'J

'\

r-- DS:R M'lD Foe I. ! FHt.t ;;'L:E/,I,:";Hf.nl .. , Ii> , fF" !F' 'In f.'O po ~.1. r•.'·...', l'J or,,;; ".: ,'.' , .':.,.'U oJ I ~ .fI, ';~'~:\E; '. ' .:: l.. -; \:'.KY

, - '.''i\qi'tFIl~j:;(ii4'-·-1.. -~~-- "..' .--_._---:---_.-

F.il. Note No. 224/1955Research ProgranmleObjective P5

D:ii;Pii.Rl'JiE!?r 01<' SOmTTIJiIC 111ID JJ:IDUSTREL l1ESEARCH BID FIRE ClIP1!'ICES' C01m:rJ!1'EEJOn,?1.' I<'illE RESEAR(,'H ORGAHIZATIOE

;---'---_._----------------This report has not been jJUblished and

should be considered as confidential advanceinformation. No reference should be made toit in any publication without the writtencOnsent cf the Directcr, Pire ResearchStation, Boreham ~iood( herts. ('.celephone:BLStree "341 and1797)~,' .

'lliE THERi,lAL PROPffiTIES OJ!' SKDI

by

D. I. La.lson, ,;p. H. Thomas and D. L. Sirrans

'.

Jm apparatus for the study of burns to the human forearm bycontact .dth a heated disk rold the theory of the method are desLribed.I<"rom' some preliminary experiments a mean v alue of skin thermalconductivity was obtained as 1'5 x 10-3 c.g.s. units. There,is someevidence that restricting the blood circulation may reduce the 'effectiveconductivity by about 20 per cent. '

. Fovember, 1955.

li'ile No. F.1000/12/156F5/2(P)

Fire Research Station,Boreham Wood', .Herts. '

© BRE Trust (UK) Permission is granted for personal noncommercial research use. Citation of the work is allowed and encouraged.

,by

D. I. Lawson, P. rr, Thomas. and _D. L. Simms.

~ ,'During recent years it has become necessD.ry to simulate the thermal

perf'ormance of human tissue by physical systems in order to know thedegree' of protection afforded by clothing in fire fighting. The workalso involves the determination of the threshold condi'tion under "thichburns occur and though a consddera' ',le amount of work has been done, onthe 4egtee' of burns caused by different levels of radiation ,1, 2, 3) 4,5, 6, 1) and also by different sldn temperatures (e, 9, 10, 11., ,12,20) thelack .of knowledge of the inter'l~~l~til:;:~of heat; flux and temperature haslimited the use to whi.ch the information could be put.

, This work has been under-taken va th the 3urns Research Unit" of thehwdical Research Council who made available apparatus by which·the fi6~'of heat into human tissue cou14 be related to the temperature at the,skin interface. lrfeasurements have so' far been' confined to the temperatures~t ~hich pain' commences.

t ••<

• :.,.t. _~

The apparatus is shown in Figure 1 and Plate 1. \'fater at .akncwn. predetermined temperature is pumped round a closed circuit and heats a.

. disle of tellurium-silver alloy (1.3, 14). The heat flow tlu-ough t he .' '.1i:i;sl~ is measured by recording ·the difference in temperature of two .thermocouples attached to. the two faces of. the dd.sk, An ,additionalthermocouple vms attached. to .th~ edge of the outer:or contact ~~ce,ofthe'diSk: for measuring the skin temperauure, . ' .', .. " '. ..', .: --.:

f ;... ': .• ' ~~ ",

The water was first r'af.aed to ·the temperature required for a' set.of', experdrnent.aj 55 - '65°C,' and the skdn was pressed fin:n~y .0I,l: ~he. disk(Plate 1). The output of the heat flow disk and the bhermccoupLe wererecorded automatically. ,S~nilar experi~~nts were ccrried. out by fourpeople using the inside of the 10\ler forearm' am' repeated vii th the bloodflow in the arm a;rrested by application of pressure. in··a: ~ph;yp:onoineter. .The, .P~ari o~ 'the experiments is shown below in Table 1. '., .' .

. " .. r'l'ABLE 1 \' 0" .' .': ' ••,,\,' •

".."':.: . .t?1an 'of e?qjeriments

......

. '.". ~/. ," ~ :'

.', '0"

Sec.

," 122"1~q.

144151·122·5123

, ., '.

.' ruration'of

exposure

.. ~ .

. ':

u ..:

30: .,'11

31'4 .....• n:.,

Initials!dn

temperature

"

II' .:

II

oc

~

13.- 5

II .. '

II

II

n'

. II'"

55

ocr't'lt"w

1dater' Ambienttemperature tempera~ure

r:....: ..:,:, .. '.:_. i .: . ~.'l-with "

Run circulationNo. Individual. yi/O-without

1 '. circulation.\ . , ".' '. .

,.I---:---~---__r----~------,- -- .-~---:-- .....,... -------~ .......-._--..,

-2- "

'""

..

