ORNL-4831 by Jon Morrow

/ti

HOME

ORNL-4831

HELP

DEVELOPMENT OF THE VARIABLE-GAP TECHNIQUE FOR MEASURING THE THERMAL CONDUCTIVITY

OF FLUORIDE SALT MIXTURES J. W. C o o k e

. .

Printed in the United States of America. Available from National Technical Information Service US. Department of Commerce 5285 Port Royal Road, Springfield, Virginia 22151 Price: Printed Copy $3.00;Microfiche $0.95 This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights.

ORNL-4831 uc-80 -Reactor Technology Contract No. W-7405-eng 26

React o r Divis ion

DEVELOPMENT OF THE VARIABLE-GAP TECHNIQUE FOR MEASURING THE THEBMAL CONDUCTIVITY OF FLUORIDE SALT MIXTURES J. W. Cooke

FEBRUARY 1973 NOTICE This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, subcontractorl, or their employees, makea m y warranty, express or implied, or assumes any legal UsMitr or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed. or representa that Its use would not infringe privately owned rights.

OAK RIDGE NA,TIOJ!IAL LABORATORY Oak Ridge, Tennessee 37830 operated by UNION CARBIDE CORPORATION for the U.S. ATOMIC ENERGY COMMISSION

iii

CONTENTS

. Page

.... ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . .... . 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . .... 2 . METHODS FOR MEASURING MOLTEN-SALT TJXERMAL CONDUCTIVITBS . . . . Selected Techniques for Fluids . . . . . . . . . . . . . . . . . NOMENCLATURE

c 0

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

Transient hot wire

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

..................... ................ . . . . . . . . . . . . . . . . .. . . . Parallel wall . . . . . . . . . . . . . . . . . . . . . . . The Variable-Gap Technique . . . . . . . . . . . . . . . . . . . General description . . . . . . . . . . . . . . . . . . . . Idealized model . . . . . . . . . . . . . . . . . . . . . . Effect of radiation . . . . . . . . . . . . . . . . . . . . Effect of natural convection . . . . . . . . . . . . . . . . Transient hot foil Necked-down sample technique Laminar heat flow

Effect of heat shunting Method of calculation MpERIMENTcu;Al?PmTus

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

................... 3. ..................... Thermal Conductivity Cell . . . . . . . . . . . . . . . . . . . Furnace . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electrical System . . . . . . . . . . . . . . . . . . . . . . .

........................ 4. EXPERIMENTCIl-IPROCEDmS . . . . . . . . . . . . . . . . . . . . Instrumentation

..................... Operating Procedure -Fluid Specimen . . . . . . . . . . . . . . Operating Procedure - Solid Specimen . . . . . . . . . . . . . . 5 . IXPERIMENTALRESULTS . . . . . . . . . . . . . . . . . . . . . . Thermal Resistance Curves . . . . . . . . . . . . . . . . . . . Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . Preliminary Procedures

1 1 2

3 3 4 4

5 5

6 6 7 9 12

16 19 22 22 30 30 32

33 33 34 34

35 40

................... Comparison with Published Values . . . . . . . . . . . . . . . .

DISCUSSION OF THE RESULTS

..................... .................. Adequacy of the Experimental Apparatus . . . . . . . . . . . . . 7. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . ACKN0WL;EDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . APPENDIX A . ADDITIONAL DETAILS OF THE DESIGN OF THE APPARATUS . . . APPENDIXB . EXPERMENTALIZATA. . . . . . . . . . . . . . . . . . . . APPENDIX C . PRECISION AND ERROR ANALYSIS . . . . . . . . . . . . . Comparison with Theory Uncertainties in the Results

40 40 42 43 44

45 45 46 51 55 99

NOMENCLATURE C P

("c)-'

Specific heat, constant pressure, c a l g"

diameter of main heater assembly, cm

r a t i o of e f f e c t i v e t o t o t a l heater wire length

heat shunting f a c t o r

Guard heater f a c t o r

â&#x201A;Ź3

Acceleration due t o gravity, cm sec-"

h r

Radiant heat-transfer coefficient, W

Current, amps

Thermal conductivity of specimen, km i s that of the metal c y l i n d r i c a l s o l i d , W ern" ("C)-'

("C)-l

-n

Mean index of r e f r a c t i o n

Heat flux, W

&'/A

Measured heat f l u x uncorrected f o r heat shunting, W em-'

Radius of c y l i n d r i c a l s o l i d , cm

Temperature, "C; TK =

Temperature difference between upper and lower p l a t e s of t h e conductivity c e l l , "C

O K

Thermal resistance a t zero specimen thickness, "C U

Heat-transfer c o e f f i c i e n t , W

voltage, v o l t s

Integration variable

x, Ax

Specimen or gap thickness, cm

Radiative function defined i n Eq. (8)

("C)-'

Coefficient of l i n e a r expans ion, ( OC)-' Coefficient of bulk expansion, ("C)-l Emissivity of cylinder surface mean absorption coefficient for radiant heat, em-' Viscosity, CP Density, g Stefan-Bolt zmnn constant

, W cme2 (

Optical thickness E l e c t r i c a l resistance, ohms

W1 cn?

Dimensionless Moduli Grashof number, g.$B KT x"/g,

NGr NPr NRa

Prandtl number, C p/k P Rayleigh number, NGr "Pr Reynblds number, pVD/p

Subscripts

film

critical

metal

at specimen thickness = 0 specimen

at specimen thickness = x

DEVELOPMET" OF THE VARIABLE-GAP TECHNIQUE FOR MEASURING THE THEFWAL CONDETrVITY OF FLUORIDE SALT MIXTURFS J. W. Cooke r

ABSTRACT The development and evaluation of the variable-gap technique for measuring the thermal conductivity of molten f l u o r i d e salts i s described. A s e r i e s of measurements were made of t h e conductivities of several substances (Ar, He, HzO, Hg, and l i q u i d and s o l i d heat-transfer s a l t ) over a wide range of conductivities W cm-l ( O C ) - ' ] and temperatures (40 t o [0.4 X loe3 t o 100 X 950째C). The deviations of the r e s u l t s from published values averaged +5$. The study demonstrates the accuracy and outstanding v e r s a t i l i t y of t h e variable-gap technique. Key words: thermal conductivity, development, design, measurement, fused salts, high temperature, MSBR.

1. INTRODUCTION

High-temperature operations i n the chemical processing and nuclear

industries have created a need for economical, e f f i c i e n t heat-transfer media whose thermal properties a r e superior t o those of organic and gaseous coolants.

Molten-salt mixtures have good heat-transfer prop-

e r t i e s compared with organic liquids, and t h e i r r e l a t i v e inertness and low vapor pressure give them d i s t i n c t advantages over l i q u i d metals. They a r e applied i n high-temperature fluxes, heat-treatment baths, and e l e c t r o l y t i c m e 1 c e l l s , and as t h e f u e l c a r r i e r and coolant for nuclear reactors, such as the Molten-Salt Breeder Reactor (MSBR) experiments

This report describes an experimental technique for determining a key thermal property of molten salts

- thermal

conductivity.

The study

evaluates t h e method over a broad temperature range using a v a r i e t y of materials representing a wide range of conductivities. Very few data on t h e thermal conductivities of molten salts, i n p a r t i c u l a r , fluoride salts, have been published. c

Most of the e x i s t i n g

measurements f o r molten fluoride s a l t mixtures were m d e by members of the

MSm

group a t Oak Ridge National Laboratory ( O m ) over 1 5 years 1

2 ago.2

To extend t h e scope of the previous measurements, we have developed

a n absolute, variable-gap technique t o determine t h e thermal conductivity

of f l u o r i d e salt mixtures i n l i q u i d and s o l i d s t a t e s a t temperatures t o -&is

technique is p a r t i c u l a r l y well s u i t e d t o t h e measurement of

the conductivity of low-conducting,

semitransparent f l u i d s t h a t must be

contained i n i n e r t surroundings a t elevated temperatures.

Most other

applicable methods s u f f e r from one o r more deficiencies if used under these conditibns. The variable-gap technique is examined i n d e t a i l and other techniques a r e discussed b r i e f l y .

The development of an experimental apparatus i s

described, and experimental r e s u l t s a r e presented f o r t h e conductivities of several c a l i b r a t i n g f l u i d s : Hg.

A r , He, heat-transfer salt

(RTS), HzO, and These f l u i d s represent a very wide range of conductivities C0.4 X low3

W cm-’ (OC)-l 1 which were measured over a l a r g e temperature to’100 X range (40 t o 950°C). The thermal conductivities of molten f l u o r i d e salts

w i l l be presented i n a separate report t o be published. 2. METHODS FOR MEASURING MOLTEN-SALT

THERMAL CONDUCTIVITIES

Thermal conductivity is one of t h e most d i f f i c u l t of a l l thermophysical properties t o determine experimentally.

The d i f f i c u l t i e s

primarily a r e due t o the u n r e l i a b i l i t y of temperature measurements, t h e inadequacy of thermal insulation, and t h e simultaneous transfer of heat by mechanisms other than conduction.

Conductivity can be measured by

e i t h e r steady-state,quasi-steady-state, or t r a n s i e n t - s t a t e heat flow systems.

Experimental determinations using t h e steady-state methods

depend upon the attainment of s u i t a b l e boundary conditions that w i l l allow the Laplace equation t o be solved f o r the temperature d i s t r i b u t i o n .

The

conductivity is then calculated from the Fourier heat-transfer equation. The t r a n s i e n t method requires the s o l u t i o n of the d i f f u s i o n equation with s u i t a b l e i n i t i a l and boundary conditions f o r the thermal d i f f u s i v i t y coe f f i c i e n t ; t h e density and heat capacity must be known t o c a l c u l a t e t h e conductivity.

*KNOs-NaN%

The quasi-steady-state methods a r e based on a s o l u t i o n of i

-NaN03 (44-49-7 mole

4).

t h e diffusion equation f o r unique i n i t i a l and boundary conditions such that t h e thermal conductivity can be d i r e c t l y determined.

I n a d d i t i o n t o conduction, r a d i a t i o n a l s o may be present w i t h transparent substances, and t h e experimental technique must be capable of i d e n t i f y i n g and separating these two mechanisms. convection may a l s o be present.

I n t h e case of f l u i d s ,

Thus, only a l i m i t e d nuniber of experi-

mental techniques are a v a i l a b l e f o r t h e determination of t h e conductivity

of f l u i d s . Several techniques found i n published investigations a r e described b r i e f l y i n t h e following section, and t h e technique used i n t h e present s t u d i e s i s described i n a l a t e r s e c t i o n . Selected Techniques f o r Fluids We w i l l describe b r i e f l y each technique and discuss i t s advantages and disadvantages f o r t h e measurement of conductivity of molten salts. Transient hot w i r e I n t h i s technique, t h e r a t e of change of temperature of a l i n e heat source s i t u a t e d i n an i n f i n i t e medium is used t o determine t h e conduct i v i t y of t h e medium.

The l i n e heat source c o n s i s t s of a wire (1 t o 5

m i l s diam) placed a x i a l l y i n a cylinder (2 t o 4 cm diam) f i l l e d w i t h t h e specimen.

The wire is heated by a steady current, and i t s temperature

i s determined by t h e change i n i t s e l e c t r i c a l r e s i s t i v i t y .

After a n

i n i t i a l t r a n s i e n t heating period, t h e log temperature becomes a l i n e a r function of time u n t i l n a t u r a l convection begins t o occur.

The

slope of t h i s l i n e a r function of temperature w i t h t i m e can be r e l a t e d d i r e c t l y t o t h e conductivity of t h e specimen.

Thus, t h i s technique is

a quasi-steady-state technique r a t h e r than a t r a n s i e n t technique.

It i s

a common technique f o r determining conductivity of l i q u i d s and has been described i n m n y publications .3-5 Its s i m p l i c i t y , quickness, precision, and accuracy make t h i s tech-

nique u s e f i l f o r most l i q u i d s .

With molten salts, however, a s i g n i f i c a n t

amount of current can be shunted through t h e s a l t i t s e l f due t o t h e r e l a t i v e l y high e l e c t r i c a l conductivity of t h e molten salts a t elevated temperatures.

Since t h e degree of current shunting is very d i f f i c u l t t o

4 predict, molten Salt conductivity r e s u l t s obtained by t h i s technique

81-8

subject t o questions which have not been s u f f i c i e n t l y resolved t o make

it s u i t a b l e f o r t h i s application. 6 Transient hot f o i l This technique7'* i s similar t o t h e t r a n s i e n t hot-wire technique except i n two respects:

(1) a t h i n f o i l i s s u b s t i t u t e d f o r t h e f i n e wire

t o provide a plane heat source instead of a l i n e source, and (2) the temperature is measured w i t h a front-wave-shearing l a s e r interferometer. Because t h i s temperature measuring technique is extremenly s e n s i t i v e , the heat f l u x f r o m t h e f o i l can be g r e a t l y reduced.

However, t h e f l u i d speci-

men must be transparent as well as compatible with the material used i n the c e l l window. The t r a n s i e n t h o t - f o i l method is more d i f f i c u l t t o apply than the t r a n s i e n t hot-wire technique.

Its primary advantage is i n t h e reduction

i n t h e molten-salt ionization that r e s u l t s from a lower voltage along t h e heat source.

Consequently, the interface between the heated f o i l and the

molten s a l t remains polarized and the flow of current i n t o t h e s a l t i s minimized.

I n practice, however, other voltage p o t e n t i a l s may e x i s t

within the c e l l , and some current w i l l flow i n t o the salt even though the surfaces a r e polarized.

Moreover, operation a t elevated temperatures

presents formidable problems i n the design and choice of materials f o r t h e c e l l windows.

Diamond i s the only transparent material s u i t a b l e f o r use

w i t h molten f l u o r i d e salts a t high temperatures, but i t s high c o s t and

f a b r i c a t i o n d i f f i c u l t i e s would r e s t r i c t i t s use t o very small apertures. Necked-down samDle techniaue This method'

i s based on t h e measurement of t h e steady-state change

i n resistance caused by e l e c t r i c a l heating of a narrow bridge of the sample material which joins two l a r g e r bodies of t h e same material.

The

theory describing t h i s phenomenon shows t h a t the change i n r e s i s t a n c e expressed by the voltage drop caused by the heating current does not depend on the d e t a i l e d shape of the narrow region.

A necessary condition,

i f t h i s is t o be t r u e , i s t h a t no s i g n i f i c a n t flow of heat occur outside

of the boundaries of t h e sample.

For l i q u i d s , t h e narrow bridge is

5 maintained by containing t h e l i q u i d i n a v e s s e l separated i n t o two parts by a t h i n wall with a small aperture.

The m a t e r i a l of t h e wall must have

both a high thermal and a high e l e c t r i c a l r e s i s t a n c e .

The technique is

c l a s s i f ied as a quas i-steady-state method. Several u n c e r t a i n t i e s are associated w i t h t h e method, t h e first of which i s t h e loss of heat by conduction along t h e t h i n separating w a l l .

A second major problem a r i s e s f r o m t h e p o s s i b i l i t y of convection.

More-

over, with molten salts t h e p o s s i b i l i t y of p o l a r i z a t i o n e f f e c t s a l s o would need t o be considered.

The important advantages of the technique

a r e t h e s i m p l i c i t y of the apparatus, t h e r a p i d i t y with which t h e measurements can be made, and t h e reduction i n t h e u n c e r t a i n t i e s i n r a d i a t i o n by t h e small s i z e of t h e heated region. Laminar heat flow The l a m i n a r flow method determines t h e conductivity of a f l u i d flowing i n a c i r c u l a r tube under c a r e f u l l y defined conditions.

