M

Fig. 1. Heat transfer constants; q = convec-tion and radiation, qc = convection only

results regarding convection from avertical surface to air was presented interms of moduli used in aerodynamics asthe Grashof number NG, the Nusseltnumber NN, and the Prandtl numberNP.NN=f(NGXNP) (13)

The value of the (NGXNP) productdetermines the nature of the air flow,turbulent or laminar. In the usual tem-perature range and at atmospheric pres-sure the air flow is laminar, along natu-rally cooled dry transformer coils. Asimplified equation is derived from equa-tion 11 and given for h in this range intextbooks,3 which may be written4 with adimension, watts/sq in, as follows

h=1.23X10-3(T-TA)O.26 (14)

Multiplying by (T- TA) gives, in watts/sq in,

1.23X10-3(T-TA)2 (15)

Typical values of q, are listed in Table Ifor L= 0.5- to 3-foot-high coils.A combination of equations 4, 14, and

15 gives, in watts, the heat wc trans-ferred by convection through A-sq-insurface at (T- TA) C temperature differ-ence.

wc-=qA (16)

Total Heat Transferred

The sum of equations 12 and 16 givesthe total watts W, dissipated from the coil,at a (T- TA) C temperature difference:

W1 =wr+w =(qrF+qc)A (17)

This is rewritten for the purpose of asimplified calculation as

W1=(qr+qc)FA +q(1-F)A (18)

q =qr+qc (19)

Within the usual limits of tempera-tures, T, to T2, which prevail in practicaldry-type transformers, both q's are wellapproximated by exponential functions,

one function for each L height of thecoil.

q(T,-TA\"q2 \T-TAI/ (20)

The logarithm of this function is ob-viously a linear function

log,o q,- logio q2=n[log,s (TL-T'A)-log,o(T2-TA)J (21)

where

n = 1.25 for q,n= 1.28 to 1.77 for qrn= 1.36 approximately for q

and the temperatures are measured in C;see Appendix I.

Straight lines represent such functionson a double-log-scaled graph paper, Fig.1, for L=0.5- to 3-foot-high coils.

Grouping of Surface Sections

It is more practical to split the totalsurface A into n sections, A,,, and to grouptogether the sections with similar heat-transfer characteristics than to consideran over-all view factor for the whole sur-face area. Equation 18 is rewritten ac-cordingly

n n

WI =q FnAIn+qGE(1-Fn)A nI I

(22)

The most practical grouping is into in-ternal and external surfaces.

Internal Surfaces

Internal surfaces are those on whichF,=O, because radiation is cancelled byan opposing surface. Such are the insidesurface of a coil facing the core, and sur-faces of cooling ducts. For these

nWI=qCEA int

Of course, the statement Fn =0 isstrictly true for these surfaces only if theopposite surface intercepting the radiationis at the same temperature and has thesame emissivity. The differences ob-

(23)

Halacsy-Temperature Rise of Dry-Type Transformers

i i- ;_ t i I I .t -tt

VILXJ

wqr.--

W =I IIII I:_T i III I I

AUGUST 1 958 457

Kw

0.5

_i - I E

8 4 8 2 8 4 8WIuM OF COOUNG DUCT. INCHES

Fig. 2. The corretion factor Kw versusradial width of a cooling duct

Fig. 3. Graphic detemination of the viewangle B between coils

Fig. 4. Graphic determination of the viewangle p between disks

served in the discussed group of trans-formers usually can be neglected, but canbe taken into account by further sub-grouping, adding correction factors toequation 22, in cases where these differ-ences warrant it.

Proper judgment has to be used to de-termine how many square inches of eacharea are heat-transfer units. For ex-ample, the part of a surface covered byspacer sticks in a cooling duct is not one.The surface of those ducts which areblocked by some obstacle at their entranceor exit and have no air circulation are notones. Such obstacles can be heavy leads,most likely in a low-voltage coil of greatkva capacity, protruding insulation oftaps, bracings or clampings of the coil,protruding core clamps, etc. The blockedducts can be considered by a factor

(number of ducts) -TIP _ (number of blocked ducts)

b= (number of ducts)(24)

An = LKb [2DnAV, duetX w-2(number of spacers) (width of one spacer)]

(25)