, ,'"

W11/0

rrrI/O'yVaH/O

\7/017

\i6,,W

, ..\//0-- _.._._ ..__.•..."' . " .

: .

, D.L.D.L.D.S.D.S.J.B.

, J. B. ~ '

- _.. ' .....~--_._-•• ,"I

~~.. _ .t ..;. ".-~.;....__' .. , •. .- --...., ~_:__._._,_._ ..J.._.•.. .• :.• ,., _ .- .. ,~.' •• _ ••. _ '., ' , J ' i'Yl-with! I I .I I

circulation I "'.-rater ! .AmbientInitial DurationIIldividual \flO-without Itemperature' ; temperature! skin ,of

.car-cuka't i.on J' , f' , I temperature exposure'. l I

...~C ' I, ,»c ' l' ~C. ,'w' . I",' , . s Sec,

.! "1.1 . .' .___ .... , ~, ., . .'.. ._, . _-_., - ... _ ...,0: _..._~ __ - ~ -_..'_ ~ 0. __I " , , ,

60 "I 14, ' 32,4 92II , 14' 25 II , ,7"/'II 13.5 30.5 .. 68II .. ' II G2

... 14 32.5 61II, II II 1:,62

i ,,'

, .. ,

65 14· 0 30,.., 33 'II II II 31II n '29 ',29II I II It .33II :: ,tt 32.8 30.5" 11' II ~, 30' 5

~__-..._,_","-- --=.. .a2__."'"....~..;..~:.._ t.~ .:.........-._.--.;._._ . ~.._

" J. B.,' .J. B.

, D, S.,D. E•.P.T.

" P,l',

ABCDEl!'

RunNo.

"p ",QRS

I ~~, lo--_-'--_

',[lhe record or'- 8J1Y experf.ment; enables t~e heat 'flow a:nd skin,temperatUre a~ any time to be f'ound , Some typi~al results for heatflow 'are shown in Pigures (2a, b, c). 'and :for skin temperatures inFigures (3a, b, c). .

3. ges-E?rS~2f ,.aPParatus,

~.1.· , ~~.E..tan~2jsc~E!L~~1~. pemperatiE:e..!!.

, ,: When' the he'ated disk is applied, to" the'~sl~in there is a temperaturech.9.nge.:rit both surfaces .amce ;i.nitialljr they'are at different temperatures.At all t~nes continuity, of heat flux must exist at, the bound~ betweenthe heat flow disle and the 'sl:in. At the moment of contact and just arter,the tom bodies 'may be regarded us sem~""infinitee in depth, so that, if Ie .l,-is the conductivity, k the diffusivityand b. the instantaneoustemperature change on the surfo.ce )the heat flux Q across the interfaceis given by (the suffices ,S and ,D· :r:eferring to skin and dislerespectively) •. ,.' .. ,;",., '

" ':, '-',,':K D g, ' ,, , .. S ", S-

O>"" "7 A G. 7T s'

."J.'

....... (1 )

, ...

Ks(9. -0.1p~

I

Hence if 9 0 ' and . ~ s are: the disk and skin temperatures before

co~.taot':and ',9~ is~ th~" ina~antaneou~"contacttemperature, it ,followsfrom equatio~ (1.)' that ' '

... :,,'~ \Q. ~ ~D (9:1) ~ '~~ )

ir;.: '

. " ..

or

•

-3-

Although the heat flux is '-r;overned by the above equati';;~;th~' .heat flow disk does not .give the aotual f'Low because there i~"riot 'ntthis time '0. linear gradient w:l;thin it... ibroover, the thcrtloooupleused to measure the contact temperature has a time lag, .so that littlequantitative use can be made of these f'ormu Lae to dete:niline the skinproperties•. Hoi,ever,' the' equatLon does·demonstrate that if' the skinter" ,)e.rature i [) to rise' _rapidly to the value of the d isle temperature theratio (VpCI]) must be as-large. as possible.

[J<pcs. ..3. 2. !2.~!3Je.E~1~E0!).s_e..:t;~!!'.~_C;:?Jl!3_t_~t_

". '.'I'he time of half response of 'i;he centre of a disk to a sudden rise

in temperature of its two faces is approximately 0·1 l2/1CD where 1 isthe t hi.ckneas and 1:-the diffusivity. If the conductivity of the diskis. assumed' .t o be that of tellurium, (0.0144 c.g.s. units),. the above

. time constant ·.is·O· 2 seconds. .Clearly, ..even if the conductivity: of thedisk in these experiments is several times ,yeater than that of puretellurium the disk may be assumed to be in a quasi-stationary stateafter the first few seconds. The response time for the boundary layerin the water is·negleoted. Subsequent'experimehts showed that the timeconstant'Was of the order of 2 seconds," .,

3.3: P.i~k._i'r.!3~_:tll.a.e•.Cp.!'...s:t;~~.