The wall

temperature of t h e tube is maintained uniform while t h e i n l e t and o u t l e t temperatures of t h e f l u i d are measured.

I n t h i s method, r a d i a t i o n losses

can be neglected and t h e troublesome measurement of heat flux eliminated. The main problems concern t h e p r e d i c t i o n of v e l o c i t y and temperature p r o f i l e s of the f l u i d a t t h e entrance s e c t i o n of t h e tube and maintaining

a uniform wall temperature.

Furthermore, t h e assumption of constant

physical properties of t h e f l u i d over t h e temperature range can i n t r o duce s i g n i f i c a n t e r r o r .

Most of t h e published r e s u l t s of t h i s technique

d i f f e r from t h e accepted values f o r thermal conductivity because the hydrodynamic and thermal e n t r y lengths were not properly assessed .lo P a r a l l e l wall With t h i s method, t h e steady heat flow through t h e specimen and t h e

temperature drop across it are measured .ll

-â&#x20AC;&#x2122;

The specimen i s contained

between two parallel walls of plane, c y l i n d r i c a l , or s p h e r i c a l geometry. This method is t h e most commonly used technique f o r measuring thermal

conductivity.

I t s s i m p l i c i t y w i t h regard t o t h e a n a l y t i c model and

experimental setup make it most a t t r a c t i v e ; however, t h e u n c e r t a i n t i e s caused by convection, radiation, and s t r a y heat flow a t high temperatures

6 can be considerable.

Reducing the heat flow u n c e r t a i n t i e s by decreasing

the specimen thickness and temperature drop can lead t o large e r r o r s i n these two measurements as well as i n the heat flow:

Thus, although the

method is simple, it requires care i n application and may be unsuitable

f o r low-thermal conductivity f l u i d s a t high temperatures .I2 The Variable-Gap Technique The variable-gap technique f o r measuring conductivity is a s i g n i f i CSnt

tmprovement over the p a r a l l e l wall method i n that it takes advantage

of the f l u i d i t y of the specimen.

By use of t h i s technique t h e specimen

thickness can be varied continuously during t h e operation with a m i n i m disturbance t o the specimen composition o r t o t h e system temperature d i s tribution.

Also by varying the specimen thickness, the undesirable e f f e c t s

of several factors, including the e r r o r s caused by specimen voids o r inhomogeneities, n a t u r a l convection, r a d i a t i v e heat t r a n s f e r , corrosion, I ~

deposit formation, radial heat flow, thermocouple location, and thermo-

I I ~

couple d r i f t , can be g r e a t l y reduced. Since only the change i n the specimen thickness and t h e change i n t h e temperature across t h e specimen i s measured, the p o t e n t i a l e r r o r s of these measurements a r e smaller and the influence of convection, radiation, and heat losses can be detected and minimized.

In.addition, t h e apparatus can be used w i t h l i t t l e o r no modi-

f i c a t i o n t o measure the conductivities of s o l i d s and gases as well as I

liquids.

Considering t h e advantages of the method, it i s s u r p r i s i n g t h a t

only limited use has been m d e of the variable-gap technique.12'14

'I5

General description The experimental apparatus i s shown schematically i n Fig. 1. Heat from t h e main heater t r a v e l s downward through the l i q u i d sample region (labeled "variable gap" i n t h e f i g u r e ) t o a heat sink. upward and radial

Heat flow i n t h e

directions is minimized by appropriately located guard

heaters, and t h e heat flux i n t o the sample i s measured by t h e voltage and current of the dc power t o the m i n heater.

The temperature drop across

the gap is determined by thermocouples located on the a x i a l center l i n e i n the metal surfaces defining t h e sample region. The sample thickness is varied by moving the assembly containing the main heater and i s measured

7 ORNL- DWG 72- 40523R

/AIR

SPACE

GUARD HEATERS

MAIN HEATER VARIABLE GAP 'HEAT

SINK

x =THERMOCOUPLE LOCATIONS

Fig. 1. Schematic drawing of a variablF-gap thermal conductivity cell.

by a precision d i a l indicator.

The system temperature l e v e l i s main-

tained by a surrounding zone-controlled furnace. Idealized model The measured temperature difference can be resolved i n t o the tempera t u r e drop across the sample gap; the temperature drops i n the metal walls defining the t e s t region; the temperature drops i n any s o l i d or gaseous films adhering t o t h e metal surfaces; and e r r o r s associated w i t h thermo-

couple c a l i b r a t i o n , lead-wire inhomogeneities i n thermal gradient regions, and instrument malfunctions.

Neglecting the e r r o r term, we can write

m = m s + m m + m f,

(1)

where subscripts a r e sample, metal, and surface f i l m , respectively.

For t h e sample region, the temperature difference i s

ms = (Q/A)

hs/ks

(2)

where Q/A i s the heat flux, Axs i s t h e gap width, and ks i s t h e t h e m 1 conductivity of the l i q u i d sample.

It i s assumed that no n a t u r a l convec-

t i o n e x i s t s i n t h e sample region. Similarly, t h e temperature drop i n the confining horizontal metal walls can be w r i t t e n

8 where Axm i s t h e heat-flow path length i n t h e metal w a l l s , and km i s w a l l conductivity.

The heat f l u x Q/A i s t h e same as i n Eq. (2), assuming

t h a t no radial heat flow and no bypass heat flow through t h e s i d e ( v e r t i -

Since k is a function of temperature, m Eq. (3) can be w r i t t e n s e p a r a t e l y f o r t h e upper and lower metal walls; however, f o r t h e purposes of t h i s analysis, t h e two regions are combined.

c a l ) walls of t h e sample cup.

The f i l m temperature difference i s o f t h e same form as t h e AT'S given

i n Eqs (2) and (3). If surface f i l m s are present b u t of constant and known thickness, Axf, during t h e experiment, t h e r e i s no e f f e c t on t h e derived sample conductivity or on the associated e r r o r .

However, a f i l m

that grows o r decays i n a n unknown way during t h e course of t h e measure-

ment introduces a n error i n Axs. Combining t h e above expressions, we obtain:

or &I

-(i) +(?2)

-Q/A

Axs

(4)

or, simplifying t h e notation,

where [LXT/(Q/A)~]

combines a l l t h e fixed r e s i s t a n c e s .

T h i s is of t h e

form, y

(6)

where a i s t h e slope of t h i s l i n e a r expression and is t h e r e c i p r o c a l of t h e sample conductivity.

The i n t e r c e p t b combines a l l o t h e r r e s i s t a n c e s .

I n operating t h e apparatus, Q/A is kept constant and LS!~i s recorded as & i s varied.

If other modes and paths of heat t r a n s f e r e x i s t within t h e

t h e specimen, t h e thermal r e s i s t a n c e w i l l not be a l i n e a r function of t h e

9 specimen thickness.

However, t h e e f f e c t of these other forms of heat

t r a n s f e r w i l l be reduced as t h e specimen thickness i s decreased.

Thus,

t h e conductivity can be determined from t h e reciprocal slope evaluated a t zero specimen thickness. Another approach t o t h e determination of the sample conductivity can be obtained by rearranging Eq. (6) as: 1

(7)

k=-=-. a y-b

Again, if other modes and paths of heat t r a n s f e r e x i s t within t h e specimen, t h e value of conductivity obtained from Eq. (7) w i l l be t h e e f f e c t i v e value which w i l l approach t h e t r u e value only as t h e specimen thickness approaches zero. E f f e c t of r a d i a t i o n Many investigators consider only t h e r a d i a t i o n emitted by t h e w a l l surfaces when evaluating t h e heat t r a n s f e r through a medium separating t h e walls.

This assumption m y be c o r r e c t when t h e medium is a gas whose mean

absorption c o e f f i c i e n t

i s small and whose mean r e f r a c t i o n index

near unity.

Many media, however, absorb and emit s i g n i f i c a n t amounts of

radiation.

This i n t e r n a l r a d i a t i o n can contribute more t o the heat t r a n s -

f e r from wall t o w a l l than t h e r a d i a t i o n emitted by t h e w a l l surfaces. Indeed, even a t room temperature, t h e heat transferred by r a d i a t i o n can approach 5% of that t r a n s f e r r e d by conduction i n some organic f l u i d s whose specimen thickness i s as small as 0.1 cm. If some simplifying assumptions a r e made, an expression for t h e

radiant heat t r a n s f e r can be derived.

These assumptions are t h e existence

of a constant temperature gradient within the medium and t h e use of mean values

E and

independent of wavelength.

The following'equation was

derived by Poltz16*17 for t h e radiant heat flux:

where y = 1 - -

3 ( 2 - 4

J-

1 0

- exp (1 -

[-(T/v)] v3 dv

exp [-(T/v)] c

and 7 =

o p t i c a l thickness of t h e medium =

-K&,

T = average medium temperature, OK, s = emissivity of the w a l l surface, (T

= Stefan-Boltzmnn constant,

5.71 X 10-1 W cm-2 (

v = dummy i n t e g r a t i o n variable.

I n Fig. 2, where Y i s p l o t t e d as a function of T for various values of E, t h e curve for c = 0 represents t h e hypothetical case i n which t h e r a d i a t i o n heat t r a n s f e r between t h e walls i s accomplished s o l e l y by t h e inner r a d i a t i o n within t h e medium. E

The distance between t h e curve f o r

= 0 and one of t h e upper curves (the appropriate plate emissivity

ORNL- DWG 72- 10524

0.6

I-

o z

1-0.4

0.2

n "

0.2

0.5

T IOPTICAL THICKNESS

Fig. 2. Radiative f'unction (Y) vs p l a t e emittance and o p t i c a l thickness of t h e specimen.

curve) represents t h e contribution of t h e r a d i a t i o n emitted by t h e w a l l surfaces t o t h e t o t a l radiated heat flow from wall t o w a l l . Equation (8) can be combined with t h e previously derived Eq. (5) t o obtain a n expression f o r t h e t o t a l thermal r e s i s t a n c e across a medium separated by two p a r a l l e l walls when t h e heat i s being t r a n s f e r r e d simultaneously by conduction and r a d i a t i o n .

That is,

I n t h e l i m i t i n g case where t h e o p t i c a l thickness

approaches zero ( i . e . ,

very small infrared-absorbing medium),

3 YTK, = 4 er where

Pl;(

., .> 1

(Ref. 16)

-l

€

2 - €

for

Thus, Eq. ( 9 ) s i m p l i f i e s t o

Figure 3 i s a p l o t of t h e thermal r e s i s t a n c e as a function of specimen thickness f o r various values of t h e a b s o r p t i v i t y c o e f f i c i e n t f o r a -n = 1.5, cmll = 0.5, specimen assumed t o have a k = 0.0034 W cm-I ("C)-', and T = 1000°C. For t h e s e values of conductivity and temperature, t h e percentage of heat t r a n s f e r r e d by r a d i a t i o n i s q u i t e l a r g e . absorption c o e f f i c i e n t ; Idecreases from ; I=

(13

(pure conduction) t o

t h e percentage of radiated heat increases t o a maximum a t about decreases u n t i l

IC =

Within t h e i n t e r v a l

As t h e

;;= 0,

;;= 2

and

> 0 these curves have

ORNL DWG 72- 40525

64 I

0.05

0.10

0.30

0.35

A a

0 0

0.45

0.20

0.25

0.40

SPECIMEN THICKNESS (cm)

Fig. 3. Thermal resistance of a n i n f r a r e d absorbing f l u i d having assumed properties at various values Of absorptivity, K (cm-') vs specimen thickness.

. an i n f l e c t i o n point producing w h a t could be described as "lazy S" curves.

Also shown i n Fig. 3 is the resistance curve for a gas whose absorptivity i s near zero and whose index of r e f r a c t i o n i s near one.

If t h e o p t i c a l

properties of a specimen a r e known, Eq. ( 9 ) can be f i t t e d t o t h e experimental data t o obtain the slope (and thus the conductivity) a t a specimen thickness approaching zero; however, the mean o p t i c a l properties must be used and the temperature gradient within t h e specimen must be nearly linear. Effect of natural convection Under i d e a l conditions, no natural convection would be expected i n a f l u i d enclosed between two horizontal, p a r a l l e l p l a t e s with one-dimensional downward heat flow.

I n t h e r e a l s i t u a t i o n , however, smll departures from

t h e i d e a l conditions can i n i t i a t e and s u s t a i n convection currents within the f l u i d .

If t h e p l a t e s a r e not horizontal o r p a r a l l e l o r i f a tempera-

t u r e gradient e x i s t s i n t h e horizontal direction, convection c e l l s can

If, i n addition, the v e r t i c a l temperature d i s t r i b u t i o n within t h e

occur.

specimen is not l i n e a r , b u t d i s t o r t e d by i n t e r f l u i d i n f r a r e d absorption, t h e natural convection can be enhanced.

Finally, vibrations, e s p e c i a l l y

those i n resonance w i t h the n a t u r a l frequency of t h e enclosed f l u i d , can induce and enhance n a t u r a l convection. I n order t o i n i t i a t e and s u s t a i n buoyancy convection c e l l s within enclosed spaces, c e r t a i n i n s t a b i l i t y c r i t e r i a must be satisfied.

Rayleigh

w a s one of the f i r s t investigators t o recognize t h a t t h e i n s t a b i l i t y

c r i t e r i o n could be r e l a t e d t o c e r t a i n l i m i t i n g values of t h e dimensionless moduli NRa known as t h e Rayleigh number, which i s

NRa = NGr NPr

)(e)

gp2B AT Ax3 gc 1-I

1-I

where g

= local a c c e l e r a t i o n due t o g r a v i t y ,

Cm/SeC2

gc = dimensional constant = 1.0 g c m dyne'1*sec'2, p

= density of f l u i d , g/cm3,

= v i s c o s i t y , cP,

= gap distance, cm, = thermal conductivity, W cm-I

("C)-', = ( s p e c i f i c ) heat a t constant pressure, c a l g-l ("C)-l, cP B = c o e f f i c i e n t of bulk expansion, ("C)-l k

The Rayleigh number, i n essence, i s t h e r a t i o of t h e product of t h e buoyancy and i n e r t i a l forces t o t h e viscous forces.

The l i m i t i n g value

of t h e Rayleigh number t o i n i t i a t e and s u s t a i n convection c e l l s has been calculated t o be 1700 when t h e f l u i d l a y e r i s bound on both sides by s o l i d p a r a l l e l and horizontal walls and is heated from below. 18 Recent 19

,experimental s t u d i e s by Norden and Usmanov

using a n interferometer technique show, however, that t h e departure from conductive t o convective

mode of heat transfer can occur a t N < 1700 f o r small specimen thickRa nesses. Figure 4 shows a p o r t i o n of t h e data taken from t h e above experi8

mental s t u d i e s i n which t h e c r i t i c a l temperature difference,

(the

temperature difference above which convection occurs), i s p l o t t e d as a

14 ORNL-OWG 72-fO526 102

IO'

u z W a W E W

a = 5 a

e t-

40'

a 0 z! L!

