NATIONAL BUREAU OF STANDARDS REPORT

2720

SURFACE TEMPERATURESWITH

THERMAL INDICATORS

by

S. M. GenenskyA. F. Robertson

Report toQuartermaster Corps

Philadelphia Research & Development LaboratoriesU, S. Army

U. S. DEPARTMENT OF COMMERCE

NATIONAL DUREAU OF STANDARDS

U. S. DEPARTMENT OF COMMERCESinclair Weeks, Secretary

NATIONAL BUREAU OF STANDARDSA, V. Astin, Director

THE NATIONAL BUREAU OF STANDARDSThe scope of activities of the National Bureau of Standards is suggested in the following listing ofthe divisions and sections engaged in technical work. In general, each section is engaged in special-

ized research, development, and engineering in the field indicated by its title. A brief description

of the activities, and of the resultant reports and publications, appears on the inside of the backcover of this report.

Electricity. Resistance Measurements. Inductance and Capacitance. Electrical Instruments.Magnetic Measurements. Applied Electricity. Electrochemistry.

Optics and Metrology. Photometry and Colorimetry. Optical Instruments. PhotographicTechnology. Length. Gage.

Heat ana Power. Temperature Measurements. Thermodynamics. Cryogenics. Engines andLubrication. Engine Fuels. Cryogenic Engineering.

Atomic and Radiation Physics. Spectroscopy. Radiometry. Mass Spectrometry Solid State

Physics. Electron Physics. Atomic Physics. Neutron Measmrements. Infrared Spectroscopy.Nuclear Physics. Radioactivity. X-Rays. Betatron. Nucleonic Instnunentation. Radio-logical Equipment. Atomic Energy Commission Instnunents Branch.

Chemistry. Organic Coatings. Surface Cheipistry. Organic Chemistry. Analytical Chemistry.Inorganic Chemistry. Electrodeposition. Gas Chetnistry. Physical Chemistry. Thermo-chemistry. Spectrochemistry. Pure Substances.

Mechanics. Sound. Mechanical Instruments. Aerodynamics. Engineering Mechanics. Hy-draulics. Mass. Capacity, Density, and Fluid Meters.

Organic and Fibrous Materials. Rubber. Textiles. Paper. Leather. Testing and Specifi-

cations. Polymer Structure. Organic Plastics. Dental Research.

Metallurgy. Thermal Metallurgy. Chemical Metallurgy. Mechanical MetaUurgv. Corrosion.

Mineral Products. Porcelain and Pottery. Glass. Refractories. Enameled Metals. Con-creting Materials. Constitution and Micrr^structure. Chemistry of Mineral Products.

Building Technology. Structural Engineering. Fire Protection. Heating and Air Condition-ing. Floor, Roof,,and Wall Coverings. Codes and Specifications.

Applied Mathematics. Numerical Analysis. Computation. Statistical Engineermg. MachineDevelopment.

Electronics. Engineering Electronics. Electron Tubes. Electronic Computers. Electronic

Instrumentation.

Radio Propagation. Upper Atmosphere Research. Ionospheric Research. Regular Propaga-tion Services. Frequency Utilization Research. Tropospneric Propagation Research. HighFrequency Standards. Microwave Standards.

Ordnance Development. These three divisions are engaged in a broad program of research

Electromechanic^ Ordnance, and development in advanced ordnance. Activities include

Ordnance Electronics. basic and applied research, engineering, pdot production, field

testing, and evaluation of a wide variety of orwance materiel. Special skills and facilities of otherNBS divisions also contribute to this program. The activity is sponsored by the Department ofDefense.

Missile Development. Missile research and development: engineering, dynamics, intelligence,

instrumentation, evaluation. Combustion in jet engines. These activities are spf'nsored by theDepartment of Defense.

• Office of Basic Instrumentation • Office of Weights and Measures.

NATIONAL BUREAU OF STANDARDS REPORTNBS PROJECT NBS REPORT

1000-10-4803 August 3, 1953 2720

SURFACE TEMPERATURESWITH

THERMAL INDICATORS

by

S. M. Genenskyand

A. F. RobertsonFire Protection Section

Building Technology Division

To

Quartermaster CorpsPhiladelphia Research & Development Laboratories

U. S. Army

Requisition No. 49-106-567-53Project No. 7-12-01-001

The publication, reprii

unlesi permission Is ob

25 . D. C. Such pertr

prepared IT that age

Approved for public release by the '* p"’’’'*’'*®'*

Director of the National Institute of

Standards and Technology (NIST)

on October 9, 2015.