There is also a .second time constant associated with the assembly,namely the time af'ter which heat is ·lost laterally and the temperature'I.1I1d heat flux. .ciw.ro.cteristics of the small disk heo.ters are no"longer( )sensibly equal to that of' a large heater. This ,time is greater··than .17

T o

.-

where I' is the disk radius •.

i!'or the disk used in these experiments, To is of t'he"order100 seconds so thut thi's is ·the maxamum permitted durata on of any test.

Within the above limits, it is possible to develop theoretical. expressions for the rise in surface temperature and for ·the heat flux.

In addition to.the abo;e notatiQn let

8 w = circulation of water temperature

g 5 = surface temperature of skin at time t

R' ~oinbined thermal,resistance "' ,disk ·c.."id water.= 0 ...

..In the skin s ,

. . 2).( t I... O~H-"t, , "

.s (3)

The. above expression assume's .that '"he thermal characte~istic~ ;;) f. andc of skin remain constant with temper-ature, distance and t:!-me •

.:,• '•• J

..'

.........

-4- .-,. '... •. . : j: ,'. 4,.. • -• ~ -: '

The. surf'ace boundary 'candition' is given by' the heat flux ..Q acrossthe interface . . , . ,. .

·1. .'

, . . 1/' '!"bQ»" .o. ";' '~.'w,s ~~.x o' -

t > 0,) 'X.::: 0 . .

At time zero the distribution of.temperature in the'skin isassumed to be represented by (Appendix I)-

1\. . . ~ .>}~, .-t Qt..' (I '--. .J2 - atX ) •• '. • •• (5)(:;1.")(. . .. . '

\~here' G"1 i~" the diff~rence between the sldn and body temperature

37°0 and ex, is a ccnatant ... .;,

The effect of the instantaneous rise in surface temperature oncontact is neglected, as thi.s is only important at very shor-t times.',

Applying the Laplace.Transformation to equations (3) and (4) J' .

d. "JoGs .. =;'P~/ Q :~ ..':·..·_:9..· '('1 ~ ..()~ : . Q':./. (6)/J., s -.-e - 1.1- s' ., . . . '. -,J _ '- . . 0..... "'f"l!.

O-~ 'Rs' .

Q. I Q'rJ - \ .'R ( :p- 9$) .... .. (7)'

t .> 0.J

X.::-O··'The.solution to equatdons (G) and (7) is'

-= 9'<"1.. . "+ (9;. +"Q/~) ~ K s RQs 1>(1 -I-q Ksl~) . '~ p Q+ ~ Ks I~)

• • • • ... (8)

1 .~

,.1

'rhe heat flow Q is obtained frail equations (7)' and (8). .

....

,=" •

. --

i.e.

Q..

':-,.' ~ .

f9w '_. ((is. +Q~ KS " .'.

.. ~ 11 . . .' --p. : I + ~ .Ks R)

K's 91

.......

'.' "

""

1',' , :

-5- ,

Inverting' the, transf'orm in equationj 9) "

. ',,'

•

; . .".\ :'- ~

. , .,

.... , ..

•

:":' ,-:;: J ..... . ; .. ' .....:: I . .p

'"" Hence the resJ.s.ance 0, the .appaz-atus '!=lontrols the time responseof: skin temp'eratu:r:e at' short times.

" '

'.

:" . ,. I'... ..,' . ' .The correction for the fact that the bu'lk of ,the skin: is not at

the sk'iI:l's,urface temperature depends' on' the values 'of:0( , anapProxim~te value'f'or,which is 3;0.which gives a,value for ~ KsRof' 0'5 (Appendix I). .,,', '. ", . ,--'" " , '

..' .. . . ., "

, ,

If' the second term in equation ,(9) is'assumed negligible; i.e.,thetinies'consid!Jred are small enough for heating not, to have penetratedto a region where the skin temperature is sensib~ greater'than the'normal surf'ace temperature, then from equation (10)

, :, "

" •••••• (11')'

, • '..... ( 12)

­.

", : .

:Q.R' ,

,~ 8s)

'" -,'/b);" -, If' Q< R):J. '> ?' '1 equation '(1:1) ,;educesto

,~', @~ ~ e):jC~(?~',-

.',, ,L, e. a graph of' 1. agains1;[ttends to linearity with a slope of"

" ,Q," ,. "

,:W, ,I " ,. Actually a :gr~ph of1~ainst[twill(Ow~f)sl-JQ<.pc)s . .. ',' ," Q"'<tehav"i allthe .f'unct Lon ,(ex2erfc x)-:-1, behaves as a function of' x, andthis is iriearJj:linear in the range considered (l!'igure 4). ' '

, Usi~g Ii. ,value '.of'O( me equal to 0: 5 , 'the v~lue'of 1. as a :ruilctionof ITis. also :shown in l!'igurel':A In equation (101theQcoef'f'icients:

of thE;! correctiori term involve 6' s,' GI and . 19- w•. The correctedcurveehcwn iri' l!'igure 4' strict~ ref'ers to a water temperature of' 6000only, the middle value of the exper-irrerrta.L ra.lll:;'e" but this is consideredtOibe suff'icient in vie'w, of, the approximate derivation of' the correction.The 'best, approximation ;to:equation (11) for the range of values ', '

.r.