. 2

16'

10-2

10-1

I00

401

SPECIMEN THICKNESS (cm),

Fig. 4. C r i t i c a l temperature above which convection occurs as a function of specimen thickness f o r three l i q u i d s showing t h e departure ~ 1700. from t h e o r e t i c a l c r i t e r i a , N R =

f'unction of t h e specimen thickness f o r t h r e e liquids:

ethylene glycol,

Also shown p l o t t e d a r e t h e curves for t h e t h e o r e t i c a l values of NRa.= 1700. The area below each of t h e curves p l o t t e d i n Fig. 4 i s stable (i.e., conduction only) and above t h e curves i s unstable (i.e., convection occurs). The experimental data can be

water, and e t h y l alcohol.

seen t o have two l i n e a r slopes (n = 0.45 and 2.0) which merge with t h e t h e o r e t i c a l curve (n = 3) where

arc ~

v = r constant ~

The NRa = 1700 c r i t e r i a could lead t o a gross overestimate of ATc f o r small specimen thicknesses. Heat-transfer measurements made during Norden and Usmanovfs studies showed the r a t i o of t h e effective conductivity t o the t r u e conductivity of f o r water t o be 1.10 a t a specimen thickness of 0.15 cm and a n N Ra only 260. Thus, considerable care must be exercised t o prevent natural

convection i n f l u i d s contained between p a r a l l e l p l a t e s heated from below as well as inclined, cylindrical, and spherical annuli heated from e i t h e r side. A similar experimental study by Berkovsky and Fertmar?'

was m d e

recently i n which the specimen was heated from above and had a nonuniform upper p l a t e temperature d i s t r i b u t i o n .

This study showed that

when t h e nonuniformity of the temperature (T ) exceeded a c e r t a i n mx Tmin no convection value w i t h respect t o the lower p l a t e temperature T 0 '

occurred.

It was found t h a t i f

Tmax

- TO

no s i g n i f i c a n t convection occurs a t a Rayleigh number of l e s s than lo4. No experimental r e s u l t s a r e reported f o r the amount of convection taking place when the specimen is heated from above and t h e p l a t e s a r e not exactly p a r a l l e l or a r e s l i g h t l y t i l t e d . If we consider t h i s case analogous t o the BerkovsQ and F e r t m n study, convection would be avoided

a t an NRa of less than l@

if t h e AT of t h e t i l t e d l a y e r above that of

t h e horizontal layer d i d not exceed that of t h e average AT across the plates.

Since AT

t h e difference i n t h e edge-to-edge separation

distance between t h e p l a t e s w i t h respect t o each other, o r w i t h respect t o the horizontal, should not exceed t h e i r average separation distance. To minimize convection due t o vibrations, t h e conduction c e l l should be well i s o l a t e d from all sources of vibrations, p a r t i c u l a r l y those withi n the resonance frequency of the c e l l .

16 Effect of heat shunting Some shunting of heat around t h e specimen is unavoidable even f o r t h e most c a r e f u l l y designed thermal conductivity c e l l s .

The percent of

shunted heat as compared t o heat flow through t h e specimen can be minimized by c a r e f u l use of i n s u l a t i n g materials, by guard heating, by using large c e l l diameter t o thickness r a t i o s , and by using zoned heat sources and sinks.

The shunting problems becomes most acute f o r low-conductivity

specimens a t elevated temperatures. The apparatus described i n t h e present r e p o r t i s designed t o minimize the shunting e r r o r with specimens having e s t i n a t e d thermal conducThe c e l l wall ("C)-'. thickness and the r a t i o of c e l l diameter t o sample thickness are

t i v i t i e s i n the range of 0.05 t o 0.10 W cm-I

optimized t o reduce the heat shunted t o l e s s t h a n l$ of the t o t a l heat flow i n t h e absence of heat guards. Unfortunately, t h e conductivities of the salts of i n t e r e s t t o the mm program were found t o be an order of magnitude lower than t h e range f o r which t h e apparatus was designed. As a r e s u l t , t h e radial guard heating was not adequate i n a f e w cases t o

prevent some heat shunting, and corrections were required. Figure 1 shows t h e complexity of t h e possible heat-transfer modes and paths within the conductivity c e l l .

Since n e i t h e r t h e temperature

d i s t r i b u t i o n along t h e c e l l wall nor t h e heat-transfer c o e f f i c i e n t s a r e well known, t h e simplified model s h a m i n Fig. 5 was selected as a n appropriate model f o r c a l c u l a t i n g t h e amount

heat shunting i n t h e

system. ORNL- OWG 7 2 - 40527

r=o MODEL

Fig. 5 . tion.

Model of t h e conductivity c e l l f o r heat shunting calcula-

By assuming a uniform heat f l u x and a uniform sink and wall tempera t u r e equal t o OOC, a n easy s o l u t i o n for t h e c e n t e r - l i n e heat f l u x m y be obtained from t h e generalized heat conduction equation [Eq. (12) 1.

The radial heat-transfer c o e f f i c i e n t U2 m y then be decreased t o account f o r t h e guard heating. The temperature d i s t r i b u t i o n within t h e c y l i n d r i c a l s o l i d can be described by t h e general heat conduction equation, a2T

1aT

-+ - ar2

a2T

+-=o

az2

where T i s t h e temperature ("C) and r and z a r e t h e radial and a x i a l coordinates (cm) measured as shown i n Fig. 5 .

Dividing t h e model i n t o

two regions, t h e boundary conditions for e i t h e r region can be written:

where k' is t h e conductivity [W cm-I

("C)-l

of t h e c y l i n d r i c a l s o l i d w i t h -

i n t h e region, L i s t h e thickness of the s o l i d (cm), R i s t h e radius (cm), C i s a constant, and U1 and U2 are t h e a x i a l and radial o v e r a l l heat-

transfer c o e f f i c i e n t s respectively.

The s o l u t i o n of Eq. (12) for t h e r a t i o of t h e a x i a l c e n t e r - l i n e heat fluxes e n t e r i n g and leaving region I, using t h e above boundary conditions, is

18 where N1 sinh (anL/R)

+ an cosh

(anL/R)

cosh (anL/R)

+ an s i n h

(anL/R)

Dn Nl

and an are t h e r o o t s of

and

There is a similar equation f o r F I1 The heat-transfer c o e f f i c i e n t s Ifi and U2 were calculated assuming s e r i e s and p a r a l l e l paths of a l l t h r e e heat-transfer modes (convection, conduction, and r a d i a t i o n ) .

The r a t i o F of t h e heat flux e n t e r i n g region I t o t h e heat flux leaving region I1 w a s c a l c u l a t e d as F = F F I I1 To account for various degrees of guard heating a f a c t o r G was

defined as rn I

G Z

-rn

heater

wall

such t h a t

Plots of t h e percentage of heat shunted around t h e specimen, 1

- F,

vs t h e specimen thickness, &, f o r various specimen conductivities as determined by a computer s o l u t i o n of Eq. (16) a r e shown i n Figs. 6 and 7 f o r temperature l e v e l s of 300 and 9oO째C, respectively.

Both of t h e s e

p l o t s assume partial guard heating; G = 0.5 was employed.

The dashed

curves assume t h e specimen t o be transparent t o i n f r a r e d r a d i a t i o n and t h e w a l l e m i s s i v i t i e s t o be 0.5.

From these p l o t s , it can be seen t h a t

t h e amount of heat shunted around t h e specimen can approach 1 0 6 for l a r g e Ax and very small specimen conductivities.

I n our conductivity

Fig. 6 . Percent of heat shunted around specimen vs specimen thickness f o r various specimen conductivities with and without r a d i a t i v e heat t r a n s f e r a t 3OO0C f o r G = 0.5.

measurements, t h e guard heating f a c t o r G was near zero and a specimen thickness of cO.1 cm was used i n determining t h e conductivity. Method of c a l c u l a t i o n I n t h e variable-gap technique, t h e thermal conductivity c o e f f i c i e n t can be determined (1) from t h e reciprocal slope of the t o t a l thermal

r e s i s t a n c e across t h e specimen (including metal walls, deposits, e t c . )

402

5 P

40-~

lo-2

2 5 40-' A X , SPECIMEN THICKNESS (cm 1

roo

Fig. 7. Percent of heat shunted around specimen vs specimen thickness f o r various specimen conductivities with and without r a d i a t i v e heat t r a n s f e r a t 900째C f o r G = 0.5.

as a -function of specimen thickness as it approaches zero or (2) from t h e effective conductivity as t h e specimen thickness approaches zero. Except f o r a few spot checks, method (1) was used t o reduce t h e data

.in t h i s r e p o r t .

The thermal r e s i s t a n c e i s calculated from t h e measured

heat flux &'/A and from t h e measured temperature difference, where

Q' -=-

4EN

7iDZ

and I = heater current, amps,

= heater voltage,

D = diameter of upper heater p l a t e , cm,

E = r a t i o of e f f e c t i v e t o t o t a l heater wire length.

The heat f l u x Q/A i s obtained from t h e measured heat f l u x by correcting f o r t h e heat shunting.

If t h e guard heating f a c t o r G [see Eq. (21)] i s

g r e a t e r than about 0.01, a heat shunting f a c t o r F i s interpolated from t h e p l o t s of 1 - F vs Cur (Figs. 6 and 7) obtained from computer solutions of Eq. (16). From these solutions, t h e percentage of shunted heat, 1 - F, i s found t o be very nearly proportional t o G o o 8 . Thus, t h e heat shunting f a c t o r f o r any degree of guard heating i s calculated using t h e r e s u l t s from only one heat shunting f a c t o r a t G = 0.5:

The heat f l u x i s then calculated as Q/A = F (Q'/A)

and t h e t o t a l thermal

r e s i s t a n c e is AT/(Q/A), where LSF i s t h e previously defined t o t a l tempera t u r e difference across t h e specimen. The t o t a l thermal r e s i s t a n c e i s then p l o t t e d as a function of t h e specimen thickness f o r a given specimen temperature.

The specimen temper-

a t u r e i s defined as t h e average of t h e upper and lower p l a t e temperature and both t h e specimen temperature and t h e measured heat f l u x a r e kept nearly constant as t h e specimen thickness i s varied (see Experimental Procedures). Three methods were used t o determine t h e slope of t h e r e s i s t a n c e curve a t Ax = 0.

F i r s t , v i s u a l inspection of t h e curve gave good r e s u l t s

when t h e d a t a were smooth and t h e r e s i s t a n c e curve was l i n e a r .

Second,

when t h e curve was not l i n e a r , numerical f i n i t e - d i f f e r e n c e techniques were used t o obtain t h e slope a t Ax = 0. were f i t t e d t o Eq. ( 9 ) [or Eq. (10) i f

I n t h e t h i r d method t h e data = 01 i f adequate information of

t h e o p t i c a l properties of t h e specimen were known.

q h e t o t a l wire length between voltage taps includes two 0.875-in.long lead wires.

22 Most of t h e data reported i n t h i s study were analyzed by v i s u a l inThe data were f i t t e d t o

spection or t h e t h i r d method mentioned above. Eq.

(9) i n fhe followingâ&#x20AC;&#x2122; way.

The fixed resistance,

i s found by extrapolating t h e thermal r e s i s t a n c e vs Ax t o Ax = 0; the p l a t e emissivities a r e determined by carrying out t h e experimental procedure w i t h t h e conductivity c e l l evacuated; and t h e index of r e f r a c t i o n is taken from t h e l i t e r a t u r e , a n average

wavelengths.

over t h e range of infrared-

From a n estimate of t h e conductivity by v i s u a l inspection

of t h e data f o r Cur C 0.1, t h e absorptivity, f i t t i n g Eq. ,(9) t o t h e l a r g e r values of Ax.

-tc,

can then be found from

Using these values of t h e

fixed resistance, t h e p l a t e emissivities, t h e average index of refraction, and t h e calculated absorptivity, the thermal conductivity i s determined by t h e b e s t f i t of t h e data over t h e complete range of Ax.

3. MPERIMENTAL APPARATUS The design and construction of t h e apparatus and a u x i l i a r y equipment

a r e discussed here.

The description of t h e thermal conductivity c e l l

i t s e l f is s u f f i c i e n t l y complete t o permit duplication; however, only

unusual a u x i l i a r y equipment is discussed i n d e t a i l .

Additional d e t a i l s

and i l l u s t r a t i o n s are given i n Appendix A. The complete, system can be considered t o c o n s i s t of four parts: t h e t h e r m 1 conductivity c e l l , t h e furnace, t h e e l e c t r i c a l system, and

t h e instrument network.

The connections and relationships between the

various components a r e shown schematically i n Fig. 8.

Photographs of

t h e apparatus are shown i n Figs. 9 and 10. Thermal Conductivity C e l l

The t h e r m 1 conductivity c e l l is shown i n Fig. 11 and i n d e t a i l i n Figs. A-1 and A-2 i n Appendix A.

The c e l l i s &de up of two components :

t h e cylindrical-shaped component, which c o n s i s t s of a sink and t h e radial

' c

n L a N

POTENTIOMETER FACILITY

ORNL-OWG

12-10530

COOL1NG COOLING WATER

I 2-PEN

CHART RECORDER

'GON

1..

0 0 0 r

VEECO

CROSSBAR SCANNER

IEL VIDAR

VACUUM STATION

D C DIGITAL VOLTMETER

sHuNTA

G@ (COARSE)

KEPCO

FLUKE

I 0

AC HEATER CONTROL

REGULATED DC VOLTAGE SUPPLY

(FINE) AC DIGITAL VOLTMETER

Fig. 8. Schematic illustration of the complete system for thermal conductivity measurements.

ru w

$ k 0

k bo 0 c,

. 26 . ORNL-DWG

72- 405321

DIAL INDICATOR

Fig. 11.

Schematic cross section of the conductivity cell.

heaters and contains t h e s a l t , and t h e piston-shaped component, which is mobile i n t h e v e r t i c a l d i r e c t i o n and contains t h e main heater and t h e guard heater assemblies. The c y l i n d e r i c a l component was machined from t h r e e pieces of s t a i n less s t e e l type 304 and welded together as shown.

The lower section,

which contains t h e molten salt, has holes d r i l l e d through t h e component f o r cooling a i r passages, and a sink heater which i s a 1/8-in.-diam Calrod sheath-type element pressed i n t o grooves machined i n t h e lower Similar heaters a r e placed around t h e cylinder a t t h e l e v e l

section.

of t h e s a l t f o r t h e radial guard heaters.

Figure 1 2 shows t h e l o c a t i o n

and designations of t h e thermocouples and heaters.

Several dimensions

of t h e cylinder component are maintained i n c l o s e tolerances t o insure t h a t the specimen thickness is uniform across t h e diameter (Fig. A - 1 ) .

The cylinder i s about 4 i n . OD

x 3.5 in.

ID, and 1 2 i n . long.

The

f i n a l m c h i n i n g of these surfaces was mde a f t e r t h e e n t i r e cylinder had been dimensionally s t a b i l i z e u by heat treatment. The mobile p i s t o n component containing t h e main heater assembly is

shown i n d e t a i l i n Fig. A-2 i n Appendix A .

The main heater i s con-

s t r u c t e d w i t h 10-mil Pt-lo$ Rh wire, wound, embedded, and buried i n a high-density A1203 i n s u l a t o r . s i t s above t h e m i n heater.

A duplicate heater, t h e main guard heater, Between these two heaters i s a 1/16-in. gap

containing t h r e e platinum-foil r a d i a t i o n s h i e l d s .

The temperature across

t h i s gap i s monitored by two thermocouples and balanced w i t h t h e guard

heater t o prevent a x i a l heat loss.

A gold f o i l provides high contact

conductance between t h e m i n heater and t h e bottom of t h e p i s t o n container.

All t h e e l e c t r i c a l wiring, t h e platinum wire, and t h e thermo-

couples extend through a hollow rod connecting t h e p i s t o n w i t h t h e upper p l a t e and support.