The length L is of course always thecooling length, which does not includethe end fillers or spacers made of insula-ting material, but only the length from thebottom to the top face of the copper,minus the axial width of any gap in thesurface; e.g., the cooling length of apancake coil is L= (number of pancakes)X (axial width of one copper pancake).The cooling length of an uninterruptedbarrel coil is L= (length of copper coil) -(end pitch).The narrower the cooling duct, the more

it chokes the airstream and reduces cool-ing. Published test results proved thatair masses farther than 3/8 to 1/2 inchfrom the vertical surface do not partici-pate appreciably in the cooling, so thatthe influence of the width of the coolingduct levels off around 1-inch width. Fig.2 shows the values of a correction factorK. for the width of the duct. Com-bining equations 23 and 25, and K,, gives

n

Wi= qcl {IL[2DnAv,duotX T-2(number of spacer, n) (width of

spacer, n]Kb,, Kj,,,} (26)

External Surfaces, View Factor

External surfaces are the ones fromwhich radiation is not fully cancelled.The view factor for a point P of such asurface is, by definition,

Fp= 1--2)(27)

The view angle a is the solid anglewithin which the point views an obstruc-tion to radiation, and 2,r solid angle is thesurface area of a half-sphere of unit radiusseen unobstructed. Parts of the same orof anotlher coil and phase barriers betweencoils obstruct radiation. Averaging for acertain area A. gives the view factor ofthat area

p

ZfapFn=l-- I

2rP

can be averaged from few values. Thecalculation is carried out for the centerphase, the hottest in a 3-phase trans-former, where, by reasons of symmetry,it is enough to consider only one quarterof the circumferential circle. The shadedview angles 3,B see obstruction as shown inFig. 3, at points p= 2 and p= 6.The same treatment can be applied to

surfaces between disks, where the sur-faces are rings and have a circular sym-metrv. Thus, the view factor can be cal-culated for their axial section, see Fig. 4.

Solid Insulation Layers

Any solid insulation 1/32 inch or morethick over the copper must be taken intoaccount because a temperature dropoccurs across solid insulations accordingto equation 5. This drop is negligible forless than 1/32 inch of insulation, andapproximated well enough by reducing theq's for 20 C by 0.01 watt/sq in for each1/32-inch thickness.

Summation of the Heat Transferred

The watts transferred through eachpart of the coil surface are totaled accord-ing to equation 22, and this calculation iscarried through for a series of tempera-

Soc -I

roo ___ I_PWTOC I ---.-

600 - I

500 -_- 1_-_- -

I- I _I0 I/ _ _400

I CAM ENT I--- -

TO(28) 40

The outer surface of a coil has cylin-drical symmetry. Fringe effects canbe neglected, therefore the surface can bereduced to a circular circumference of asection across the axis, and the solidangles to plane angles 0,,; see Fig. 3.Equation 28 reduces to equation 29

p

I F=l- (29)7rp

The view angle ,B changes continuouslyaround the circumference; therefore it

s0

50

110- C TOTAL

CO* C RISE

Fig. 5. Graphic determination of tempera-ture of coil shown rn Fig. 6

0

Fig.6.High-voltage pr of2 NQ3

14 STICKS 5 75

Fig. 6. Hi'Sh-voltage part of coil

Halacsy-Temperature Rise of Dry-Type Transformers A.UGUST 1.958458

tures in the range where the final tem-perature is expected. It is sufficient toselect certain significant temperatures,such as 55, 80, 110, 150, and 180 C riseabove 30 C ambient and suppose a linearcontinuity of W1 between them.

Of course, such a calculation is doneeasily in a preprinted tabular form and bya single setting of the slide rule, as the onlyterms changing with the temperature areq and q, in equation 22. The resultingtabulated function represents equation 1.

Heat Generation

Equation 2 shows the total watts gen-erated versus temperature. D-c lossesaccount for the largest portion of the totalwatts generated. These d-c losses are,at T C,

VT"P01 (234.5+T) (30)VrI'P25 A 254.5

I is the rms value of the coil current inamperes; pw=0.67X1104 ohm/in/sq infor copper, and a corresponding value forother conductor materials. Values ofthe factor (234.5+T)/254.5 are given inTable I.The stray losses'-" are Y % of the d-c

losses and can be accounted for by aniultiplise

yfy=l+- ~~~~~~~(31)100

Since fy, is small in practical dry trans-formers, it is permissible to write

W2=fy vW(234.5+ T)/254.5 (32)

Equation 32 is the amplified form ofequation 2.