, ' -

r-

-6-

. The factor 1.85' replaceJ~W f:~~ the ~l~~e····~~"gi'v~n byequation (12) and th~refore g1v;es vcl.~es orCI\. p c"Jilhich are 8 per cent 'higher. Equation (13) is £llso ahown in Figur~ (4.;'

6. ~t':~i~~~:,::.~_~~~,~~'~~.~~f~ctive w~t~r-"::m~:a~~=_ GN

The ex.~er~ento.l'data are plotted as ~: against. [tCli"igure 5a-c).

This cU!"'J'~'apprcxfmat.es :to 8.. straight line in .-the .. rxnge 2-4 times theintercept 'and ita cl~pel if v~~ues for ·9 ~ and' ~. 6 are known, enablesthe val.uea of I~-t'~Ci;> to be qalculn.ted. 'These are shown in Table 2.' Itdoes not aacume~ that R is the same, for different experimental runs butonly that R ;\.;;; conecarrt dur-Lng iany one run. \

. R could be found by extrapolating the line '~o the ms of :I. and

using the same values of () wand 9 I S J but a method making u~e ofequation .(4) ·:18 mor-e d:lreet and thus' preferable. The measur-ed heatflow and the c(")l'l'('~1?0jJdin~ measured skin temperature at any time are .. '.plottRd against one uncther (:B'igures Ga-c) and the slope of the line is. ..:,a meanuz-e of n •. 2.'he results for R obtiUned by this method are also shownin Table 2. In &ddition to giving values o~ TI, equation (4) enables the:ll.ppiied water temperature.·to be calculated. This is given by the intercept' . '.on the temperature axis for zero heat flow. Tr~se values are also listed .in 'l'able 2.

IJ.'ABLE 2

•

......_~ "-- --' _ ..- - ."j'''';_ - ,_, •.'.-_. .... ·····_··r·--..-..- ..~-------_.~--~

Actu~~ . Calculatedwl'lter' . " . . water

temperature temperatureRun

L-...__

(1 )

R' ." ..

qgs,units

_.._...-....... -- .... . .

(2), .

I~cq~Ji•.

.' unitsx 10-3

2'.030·95f·381.. 352'81

·0·96

" .

Circulation

.. '

!C~ (1) by heat flciw method (equation' (4().. (2) bY .~qu~t~~n: .~':(13) using nominal applied temperature for e v, , '

-7:'

7~1. Discussion of results' for R,'._.-.-.-,...'-, ...._-~_ ..•.-......,-_•...--:--.. ,

,,' ,Typical"?raphs of heat flow against skin .temper'ature are-shown inl!'igu.i::es( 6a-c). They are straight lines curving at,the extremeties.'

" ,The reasons for this have already been df.scusaed (Sections 3.2. 'and3•j~). A.'la.lysis shows that the val.ue of R, t he combined thermal'resistance of disk and vlater, obtained from the slope of the line maydepend upon 1;,,-e applied temperature but that the variation is much 'greater than t he ntlru.mum.vafue predicted fQr' trevarlation -Ln waterresistence(Appenilix II). '

7. 2 0 P:LE?I:~~J;L9!.1_g~:..~eff~R~j,y~. !'!l-~!_j;jrn:p~!~:t~!i. ', .

The"v:ilues of the effect'ive'wat~r temperature are' aeen ,to'be asmuch-as 70 0 Lower- than the nominal :values. 'rhis implies ,toot the heatcapab'l,e of being absorbed by the 'sk'in, is',greater than'the source cansupply, and "tl13.t the actual applied temperature varies in the initial','~tage~ 'of' t he. ezper-ament ,

, 7~ 3. .P;L~9!151.f!i9~..9!...!:~§)1;J,~!!..f9.:r:..1y?!:'.,:" ,.' In Table 2 values of Kpc are given using only the nominal values'

of ~ w. The scatter amongst 'individual results is too large topermit satisfactory analysis, but' a ,partial' analysis of the resultsobtained'using'the,nominal water, temperature suggest that there might'be a reduction inI~c.when'the c1rcillation"is restricted. , '~he magnitude

, of the reduc,tion, if real, would lie from 1. 6 x 10-3 c. G.S. 'units to,1·3 x 10-3 C.'G. S. units, Using the' crJ.6ulated values of Vlater temperaturegives somewhat higher v~ues,of Kpc, but since these may be shown to becorrelated with R it follows,that errors in estimating R effect ,the valuesof lcpc and this'method is therefore to be, rejected'. Assuming that. pcis unity, gives','a: mean value for Kfor -al.L results of 1'5 x 10":3 C.,1]:.S.units c~wred ,lith a value of 0·6 - 1 x 1O-3,C:G.S. units given byReader \ 1tJ) • ' '" " '

A probable reason, for this difference is the variation Ln thepressure .7itb ,ihich' the ~ is brought into /contact with 'the disk.This has beerinoted by, lviorltz and Henriques (9).. , ' .