A f l e x i b l e bellows welded t o t h e p i s t o n rod and t h e

upper flange allows mobility of t h e p i s t o n while providing a vacuum t i g h t seal.

The v e r t i c a l movement of the p i s t o n i s adjusted by a threaded

nut whose microthreads are p r e c i s i o n machined.

The v e r t i c a l movement of

t h e p i s t o n i s measured with a d i a l i n d i c a t o r connected t o t h e bottom of t h e p i s t o n with a fused quartz rod t o minimize t h e e f f e c t of t h e r m 1

expansion.

Several dimensions of t h e mobile p i s t o n component are a l s o

ORNL-DWG 72-10531

Fig. 12.

P o s i t i o n of thermocouples and heaters.

l i -

maintained i n c l o s e tolerances (See Fig. A-2).

The s p e c i f i c a t i o n s of

these tolerances insure that t h e p a r a l l e l i s m of t h e two p l a t e surfaces does not vary by more than 0.005 i n .

This tolerance was measured i n s i t u

by placing a b a l l bearing i n t h e gap of t h e specimen, r o t a t i n g t h e apparatus i n a n inclined position, and measuring t h e v a r i a t i o n i n t h e gap s e t t i n g with t h e d i a l indicator.

A t y p i c a l p l o t of t h i s v a r i a t i o n around

t h e edge of t h e c e l l i s shown i n Fig. 13.

The maximum edge-to-edge varia-

t i o n of t h e thickness i n t h i s case of 0.0017 in. demonstrates excellent conformity t o t h e 0.005-in. tolerance. The t e s t c e l l described here and i n considerably more d e t a i l i n Appendix A i s t h e f i n a l design (Model 111-B) of t h e conductivity c e l l . Several modifications were made i n t h e course of t h e development of t h i s apparatus.

The notation, description, and chronological appearance of

these modifications a r e l i s t e d i n Table 1. The locations of the thermocouples used i n t h e conductivity c e l l a r e I n i t i a l l y , t h e thermocouples were 1/16-in. -OD sheathed

shown i n Fig. 12.

Chromel-Alumel thermocouples; later Pt vs Pt-16 Rh thermocouples were used. I

Thermocouples 1, 2, 5 , and 6 a r e a r c welded t o t h e bottom of t h e i r

respective thermal wells t o insure t h a t they remain fixed during t h e

measurements.

ORNL-OWG 72-40533

4 35 480 225 270 ANGLE, ROTATE0 CLOCKWISE (deg)

315

360

Fig. 13. Variation i n t h e gap thickness around t h e circumference of t h e conductivity c e l l .

Table 1. C e l l modifications Model

Heater assemblya

I-A

11-A

Cylinder

Thick one-piece heater core; D = 8.572 cm, E = 0.969

Original cylinder

1/16-in. -OD SS-sheathed, Chromel-Alumel grounded junctions, MgO i n s u l a t ion

Thinner two-piece heater core with 1/32-in. a i r gap between rmin and guard heaters; E = 0.971

Original cylinder

1/16-in. -OD SS-sheathed, Pt vs Pt-16 Rh un-

11-B

111-B

Thermocouples

grounded junctions, MgO insulation

Wall of t h e o r i g i n a l cylinder was underc u t and grooved t o reduce heat flow down t h e w a l l ; 'IC 9 added

New heater with 1/16-in. a i r gap ' w i t h three P t f o i l baffles;

E = 0.966 a

D diameter of heater assembly and E = r a t i o of e f f e c t i v e - t o - t o t a l heater wire length, where t h e t o t a l wire length between t h e voltage t a p s includes two 0.875-in.-long lead wires. E

Furnace The f'urnace c o n s i s t s of two 6 - i n . - 1 ~ x 8-in.-long individually cont r o l l e d clamshell heaters of t h e embedded wire type.

The annular space

between t h e heater and t h e 12.5-in.-OD water-cooled f'urnace s h e l l was f i l l e d with Fiberfrax i n s u l a t i o n .

This f'urnace is capable of r a i s i n g t h e

ambient temperature of t h e molten s a l t t o 1000째C. E l e c t r i c a l System The heater e l e c t r i c a l system is diagrammed i n Fig. 14.

The a c supply

voltages t o t h e sink, guard, and furnace heaters a r e regulated with a

31 ORNL-DWG 72-10534

FLUKE AC DIGITAL VOLTMETER

K ROTARY

VARIAC AUTOMATIC VOLTAGE REGULATOR r----l

20-A VARIAC (COURSE ADJ) r--1

GUARD HEATER

VARIAC AUTOMATIC VOLTAGE REGULATOR

TOP HEATER \

KEPCO DC VOLTAGE SUPPLY

;

Fig.

14.

0.4 0 SHUNT

MAIN HEATER

Diagram for e l e c t r i c a l heater system.

Variac a u t o m t i c voltage regulator.

The voltage through each of the

heaters i s adjusted by two Variacs, coarse and fine, and by a filament transformer.

The f i n e adjustment extends t h e coarse Variac s e t t i n g

with t h e a d d i t i o n of 6 V of increased s e n s i t i v i t y (0.038 V ) . ac d i g i t a l voltmeter

A Fluke

i s used f o r s e t t i n g and reading t h e voltages.

Two Kepco dc voltage supplies provide t h e e l e c t r i c a l power t o t h e m i n and top guard heaters.

The supply voltage t o t h e two Kepco u n i t s

i s a l s o regulated by the Variac automatic voltage regulator.

The power

t o the main heater i s determined from measurements of t h e voltage and t h e current w i t h a Vidar d i g i t a l microvoltmeter and a Leeds and Northrup precision r e s i s t o r .

Specifications of these instruments a r e given i n

Table A - 1 i n Appendix A. Instrumentation The thermocouple c i r c u i t diagram is shown i n Fig. 15. The temperature measurements a r e m d e w i t h grounded 1/16-in. -OD Chromel-Alwnel

O R M L - OWG 7 2 - 40535 r

L&N MODEL K-5 POTENTIOMETER

VlDAR DIGITAL VOLTMETER

ROTA RY

ROTARY

HONEY W E L L 2- PEN RECORDER

ROTARY

CROSS BAR SCANNER

---_ --- --- I : _.--- - _ -- + - j ! -- - .--

I 1

L & N DC M I C RO VOLT SUPPRESSOR

.--. I

L--

ICE BATH: COLD JUNCTION AND ZONE BOX

---0.040 Pt WIRE -- -- 0.010 P t IOVo R h ----- 0.020 PP tt -WIRE I .

-.- -.- .---0.020P t - P t PURE Cu

Fig. 15.

Thermocouple c i r c u i t diagram.

WIRE

10% Rh WIRE WIRE

33 thermocouples or with,ungrounded

1/16-in. -OD P t vs Pt-16 Rh thermo-

couples; both a r e sheathed i n 304 type s t a i n l e s s s t e e l .

Lead w i r e s from

each thermocouple a r e joined by a r c welding t o high-purity copper c i r cuitry w i r e .

To minimize and cancel ex-lqaneous thermal emf's, each of

t h e s e junctions i s contained i n a mineral-&l-f i l l e d g l a s s tube i n s e r t e d i n a hole d r i l l e d i n t o a high-purity copper block, 3 X 2 i n . diameter, and the whole assembly i s immersed i n a d i s t i l l e d water i c e bath.

Low

t h e r m 1 emf holder i s used i n other c i r c u i t r y junctions. Each thermocouple emf can be read by e i t h e r a Vidar d i g i t a l microvoltmeter, a Honeywell pen recorder, o r a Leeds and Northrup K-5 potentiometer f a c i l i t y . Table A-1,

The specifications of these instruments a r e given i n

Appendix A .

EXP~IME3lTALPROCEDURES Preliminary Procedures

The conductivity c e l l surfaces a r e cleaned w i t h detergent, rinsed with demineralized water, and d r i e d with f i l t e r e d a i r .

After use, t h e

corrosion products a r e removed by polishing with r o t a r y s t a i n l e s s s t e e l brushes, 600-grit cloth, and crocus c l o t h t o r e s t o r e t h e surfaces.

assembling t h e apparatus, t h e p a r a l l e l i s m of t h e p l a t e s i s checked f o r t h e s p e c i f i e d tolerance (0.005 i n . ) , and t h e thermocouple readings a t room temperature match within <0.2pV.

The p u r i t y of the specimens

used i n t h e determinations meet t h e ACS s p e c i f i c a t i o n s f o r reagent-grade chemicals : 99.997% pure argon, 99.995% pure helium, doubly deionized and t r i p l e d i s t i l l e d water, t r i p l e d i s t i l l e d mercury, and reagent-grade KN03,

NaNO,,

and NaN03 salts d r i e d i n vacuum.

The specimen i s introduced i n t o t h e c e l l , t h e apparatus leveled and leak t e s t e d w i t h a helium leak detector.

heating overnight a t about 150째C.

The system is then outgassed by

Voids i n t h e specimen are removed by

a l t e r n a t e l y increasing and decreasing t h e specimen thickness after it has

For l i q u i d and s o l i d samples, an argon cover gas i s introduced i n t o t h e c e l l a t s l i g h t l y above atmospheric pressure.

'been melted under vacuum.

34 Operating Procedure

- Fluid

Specimen

The furnace heat i s applied t o t h e system t o reach t h e desired temperature l e v e l .

The tmin heater i s adjusted t o obtain t h e required heat

f l u x through t h e specimen (0.02 t o 0.7 W em-'),

and t h e guard heaters a r e

adjusted t o maintain a close temperature balance between thermcouples t h r e e and f i v e (< kO.5"C)

and thermocouples t h r e e and four (< +1"C)

* to

minimize heat losses (see Fig. 1 2 ) . After steady-state conditions a r e reached, t h e measurements a r e recorded; the c r i t e r i o n f o r t h e steadys t a t e condition is a temperature d r i f t of l e s s than l 0 C / h r .

Recordings

a r e made of a l l thermocouple readings, air flow r a t e i n the cooling sink, d i a l indicator reading, and voltages and currents from parer panelmeters

and d i g i t a l voltmeters a t each gap distance.

The gap is then changed,

steady-state conditions a r e reestablished, and the recordings repeated. A number of gap spacings a r e used (0 t o 0.4 cm) depending on t h e l i n e a r i t y of the data.

The heat flux and average specimen temperature are kept con-

s t a n t f o r each gap spacing (> kO.005 W

k1"C).

The above procedure i s repeated f o r each specimen temperature l e v e l . Operating Procedure

- Solid Specimen

If the measurements a r e made with t h e specimen i n t h e s o l i d s t a t e ,

t h e specimen is melted before each gap spacing is selected, and then the gap spacing is fixed by cooling the specimen t o t h e desired temperature.

The experimental r e s u l t s from t h i s study demonstrate the successful development of the variable-gap5 technique f o r the measurements of moltens a l t thermal conductivities.

Concurrently w i t h t h e development of the

method, we measured conductivities of several molten f l u o r i d e s a l t m i x t u r e s which w i l l be presented i n a subsequent report.

*I n

some cases the r a d i a l guard heating was inadequate t o reduce the r a d i a l LfT t o < +lot, and a correction f o r heat shunting was necessary (Chapter 2 ) .

35 The thermal conductivities of f i v e materials were determined over a temperature range from 38 t o 9 4 6 " ~f o r a t o t a l of 31 s e r i e s of measurements.

Argon, helium, water, H"S,

* and

mercury were s e l e c t e d t o c a l i b r a t e

t h e apparatus because t h e i r conductivities a r e w e l l established and cover

0.4

a wide range of values:

t o 100 x

loe3

W cm-I ("C)-'.

The con-

d u c t i v i t y of HTS i s not as w e l l established a value as those of the other substances.

However, HTS can be heated t o temperatures required t o melt

t h e f l u o r i d e s a l t mixtures.

Nearly 350 measurements were made of t h e

thermal r e s i s t a n c e as a function of specimen thickness t o obtain t h e 31 determinations of conductivity.

I n addition, another 50 measurements of

r e s i s t a n c e vs thickness were made w i t h t h e system evacuated t o evaluate t h e surface e m i s s i v i t i e s . The o r i g i n a l and reduced data a r e presented i n Tables B-1 t o B-22 i n Appendix B.

The data were reduced as indicated i n t h e method of c a l -

c u l a t i o n i n Chapter 2.

The t o t a l thermal r e s i s t a n c e i s p l o t t e d as a

function of t h e specimen thickness, and t h e thermal conductivity is determined from t h e r e c i p r o c a l slope as t h e specimen thickness approaches zero. Thermal Resistance Curves Several representative p l o t s of t o t a l thermal r e s i s t a n c e as a funct i o n of specimen thickness a r e shown i n Figs. 16 t o 20.

A t t h e lower

temperature t h e thermal r e s i s t a n c e i s a l i n e a r function, as shown i n Figs. 16 and 17 f o r mercury a t 6 0 . 8 " ~and HTS at 197째C.

A t t h e higher

temperatures, t h e influence of i n f r a r e d r a d i a t i o n on t h e heat t r a n s f e r can be seen by t h e curvature of t h e r e s i s t a n c e curve f o r HTS and argon a t 5 2 6 0 ~and helium a t 946째C (Figs. 18 t o 20).

The f i x e d thermal r e s i s t a n c e of t h e conductivity c e l l ,

' varies from 5 for mercury t o 30 f o r argon.

*ms:

KNO,-NaNO2-NaNO3

(44-49-7 mole

Model changes i n t h e m i n

4).

36 ORNL-DWG 72-40536

f I

3 00

0 0

0.2 SPECIMEN THICKNESS

0.1

0.3

0.4

(cm)

Fig. 16. Total thermal r e s i s t a n c e vs specimen thickness of mercury at 6 0 . 8 ~( R~u n 2, Apparatus I-A).

420

400

tu E

- 80 0

0.1

0.2

0.3

0.4

SPECIMEN THICKNESS (cm)

Fig. 17. Total thermal r e s i s t a n c e vs specimen thickness of HTS at 1 9 7 O C (Run 10, Apparatus I-A).

440

420

0 0

0.4

0.2 SPECIMEN THICKNESS (cm)

0.3

0.4

Fig. 18. T o t a l thermal r e s i s t a n c e vs specimen thickness of HTS at 5 2 6 ' ~ (Run 1, Apparatus 11-B).

ORNL-DWG 72-40539

0.4

0.2

0.3

0.4

SPECIMEN THICKNESS (cm) -

Fig. 19. T o t a l thermal r e s i s t a n c e vs specimen thickness of argon at 503OC ( R u n 1, Apparatus 11-B).

38 ORNL-OWG 72-40540

0.4

0.2 SPECIMEN THICKNESS (cm)

0.4

0.3

Fig. 20. Total thermal r e s i s t a n c e vs specimen thickness of helium a t 946OC ( R u n 2, Apparatus 11-B).

heater assembly (Table 1) account f o r most of t h e v a r i a t i o n i n fixed thermal resistance.

tures up t o

Model I-A was operated s e v e r a l months a t tempera-

8oo0c with

f l u o r i d e salt mixtures during a t i m e between

mercury and HTS c a l i b r a t i o n runs.

The Chromel-Alumel thermocouples of

model I-A would be expected t o show s i g n i f i c a n t emf d r i f t under these conditions. Thermal r e s i s t a n c e as a function of gap spacing w i t h t h e c e l l evacuated i s shown i n Fig. 2 1 f o r two temperature l e v e l s (200 and 510째C) and two values of heat f l u x (0.100 and 0.224 W cm'2). specimen r e s i s t a n c e (i.e., t h e evacuated runs.