Temperature Rise

The curves representing equations 1 and2 or rather, 22 and 32, intersect where justas much heat is transferred as is generated,so that balance is reached. The tem-perature read at that point is the steadystate of temperature of the coil; Fig. 5.Appendix II is a sample calculation forthe sample coil, Fig. 6.The temperature calculated in this

way is the average temperature ofthe respective high-voltage, low-voltage,tertiary, etc., part of the coil shown inFig. 6.

Table II. Calculations and Test Results Compared

High-Voltage Coil Low-Voltage CoilTemperature, C Temperature, C

Three-PhaseTransformers, Calcu- Calcu-

Kva Voltage lated Test Difference Voltage lated Test Difference

112!/2 ........ 600... .81 80.......1.. 120. 73. 79 ..... -6112/ ........712,400 71 73.......-2 120. 70. 76..... -6112'/2 ....... .480 77 70 7. 120. 69. 69 ..... 0150 ........ 480.. 48. .55 ......-7 ... 66 ...... -3150 ........ 480 53....59.. -6 120 70 78 ... -8150 4,160 .57 61 ...-4... 120 70.....74 -4150 4,160 65 i68 ...-3... 120. 68 69 ..... -1225 480 55 61 -6 120.. .72 6 ..... 6225 ... .400. ...... 87 76 11 480. 6767...2225 ... ..... 480...... 72 74.. .. -2. 80...... 74.. .. 71 3225 ........ .......160 68...... 71 -3 480.- 4 71 .... -7300 ...... .. 480. 63 62...62 I...... 120 i68 79 -11300 ........ 2,400 .. 60 ... - .12 0 70 75 -5500 ........ 6,763...7272..... 78. -6 . 4 5 67 -2500 ........ 6,763.. 76. 71 5.60 480 Rffi O500 ........12.000 ...74. 84... -10. 120. 92 .....90 2750 ........ 4,160... 58. 62. -4. 480 72..... 66 6750... 4,160. 56...... 60. -4. 480. 75 70 . 5

1,000 ... 12.000. 76...... 76. 0. 480. 78 72. 6

test values were generally consideredsatisfactory. There were two casesamnong the 30 reported where the differ-ence was 11 C, one positive, the othernegative. These cases will probablyprove to be extreme or erroneous if moreresults will enable a statistical evalua-tion.

Appendix 1. Calculation oFHeat-Transfer Function

From equation 15,

qc2 T2-TA

log q¢,-log q47s-1.25!log(Ti-TA)-log(Tg-TA)] (34)

From equation 11,

qri T14-TA (35)qT2 T24-TA4 (5

log qr,-log qr2 =10(T4- TA4)-log(T24-TA4) (36)

It is more convenient to have an ex-ponential function, though arbitrary, onthe right-hand side, thus

log q'-lIog q,2([log(T,-TA)-log(T2-TA)] (37)

where n by combination of equations 36 and37 is as follows

log( Ti4- TA4)-log( T24- TA4) (38)log( T, -TA ) -log( T2 -TA)

The values of n calculated from equation38 for a series of temperatures are as follows:

Appendix IL. Temperature Riseof Coil Shown in Fig. 6

Heat Transferred

The initial calculations for the cylindricalinner surface (one side of a duct) of the coil,shown as no. 1, are as follows:

diameter= 12. 7circumference- 11. 75X -36. 85less (14 spacersX0. 375 inch each) -5.25cooling circumference-36.85-5.25=31.60k, for 3/8-inch-wide duct -1circumference cooled by convection= 1 X

31.60= 31. 60 inches

The calculations for the cylindrical innersurface (both sides of a duct) of the coil,shown as no. 2, are as follows:mean diameter= 13. 675 inches2X (mean circumference) -2(13.675X T)

-85.60less (14 spacersX0.375 inch eachX2)

=-10.50cooling circumference -85.60-- 10.50

-75.10k. for 3/8-inch-wide duct=1circumference cooled by convection =1 X

75.10=75. 10 inches

The calculations for the cylindrical outersurface of the coil, shown as no. 3, are asfollows:

diameter= 14. 65circumference= 14. 65X =46. 00view factor derived geometrically, 1-F