8. General discussion•. ., ...... ~, ••••••,.~.'••M ......... • .......,_....

, '

The results using the apparatus in its present form are not likely'to be accurate since:-

(a)' the theriiuU' resistance 'betwee~ tht3 water, the disk' and .t heskin means that th(l' heat'.:n0\7 to the' skdn is not necessarilychar'actier'Latri.c 'of" the "nbrrin8.l water temperature (Appendix II).' 'l'hisraises some doubt as to the correct value of, the ,effective'vlatertemperature. ' This phenomena haa been reported by other inve'stigators (9).

(b) the, skin~temperaturemay be being measured at a different,point fr9ffi where the' heab .f'Low is being measured (Appendix III)., .

'(~) the pressure vlithVlhich tl,1<;l,skin was pressed against thedisk VIas uncontrolled'and this seems'a,lllcely cause of variation inthe value obtained for Kpc.Although ,,/Oritz and Henriques (9) do not.clm that there is an ef'f'ecf due to compression of. the' sldn,' they'tried to avoid, it during th6ir experdmerita, ' ~l)ey.donot rei>ort.;3W:increase in burn severity with compression. ", " '.

", .

.,.8-

Since the damage to the skin ~aries markedly ~lith temIJBrature inthis range of experiments, it is neceasary to' knovi the' skin temperaturew),th some accuracy• Both, the heat' fl.ow and skin temperature vary durine'~he _course .ot: an experiment ylith ~lie :present apparubus 'and somemOC;'ificationHould appear to be. necessary. '. .

" . . - .

~'or periods of' heating longer ,than 100 seconds a ddsl; of largerarea wiil be 'neceeaary, Two importan't conscantis of' the disle areunknown ,', thermal' conductivity, and thermo-electric output of thejunction;' a slight modification of the electrical system introducingextra thermocouples wouLd .enable ;;hese quantities to be measured, andcheck the accuracy of the system. The pressure with 'Ihich the skin isapplied to the heat disk is applied' needs·.to be controlled. A checkon the accuracy o~ the method can be obtained by using a material ofknown l~c;- This woul.d 'also enable the importance of the term due. toheat flow from the blood out to.the skin. to be estimated•. It shoulde.Lso bejloelsible to' use the apparatus in r'ever'se to examine low .temperature values' of x, p. and c. If cold Ymter floYisthrough the .tube and extract heat from the skin, the effect of the initial conditionsl7ill have vanished by equilibrium, and the difficulties in interpretingthe results will be correspondingly reduced•.

. Ref'er-ences .-"- _.-: •.. ":-- i .

1. . i\Iortoni j •. H., Kingsley, J,f.' ·D. and Pe¥se, H. E. Studi¢s on flas,h .. ?.u=s:' Thresh(old). burns; §!!-EB!l;SY..l_GJ'!l~9f;L~... _Jl-!1?..9J?;;~~~rt~l§.Jl~Ch.? 1952, 94. pp. 317-22.',

'.:'.:

,. r 2. fuettner, i~. Effects of. extreme hec.t· and cold on human skdn,'1. ',4nalysis of temperature changes caused by different kinds

" of.hea:ti application•. :!:..::~PP!:~fu~3-.9;!,.. · 1951, 2J (12) 691- 702.,

Buettner,;C; Effects "of extreme heat and cold on human skin; II•.. ,?-,-·£tE.l2±.!-!l1,Y~iol. 1951, l (12) 703-

4. fuettner, K. Effects of extreme heat and cold on human skin; III.l"umerical 'analysis and pilot experiments on penetrating flashradiaticineffects. J. APJ2h-~:S~9~. 1952, 2. (5) 297-20;

5.

6. !)rake-Seager,. E. R., 'fread,:eU, ~. E. E. and mttorfiald, v, J.' H.High temperat~ radiation .and pain: Location and blacl=i~e; o:f·the test .site'., AORG Report Ilo-, 18/1950.' November, .1950;.

7." .

fuettner, K.· Effects of· extreme .he at on man..(1~), lio. 9, October 28tll, 1950,' 732-'38.

,.'1!oritz;A.R. and Henriques, ·1'. C. Studie~ 'or thermal iiljury, , II.''l'he relative importance of time and' ·surface· temoerature iilthe . .causation of cutaneous burns. Ame.r-, ..~:. ja~h: ;1947, ?2J 695-:;729.

iienriq~es,J!'.· C•. and lJoritz, A. R..Studies. of' thermal injury, I •.The'conducti9n of heat to .and t~ough skin and the temperatures '.attained .bhez-edn, .A theoretical and .an experimental investigation.Amer.",J'...]attl.• ,1947,~531-49;,. '. '. . . . . '.

8.

9.

10. Lea~, E. C., l~ters, R. A. and Rossiter, R. J. Experimentalthermal burns, especially the moderate temperature burn.Quar:t.!...~.!._~. !'J!.'y'si~. 19L>3-44, 32, 67-86.