SURFACE TEMPERATURESWITH

THERMAL INDICATORS

by

S. M. Genensky and A. F. Robertson

Abstract

At the request of the Quartermaster Corps,analytical and numerical solutions havebeen obtained for the surface temperaturerise of homogeneous, semi-infinite solidsand similar solids with one or two finitelamina of other materials on the exposedsurface when heated by a time invariantradiant energy source. By the use of thesetwo methods of calculation it has been pos-sible to estimate the surface temperaturerise for skin and inert assemblies intendedto simulate skin when these are heated byradiant energy which is totally absorbed atthe surface. It is shown that, as a resultof their thermal properties, the temperaturerise of the Quartermaster temperature indi-cators is very different from that to beexpected of skin under similar conditions.

1, INTRODUCTION

The Quartermaster Research and Development Laboratorieshave developed thermal indicators and requested that an anal-ysis be made of the extent to which these indicators withvarious types of backing materials may be considered as simu-lating temperature changes on the surface of opaque skin whenexposed to thermal radiation.

2

This report presents some results of analytical and

numerical calculations which may be of assistance in eval-

uating the usefulness of these indicators. The calculationshave been made with the objective of estimating the maximumsurface temperature rise of homogeneous or laminated materi-als which have been exposed to a time invariant pulse ofradiant energy of one-half second duration. Calculationshave been performed with the use of thermal data furnishedby the Quartermaster Corps on various assemblies proposedas representing:

a. Human skin

b. Homogeneous skin simulants

c. Quartermaster temperatureindicator assemblies

Most of the calculations have been made by means of ananalytical solution of the problem for the case of a finitelamina in good thermal contact with a semi-infinite backing.A few additional numerical solutions have been obtained bymeans of SEAC, the National Bureau of Standards digital com-puter, for the more complex assembly of two finite lamina incontact with a semi-infinite backing.

Because of limited funds available for the work, noattempt has been made to obtain solutions for all the assem-blies proposed. The solutions for the one, two, and threebody composite systems considered have been obtained for awider range of thicknesses and thermal properties than wasrequested, in an effort to make the work more general.

2. THE PROBLEM AND WORK DONE

The work requested (1) was very broad. It included thefollowing "jobs":

1. Investigate the effect of fabric covering on thetemperature rise of skin or indicator and backingexposed beneath the fabric.

2. Calculation of surface temperature rise of skin,using the assemblies and thermal properties fur-nished.

(1) Philadelphia Quartermaster Research and Development Lab-oratories letter QMDP 4-23.112 RP

,30 March 1953? signed

by John M. Davies.

- 3 -

3. Calculation of the surface temperature rise of semi-infinite materials which have been proposed as skinsimulants.

Calculation of the surface temperature rise of avariety of temperature indicator assemblies withseveral different backing materials.

It was suggested that items 2 to ^ be calculated for an energypulse of one-half second duration. An investigation of item 1

was considered too complex in view of the funds available.Work was, therefore, confined to items 2, 3 5

and 4 .

The thermal properties used in performing the calculationsare shown in Table 1. Most of these were obtained from theQuartermaster Corps. (1)

Table 2 presents the eight different skin assemblies forwhich calculations were requested (Job 2). The manner in whichthe suggested assemblies were modified in solving for tempera-ture rise by both analytical and SEAC calculations is indicated.

Table 3 presents the thermal properties of four finitesimple slab materials and one semi-infinite composite assemblywhich have been proposed as simulating behavior of skin (Job 3 )«

For the finite specimens a number of thicknesses were proposedfor solution. However, for the half-second pulse used, all ofthese can be considered as semi-infinite at the time when surfacetemperatures are a maximum and thus one solution serves for allthicknesses requested.