=0.4860.486X46.00=22.40total of circumferences cooled only by con-

vection = 129.10 inchescooling length=15.75-0.22=15.53

Test Results

Table II shows a series of test resultscompared with calculations made accord-ing to the method of this paper. Differ-ences of 8 C between calculated and

log (Ti-TA)- log (T,4-TA4)-Ti (Ti-TA) T2 (T2-TA) 10 (T2-TA) 10 (T2'-TA') D

358 ...... 55 30.0 ..... -0 162 ..... -0.208.... 1 .28383 .. 80 413 110.......... -0.139 .. .. -0 197 . 1. 42413 110 453 150 ... -0 135.. .. -0 215 . 1.59453.. 150. 483. 180. -0.078. -0 138.... 1.77

Halacsy-Temperature Rise of Dry-Type TransformersAUGUST 1958 459

area cooled by convection=15. 53X129.10-2,005 sq in

circumference cooled by radiation and con-vection = (1-0 . 486) X46. 00= 23.60

area cooled by radiation and convection-15.5.3X23.60=366.5 sq in

The total heat transferred is as follows:

C riseabove 30C= 45. 5.80... .110

C total = 75. 85.... 110. ..1402,005Xq= 260.6. .322.8..535... .740366.5Xq= 122.0..158... .257...397.6WI, watts= 382.6. .480.8. .792.. 1,137.6

Heat Generated

The calculations for the heat generatedare as follows:

DiscussionN. A. Hills (Moloney Electric Company ofCanada, Ltd., Toronto, Ont., Canada): Indry-type transformer temperature-risecalculations, designers are interested inobtaining rises that are close to the tem-perature class limits. With this in mindI would think the process as outlined inthis paper could be simplified by estab-lishing the watts loss at the temperaturelimit for the class and obtain the tem-perature rise by reference to Fig. 1,rather than by a graphical plot as in Fig. 5.If the rise is close to the desired limit, as itshould be, the error introduced would bequite small.

This approach in effect establishes rela-tionships between surface watts/sq in andtemperature rises for different duct lengthsand with duct-size corrections that could belisted in a relatively short table. This formfor the information would be easy to in-corporate into a computer design program.

I would appreciate the author's commentson the following:

1. How great an error is introduced byassuming that the correction for ductlength and the correction for duct size canbe considered independently.2. Fig. 2 would indicate that two 1/4-inchducts would be preferable to. one 1/2-inchduct. Our experience would indicate thatthis is not so.

3. No mention is made of the relativeeffectiveness of ducts which have hot sur-faces on one side only as compared withducts with hot surfaces on both sides.

J. J. Kunes (Westinghouse Electric Cor-poration, Sharon, Pa.): This paper de-scribes an interesting method of calculat-ing the temperature rise of dry-type trans-formers, derived from the familiar equationsfor the three modes of heat transfer. Be-cause it will be placed in the literature, how-ever, I would like to argue the followingpoint for the record.Equation 18 seems an unnecessary comn-

plication of equation 17. It would be more

straightforward to calculate directly thetotal heat dissipated by convection, andthen calculate the heat dissipated by radi-

copper wire, 0.112 X0.220=0.024620 sq indeduction for round corners= 0.000838cross-sectional area A =0.024620-0.00838

=0.023782 sq inlength of wire=42.80X240 turns= 10,260

inches-=41.7 amperes, 12= 1,740

Substitution of these values in equation 31gives

V2o= 1,740 X 0.67X 10-6X 10,260/0.023782= 503 watts

For different temperatures (in C) thetotal watts generated (from equation 30)are as follows:

C= 220... 75...85... 110...140W2, watts=503.. .606.. .626.. .676. ..737

ation, using the areas involved in each case.This would eliminate the approximation in-volved in the value of the exponent n for q.Also the view factor F would be used withradiation, where it has physical significance,instead of in a convection term.

M. F. Beavers (General Electric Company,Pittsfield, Mass.): The author has pre-sented an analysis of a rather complexproblem of heat flow as applied to dry-typetransformers. As indicated in this study,convection and radiation play a large partin the heat-flow problem in such arrange-ments as concentric coil surfaces and adja-cent core surfaces in dry-type transformers.However, in an oil-immersed transformer,radiation plays such a minor role, that theproximity effect of the winding and of thecore on each other is negligible. Therefore,for the purpose of determining temperaturerises, it has been found entirely satisfactoryto make compromise tests (such as the short-circuit temperature-rise test) on oil-im-mersed transformers in which the core isexcited at a very low value-essentiallyimpedaince voltage.