•

-9-

11. 1britz, A. R., Henr-Lques , Iv. C., Dutra, :'6:. H. and '.:e~s~ger, J. R."S'cudies of thermnl injury, IV. 1m exploration of the casual.ty­producing attributes of conflagrations; local and sys t emr.ta,c . :.erfects of general outaneous exposure to excessive circwnarabientair and circwnradiant heat of' varying duration and intensity.Arc!.l..:..!,§-_t!:i, ..iI,il!?". _!:~?~1 1947, !.?~ 466-88.

12: Henriques, 1'" C. Studies of '"hermal injuF.f, V. The predictabilityand the significance of themally induced rate processes leading toirreversible epidermal injury. Ar.'?E.,.Paths., (Lab, ..1~~s:l. 1947, !!:2J489-502 •.. .

13. Hatfield, H. S. and '!ilJdns, .1<'. S.. ,~new heat flow meter;:!..... §.c:!:-'-}!1_"i~E .• , 1950 , ?:7..., (1) (Jan.). 1·-3..

Hatfield, H. S. An apparatus for tho mecsurement of the thermalconductivity of biological tissue. ~~~!.• .A~~E.:.. 1 953 , .lQ~(12), 1.60-1.

'. 15. conduction in solids.

17. Thomas, p. Il, and Simms, D. L. Some practical limitations to theuse of small irradiated areas on solids for the study" of thermaldamage" Departmenj; of_!3.cientific and I!)311!1trial g~£.~E.9h ~nd

L~_.Qffi~§;g£,,~!!.~!,_:!o~~:t]E.::eRese§,!,.9h Organi.z£·~_lL,-H•.Hote No. 163/1955. . ....-_...~ . .

19. ECkert, E. R. G, "Introduction to the transfer' of heat andilicGraw-Hill, 1950, (92-3).

20. Lindwell, 0; lIL. Production of' skin burns by hpt. gases•. 1J~.~!J.!'~,

156, .1945.; p. 298.

:-; .. "

roo

•

-10-

APf'EHDlX I

theThe bemperabure d::Lstrib~tion within

• _ . • ,L

f'.9rm .the· skin i" aasumed to t oke

- Q+ ,Qs

'(_ . ..' .; cJ.Y...)I --' .Q, .' .• ••••• (1A)

-This expression vroula'gi~e Q7_::' Q~.,LOI·(the body t~iaperature) when

the exponent term is small i. e. at Lar-ge depths. The vulue of 0( mustbe determined fr~n the poundary conditions.

The heat flux across the surface 'x =0 is, .

Q. ·..... (2A) ..»

Q is also given by,

9--= • • •• •• (31\)

where .H is the ~attransfer coefficient at the sldn surfo.ceto the surrounding air.

hence from (21\ and 3A)

. I

c<1:-/ Os, (l.,A)- ·.', ...- K ~

~'or a blacl: body at 30°C 11 is approximately 0.0004-6 e.G. S. units.

Since the correction term is small,' approximate. values for i(pcand R may be assumed I

viz. " ... 1 x 10-3· c.c.s, units,l.\, ..

p~ 1 C .~~ VJ.....;t~

wv.d::e • 1 c. S. ~9 s ~ 31'50 e

Q1 : 37-31·5 = 5'5°0

R = 170 e.G.s. units.

01. is then found to be approximately 3 cm-1•

A value of 3 for 0( implies that the skin temperature at 8 rom .depth is 36· 50C within -!rOC of the bulk body temperature.

/

-11':'

AP2NIDJX II

Effect of thermal resistance of disk ro,d water~--- _._-_ •._.--_._---_. _ _-_._---.-.-----

. ~'he amount of heat being takerrfrom the' water 'system is comparativelylarge and the resistance in the boundary layer is high, so .t hat the anourrcof he0.t passing through the disk mf.\~r not be char-actez-Le.c Lc of the'cel"1i::erature of the main stream of water, An approximate calculation oftlllf comparative resistance to .hea'c f'Low of' disk and .tater may be made asfollo~s.· -

D. -:I,7' D

,

1Disk.} .III

. Ii

---£-~1!

1'1

be~ "'J'Uf I.

~;rater s tr,'eam. I

,

PI

.IBoundary layer

'rho' heat flux .Q_ through t he boundary layer is

I

G- •••• ! •

,rlrere 1\, is the heat transfer coefficient ·across the water boundarylayer and 6 Q- w is the bemper-a'tuz-e drop in this Layer',

11'he heat flo\/. through disle is given by

.... ~ . (2)

where. ,"ij.Y.. ~s'., the tempez-abure drop across the disl::

and /!;...i::;.',its :.:thickn~s8.

I~~/ . .I . 0 •• '. • • .0)

. \

... ::.rh~· value o,f'1~7 depends ~pon·the local velocity o~ the water end,the geometry of the apparatus.' If it':can be assumed t):iat 'the .LocaL. '... ,velbci'-ty~ ~Vl' ~s the same as' in the- lIIB:iri stream,' i.e. '100'cm/sec, a . ''',. ' .