Table 4 presents the fifteen different indicator mountingand assembly arrangements for which calculations were requested(Job 4 ). As a result of discussions with Quartermaster officials,it was decided to concentrate work on solution of indicatorshaving type C assembly. This table shows the manner in whichthe six-layer system was simplified. The fact that the thermalproperties of the thin surface indicator layer were differentfrom those of the backing was neglected and a constant value ofk was assumed for the next four layers; the semi-infinite back-ing representing the sixth layer completes the system.

:--V >

U > f

:\Ci r-

f.' /v * r, ;i .

• t

"i/1

,:,v

!/ tffl

•

i-!-. '^>?A/>•:

L.

I

“>.

''V

- 4 -

3.

ANALYSIS AND RESULTS

As mentioned earlier, Loth an analytical solution of a

two material composite semi-infinite body, and a numericalsolution for a three material semi-infinite slab were ob-tained. The latter made use of SEAC. All solutions weredeveloped with the following assumptions:

1. The input energy pulse is zero at time zero andequal to ^ between time zero and one-half second,after which it is again zero.

2. The materials are opaque.

3 . The thermal properties of the bodies being heatedare constants.

4 . There are no losses from the heated body to thesurroundings and all of the incident energy isabsorbed.

5. At all solid interfaces both temperature and heatflux are continuous functions of distance.

6. The bodies being heated are inert.

It was agreed that computations should be made for themaximum temperature rise at the surface of the specimen.This would occur at the end of the radiant exposure or one-half second. It was hoped that an analytical solution mightbe found or developed for the multi-layer specimens. Such asolution was not found and appeared impractical to develop forassemblies more complex than those of two materials.

The analytical solution for a finite surface layer on asemi-infinite solid was developed as follows. Consider a semi-infinite solid having a surface layer of finite thickness Bin intimate contact with the remainder of the solid. The tem-perature within the solid is considered a function of depth xand time t and may be written @(x,t). Initially the solid andsurrounding medium are assumed to be at temperature •©•(x,0) =

0 (-oo<x<oo). Further, the exposed face of the solid is subject-ed to a constant flux |) from time t>0 to t=T. the terminationof the experiment, and the temperature ^(x,t) as x tends towardinfinity is zero for all time t. The exposed solid has thermalconductivity k]_ and thermal diffusivity ^ ^ and the backing or

- 5 -

underlying layer has thermal conductivity kp and thermaldiffusivityX 2* solid interface both the tempera-ture and conductive flux are assumed continuous. Mathe-matically the problem may be expressed as follows:

39(x, t) e(x,t)

dx(0<x<B) (0<t:^T)

-k-,59(0,t)^ X =

f)(0« t;$T)

lim 9(B - x,t)x-^o

= lim 0 (B + X, t

)

X ->o( X > 0 , 0$ t^ T )

limX^o

. , d©(B+x,t)^ lim ko-— 2

X-^ 0 ^ dx (x>0, 0^ t<^T)

^©(x, t )

^t<y s(x,t)

^ 5x2(B<x<oo) (0<t^T)

lim 0 (x, t

)

x->oo-4* 0 for all t

^(x,0) = 0 ( - 00< X<00 )

and the solution of this problem, which of course assumeslinear heat flov/, may be expressed as follows:

, J -p- i

fr«-

- 6 -

0(x,t)

$

2B(n+l)-x

.

2

2B(n+l)-x . (2B{n+l)-x\— erfcf-

1 2

r ^ ^2B(n+l)+Xf

+ 2 eL t a

2B(n+l)+x / 2B ( n+1 ) +xJ

Spa ' >= J

P 2”

X_ X

»r(1)

for <0$x^B)

- 7 -

and

00

(j)0 '5

"2E^lir ®V

(2n+l)B,

x-B”h

V 1

2^

(2n+l)B x-B _,——r— + 7=_erfc

s/^ J^2*“

(2n+3)B x-B~1^

( 2n+l)B ^ x-B

\/^ .

j

2fT ^

*# 2./T

“ “

(2n+3)B x-Beffc

1 2

( (2n+3)B^x-B

j'El

\2ft

B x-B

2

Ak1

B ^ x-B

y^T 2 -

B x-B

erf c1 2 I

2/r

for (E<x<oo)

8

where 6(x,t) is the temperature, a function of position x andtime t.

This equation served as the basis upon which all analyses in-volving hand and desk calculator computations were carried out.