The values of t h e

t o t a l minus fixed r e s i s t a n c e ) were used f o r

The expected l a c k of v a r i a t i o n of t h e r e s i s t a n c e as

a function of t h e gap spacing can be seen i n t h e f i g u r e .

A s l i g h t change

i n t h e emissivity of t h e p l a t e surfaces w i l l account f o r t h e small d i f ference i n t h e r e s i s t a n c e between t h e two heat f l u x values a t 200OC. The t o t a l hemispherical emissivity e, calculated from t h e thermal resistance using Eq. (10) i n Chapter 2 (assuming equal emissivity f o r t h e two p l a t e s ) , varied from 0.4 t o 0.5.

200 200

513

-- 1600 3

0.40 0.45 0.50

0.224 0.100 0.090

el E

- 1200 W

z a III

;800 v)

I a

0.I

0.2

0.3

SPECIMEN THICKNESS (cm)

Fig. 21. Thermal resistance vs gap spacing w i t h t h e conductivity c e l l evacuated.

The i n f l e c t i o n i n the slope of the resistance curve f o r HTS a t 5 2 6 " ~ (Fig. 18) i s similar t o those shown i n Fig. 3 for smll infrared absorbing mterials.

The s o l i d curve drawn through the data was derived from

Eq. (9), using t h e procedure outlined i n Chapter 2.

A value of

1.4

was derived from t h e Molten Salts Handbooka1 for the e u t e c t i c composition

of NaN03-KN03 (47-53 mole $) a t 525째C and the previously measured value of e = 0.45 was used for t h e p l a t e e m i s s i v i t i e s .

Incorporating these

values i n Eq. (9), a b e s t f i t of the experimental data over the e n t i r e range of specimen thicknesses (0 < Ax < 0.3 cm) gave values of the specimen conductvity and mean a b s o r b t i v i t y of 3.28 X 12 cm-l

W cm-' ("C)-l

and

, respectively.

The thermal resistance curves shown i n Figs. 19 and 20 resemble those

shown i n Fig. 3 f o r nonabsorbing gases (n = 1, K = 0).

Using t h e pre-

viously determined p l a t e emittance, the values of the conductivity were found from a b e s t f i t of the resistance data t o Eq. (9) t o be 0.34 X and 3.3 X respectively.

W cm-'

(OC)-l

f o r argon and helium at 503 and 946"C,

Thermal Conductivity The experimental r e s u l t s f o r t h e thermal conductivity f o r t h e d i f f e r e n t c a l i b r a t i o n speciments used w i t h t h e various apparatus models are presented i n Table 2.

One value f o r t h e conductivity of s o l i d HTS a t 12OOC

i s 14% l a r g e r than a published value.'

The mximum deviation of t h e other

r e s u l t s from published values a r e +9.@ and -18. positive deviations i s 4.9$,

The average of t h e 18

and the average of t h e 12 negative deviations

is -4.4$.

DISCUSSION OF THE RESULTS

The accuracy of the r e s u l t s , comparison w i t h previously published values, and t h e o r e t i c a l c o r r e l a t i o n s a r e discussed i n t h i s chapter. C o m p a r i s o n w i t h Published V a l u e s

The values of t h e conductivity of t h e substances used t o calibrate t h e variable-gap apparatus were w e l l established with t h e exception of HTS.

Touloukian's recommended values"

for argon and helium and Powell * s

values13*83 f o r water and mercury are representative of accepted cond u c t i v i t i e s f o r these m t e r i a l s .

Of the two s t u d i e s on the conductivity

of HTS, w e selected t h e more recent r e s u l t s of "urnbull'

over those of

Vargaftik2* because, as Turnbull points out, Vargaftik's c a l i b r a t i o n t e s t s w i t h "Dowtherm A" do not agree w i t h other published values.

How-

ever, Turnbull employed t h e transient-hot-wire technique with its attendant current-shunting problems (Chapter 2 ) ; consequently,. t h e conductivity of

HTS cannot be regarded t o be as well established as that of t h e other specimens measured. The individual deviations between t h e experimental r e s u l t s and t h e published values were examined as a f'unction of t h e specimen type, specimen conductivity, specimen temperature, and apparatus model. c o r r e l a t i o n could be found.

No obvious

Tsble 2.

1-A

a30

3 4 5 6 7 8 9

277 549 285 199

198

x io3 6-71 6.71 6.78 83.1 93.2 4.24 4.1 5 3*45 3.34 4-78 4.4 3 3.47 4.64 4.83 4.71

552

3*07

554 172 509 519 946

3 Hg

RTS

11-A

1 2 1 2

1 2

11-B

1 2

3 RTS 111-B

fITs

Experimental results

1 1 2

45.2 51.9 38.0 60.2 60.8 307 308 546 545 197

503 860

859 526 525

527

105

517 317

120

x io3 6.38 6.47 6.30 93.2 93-2 4.30 4.30 3.24 3.24 4.80 4.38 3.22 4.40 4.80 4.80 3.21

5.2

3.7 7.6

-10.8

0.0

-1.4 -3.5 6.5

5 5 5 5 5 5 5 5 5 5 5 5

3.1

-0.4 1.1

7.7 5.5 0.6 1.9 -4.4 8.7 6.2 0.7

3.48

3-20

2.0

5 3-04 2.70 3.70 0 3k0

1-93 3.02 3.04 4.21 0.361

0.49

0.463

6.5

0.463 3.33 3-07 3.07 1-77 3.37 4.26 5 -5

-2.4

3 0.452 3.28 3.20 3*00 1-94 3.34 4.4 9 6.27

-11.2

-12.1

-5.8

-1.5

4.2

-2.3

9.6 -0.9 5 t4 14.0

5 5 5

The average deviation of &5$ from t h e published values f o r t h e thermal conductivities i s considerably less than expected considering t h e specialized design of the apparatus. Comparison with Theory The experimental r e s u l t s f o r HTS a t 5 2 6 " ~(Fig. 18) are a n example of a t e s t of t h e theory of Chapter 2 f o r infrared absorbing materials. Equation (9) i n conjunction with t h e values of

-K , -n,

e, and k (selected

i n t h e manner previously described) agrees w e l l w i t h t h e experimental thermal resistance data over t h e range of specimen thicknesses examined. I n addition, t h e i n f l e c t i o n point of Eq. (9) and t h e apparent i n f l e c t i o n point i n t h e thermal r e s i s t a n c e d a t a both occur i n t h e v i c i n i t y of x = 0.1 em.

Such agreement gives us confidence i n t h e use of Eq. (9)

t o *represent t h e thermal resistance data of mildly i n f r a r e d absorbing However, as Poltz17 points specimens l i k e HTS a t 500째C (E = 12 em-'). out, t h e Kirchoff theory ceases t o be v a l i d i f t h e r e c i p r o c a l of t h e absorption c o e f f i c i e n t is of the same magnitude as t h e wavelength i n some regions of the absorption spectrum.

Fortunately, when t h i s con-

d i t i o n occurs, t h e thermal r e s i s t a n c e i s very nearly a l i n e a r function of t h e specimen thickness. From a t h e o r e t i c a l standpoint, t h e disruption of t h e l a t t i c e cont i n u i t y by melting should lower the conductivity s i g n i f i c a n t l y . If we extrapolate our one r e s u l t f o r the conductivity of s o l i d HTS a t 120째C t o the melting point a t 142째C by assuming that thermal conductivity is proportional t o t h e inverse of t h e absolute temperature k

1/T

(OK)

(according t o the Debye phonon-scattering theory), a r a t i o of t h e l i q u i d to-solid thermal conductivity a t t h e melting point is found t o be 0.85. Turnbul12' reports t h e average r a t i o of liquid-to-solid conductivities

a t t h e melting point f o r a l a r g e number of salts t o be 0.86 f 0.13. However, Turnbullrs reported values f o r HTS5 do not show a discontinuity

a t t h e melting point.

Accordingly, our value of t h e conductivity of

s o l i d HTS, 14% higher than Turnbull's, appears t o be the more reasonable one.

I )

Uncertainties i n t h e Results A d e t a i l e d e r r o r analysis of t h e system is given i n Appendix C, and

t h e r e s u l t of t h i s a n a l y s i s is shown i n Fig. 22.

The estimated maximum

and standard e r r o r l i m i t s i n t h e conductivity measurements using apparatus The e f f e c t s

111-B a r e p l o t t e d as a function of t h e specimen conductivity.

of t h e specimen temperature rarge (300 t o 900째C) and of t h e degree of

r a d i a t i o n e f f e c t s (zero t o maximum r a d i a t i o n a t 900째C) do not contribute g r e a t l y t o t h e e r r o r and a r e shown by t h e areas included within t h e small bands i n Fig. 22.

It is apparent f r o m t h e figure that t h e e r r o r i s sensi-

t i v e t o t h e magnitude of t h e specimen conductivity except a t l a r g e r values of t h e conductivity.

Much of t h e increase i n e r r o r a t low values of con-

d u c t i v i t y r e s u l t s from an increased uncertainty i n t h e measurement of t h e This uncertainty, caused by t h e thermal

change i n t h e specimen thickness.

expansion of t h e conductivity c e l l as t h e guard heating i s adjusted, can be minimized by a dual quartz rod, d i a l indicator system. Such a system was not considered necessary f o r t h e present apparatus s i n c e t h e conduct i v i t i e s of the molten f l u o r i d e salts were found t o be i n t h e v i c i n i t y of 0.01

cm-l

("c)-' . ORNL-OWG 72-90542

I Illll

I I I IIII

5 IO+ k, SPECIMEN CONDUCTIVITY (Wan-' %-'I

I I I Illl

to-'

Fig. 22. Estimated standard and maximum e r r o r limits i n t h e cond u c t i v i t y measurements f o r Apparatus 111-B vs specimen conductivities with and without r a d i a t i v e heat t r a n s f e r over 300 t o 900째C range. Also shown are experimental deviations from published values.

44 Figure 22 shows a l s o the deviations of each of t h e experimental res u l t s from t h e published values.

Several points a r e outside of the

estimated e r r o r l i m i t s (the conductivity of s o l i d HTS was discussed i n t h e previous s e c t i o n ) . Apparatus I-A,

Data f o r water and mercury were obtained using

i n which Chromel-Alumel thermocouples were used.

Since

t h e uncertainty of t h e temperature measured w i t h t h e Chromel-Alumel thermocouples is four times of that from P t vs Pt-lO$ Rh thermocouples, t h e e r r o r l i m i t s f o r Apparatus I-A a r e considerably l a r g e r than f o r 111-By especially a t t h e higher specimen conductivities.

Excluding these points,

93% of t h e data l i e s within t h e maximum e r r o r l i m i t s and 6% within t h e standard e r r o r l i m i t s . Adequacy of t h e Experimental Apparatus The experimental apparatus proved extremely durable despite i t s

complex design.

Model I-A endured 500 hr of operation w i t h a f l u o r i d e

salt mixture a t temperatures ranging from 500 t o 8 0 0 0 ~and f o r 850 hr w i t h HTS a t temperatures from 200 t o 500째C before f a i l u r e of a thermo-

couple required t h e replacement of t h e heater assembly.

Model 11-A

suffered a weld f a i l u r e i n t h e heater assembly a f t e r 1000 h r of operat i o n w i t h helium and argon a t temperatures from 200 t o 950째C and 800 h r w i t h f l u o r i d e s a l t mixtures from 500 t o 8 5 0 " ~ . Model 111-B i s s t i l l i n

operating condition a f t e r nearly 3000 h r w i t h f l u o r i d e salt mixtures a t temperatures from 500 t o $ 0 " ~ . We previously noted that a dual quartz-rod d i a l - i n d i c a t o r system

would be able t o account f o r thermal expansion of t h e c e l l i n measuring specimen thicknesses a t low conductivity.

For such measurements, the

upper and lower p l a t e surfaces should be polished t o a mirror f i n i s h a l s o . The accuracy and precision of the conductivity values could possibly be improved by measuring t h e heat f l u x departing from t h e specimen.

This

heat f l u x can be determined by t h e usual means of measuring the tempera t u r e drop along a well-insulated rod of known conductivity.

By meas-

uring both t h e heat flux entering and leaving t h e specimen, t h e e f f e c t of heat shunting on t h e determination should be reduced.

CONCLUSIONS

Designed as it i s f o r specialized thermal conductivity measurements w i t h molten fluoride s a l t mixtures from 500 t o 1000째C, t h e variable-gap

apparatus has demonstrated remrkable v e r s a t i l i t y .

Experimental r e s u l t s

agree w i t h published r e s u l t s within an average deviation of +5$ for a wide v a r i e t y of specimens (solids, l i q u i d s , and gases), specimen conductivities [O .4 X

loe3

and temperature l e v e l s (40 t o I n addition, t h e variable-gap apparatus has demonstrated i t s t o 100 X

W cm-'

("C)-'

950째C). a b i l i t y t o distinguish and evaluate t h e i n t e r n a l r a d i a t i o n within s m l l

infrared absorbing f l u i d s . Considering t h e wide range of application and t h e accuracy of the variable-gap method, it i s s u r p r i s i n g t o f i n d s o f e w references t o it i n the l i t e r a t u r e .

The experimental measurements of t h e conductivity of

several fluoride salt mixtures made concurrently w i t h t h e present study w i l l be reported i n a l a t e r publication.

ACKNOWLZDGMENT

The author i s g r a t e f u l f o r t h e invaluable a s s i s t a n c e of many of h i s associates who contributed t o t h i s investigation.

I n particular,

t h e author wishes t o express h i s appreciation t o t h e following persons: S . J. Claiborne,

Jr., f o r h i s vaulable a s s i s t a n c e i n assembling and operating t h e apparatus, W. K. Sartory for h i s p a t i e n t advice, J. W.

Krewson and W. A. B i r d for t h e i r design of t h e instrumentation, J. W. Teague f o r h i s expediting t h e f a b r i c a t i o n of t h e apparatus, Roberta Shor and M. R. Sheldon f o r assistance with t h e f i n a l editing, and Margie Adair and Dolores Eden for t h e i r typing of t h e report.

REFERENCES

1. E. S. B e t t i s and W. B. McDonald, "Molten-Salt Reactor Bperiment," Nucleonics, 22(1): 67-70 2.

(1964).

W. D. Powers, S. I. Cohen, and N. D. Greene, "Physical Properties of Molten Reactor Fuels and Coolants," Nucl. S c i . and Eng., 17(2): 20+211 (1963)

3. Narayanaswamy Mani, "Precise Determination of t h e T h e m 1 Conductivity of Fluids Using Absolute Transient Hot-wire Technique," s e r t a t i o n , Calgary, Alberta, August 1971.

pN> D i s -

P. Grassmann, W. Straumann, F. Widmer, and W. Jobst, '%leasurement of Thermal Conductivities of Liquids by a n Unsteady S t a t e Method," Progr. I n t e r n . Res. Thermodyn. Transport Properties, Papers Symp. Thermophys. Properties, 2nd,Princeton, N. J., pp. 447-53, Academic Press, New York, 1962.

5 . A.

G. Turnbull, "The Thermal Conductivity of Molten Salts," Australian J. Appl. Sci., 12(1): 3 G l (1961).

6 . L. R. White and H. T. Davis, "Thermal Conductivity of Molten Nitrates,

J. Chem. Phys

., 47(12) : 5433-5439

Alkali

(1967).

S. E. Gustafsson, "A Non-Steady-State Method of Measuring t h e Thermal Conductivity of Transparent Liquids, '' Z. Naturforschg., 22a(7) : 10051011(1967).