. ina.Ximu.nl'~v'alue' for- I'Iy:{ may 'be, c~leula:teq:':.•rhi.ch 'is .approprdate toa short'·:.plate of .the same "lei.1gth' lip as the disk, 1 em'in a free atz-camor we.ter •

..:"; ". ~~ : :: '", .;.~~ :". ~ ":,.-":' :'-~'~'.' . , ," .: ..... .. . .. ~. ..~

-12- •

The Reynolds ,number is

-, ru-"LV

.. ,'

where,.''V is the"ldnematic viscosity of Ilaterat 6Qoc,

hence tY R "= 20,000.,«... '1'01' this value of' the Reync'lds number the boundary layer is laminar.

The heat trc.nsfer coefficient is then obtained from (19)

1-1"", l

Kr

where lCw is the thermal conductivity of Vlaterand l~ is its thermal diffusivity.

1\./ = 0'2 c.g.s. units.,

The disk is 1 mm thick and if' the thermal conductivity of the diskis assumed to be O.0144,cal/cmVsec/oCequation (3) gives

•

0·144 cal/cmVsec/oC

D. Qv:rLJ 'Lft] = O· 72

The boundary layer resistance is therefore important since thetemperature drop across it is comparable with the temperature' drop'across the disk.

!l r-,l is of the order BOc and f\ will then be of the order~ ~ IV6°C a" BnY bo less then tho vnJ.uo calculated above and Kn [leY bo

larger than the value for pure tellurium, this would increase theestimate of ~ .' The Reynolds number and the ITandtl number

( 'V/..-kw-) a::::, 'temperature dependent and s Lnce they control II.,-t» the

resistance to heat flow is temperature dependent. E'rom'the data' on thesephysical properties of water, H.,-(, should decrease by about' 8 per cent inthe range 550-650 and this would alter the resistance' of 'the water anddisk by at least 4 per cent. " "

Leach, Betel's, and Rossiter (10) describe experiments'using a metalchamber the base of which~wa~ ueld in contact with the skin of guineapigs. - j,Ioritz and Henriques' i 9) have exanuned the Vlater f'Low in a similar

.chamber 'and have discovered that theremperature 'of the stream of, hotwater fldfnng'through' the'upper and midportions of the metal' chamber,wassignificantly' arid v:ariably' higher than thil.t of the w1derlying: skin.' 'They

(comment that there are two hindrances .. to the conduction, of heat between, 'the site 'of the measured temperature and the surface of the skin,thenl0tallic base of the chamber and the layer of quiet fluid above it.

-13-

tlloritz and Henriques (9) do not give details of the thickness. ofthe chamber or state the metal they or Leach, ~~-":·~.;rs, :'..1"1d ~:Os::;i'~~:C' (,10)used for it. Assuming it to be COPi~r and to be 1 mm thick.

th~'· the~a'l ljQll1Lh~'~~::~(;;) i 6 9:'.2)_' = 9.3 C•.G. S. units'0.1' '

: .... .

','.' .'

.: -and

,LJ Q~ .."'" ....

.'\ 1 'I .I, =-: 1) . =1~5

..

. . . The the~~e.l .resi~tance of'-'he water bcundary layer is HUlS muchuorJ L.l~I.~'\r.·c:..:.1';~ tl~~';~~ ,"~;~.'~' ;;:;hsz-i.1.Ll rDsi8·~ ...~.!ce i.if '~l1e metal.

?i~ritz and HenrLquea claim to have eliminated th..; 3'~~'i;ic l::~l"0r ofwaber' by the use of a brass cup, the base of which WHS open so thatwater in direct contact with the skin. In fact, their system and theearlier system could' only remove the laminur boundary layer if eddieswere deliberately introduced. The fact that their thermocouple didmeasure the same temperature as the water In~ have been due to itscreating eddies in the water.

So far as the experiments described in this paper are concerned,the high resistance of the boundary l~er will not affect tl~ resultsobtained 'provided that the r-eai.s tance is linear·.lith terilperatlfre,·and'.that sufficient 1)eat·can be' obtained frcfl1 the.wate~.

'..

-11.t.-

AFPE.mn:: III·., . : '

" i i.I,

Une~_ll._tempe:r:.a_t_Ll!.:!l~fdisk .,:

The temperature z-rs'e at .the edge of a uniformly heated disk inequ librium on a semi-infinite .~ol:j.dmay.be 4D per cent below thetemperature rise at·: the" cenbre ,17) .... 'l'he difference between thecentral and ·the edge disk temperatures has been measured for differentHater temperatures (Figure 7); . since the temperatures are less than4D per Gent different the hea t flux must.·be ·greater towards the edgeof the size than at the centire, but this dii'ference may vary with theconductivity of the object in contact with the disk. The differentfon'l of the tiI;le-temperature curve near the beginning 01' the experimentis due to' the. dif:ferent time constants of the .thermocouples.

, .

•

..:,,: ~ . ',: I •

\

."PLATE .1.