Since this temperature rise is directly proportional to |), amore general solution is obtained by expressing the results ofcalculations in terms of 9/(|) which for brevity we call "tempera-ture rise". These computations were restricted to ascertainingthis surface temperature rise of various homogeneous and compo-site solids exposed to the time invariant energy pulse for one-half second. It is to be emphasized that since the analyticapproach was confined to semi-infinite solids composed of atmost one finite layer in intimate contact with the rest of thesolid, the computations can at best be regarded as approximationsto the structures offered for analysis.

Further

s = and \ = m/q

where

Q

and

k-| fjL o

For an energy pulse of one-half second, the maximum tempera-ture rise occurs when x=0 and t=0.5» Substituting these valuesin equation (1) gives;

- 9 -

e(o,o.5) _

2

(n+i)B \/ 2

00 ^ J

erfo B(n+l)\f2 ^

Figures 1 to 7 and Table 5 present the results of thecalculations. An attempt has been made to furnish generalizeddata by study of a wider range of variables than was requestedfor the specific problems involved. All these figures presentthe maximum surface temperature rise one-half second after ex-posure to a constant intensity radiant energy input pulse of

|) cal/sec cm^. In these figures the symbol^ is used to desig-nate the thickness in inches of each of the individual layers.

Figures 1 through 4 and table 5 are for two materialcomposite bodies or for homogeneous materials and representthe results of the analytical solution of the problem.

Figures 5 through 7 present results of the SEAC numericalsolution of the problem for three material composite bodies.Data are presented for both surface and two subsurface inter-faces as a function of time for the duration of the one-halfsecond exposure.

It should be remembered that most solutions presentedinvolve some simplifying assumptions and in all cases where theindicator assembly has been studied the presence of the thin,translucent indicator surface film has been completely neglect-ed. This is justified because of its very small thickness andthe fact that it cannot be considered as opaque.

10

Table 5 gives surface temperature rise of various homo-geneous solids. These calculations were based upon valuesfrom Table 3*

Figure 4 is a plot of surface temperature rise ofvarious composite solids with the same surface layer andvarious high conducting backings. The surface layer ^s

10x10 ^ inches thick and has a conductivity kp= 3xl0~^cal/cm°C sec. The figure also indicates the surface temperaturerise of a homogeneous solid made of the surface material, andcontains a band which indicates the probable range in whichthe surface temperature of human skin might fall.

4. DISCUSSION OF RESULTS

Figure 1 presents the results of the analytical solutionfor simplified skin and indicator assemblies. It shows thatthe indicator assemblies cannot be expected to demonstrate thesame thermal behavior as skin even when the conductivity ofthe backing is varied over wide limits.

Figure 2 curve B shows the surprisingly constant tempera-ture rise of the surface of a composite body when the conducti-vity of the 3x10~3 in. thick surface layer is varied over widelimits.

>The kp c of the backing is maintained constant at

17»5x10” cal^/cm °C^sec. Data presented in table 5 indicatethat the probable temperature rise of skin §. is likely to be

or 2^

between the values of 20 and 35 ^ These temperaturecal

limits correspond to kpc products of about 5t and l6 cal^/cm^°C^sec for homogeneous materials.

The importance of the k^c product may be appreciated whenit is considered that:

= 2 BT (txT)k \J 'W ^

is the solution of the analytic problem presented earlier whenX = 0 ,

kj_ = k2 ,

and ^ p “ 2 '

,T .

m

',11

I

11

This may be written as:

e(Q,t)2

When t = 0.5 sec, we have

9(0,0. 5)

An examination of figure 3 leads to the conclusion thata composite semi-infinite solid with surface layer twenty ormore thousandths of an inch thick might well be considered athermally homogeneous semi-infinite solid having the conducti-vity and diffusivity of the surface material. This statementholds with reasonable accuracy for the range of conductivitiesand diffusivities found in table 1 listed under indicatormaterials. It might be argued that figure 3 was based upon acomposite semi-infinite solid with k^_> k2 and thus the con-

clusion drawn here is not necessarily applicable to the semi-infinite solids of figure 1 where, for the most part, k^< k^.