In the case of dry-type transformers, how-ever, a compromise temperature-rise test,in which the core and windings are not attheir respective temperatures simultane-ously, is subject to error and requires eitherfurther tests or a fundamental understand-ing of the interrelations of heat flow whichpennit certain corrections to be applied tothe compromise test result.

It is not clear from the paper as to thetest method used by the author, but it isassumed that the test data presented in thispaper were obtained under the conditionsof a load-back heat run such as recom-mended in the revised Test Code for dry-type transformers proposed by the AIEEProject Group on "Methods for MakingTernperature Rise Tests on Transformers."'

This working group is hopeful of ascer-taining a compromise test on dry-typetransformers which will permit making atemnperature test on a single unit. Thewriter has recently conducted some com-promise tests on single units which, withcertain corrections, show some promise ofbeing substantially equivalent to dataobtained on the same units under load-backtest conditions. These data are beingprepared for presentation in the near future.

ReFerences1. ELECTRICAL COILS AND CONDUCTORS (book).H. B. Dwight. McGraw-Hill Book Company, Inc.,New York, N. Y., 1945, p. 51.2. THREE PHASE INDUCTION REGULATOR (DerDrehstrom Induktionsregler) (book), H. F. Schait.Julius Springer, Berlin, Germany, 1927.3. HEAT TRANSMISSION (book), W. H. McAdams.McGraw-Hill Book Company, Inc., 1954, pp. 167,173.

4. CoNvERsioN FACTORS (book), 0. T. Zimmer-man, I. Lavine. Industrial Research Service Inc..Dover, N. H., 1955, pp. 29, 77.5. Dwight, op cit., pp. 26-32.6. STRAY CURRENT LossEs IN STRANDED WIND-INGS OF TRANSFORMERS, H. J. Kaul. AIEE Trans-actions, vol. 76, pt. III, June 1957, pp. 137-49.7. PHYSICAL AND CHEMICAL CONSTANTS (book),G. W. C. Kaye, T. H. Laby. Longmans, Green andCompany, London, England, 1948, p. 81.

If the author has conducted any suchcompromise temperature-rise tests, anyinformation or comments he may have tooffer on this subject should also be veryhelpful to this working group in preparingproposals for compromise temperature risetests on dry-type transformers.

REFERENCE1. ASA TRANSFORMER STANDARDS C57.22-TEB-PERATURE RISES TESTS ON TRANSPORMERS, AIR3:EProject Group. Electrical Engineering, vol. 72,Jan. 1953, pp. 70-74.

L. C. Whitman (General Electric Company,Pittsfield, Mass.): The calculation of thetemperature rise of the dry-type trans-formers is considerably more involved thanfor liquid-immersed transformers due to thepoor thermnal conductivity of the air mediumand the existence of considerable radiationeffects. In a liquid-immersed transformer,a thin oil film suppresses radiation effects sothat internal radiation effects are practicallynonexistent.The author has outlined one approach to

the heat-transfer problem in dry-typetransformers and he is to be commended forhis basic approach. I would like to offer afew suggestions which consider some of theeffects encountered in the application of thisapproach to actual cases.The thermal gradients between compo-

nent parts of dry-type transformers are ofconsiderable magnitude, and interactionbetween core and windings, between thewindings themselves, and between thewindings and casing, must be considered.The assumption is made that, "...tem-

perature of the enclosure is considered to beequal to that of the coolant...." If Dr.Halascy is referring to the core and coils of adry-type transformer operating without anenclosing casing this is essentially correct asthe walls of a room are presumably of thesame temperature as the ambient air.However, the conventional ventilated dry-type transformer has an enclosing sheet-metal casing with ventilating louvers forsafety, appearance, and partial shieldingfrom dirt, as well as from possible waterdripping from condensate of overhead pipes.This casing temperature is somewhathigher than the room ambient temperature.From heat-run data, the average tempera-ture rise of this casing is in the range of 15%

Halacsy--Temperature Rise of Dry-Type Transformers460 AUGUST 1958