NATIONAL BUREAU OF STANDARDS REPORT

8345

THERMAL CONDUCTIVITY OF A SPECIMEN OF

ELECTROFORMED NICKEL

by

To W„ Watson and H, Eo Robinson

Report to

The International Nickel Company, Inc P New York, No Y 0

U. S. DEPARTMENT OF COMMERCE

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NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT NBS REPORT

1006-50-10642 30 April 1964 8345

THERMAL CONDUCTIVITY OF A SPECIMEN OF

ELECTROFORMED NICKEL

by

T„ W, Watson and H. E* Robinson

Heat Transfer Section

3uilding Research Division

Report to

The International Nickel Company, Inc

New York, N. Y.

IMPORTANT NOTICE NATIONAL BUREAU OF ST t for use within the Government, and review. For this reason, the whole or in part, is not authori. Bureau of Standards, Washingto

the Report has been specifically |

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST)

on October 9, 201 5.

s accounting documents intended

subjected to additional evaluation

listing of this Report, either in Office of the Director, National

the Government agency for which

pies for its own use.

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

Thermal Conductivity of a Specimen

of Electroformed Nickel

by

Thomas W. Watson and Henry E. Robinson

1.

INTRODUCTION

This report presents results of thermal conductivity and electrical

resistivity measurements in the temperature range —162° to 540° C of a sample of electroformed nickel (radially-deposited on a nickel wire)

submitted by the International Nickel Company, Inc., 67 Wall Street,

New York, N. Y.

2.

SAMPLE

The sample submitted was a bar about one inch in diameter, which

was machined to yield a test specimen having a uniform diameter of

2.54 cm and a length of 3 7.0 cm.

The chemical composition of the specimen is given in Table 1, as determined from a spectrochemical analysis made by the National Bureau

of Standards Spectrochemistry Section.

3.

TEST APPARATUS AND METHOD

The thermal conductivity of the sample was determined by means of

a steady-state flow of heat longitudinally in the bar specimen, with

measurements of the temperatures existing at the ends of six consecutive,

approximately 3‘51-cm, spans along the central length of the bar. Each

determination required a pair of tests at moderately different temperature conditions, and yielded values of thermal conductivity at six different mean temperatures. [l] a

The test apparatus is shown schematically in Figure 1.

The specimen, a bar approximately 3 7 cm long and of uniform external dimensions over the metering length, was supported at the top

(coolant) end concentrically within a stainless steel guard tube of

0.8-cm wall thickness, x^hich in turn was held concentrically within a cylindrical outer container. The specimen was drilled at each end with

a 1.35-cm hole 5.5 cm deep. An electrical heater was inserted and

secured in the hole at the bottom (hot) end by a completely-enclosing

a See references in 6. REFERENCES
2

metal cap (in lieu of the strap shown in Figure 1), and the supporting

fixture at the top end provided a liquid-tight connection for circulating

a coolant through the top drill-hole.

Temperatures along the specimen were indicated by seven thermocouples located symmetrically about the longitudinal center of the specimen, spaced approximately 3*51 cm apart, with one additional thermocouple

near the bottom end of the specimen. Thermocouples were similarly located in almost exactly corresponding longitudinal positions on the guard

tube.

The guard tube was equipped near its lower end with an external

circumferential electric heater, as shown. The guard tube was cooled at

the top by means of a copper-tube coil soldered circumferentially at a position corresponding in effect to that of the specimen coolant well.

Coolant (liquid nitrogen at —196° C or water at 40° C) was pumped through

the guard coil and specimen well in series connection, as shown.

The electrical heater for the specimen consisted of a porcelain

cylinder 1.25 cm in diameter and 5.2 cm long, threaded longitudinally

with 26-gage nichrome heater wire. Its resistance at 25° C was approximately 21 ohms. Current was brought to the heater through relatively

large heater leads , to which separate potential leads were connected at

the point where they entered the porcelain core. The heater was ener- gized by an adjustable constant-voltage d-c source. Heater current and

voltage drop measurements were made using standard resistors and the highprecision manual potentiometer used for thermocouple observations. The

guard was heated with alternating current governed by a sensitive temperature controller actuated by the guard temperature at a selected position.

The thermocouples were made from calibrated chromel and alumel

26-gage wires, welded by gas-oxygen flame to form a butt joint about

0.042 cm in diameter.

The thermocouple junctions were pressed into transverse grooves

0.04 cm wide by 0.05 cm deep and 0.6 cm in length in the convex surface

of the bar and tightly secured by peening the metal around the groove.

The bare thermocouple leads were individually insulated electrically

with high- temperature flexible sleeving, and led out into the powder

insulation in the same transverse plane as the junction (one wire in

each direction around the bar), forming a 2.5-cm circle. The wires were

brought out through the powder insulation near the guard tube. The

thermocouples in the guard tube were electrically welded to form a spherical junction about 0.10 cm in diameter. The junctions in the

guard were inserted into radially-drilled holes 0.11 cm in diameter and

0.17 cm deep, and tightly secured by punch-pricking the metal around
- 3 -

the hole. The wires were similarly brought out through the powder insulation. The longitudinal positions of the thermocouple junctions were

taken as those of the centers of the grooves, or of the drilled holes,

measured to the nearest 0.01 cm with a laboratory cathetometer.

Current leads (0.1 cm Pt) were attached to the two ends of the bar

specimen for passing a direct current of about 8 amperes along the bar

for making electrical resistivity measurements. The lead at the hot end was led in a flat spiral in the powder insulation, in a plane transverse

to the bar axis, to near the inner radius of the guard tube, from which

point it was electrically insulated with broken ceramic tubing and brought

upwards through the powder insulation near the guard tube.