However, observe that the kpc of the surface layer of compositesolids used in constructing figure 1 are less than those usedin the construction of figure 3 and thus the equation derivedin the previous paragraph indicates that, if the semi-infinitesolid were composed solely of the outer material, the surfacetemperature of the solids of figure 1 would be higher thanthose of figure 3* This means that heat finds more resistancein the surface layers of solids of figure 1 than those of figure3 . Consequently, it is not unreasonable to expect that a twenty-thousandths inch layer of the surface materials in figure 1 maybe considered semi-infinite for the purpose of calculating surfacetemperature rise.

The data presented in figure h were obtained in an attemptto "drag down" the indicator surface temperature rise by the useof highly conductive backings. It is evident that this objectivewas not obtained because of the rather thick indicator assemblyand its low kp c product. It therefore appeared desirable toprovide an indicator backing having different thermal properties.

12

The suggested change does not appear too feasible, as theabsorbent properties of the paper appear essential for properoperation of the indicator.

Figures 5> 6, and 7 show temperature rise for three mate-rial composite bodies as obtained on SEAC by numerical methods.This method of solution provides time-temperature rise data forthe surface and two material interfaces. The solution for skin,figure 5) indicates that only the first two layers are involvedin the initial transient heating process and therefore the sur-face temperature rise at 0.5 sec is comparable with data of figure1, curve c, for a conductivity of 9xl0~^cal/cm° Csec for the back-ing. It will be observed that the SEAC solution provides a sur-face temperature rise about 20^ greater than was found by analy-tical methods.

No method is readily available for checking the accuracyof the other two SEAC solutions presented in figures 6 and 7»It is likely that the error will be considerably less than thefigure mentioned above because a finer grid was used in thesecomputations. It does, though, seem hardly likely that thealmost perfect check observed for surface temperature rise forplastic in figure 7? with the similar data for polyethylene infigure 1, represents the true condition. It is likely than anerror of or more percent is present in both figures 6 and 7»

5. CONCLUSIONS

The following conclusions appear to be justified from thework which has been accomplished:

1. An analytic solution has been obtained for the surfacetemperature rise of a two material composite semi-infinite body during heating by a time invariant radiantenergy pulse.

2. A code has been devised to permit use of SEAC forsolution of surface temperature rise when two finitelamina of different materials are placed on thesurface of a semi-infinite solid.

3» The two methods of solution have been used to calculatethe surface temperature rise of a wide variety ofhomogeneous, two layer and three layer bodies after

- 13 -

one-half second exposure to a time invariant radiantenergy which is totally absorbed at the exposed sur-face.

4. It is shown that the Quartermaster temperature indi-cator assemblies have thermal properties which pre-vent their thermal behavior from simulating that ofskin when subjected to the same thermal radiationexposure.

Thermal

Properties

of

Skin

and

Indicator

o0CO

C\Jo J- CM lolococo J-

oo IrwO loo \0\0 POCM 0-0 loco

Jt- rOlOHCX) O O CM POO-4- o oQ. a O O O O O O O O O O o oM o O O O O o o o o o o o oO O O O o o o o o o o o

OJ1—

1

cd

o

o .

• • • •

loCM lo O

CJ0 0-lr\0 lo sOMD H OCMMD PO-4-0 O 1

—1 1—

1 rH O O 1—1 O 1—It—

1

H H\ o o o o o o o o o o o o\ CM o o o o o o o o o o o oao

• • • •

1

o a O CM CJNPO C\I (—1 I—

I

0-4-a o \DsO POO PO PO-4- MD CM lo CM CMO • • • • • « e 0 0 • • •

I—

1

(1

cd

0 ooa0

00 0Cm c 0 olo0 o loCO-4- H CM CM lOlOPOOO CM PO« o_i O O O H O O O O O O O O

a O O O O O O O O O O O Oa CJ O O O O o o o o o o O Oo \ • • • • 0 •

f-i 1—

1

cd

o

o

ootuO

I—

I

Oj

o

00 O-ItnONN.

0-0 l-O0-lr\H loj- ^OU^

POa 0 POlo CM 1—1 t—

1

o CO 00 OCO I 1 00 CO ONJ- O CJN lovoo • 9 9 • cd • 9

tiD •H 1

1 1

—1

p0 0-p o S4

cd cd 00 S p (—

1

I 1

1

—1 •H O pq 0 0

cd a P -p > S4 4:J

•H p 0 0 o cd (4 •H -P •H C\j

0 •H 1—

1

-p o o 0 P 0 Oh O<4 0 o a o cd •H -p 0 0 0•H -p •H Ih -P 0 o p xl Pk Phi—

1

O-14 cd Ph 0 cd 4 •H <4 cd Td Cd cd O Oca S pq Q S M o EH P-i P-t ^

atu

•Ha,

Table 2.