IiS 97D02)l /jSDO WYSCL

APPARATUS IN USE

,, ,.• 1

,Baffles

Water flow

, Skin thermocouple

FIG. I. DIAGRAM OF APPARATUS

Water thermocouple

Heat flow disk

r(1'(1"

~ciriU-

--- ~-~ ~ ~- - -~ 1 ----A·_·

-----I~'._-

~, '\. ~~~~.-- _. -

-- -

L ~ _.-

. -_. _. ", . ~,_._. -

..

,,' -, --

'~ -.-- " ............._.....• -,.,,,.-;,' ''''''-. - .

...., ..~~

._._- ---~

-"

.....-..- ..;- ~.-

j

!- .~---- ....._. __ .._.. -

,_ "u __..

- - --

I-------

-

~.'----

i

------

- - - --

---

- --

I

~_. - _..... ~---

-, ..........-

. -

~ --

I·.- -_.._-- -

,.,.-........-..~.. .- .-.-- ...--_...-

-

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

-

_.. .-- -.._.- _._~- -

.:..

2

6

·8

12

o

10

X 10"1­

14

-'J~U"I

NIE

-.J

:0.~.'. .t i";4 IPi:

ro. 0:_Ju,

t-.$!.WI

30 60 90 120

TIME-s

t"

Applied water ternpercture 65°- --~-r~ " tl 60°--. __ .-

" "If SSe

.7:/FIG.2· HEAT FLOW' INTO SKIN AS A FUNCTION OF TIME

.. .. -

45I-ZUJ

It! 40~«UJ>',

350co«

-------- ----.,-------_._----

[ • u -----j

--_. --f--------------------- . ..~--

0:!J.

Applied watertemperature 65°C

Cold junction

"

"

"

"

+---

LL

o

5 -.-.- - ------ ----- ---. ---. --- ---------

UJa:~

t­-ca:UJ0..~UJt-

FIG.3. CHANGE

I

I:

30

IN TEMPERATURE

60TIME - 5

OF SKIN

90

TH ERMOCOUPLE WITH =rIME

:t

i

... .t

j

";,

1:~t,-e5 ~O ·75 + I· 85 J-:rQR

---Approximate Equation (13)

- - - Uncorrected equation (l0)

. - . - Corr41ct~d equot ion (II). ..'

---------+-------+----1

--l-------------

l-----------T---­

.j

I

,y

---~---f---~tIC---'+---

4 r----._--------,-

31-------+--------+

d~1' cr .2I I C'afl

"

2-22·01'0I· 20·80·4O'--- ..J.-- -'--- ......I.- --l- ----!..__---J

r-:FIG.4. THEORETICAL RELATION BETWEEN HEAT

FOR· INI"fIAL TEMPERATURE GRADIENTFLOW AND TIME) UNCORRECTEDIN SKIN

AN 0 CORRECTE 0

f'

•

•

wo

•

-----------------JI

IVo

I

!IiI

"ri

..------- _.L -------- -~-~---...---.----i: I

I

-I 2RECIPR.OCAL OF HEAT FLOW - cal em s

o

\\\

\\I \ i\

'" ~ ._~ .. . ._._ ..~ ~ ..\ _L _. ..__• ---'

0- _.- '--' ... - _._~_.- _.~ - --~--- ,

ctJ .--...- -

~rn

.-t'",7'

I.........4

1/\

--'';1-

(Pm-;~rnrnZ

)J

~"U::0o()»r

o"

"G)

Ln

::0o~

:rrn»~

I

"6~

»zo(J).()c»JJrn

-.::0om~0­.- 0(J)z

A

o.."

-;

~rn

o.."

»"U"Urn~oz

•.

11 .' •

'j

----.--.--------t-----

61-----~--·

8

4 ·-------1f----·--~-·---I-- - ------1- .I I I

2 -----t-------- ----------~-. -- 1--- ----..--.--.- --- -----.----.-----=p-..-..=---------l

10ou

~V)

or~

:::>ocrI~

- '&.I X 10V) _

c4 .12r----r------~----__r-----~-----_..,....------,

IEU

383634323028O'- l.....- .L-- -..l --L --L ---J

~-cUJ:r

nD

SKI NTH E R MOe 0 UPL E - °c ABOVE AM BI EN T iI.,1

IIl

--~ FIG.6, RELATION BETWEEN HEAT FLOW ACF\OSS DISK AND SKIN THERMOCOUPLE READING-

• •

• .. " 11''' .,

•

,

I.-

I I--

I -- -- - ,I - - I I--- I II - I

I <->: I I.I- 'j- -I

\. ."---. '-.-----I

45

0,UJtr:::>

~tr 35UJCL~UJ~

UJ...JCL:::>

3 25o~a:UJJ:~

Z~

l/l . 15o 10 20

TIME - s

30 40 50

o· - -0--0 Central thermocouple

x x ----.l( Edge thermocouple

Applied water temperature 600

Cold junction temperature 160

FIG.7. DIFFERENCE IN TEMPERATURE BETWEEN CENTRAL AND EDGE OF DiSK• •