S. E. Gustafsson, N. 0. Halling, and R. A. E. Kjellander, "Optical Determination of Thermal Conductivity w i t h a Plane Source Technique (I1 Molten LiN03, RbNO3, and C s ( N O 3 ) , " Z. Naturforsch., 23a(5): (1968).

9- C . E. Mallon and M. Cutler, "Thermal Conductivity of E l e c t r i c a l l y Conducting Liquids," The Rev. of S c i . I n s t r . ,

(1965)

36(7): 103&1040

10. P. Y. Achener and J. T. Jouthas, %Alkali Metals Evaluation Program, Thermodynamic and Transport P r o p e r t i e s of Cesium and Rubidium, Thermal Conductivity of t h e Vapor," AGN-8192, Vol. 2, Aerojet General Corp., October 1968.

11.

J:E. S. Venart, "A Simple Radial Heat Flow Apparatus f o r Fluid 41: 727-731 Thermal Conductivity Measurements, '' J. S c i . Instr

(1964)

12. W. F r i t z and H. Poltz, "Absolutbestimmung Der Wdrmeleitfghigkeit von F l s s s i g k e i t e n -1,"'Intern. J. Heat Mass Transfer, Vol. 5, pp. 307-316, Pergamon Press (printed i n Great B r i t a i n ) , 1962.

13. A . R. Challoner and R . W. Powell, "Thermal Conductivities of Liquids: New Determinations f o r Seven Liquids and Appraisal of Existing Values, Proc Roy. Soc (London), ~ 2 3(1212) 8 : 9 ~ 0 (1956) 6

14.

J. Matolich and H. W. Deem, "Thermal Conductivity Apparatus f o r Liquids; High Temperature, Variable-Gap Technique," Proc. 6 t h Conf. on Therml Conductivity, Oct 19-21, 1966, Dayton, Ohio, PP* 39-51.

15.

J. W. Cooke, "Therm1 Conductivity of Molten Salts," Proc. 6th Conf. on T h e r m l Conductivity, Oct. 19-21, 1966, Dayton, Ohio, PP* 15-27.

16. H. Poltz, "Die Wgrmeleitfahigkeit von F l k s i g k e i t e n 11, Erschienen i n der Z e i t s c h r i f t , " Intern. J. Heat Mass Transfer, 8: 515-527 (1965) 17. H. P o l t z and R. Jugel, "The Thermal conductivity of Liquids

- IV.

Temperature Dependence of T h e m 1 Conductivity," Intern. J. Heat Transfer, 10: 107488 (1967).

mss

18. H. GrbSser and S. Erk, Fundamentals of Heat Transfer, 3rd ed., rev. by U. Grigull, Trans. by J . R . Moszynski, p. 315, McGraw H i l l , New York, 1961. 19. P. A. Norden and A . G. Usmnov, "The Inception of Convection i n Horizontal Fluid Layers," Heat Transfer 155-161 (1972).

- Soviet Research,

4(2):

20.

B. M. Berkovsky and V. E. Fertman, "Advanced Problems of Free Convection i n Cavities," 4th Intern. Heat Transfer Conference, Paris, September 1970, Vol. 4, Paper NC 2.1, E. L. Seiver Publishing Co., Amsterdam, 1971.

21.

G. J. Jantz, Molten Salts Handbook, p. 92, Academic Press, New York, 1967.

22.

Y. S. Touloukian, P. E. Liley, S. C . Saxena, Therm1 Conductivity; Nonmetallic Liquids and Gases (Vol. 3 of Thermophysical Properties of M t t e r ; t h e TPRC Data S e r i e s ) , Plenum Press, New York, 1970.

23.

R. W. Powell and R. P. Tye, "The T h e m 1 and E l e c t r i c a l Cmductivity

24.

N. B. Vargaftik, B. E. Neimark, and 0. N. Oleshchuck, "Physical Properties of High Temperature Liquid Heat Transfer Medium," Bull. A l l - U n . PWR Eng. Inst., 21: 1 (1952).

25.

A. G. Turnbull, "The Thermal Conductivity of Molten Salts," Australian J. Appl. Sci., l 2 ( 3 ) : 324-329 (1961).

of Liquid Mercury, I' Proc Heat Transfer Conf , 1961-62; University of Colorado, 1961 [and] Westminstry, England, 1961-62, Intern. Developments i n Heat Transfer, Paper 103, pp. 856462, ASME, 1963.

APPENDICIES

51 APPENDIX A

ADDITIONAL DETAILS OF DESIGN OF THE APPARATUS

S u f f i c i e n t d e t a i l i s given i n t h i s s e c t i o n of t h e Appendix that t h e thermal conductivity c e l l can be duplicated.

Details of the various

components a r e shown i n Figs. A - 1 and A-2. The discussion of t h e methods i n Chapter 2 and Appendix C suggests that t h e geometry of t h e apparatus e x e r t s considerable e f f e c t of t h e

accuracy of t h e conductivity determination.

However, i n most cases, t h e

consequences of gross s i z e , corrosion, and high-temperature s t r e n g t h counteract other changes which might improve i t s accuracy.

We concentrfted

on minimizing s t r a y heat flow because t h e heat-transfer model i s unidimensi o n a l

The cylinder containing t h e specimen is constructed from s t a i n l e s s s t e e l (304) and i s i l l u s t r a t e d i n Fig. A-1.

The dimensions of t h e cylinder

were s e l e c t e d t o minimize heat shunting around t h e specimen without sacrificing its structural integrity.

The length of t h e cylinder was

chosen t o fit a standard furnace, 5 in. I D X 18 i n . long, s o that t h e specimen would occupy i t s center.

A uniform a i r gap, 3/32 in., between

t h e cylinder and t h e s i n k provides an even heat f l u x d i s t r i b u t i o n t o t h e sink. The mobile heat assembly, shown i n Fig. A-2, i s designed t o reduce t h e upward flow of heat from t h e specimen a r e a .

The most important p a r t of t h e assembly i s t h e A L 0 3 heater core machined from a high-purity, highdensity A1203 ceramic.

The core i s fabricated i n two pieces and is designed

so that a 60-in. length of O.OlO-in.-diam

Pt-lO$ Rh wire could be uniformly

wound on each piece forming t h e =in and guard heaters.

The grooves con-

t a i n i n g t h e wires were then f i l l e d with A l z 0 3 cement and f i r e d . f a c e of t h e main heater was ground f l a t and smooth.

The sur-

Several dimensions of

t h e mobile heat assembly were c l o s e l y controlled t o insure a uniform specimen thickness.

These a r e shown i n Fig. A-2.

Other considerations contributing t o t h e design of t h e apparatus in-

clude the ease of assembly and disassembly and t h e convenience of f i l l i n g ,

ORNL-DWG 72-40543

L--4.000

Fig. A-1.

OlAM

Detail of t h e conductivity c e l l cylinder.

ORNL-OWG

12-10144

UNF 2 A THO

DIMENSIONS ARE I N INCHES

r.1

0.100 DEEP I 0.040 WIDE .0.425 PITCH GROOVES WOUND WITH 0.010 P I + ( O X Rh WIRE IMBEDDED IN Alz03 (FIRED1 6"' (TYPICAL E M H SIDES)

Fig. A-2.

''"

HEATER CORE %e AIR W P WITH 2 LAYERS OF

0 . b TK PLATINUM FOIL RADIATION SHIELD

D e t a i l of movable ipiston assembly 'of t h e conductivity

cell.

draining, and cleaning t h e apparatus.

I n addition, t h e specimen volume

and t h e t o t a l heated mass of t h e apparatus were made as small as possible. The more important experimental equipment used i n t h e present inv e s t i g a t i o n i s l i s t e d i n Table A - 1 .

Model and s e r i a l numbers, capacities,

accuracies, and l e a s t count a r e given when known or applicable.

54 Table A-1. L i s t of P e r t i n e n t Experimental Equipment (heading values are given if known) Equipment Potentiometer

Lm 7555 type K-5, 177362, Leeds L Northrup

Capacity o r range

Accuracy

Least Count

o - 1.6 v

?(0.001$ of reading + 2 PV)

2.0

o - 0.16 v

+(0.003$ of reading + 0.02 pv)

0.2

- 0.016 v

f (0.00%

+ 0.1

of reading pv)

0.02 pv

Voltage regulator Variac, automatic Model 1581-~

Output 115 V, a d j . +lo$, 50 A

ko .25$

Null detector Leeds & Northrup

9834-1

0.07 pV/m for source resistances

up t o 2000

0.1 pv

Dc d i g i t a l voltmeter Vidar 521 i n t e g r a t i n g voltmeter

t o k1000 v i n six-decade stages

+lo pv

?0.01$ of f u l l scale

1.0 pv

Thermocouples P t vs Pt-16 Rh

k0.2

Chromel-Alumel

k O .75

P r e c i s ion r e s i s t o r Leeds Be Northrup Model 4360

0.1 n,

15 A

E voltage supply Kepco Model SM 75-~MX Input l O F l 2 5 V, 60 cps, 9.6 A max; output 0-75 v, 0-8A

k O ,045

Line: <0.01$ voltage v a r i a t i o n o r 0.002 V, whichever greater a f t e r stabilizing

D i a l indicator

Federal Model E3BS-Rl

20 revolutions (0.4 i n . )

one-half of one division

0.0001 i n .

APPEXDM B

The uncorrected, r a w data, experimental thermocouple emfs, heater

current and voltage, and gap-dial indicator readings are given i n Tables B-1 through B-11.

The reduced experimental r e s u l t s , which in-

clude specimen thickness, t h e average temperature l e v e l , temperature drop, heat flux, and t o t a l thermal r e s i s t a n c e are tabulated i n Tables B-12 through B-22.

A l l these data a r e grouped by specimen and apparatus model

numbers (Table l), and appear i n chronological order. The guard and shunting f a c t o r s a r e determined as indicated i n t h e

method of c a l c u l a t i o n given i n Chapter 2, where t h e guard f a c t o r i s s p e c i f i c a l l y defined as (see Fig. 12):

G Z

T3 T3

- T5 T2

The heat flux i s determined as

The data f o r vacuum runs were reduced i n a s l i g h t l y d i f f e r e n t way

from t h e other runs.

The p l a t e - t o - p l a t e temperature drop w a s determined

from t h e t o t a l drop minus t h e estimated wall temperature drops and w a s used t o c a l c u l a t e t h e thermal r e s i s t a n c e .

If t h e average temperature

l e v e l varied s i g n i f i c a n t l y i n t h e vacuum runs, t h e calculated thermal r e s i s t a n c e s were normalized t o a mean average temperature by t h e r a t i o

where T i s i n OK.

Experimental Data for HpO Using Apparatus I-A

Table B-1.

Run No. +

1-B

1-A

1-c

1-D

1-E

1-F

1-0

1-8

9-1-65

9-2-65

9-3-65

2:15

4:07

1:25

2: 55

4:25

11:22

12:50

1:50

0.05600

0.056aI

0.04930

0.00000

0.25764

0.20802

0.15819

0.05123

0.01976

0.09889

0.04g05

0.02462

1.2504

l.OOO8

1.4407

1.3170

1.2540

2.2628

2.0435

1 9368

0.5760

0.4728

0.919

1.0415

1.0689

1.479

1.5936

1.6585

1.3996

1.1438

1.6457

1,5176

1.4246

2.5753

2.3414

2.2241

1.3948

1.1391

1.6432

1.5165

1.4248

2.5716

2.3402

2.2245

2.5775

2 3370

1.3974

1.1473

1.6496

I.5202

1.4202

2.2261

1.2503

1.0003

1.4400

1.3204

1.2356

2.2632

0.5760

0.4720

0.9122

1.0436

1.0523

1.4800

1.5930

1.6553

2:20

4: 12

1:35

3: 10

595

11:27

12: 55

2:14

0.0 0.0

0.0

0.5n

0.571

0.0

0.0 0.0

6-98

11.1 0.9474

11.1

0.7875

0.9512

0.9532

13.92 1.1356

13.92 1.1429

13-92 1.1470

0.0 0.0

11.6

4.4 -

6.7

6.1

5.6

7-15

6.0

4.5 -

9.4

5.6

0.7810 0.0 0.0

5.0

4.9

5 -2

5.5

4.1

5 -8

5.3

5.5

4.1

5 -8

4.5

0.0 0.0

0.0

0.0 0.0

0.0

4.7

2.0430

1.9330

4.4

7-15

6.0

5.6

0.0 0.0

0.0

0.0 0.0

0.0

Table B-1 (Continued)

__ Run No. +

2-A

2-B

2-c

2-D

3-A

3-B

3 4

9-5-65

9-16-65

9-17-65

9-21-65

4:05

3: 40

11:52

1:02

3:50

2:32

340

4: 12

0.00000

o.oo0oo

0.00000

0.01240

0.14982

0.14485

0.09503

0 .Owl80

0.14730

0.0888

0.0669

1.8876

2.6371

2.6578

2.4748

2.2562

1.9287

1.8153

1.7575

1.0932

1.2268

1.3244

1-1

1.6953

1.5749

1.5979

1.7l-52

1.8331

2.1651

2.9784

2.9923

2.7848

2 5576

2.1783

2.0455

1* 9837

2.5551

2.1728

2.0440

1 9830

2.1649

2.9671

2.9810

2.1664

2 9743

2.9843

2.7805

2.7777

2.5598

2.1787

2 .Ob08

1.9802

1.8876

2.6411

2.6560

2.4742

2.2592

1.9306

1.8147

1.7565

1.6953

1.5790

1.5966

1.n 4 8

1.a374

1.0951

1.2250

1.3236

3:51

12:03

1:07

4: 05

2:42

3: 50

4: 18

0 .o

0.0 0.0

0.0

0.0 0.0

13.92 1.938

13-92

13-92 1-949

13.96

1.968

12.00

12 .oo

12.oo

1* 938

1.733

1.739

1.742

0.23 13.80 1.1385

14.8 5.3 -

0 .o

0.0

0.0 0.0

8.7

14 .O

0.0

7.3

10.2

7.3

6.7

6.1

5.9

5.3

7.3

6.8

5 .8

5.9

5 .8

5.3

0.0

5.5

7.3

6.8

5 .8

5.9

5.8

5.3

0.0 0.0

.o.o

0.0 0.0

0.0

0.0 0.0

0.0

lhble B-2.