Some of the Suggested Calculations of Skin Temperaturesand Manner in which Assemblies were Changed

for Actual Calculations

Item NumberProposed As Calculated

Thickness k Thickness k

1

in.

3x10"^8080

160

cgs

5x10”^94

11

in,

3x10“^00

cgs

5x10"^9

K a) SeacSolution

3x10"^8080

160

5x10“^94

11

3x10“3

8000

5x10"^94

2 3x10-3808000

5x10-494

11

3x10~300

5x10“4

9

3 3xl0~^808000

5x10"^254

11

3x10"300

5xio""*-

25

4 3x10"3808000

5x10"^251011

3x10"300

5x10"^25

5 3x10“^808000

-45x10

^

251025

3x10"^00

-45x10

^

25

6 3x10"^8080oo

10x10"^251025

3x10'300

10x10"^25

7 3x10-3408000

5x10"^

11

40x10"3oo

9x10"^4

8 3x10-38o

5x10-^ 80x10-300

9x10-^4

••' #>

'i

I 'I

4

I'.V-

ms'-'*' aT,S»

‘..'.iiJrli-h

,. '.y:

>v;f,

',v,.

''AK?'A*3P

'

v:^A"f5

Table

rr)

m

cd

I—

I

::i

a•Hca

a•H

ca

w:=5

o0

•H-PCd

I—

I

oI—

I

cd

onzi

0-P00txO

to

ca

p0

00fd

Ha

a

0;=s

o•H

•H

pq

000

o•HPdEH

0sd

0UAH p

>> 0Pd >p> o0

r—

I

oOh

oo;s

0fd

•HOh

C\J

Ed Ed

CO vO *H CO rO-Ho 1 1 O 1 1

.o I

—

1 OMD O O O J-o Er\ O O O P O ON

II II II II II II II II

Ho •

P P CMo o •

Qh 0'H

iLi ^

cjPdPii P dij p

COO «

O oo p• • \o

O Etn

II II• •

Psj o

0 p 0bO 0 Ed

O > 0 COa 1

—1 O

o p O POd o Pd O Ei^

p CO p • •

p 0o 0 >s II II

p 0 r—

1

Pd O dsj o0 o PEd Ed

o •H

OJ

•H

0

TdP 00 0Od p

pi

P> tyOd^0 *H 0

Cp0 P0+0 00 0 Phpi 0txopp

SO’

0Pi 0o P Ed

Ed -H0tuO*H 0

H cd PiP P0 Od O> ^ P*

POO CN-

nbd O

COooO [>-

Psj oQc

MDO

\0O

vDO

ETnP Eca

Eta

Er\

P Er\ Moritz

&

Henriques

i

\

i

'!

i

uao oj

lr> oo 8• •

p 1r\

W3 O CMs=! ph O O ^•H o o 8-P 9 •

d •

P sH

o •Hs

•N

u Wo Pp> P Cr\

cci O (Mo P r>~ O O vOph•H PI o o o J-

d • • •

P Cm• M O

phP m

(D O in

H Cm prP sq

cd P M lc> PH P o O CM >

O •H CM O O -H•H O O in

P> EH . • • Pcd

1—

1

'PP <do O

1—

1

Pp 1—

1

-po m •H

i:a :s

p O CM(U o \

1 O O Pp> O O 1-rN CD

m p • • • pCD p PWD o PhtxD

P p PCO o o

1—

1

1—

1

p p•H HP PP PP> -PP Ps ^ P s

p pp p p p> Pi—1

1—

1

•rH O PP -Hp> P ^ P>o P P P’ oOOP <c!

•H rPTd P H o

• p p o p .