Run+

Using Apparatus I-A

1-A

1-B

1-C

1-D

1-E

2-A

2-B

2-D

2-E

2-F

9-14-65

9-15-65

12:55

2:05

3:50

4: 06

6: 05

10: 40

12:lO

1:25

2:45

4:45

6:40

.Ooo50

-0.00050

0.00000

0.09451

0.04446

0.02237

0.09500

0.04480

0.14975

0.09508

0.04484

0.0057a

-0.00050

0.19469

0.09462

2.5855

2.5774

2.5800

2.5498

2.4645

2.5861

2.5673

2.6130

2.5707

2.5312

2.5167

2.2959

2.3658

2 * 3585

2.3648

2.3048

2.3815

2.3989

2.3620

2.3626

2.3621

2 * 3766

3.0665

2.9982

3.0192

2.9771

2.8796

3.094

2.9891

3.0881

2.9889

2 * 9476

3.0351

2.9842

3.69

2 * 9658

2.8766

3.019

2.9827

3.0662

2.9773

3.0285

2.9849

3.652

2.9751

0.Q735

0.8389

0.8820

3.0348

2.9830

1.0832

0.8723

3.0136

2.9956

0.8765

2.8535

-8505 -

2.9216 2.9228

2.9517

2.9l28

2.5841

2.5728

2.5793

2.5438

2.4638

2.5862

2.5657

2.6143

2.5498

2.5291

2.5181

2 * 3635

2.3441

2.3600

2.3776

1:35

3: 35

4:50

6: 46

0.0 0.0

16.96 2.323

16.96 2-39

2.2941

2.3612

2.3579

2 -3639

2 * 3038

2.3815

2.3971

1:12

2:16

3:55

4: 46

6:15

io: 50

12:20

0 .o

0.0

0.o

0.0 0.0

16.60 2.265

17.02. 2.326

17.06 2.333

17.03 2 * 330

17.00 2 330

17.00 2 331

16.96 2.317

0.0

17.08 2.26

7.3

0.0 0.0

2.2

0.0 0.0

5.5

0.0 0.0

3.7

8.2

7.5

7.6

7.5

7.8

7.6

8.O

7.6

7.5

7.6

8.0

7.3 -

7.6

7.5

7.9

7.6

0.0

0.0 0.0

0.0

0.0 0.0

0.0

0.0 0.0

0 .o

16.62 2.265 0.0

0.0

0 .o 0.0

ESrperimental Data for

---

7.9

7.9 -

7.6

7-6

7?3

7.3

0.0 0.0

0.0

0.0 0.0

0.0

Table

Run No.

1-A

.l-B

B-3. EXperimental Data for

Using

1-D

1-E

1-F

1-0

Apparatus I-A 1-8

1-1

1-J

2-A

2-B

2-D

7-7-66

7-8-66

7-11-66

&gun

12:50

2:45

4:05

8: 50

io: 30

11: 30

12:40

1:50

3:00

4115

8: 50

10:aY

11: 50

1:aY

z ~ r o(in.)

0.~0280

0.00280

0.w280

0.00280

0.15240

0.12758

0.08246

0.05238

0.0227l

0.01269

0.03782

0.06740

0.10502

0.00791

0.00752

0.02289

0.03031

0.09340

12.816

12.770

12.683

12.634

12.627

12.631

12.668

12.729

12.596

12.722

12.711

12.693

12.760

12.087

12.164

12.242

12.352

12.395

12.416

12.349

12.290

12.216

12.398

12.523

12.470

12.426

12.287

Date

Dial Readiw (in.)

12.967

12-99

12.809

12.789

12.743

12.739

12.738

12.784

12.857

12.n3

12.830

12.819

12.806

12.887

12.931

12.879

12.786

12.776

12.729

12.724

12.726

12.767

12.834

12.695

12.e16

12.805

12.790

12.865

12.m

12.894

12.774

12.725

12.684

12.687

12.666,

12.724

12.823

12.670

12.768

12.754

12.748

12.856

14.l&

14.163

14.129

13.474 -

14.105

14.W

14.084

14.074

14.082

14.104

14.076

14.137

14.13

14.116

14.128

13.545

13.540

13.539

13.523

13.501

13-56

13.629

13.604

13* 562

13.513

12.634

12.628

12.63

12.668

12.729

12.ni

12.693

12.761

14.196 13.424

13.452

13.482 -

12.8lb

12.769

12.683

12.597

12.722

12.085

12.165

12.242

12 352

12 394

12.416

12.350

12.287

12.216

12.398

12.523

12.468

12.428

12.290

1:OO

2: 55

4:lO

g:oo

lo:&

ll:Jm

12:50

2:oo

3:lO

4:20

9: 00

10: 30

12:oo

1:30

0 0

% :a

8.65 0.8850

8.73 0.8949

8.78

8.60 0.9016

8,82

8.77

8.78

0.8769

8.63 0.8768

0.9033

0.8955

0.8990

8.87 0.949

8.72

0 0

4.1 4.0

4.1 4 -0

4.1

4.1 4.0

4.1 4 .O

4.1

4.0

4.1 4.0

4.0 3.9

6.3 6.7

5.7 6.0

4.9 5.2

4.3 4.3

4.0 4.3

4.0

4.0 4.3

4.6 4.9

5.25

4.3

5.6

4.1 4.3

4.3 4.6

5.2

6.1 6.5

5.6 6.0

4.9 5.2

4.2 4.4

4.0

4.0 4.3

4.4 4.7

5.2

4.0

4.3

4.0

4.1

4.2

4.3

4.4

5-0

8.63

3.75 -

3.8

3.75

3.8

3.75 3 .8

0.8*

3.75

4.2

3.75

3.75 -

3.8

4.3

3.7 3.8

5.5

3.7 3.8

3.7 -

3.8

3 -7 -

3.8

0.8500

3.7 3.8

0.8905

0.8887

5.5

5.4

3.7

3.8

lhble B-3 (Continued)

Run No.

2-9

-8

2-F

3-B

3-D

3-E

3-F

3 4

3-J

3-1

7-K

3 4

7-11-66

7-12-66

7-13-66

7-14-66

2: 35

4:05

2: 10

3:15

4:05

9:20

10:45

11~50

1:lO

2: 15

3:20

4:17

8:50

10:25

Mal ZCM (in.)

0.00280

0.00645

Mal Reading (in.)

0.11650

0.14027

0.15656

0.14649

0.12648

0.11410

0.09417

0.07421

0.05418

0.03422

0.01415

0.62422

0.04443

0.06411

12.804

12.826

22.846

22.856

22.824

22.858

22.820

22.807

22.177

22.760

22.n2

22.734

22.686

22. I48

12.244

12.185

22.244

22.285

22.307

22.384

22.395

22.433

22.456

22.476

22 * 503

22.492

22.381

22.404

12.940

23.019

23.025

22.989

23.020

22.979

22.961

22.944

22.922

22.888

=.go6

22.851

22.9l5

12.913

12.935

22.95

22.996

22.960

22.993

22.952

22.939

22.911

22.889

22.850

22.871

22.816

22.883

12.921

12.948

23.023

23.027

22.990

23.020

22.977

22.963

22.941

22.921

22.906

22.918

22.852

22.913

14.139

14.1w(

24.329

24-33

24.299

24.251

24.224

24.205

24.196

24.176

24.154

24.157

24.094

24.124

13.486

13.458

24.059

24.069

24.074

24.053

24.040

24.045

24.053

24,056

24.060

24.058

23-97

23.965

12.805

12.826

22.843

22.856

22.825

22.857

22.819

22.806

22.777

22.758

22.7ll

22.734

22.684

22.749

12.244

12.185

22.247

22.286

22.305

n .383

22.394

22.431

22.455

22.476

22.503

22.492

22.380

22.405

2:45

4:lO

2:20

3:20

4:15

9:25

10: 50

12:oo

1:15

2:25

3: 32

4:20

9200

10: 30

0 0

8.72

8.72 0.8868

9.62 0.7946

9.62 0.7942

9.62

9.62 0.7946

9.62

0.7949

0.7959

9-62 0.1963

9.62 0.7959

9.68

0.7948

9.62 0.1954

9.60

0.8872

0.7956

0.8009

0 0

4.6 3.9

4.0

3.3

4.0 3.3

0.2

0 0

1.0 0.5

6.1

Date

0 0

-7947

4.0

4.7

3.9

4.0

4.6 3.9

5.6

5.8

3.7 3.5

3.1 3.0

2.8 2.6

2.3 2.1

1.2

6.2

3.8 3.7

2.0

6.0

1.5

0.8

5.5 5.9

5.8

3.7 3.5

3.1 3.0

2.8 2.5

2.3 2.1

2.0

1.2

6.2

1.6

0.8

0.2

3.7

6.1

6.i

6.1

3.8

6.1

6.1,

963

6.1

1.6

6.1

0.5 0.5 6.1 6.1

3.3 1.7 1.2 1.7 1.2

6.1

c' Table B-3

Run

NO.

3-M

3 4

3-0

4-A

4-B

(Continued)

4-D

4-E

4-F

5 4

5-B

5-D

5-1

Date

7-14/66 7-14-66

7-14-66

1-14-66

7-15-66

1-15-66

7-15-66

7-18-66

7-19-66

Tiw Begun

11:30

1:00

2:42

4:lO

9:10

10:50

12:b

2:20

3833

12:45

2:30

3: 50

9:20

11: 10

Dial zero (in-)

0.00645

0.05269

(in.) 0.08432

0.10430

0.13669

0.03915

0.03891

0.01910

0.01188

0.02239

0.03054

0.20243

0.18253

o.lQb

0.14226

0.12232

22.691

22.69

22.691

8.319

8.2950

8.2555

8.2980

8.2450

-1

*-ai=

22.774

22.778

22.845

.ass

22.672

22.671

22.378

22.335

22.316

22.418

22.385

22.448

22.495

22.457

22.433

7.6417

7.6W

7 7421

7.8495

7.a53

22.854

22.856

22.936

22.W

23.006

22.861

22.828

22.834

8.4584

8.4351

8.38Il

8.4301

8.3772

22.907

22.96

22.979

22.828

2 2 . m

22.802

22.822

22.824

8.4406

8.41n

8.373

8.4159

8.3625

22.932

22.951

23.015

22.858

22.821

22.838

22.866

F.854

22.853

8.4288

8.3976

8.3381

8.3832

8.3315

24.143

24.146

24.166

24.083

24.013

24.017

24.035

24.033

23.027

9.2262

9.2213

9.19

9.2147

9.m5

8.7530

8.7556

8.865

8.8067

23.961

22.856

23.929

23.930

23.941

23.903

23 9 5

23-943

23.925

23.939

8.8046

8* 3193

8.2942

8.2551

8.29l5

8.2438

2 2 . m

22.786

22.843

22.694

22.673

22.672

22.69

22.689

22.690

22.375

22.330

22.37

22.418

22.386

22.447

22.493

22.455

22.432

7.6417

7.6882

7.7410

7.8495

7.8652

1h40

1:10

2:50

4:15

9:20

11: 00

12:50

2: 34

3:43

12:50

2: 35

3: 55

9:35

11:m

0 0

9.68 0.8008

9.67

9.64 0* 7983

9.68 0.8018

9.59 1.0995

1 .io03

1 .io16

9.59

0.8018

9.68 0.8018

9.59

O.@Q23

9.68

0.8022

1.1001

9.59 1.1016

0 0

4.0, 3.3

4.0 3.3

4.0

2.4 2 .o

2.4 1.9

2.4.

2.4 1.9

2.4

1.9

1.9 1.7

1.9

2.0 1.7

2.6

3.3 3-2

a.0 0.3

a.0

0 0

1 .o 0.5

5.6 6.2

5.4 6.0

5.1

4.9 5.4

4.7

2.3

2.0

2.6 2.4

3.3 3.1

a.o

a.0

1.0 0.5

5.5 6.2

6.0

5.0

0.3

0 0

5.3

0.4

0 0

1.7

5.5

4.9 5.5

4.7 5.2

6.1

2.8

2.7

2-7

2.7

2.8

2.75

2.7

6.1

0-7m

3.3

6.1

9.68

0.2

6.1

9.68

6.1

6.0

6.1

2.8

2.7

9.59

5.5

1.7

0 0

1.9 1.7 5-2

(Continued)

Teble B-3

Run no. +

5-p

5-0

5-8

5-1

Date

7-19-66

7-20-66

Time Begun

12: 37

2: 35

3: 30

8:50

1O:lO

Mal Zero (in.)

0.05269

Mal Readillg (in.) 0.10241

0.10241

0.08248

0.06258

8.1800

8.1360

8.0474

8.1878

5-n

6-A

6-c

5-L

5 4

7-20-66

7-m66 7-21-66

7-21-66

7-n-66

11:20

12:20

1:35

2125

10:10

12:lO

1:55

3:m

0.05269

0.04258

0.4258

0.04258

0.05soS

0.05495

0.05269

0.07248

0.09245

0.19544

0.17540

0.15540

0.13518

0.11540

8.0307

8.0424

8.0356

8.0621

8.1019

11.5063

11.4776

11.4570

11A 9 8

11.4631

10.9625

10.9873

11.0294

11.1131

11.1363

5-It

6 B

6-E

6-D

7.8830

7.8772

7.9015

7.8885

7.8893

7.9127

7.9115

7.8702

7.8388

8.399

8.319

8.2684

8.1776

8.1563

8.1660

8.1600

8.1881

8.2296

11.6280

11.6017

11.5769

11.6122

11.5832

8.3056

8.2971

8.2530

8.1629

8.1433

8.1532

8.1470

8.1748

8.2161

11.6076

11.5806

11.5567

11.593k

11.5631

8.2738

8.2619

8.2288

8.1438

8.1170

8.1262

8.1231

8.1440

8.1768

11.6136

11.5815

11.5466

11.593

11.5625

9.1811

9.1630

9.1508

9.1049

9.1021

9.1001

9.059

9,1030

9.1088

13.3060

13.2899

13.2726

13.2809

13.2832

8.8037

8.7926

8.7932

8.7816

8.7835

8.7840

8.7744

8.7688

12.9338

12 99

12.9388

12.9700

12.9839

8.1878

8.1800

8.1349

8.0473

8.030.7

8.0416

8.0356

8.0657

8.W

n.5050

11.4778

11.4565

11.4931

11.4626

7.8833

7.8772

7* 9016

7.8883

7.8903

7 * 9121

7.911

7.8725

7.8356

10.9625

10.9873

11.0280

11.1142

11.1366

12:20

2: oo

3: 10

8.7838 -

12:45

2:40

3: 40

9:oo

10:20

11: 35

12: 30

1:45

2: 40

9:13

1R15

0 0

9.59 1.1034

9.59

9.59 1.1056

9.59 1.10%

9.59 1.1093

9.59

9.59 1.1083

9.59 1.1072

8.645

8.64

1.109

9.59 1.1093

8.64

1.lo43

0.W

0.9092

0.9W-l

8.64 0.W7

8.64 0e-3

0 0

1.8 1.6

2.0

1.6

2.0 1.6

4.4 4.9

4.5 4.9

4.35 4.8

4.1 4.6

3.9 4.3

4.1 4.6

4.3 4.7

4.2 4.4

3.9 4.1

3.6 3.9

3.4 3-65

3.2 3.4

4.5 5 .O

4.5 5.0

4.35 4.7

4.0 4.4

3.9 4.3

4.1 4.6

4.3 4.7

4.1 4.3

3.9 4.1

3.4 3.0

3.4 3-65

3.2 3.3

2.7

3.8

2.7

2-7

2e 7

2.7

3.8

3.e

3.8

5-5

1.6

c Table B-3 (continued) ~~

Reading (in.)

7-26-66

1:15

3:05

0.00672

0.06636

0.04628

0.02657

0.01661

0.01162

0.02163

7-25-66

3: 30

11:lO

12:35

2:lO

0.04258

0.00672

0.12653

0.10650

0.04258

Dial Zero (in.)

-1

7-26-66

0.08641

7-22-66

11:m

l2:O5

0.00672

7-22-66 1:lO

7-22-66

3:55

10:30

4:17

7-22-66 12:20

7-21-66

7-26-66

7-25-66

7-C

TI- Begun

I-%

3:20

7-B

6-A

7-G

7-25-66

7-A

Date

7-F

6-5

6-G

NO.