M o a. !s pq

CM J- CM H CMO O O O OO O O O OMh

llH

Oxf- CM H CMO o o o o^o j-O O O O O OM-

IPs

CMJ- CM O J- CM H CMO O O O O O O OO O O Ua O O O O O

« « • •

PO l>-

P O CMP, o oP o oEH • o

lr\ POPh CM > O J- CM H CMO O O •H O O O O OO O O lr\ in O O O O O EcH

c • • • pxdTd

<y~) CO fcuO

o o pXJ o o •Hp> o o•H o e o

1-!^ EP. pO J- CM O ^4- CM H CM^ pqo o o p O O O O OO O O Ec\ p O O O O O Es^ p

• • • • Ph •Hp(X

p po p

fXrH pP P-.

•Hp pp oH>P p

P S p oP P -p

P P p p?H 1—

1

> P 1—

(

oO P t>» *H O p p >> •Hp> > ^ 4-> -P > > ^ X!P -H P> O P •H -H -P pO p P P o P P P P M•H p P >^Pd •H P P P P ^^TdT3( H O T5 fXXl P^x! H OP P Td O O • P p Td P xd o o o

M O, <aj (X, IS O 1—i P-i <ij EH Ph S Q

CM J- rnO OMDO O O

O roO OMDO O O

Ph

O-Pcti

O Ph Q)

•H 0) O Tli

cd Oaj Ph O

M a, CO ^

Table 5*

Surface Temperature Riseof

Various Homogeneous Semi-Infinite SolidsReference Table 2

Solid k pc Temperature Rise

cal/sec cm°C cal/cm-^° C °C sec cm2/cal

* 25x10"^

0.7 19.1

** 8 0.7 33.7

Polyethylene 8 0.5 39.5

Wood 3 0.2 103.0

€

T

* QM guess at Hardy's best figures for skinAverage of Moritz & Henriques ' figures for skin

j

I

I- ^

rm

]

1

i

r

1

/•"

C.

SK

CH

soKFACE

~rEMPeE^oe^

ei$

\

c^w

—r~

jR—1—1

'1 1

I is

EBJlL^l iH-rnf

'!I

!'

_L

! I

J-I _1

rr^

.4 .. 1 .

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THE NATIONAL BUREAU OF STANDARDS

Functions and Activities

The functions of the National Bureau of Standards are set forth in the Act of Congress, March

3, 1901, as amended by Congress in Public Law 619, 1950. These include the development and

maintenance of the national standards of measurement and the provision of means and methods

for making measurements consistent with these standards; the determination of physical constants

and properties of materials; the development of methods and instruments for testing materials,

devices, and structures; advisory services to Government Agencies on scientific and technical

problems; invention and development of devices to serve special needs of the Government; and the

development of standard practices, codes, and specifications. The work includes basic and applied

research, development, engineering, instrumentation, testing, evaluation, calibration services, and

various consultation and information services. A major portion of the Bureau’s work is performed

for other Government Agencies, particularly the Department of Defense and the Atomic Energy

Commission. The scope of activities is suggested by the listing of divisions and sections on the

inside of the front cover.

Reports andi Publications

The results of the Bureau’s work take the form of either actual equipment and devices or

published papers and reports. Reports are issued to the sponsoring agency of a particular project

or program. Published papers appear either in the Bureau’s own series of publications or in the

journals of professional and scientific societies. The Bureau itself publishes three monthly peri-

odicals, available from the Government Printing Office: The Journal of Research, which presents

complete papers reporting technical investigations; the Technical News Bulletin, which presents

summary and preliminary reports on work in progress; and Basic Radio Propagation Predictions,

which provides data for determining the best frequencies to use for radio communications throughout

the world. There are also five series of nonperiodical publications: The Applied Mathematics

Series, Circulars, Handbooks, Building Materials and Structures Reports, and Miscellaneous

Publications.

Information on the Bureau’s publications can be found in NBS Circular 460, Publications of

the National Bureau of Standards ($1.00). Information on calibration services and fees can be

found in NBS Circular 483, Testing by the National Bureau of Standards (25 cents). Both are

available from the Government Printing Office. Inquiries regarding the Bureau’s reports and

publications should be addressed to the Office of Scientific Publications, National Bureau of Stand-

ards, Washington 25, D. C.

V-

NBS