7-E

6-1

6-P

Run

7-D

7-1

0.04258

0.09541

0.07560

0.05535

0.04535

0.05039

11.432

11.3900

11.3670

11.3427

11.3306

22.976

22.949

22.929

22.934

22.914

22.881

22.853

22.854

22.864

11.1613

11.1736

11.2lo1

11.2173

11.1923

22.492

22.509

22.533

22.580

22.612

22.639

22.640

22.660

22.634

11.5516

11.5136

11.4910

11.4636

11.4467

23.139

23.107

23-09

23.095

23.084

23* 063

23.041

23.036

23.043

11.530

11.4908

11.4680

11.4413

11.4266

23.116

23.081

23.061

23.066

23.050

23.024

22.996

22.992

23.002

11.596

11.4959

11.48%

11.4548

11.4289

23.159

23.118

23.096

23.089

23.077

23.064

23-65

23.068

13.2579

13.2336

24.170

24.242

24.236

24.225

24.224

24.212

24.204

24.194

24.190

12.9936

12 9919

12.9759

13.2789

12.9

13.2767

12.9993

13.2655

11.496

11.3900

11.3676

11.1620

11.1734

11a 1 0

4:05

11:25

8.64

0.9101

24.041

24.048

24.057

24.074

24.089

24.068

24.062

24.063

24.053

11.3435

11.3310

22* 975

22.947

22.99

22.935

22.915

22.@7

22-853

22.853

22.864

11.2175

11-1935

22.492

22.510

22.535

22.581

22.613

n .639

22.639

22.659

22.634

12:32

1:15

3:35

11:m

12:45

2:20

3:25

4:22

lo:40

12: 10

1:25

3:10

0 0

8.64 0.9~6

8.64

9-58

0.7894

9.58 0.Wl

9-58

0.7893

0.7896

9-58

0.7888

9.58 0.7894

9.58

0.9121

0.9126

9.58

0.9112

0.7906

0* 1907

0.7907

0 0

2.0 1.6

1.8 1.05

1.4

1.0 0.2

0.8

0 0

2-9 3.1

2.7 2.7

2.4 2:5

2.1 2.2

2.2 2.2

3.1 3.0

2.3 2.3

2.0 1.7

1.5 1.2

1.0 0.5

0 0

2.9 3-1

2.8 2.8

2.5 2-5

2.1 2.1

3.1 3.0

2.3 2.3

2.0 1.8

1.5 1.2

0.1 0-5

0 0

3.8

6.2

3.8

6.2

6.1

6.2

Table B-3 (COntinUCd)

7-J

7-K

7-M

7-n

7-0

7-P

7-26-66

7-27-66

7-28-66

4: 00

5:15

6:io

7:25

8: 50

10:10

11:lO

6:50

8:05

9:10

10:05

ll:05

11:45

1:05

0.00672

0.04190

0.01190

0.041gO

0.04190

0.05270

0.03673

0.05632

0.07633

O.Og649

0.11653

0.13652

O.Oo680

0.13~3

0.09208

0.05191

0.0-

0.7228

0.09239

0.10122

22.888

22.99

22.926

22.940

22.91

23.025

22.046

11.7853

11.7254

11.6649

11.6520

11.6954

11.7167

8.2710

22.619

22.609

22.567

22.532

22.516

22.5ll

22.673

11.4130

11.459

11.5151

11.5334

11.4881

11.4534

7.9658

23.057

23.084

23.089

234"+

23.131

23.185

23 -035

11.9122

11.8196

11.7901

ll.VO6

11 .a156

11 .E353

23.052

23.058

23.067

23,109

23.159

22.w

8.4088

23.022

11.8874

11.8264

11.7667

11.7496

7951

11.8159

8.3912

23.062

23.084

23.W

23.096

23.139

23.209

23.076

ii.8941

11.8313

11.7853

ll.7593

11.7976

ll.8118

8.3802

24.19

24.194

24.202

24.026

24.209

24.238

24.206

24.054

24.050

24.035

24.015

24.002

24.000

24.046

22.007

22.98

22.96

22.937

22.982

22.618

22.608

22.570

22.526

4:05

5:20

6:20

0 0

9.58 0.7905

9.58 0.7902

0.7902

1.1 0.5

Run No. + lhte

Begun

Mal zero (in.)

-1

Readinn (in.)

8-A

8-B

8-D

8-E

9-b

8-p

13.5636

13.5189

13.4953

13.1794

13.4810

13.4829

9.3344

13.1829

13.2026

l3.2l66

13.2243

13.2174

13.2089

8.8453

23.025

22.845

11.7845

11.7221

11.6650

11.6501

11.6950

11.7169

8.2728

22,517

22.514

22.672

11.4129

11.4553

11* 5159

11.5320

11.4874

11.4556

7.9672

7:35

8: 57

10:20

11:m

7200

8:15

9:20

10:15

11:l2

11:55

1:13

0 0

9.58

9.58 0.7900

9.58

9.58 0.7888

9.58 0.7909

0.9033

8.66 0.946

0 0

1.1 0.5

2.1

0 0

1.1 0.7

1.7 1.4

2.2 2.0

2.7 2.6

3.5 3.4

0 0

1.2 0.9

1.7 1.4

2.2 2.0

2.7 2.6

3.6 3.5

6.2

6.1

6.2

0.7893

6.2

8.66

9-56

0.-

O.gO63

O.gO54

0 9050

1.0938

0 0

1.6

2.1 1.6

1.8 1.6

0 0

3.3 3.5

2-9 3.1

2.4 2.5

2.0 2.0

2.6 2.8

2.8 3.0

3.3 3.5

2.9 3.1

2.4 2.5

2.0 2.0

2.6 2.8

2.8 3.0

3.8

8.66

3.8

Table B-3 (Continued)

Lnte

Begun

7/28/66

7-28-66

7-29-66

8-1'66

2:15

3:23

4: 40

6:00

7:10

9:45

10:50

11:40

1O:lO

11:35

12:55

2:40

4:Oo

12:20

0.05270

Dial Zero (ln.)

0.05270

o.OsTI0

0.05270

D l a l Reaalng (lu.)

0.08116

0.w117

0.06130

0.05270

0.09268

0.12261

0.14269

0.16275

0 .18262

0.20270

0.08715

0.06170

0.05778

0.06632

82Q34

8.1590

8.1546

8.2361

8 * 2799

8.3103

8.3630

8.3861

8.4409

8 1994

8.1725

8.1540

8.1588

8.0083

8.0013

8.0289

7.9677

7.8961

7.8446

7.8352

7 * 7750

7.7618

7.9485

8.009

8.0101

7.9845

8.2871

8.2798

8.3639

8.4163

8.4507

8.5004

8.5285

8.5798

8.3289

8.3078

8.2800

8.2854 8.2712

8.3359

8.3977

8.4296

8.4831

8.5074

8.5610

8.3139

8.2884

8.2651

8.372

8.3755

8.4203

8.4620

8.4972

8.5515

8.2852

8.294

8.2474

8.2525

9.256

9.2600

9.2881

9.2969

9.3006

9 3194

9.3309

9.2841

9.2613

9.2526

9.2387

8.8456

8.8344

8.8016

8.775C

8.mO

8 * 7391

8.7356

9.2841

8.8243

8.8354

8.8306

8.1540

8.2367

8.2803

8.999

8.3635

8.3861

8.4406

8.1987

8.1726

8.1540

8.1574

7.8336

7.7748

7.7618

7.9483

8.0104

7.9850

8.2719

8.2649

8.3092

8.2560

8.24%

9.2848

9.2617

8.398

8.8437

8.893 -

8.3504

8.2045

8.1590

8.-

8.0015

8 - W

7.9686

7.8970

7.8446

3: 3

4:50

6: 15

7:20

9: 50

11:OO

11:45

10:15

11:40

1:OO

2:55

4:05

12:30

0 0

9.56

9-56

l.l@

1.lo10

1.8 1.6

4.6

2.7 2.7

0 0

9-56

9-56 1.0987

9.56 1.0967

9-56 1.0963

9-56 1.0949

9-56 1.0941

9.56

9-56 Logy5

9.56 1.io03

9-56

1.1012

1.1010

0 0

1.8

1.6

1.8 1.6

1.8

1.6

1.8 1.6

4.3 4.7

4.7 5.2

5.0 5.5

5.1 5.7

5.4 6.0

5-65 6.25

4.6

4.65

3.9 4.35

4.45

3.9 4.3

4.3 4.7

4,7 5 -2

5-0 5.5

5i i 5.7

5.4 6.0

5-65 6.25

2:;5

4.45

2.7

4.7

2.7

0 0

1.8 1.6

4.0 4.4

3.9 4.3

4.0 4.4 2.7 2.7

1.lo11

0 0

1.093

2.7

4.65 2.7 -

2.7

8-1-66

8-8-66

Timc Begun

1:55

8: 9

9:21

Dial Zero (in.)

0.05270

0.01540

D i a l Readlng (in.)

0.07648

0.13551

0.13257

0.12956

8.1m

23.031

23.024

23.022

Date

8-8-66

8-6-66

10:05

11:00

2:00

1:00

2: 10

3:15

4: 20

0.01540

0.12655

0.12345

0.12050

0.11550

0.11249

0.10250

23.006

23007

22.997

22.992

22.99

22 991

8-8-66

5:20

6: 20

7:lO

8: 30

0.01540

0.09406

0.06815

0.08230

0.07638

22.988

23.000

23.005

22.996

8-8-66

7.9846

22.546

22.539

22 * 558

22.556

22 * 563

22.558

22.567

22.576

22-59

22.602

22.625

22.640

22.638

8.3264

23.191

23.186

23.181

23.164

23.162

23.154

23.149

23.153

23.148

23.149

23.159

23.162

23.156

8.3117

23.165

23.158

23.154

23.137

23.128

23.124

23.129

23.121

23.119

23.129

23.134

23.130

8.2909

23.210

23.206

23.203

23.179

23.175

23.165

23.157

23.161

23.154

23.151

23.158

23.160

23.156

9.2525

24.259

24.256

24.251

24.243

24.236

24.233

24.228

24.226

24.228

24.232

24.236

8.8282

24.036

24.055

24.061

24.025

24.020

24.021

24.023

24.021

24.024

24.029

24.033

24.036

24.046

8 * 1975

23.030

23.023

23.021

23.005

23.007

22.996

22.992

23.000

22.990

22.989

23.001

23.006

22.993

7.9850

22.546

22.540

22.559

22.554

22.564

22.558

22.566

22-57

22.593

22.603

22.627

22.640

22.635

2:05

8: 37

9:27

10:15

11:17

2: 10

1:15

2:15

3:20

4: 30

5:25

6:25

R20

8: 40

0 0

9-56 1.0997

9.61

0.7907

0.793

9.61 0.7904

9.61 0-7904

9.61 0.7904

9.60 7903

9.60 0.7903

0.7900

% :8

0 0

1.8

1.6

1.7 1.05

1.05

1.7

1.7 1.05

1.7

1.05

1.7 1.05

4.2 4.65

3.0 3.0

2.8

2.7 2.6

2.5 2.45

2.4 2-35

2.3 2.25

2.2 2.1

2.0

2-7

1.95

1.8 1.6

1.7 1.45

1.7 1.05

4.2 4.65

3.0 2.9

2.8 2.8

2.5 2.5

2.4 2-35

2.3

2.2 2.1

1.75

1.95 1.7

1.8

2.2

1.5

1.o

2.7

6.2

2.7

6.2

2.7 2-55

6.2

8-8-66 â&#x20AC;&#x2122;

6.2

1.95 6.2 6.2

1.75 2.0

9.60

6.2

9.60

0.7898

1.5

6.2

.. .

8-8-66

8-10-66

10:40

11:20

9:00

lor15

1l:lO

12:m

12: 50

1: 35

2:25

3: 30

4:lO

4:57

6:40

0.01540

0.06458

0.05878

0.05435

0.05168

0.0467l

0.04232

0.03826

0.03449

0.03072

0.02675

0.02270

0.02132

0.01954

23.056

23.052

23.056

23.047

23-02?

23.018

23.012

23.027

22.810

22.800

22.820

22.816

22.836

8-10-66

Z.%3

22.970

22.959

23.67

23.068

23.058

22.610

22.627

2 2 . M

22.764

22.778

22.781

22.789

22.795

22.all

23.131

23.134

23.123

23.222

23.227

23.222

23.a9

23.216

23.220

23.213

23 * 198

23-19

23.202

23.103

23.101

23.091

23.197

23.198

23-19

23.189

23.185

23.189

23.179

23.163

23.157

23.153

23.165

23.19

23.127

23.122

23.221

23.224

23.220

23-223

23.222

23.227

23.221

23.212

23.214

23.213

23.224

24.230

24.221

24.276

24.273

24.272

24.269

24.264

24.263

24.262

24.264

24.152

24.149.

24.152

24.151

24.164

24.050

24.049

24.219

24.646

24.277

24.143

24.277

24.145

24.276

24.140

24.137

24.141

24.149

22.9

22.970

22.959

23-67

a3.a

23.057

23.056

23.052

23.057

23.045

23.026

23.018

23.009

23.026

23.609

2 2 . w

22.764

22.m

22.780

22.790

22.796

22.812

22.809

22.800

22.820

22.815

22.836

9:45

l0:45

ll:25

9:oS

10:25

11: 16

12: 10

1:00

1:45

2: 35

3: 35

4:17

5:07

6:45

0 0

%99

9.60 0.7900

9.60

9.595

9:595

9.585

0.7880

0.7881

9.585

0.7881

9.585 0 7879

9.585

0.7881

0.7878

9.585

0.7881

09#9

9.585

0.7903

0.7881

9.585 0.7878

0 0

1.7

1-7 1.05

1.7 1.05

1.8 1.05

1.8

1.8 1.05

1.8

1.3

1.05

0.8

0 0

1.0 0.5

1.o 0.5

q.0

a.0

0.8

a.0

a.o

0.3

0.2

0.1

0 0

1.2 0.9

1.0 0.5

a.0

0.2

0.1

0 0

6.2

0.3

6.2

0.3

6.2

1.05 1.1

* 13

8-8-66

6.2

(3\

Table B-3 (Continued)

Run NO. +

11-EB

12-A

12-8

124

12-D

12-~

12-F

12-G

12-H

12-1

12-J

124

12-1

Date

8-10-66

6-11-66

8-11-66

Time Begun

7:23

8:05

8: 55

9:35

l0:15

10: 50

11: 35

8:40

9:56

10: 45

11: 35

12:25

l:20

2: 30

D i a l Zero (in.)

0.01540

Mal Read-

0.01742

0.015p

0.02336

0.03125

0.03511

0.03908

0.04301

0.04691

0.05095

0.05481

0.05870

0.06461

0.07C63

0.07652

23.087

23.086

(in.)

23.014

23.005

23.009

23.021

23.026

23.029

23.043

23 0%

23.085

23.087

22.837

22.829

22.805

22* 791

22.785

22.780

22.782

22.822

22.809

22.805

22.801

22.795

22.7%

22.784

23.198

23 -185

23.188

23-19

23.196

23-19

23.207

21.257

23.251

23.252

23.250

23.248

23.157

23.146

23.148

23.158

23.162

23.165

23.176

23.225

23.219

23.220

23.219

23.n9

23.222

23.217

23.207

23.204

23.203

23.201

23.211

23.259

23.252

23.251

23.250

23.249

23.251

24.266

24.265

24.261

24.256

24.254

24.261

24.299

24.293

24.2%

24.287

24.286

24.279

24.278

24.149

24.143

24.140

24.134

24.133

24.132

24.159

24.150

24.137

24.128

24.125

24.l23

24.124

24.163

23.003

23.W

23.02l

23.026

23.030

23.043

23* 092

23.086

23.087

23.085

23.086

23.087

23.086

22.8%

22.829

22.805

22.791

22.784

22.780

22.782

22.821

22.809

22.807

22.800

22.795

22.792

22.784

7:28