After installation of the specimen, the space between it and the

guard tube was filled with diatomaceous earth powder insulation, which

also was used to insulate the space surrounding the guard tube. The

tests were conducted with the insulation exposed to atmospheric air.

In principle, if there were no heat exchange between the specimen

and its surroundings, the conductivity could be determined from the measured power input to the specimen and the average temperature gradient

for each of the six spans along the specimen, all of uniform known

cross-sectional area. In practice, a perfect balance of temperatures

between the bar and guard all along their lengths is not possible be- cause of differences in their temperature coefficients of conductivity,

and the effect of the outward heat losses of the guard. In addition to

heat exchanges between the bar and guard from this cause, a relatively

smaller longitudinal flow of heat occurs in the powder insulation sur- rounding the specimen, and the contribution of the specimen to this heat

flow must depend somewhat on the bar-to-guard temperature unbalance.

In order to evaluate the heat flow in the bar at the center points

of each of the six spans, a partly empirical procedure was used. Two

steady-state test-runs were made with slightly different bar and guard

temperatures and power inputs. In the two tests, the heat flow and the

observed temperature drop from end to end of a given span differed, as did also the approximate integral with respect to length of the observed

temperature differences between bar and guard, summed from the hot end

of the bar to the span center point. It is thus possible to write for

each span two equations (one for each test-run) of the form

AkAt

Ax

+ fS Q

where A is the cross-sectional area of the specimen,

k is the specimen conductivity at the mean temperature of the

span,
4

At is the temperature drop from end to end of the span,

Ax is the length of the span,

fS represents the total net heat loss from the bar from its

bottom end at the heater to the midpoint, x, of the given

span, expressed as the product of S, which is the integral

J 0

(^~ o ^ r “ t guard^X} anc* an avera8e heat transfer coefficient

f for the thermal path from bar to guard,

Q is the measured power input to the specimen heater.

The two equations written for each of the six spans of the bar can

be solved simultaneously to determine k and f. For this to be strictly

valid, k and f must have equal values in the two equations. Since the

mean temperatures of the span in the two tests will in general differ

slightly, and the conductivity of the bar may vary with temperature, a slight adjustment is made to the observed values of At so that k corresponds to the mean of the span mean temperatures in the two tests. The

equality of f in the two tests is not so readily assured, but because

the magnitude of fS in these tests was generally on the order of one percent of Q, a moderate difference in the values of f in the two equations

would affect the solved value of Ak/Ax only slightly.

Electrical resistivity measurements for each span were made at the

end of, but at the temperature conditions existing at, each pair of runs

for determining the thermal conductivity, by passing a d-c current of

about 7.7 A along the bar, and observing the potentials of the chromel

leads of the span thermocouples, with the current direction forward and

reversed. The average of the two potential drops between two adjacent

chromel leads indicated the net potential drop due to the current flowing

in the span, and thus enabled calculation of its resistivity. Due to a slight warming of the bar during the period of current flow, the resistivity was assigned to correspond to the time-average of the span mean

temperature over this period. The same electrical and temperature measurements also enabled calculation of the thermoelectric power of the

nickel relative to the chromel P thermocouple wire used.

The computation of results directly from the observed data was effected by an IBM 7094 digital computer suitably programmed to compute

the thermal conductivity, the electrical resistivity and the thermoelectric power, and the corresponding mean temperatures, for each of

the six spans.
- 5

-

4. RESULTS

The results of the thermal conductivity and electrical resistivity

determinations are shown in Figure 2 and Table 2. The 36 individual

values plotted in each case represent six sets of tests, each with values

for the six spans. The open circles represent values obtained in tests

made with increased values of span mean temperatures; solid circles

represent values obtained on cooling from the maximum temperatures attained. The solid lines represent the trend of the data from which the

values tabulated in Table 2 were taken.

The calculated values of the thermoelectric power of the electroformed nickel relative to the chromel P thermocouple wire used are plotted in the upper part of Figure 3» Values of the Lorenz function,

kp/T, were calculated from the values of thermal conductivity, electrical resistivity, and temperature tabulated in Table 2. They are given

in Table 2 and represented by the smooth curve in the lower part of

Figure

5. DISCUSSION OF RESULTS

The individual values of thermal conductivity and electrical resistivity plotted in Figure 2 show moderate scattering from the smooth

curve. The extreme departure of an individual value of thermal conductivity from the smooth curve is less than two percent. The uncertainty

in the smoothed conductivity values is believed to be not more than

one percent.

As shown in Figure 2, the thermal conductivity decreased as the temperature increased to the Curie point, and thereafter increased. The curves are shown dotted in the region where a part of a measuring span was at the apparent Curie temperature, because of increased uncertainty

in the values obtained in this region. The dashed lines in Figure 2

represent the values of Van Dusen 19^4 [2] for nickel of 99.94 percent

purity.

The obtained values of electrical resistivity are shown in the upper

part of Figure 2. The resistivity increased with temperature to the

Curie point, and thereafter increased more slowly. The points plotted

as triangles near the resistivity curve show values of resistivity re- ported by Roeser 1941 [3 ] for nickel of 99.94 percent purity; the squares

show values of White and Woods 1959 [4] for nickel of "ideal purity."
6

The obtained values of thermoelectric power of the electroformed

nickel, relative to the chromel P thermocouple wire used, are shown in

Figure 3> with symbols consistent with those of Figure 2. The plotted

triangles represent values of thermoelectric power of nickel relative to

chromel P derived from data on thermal emf of nickel, and of chromel P,

relative to platinum [5].

The lower curve of Figure 3 represents the values of the Lorenz

function (kp/T) given in Table 2, derived from the thermal conductivity

and electrical resistivity results. The theoretical (Sommerfeld) value

2.443 x 10"® V

2 /deg2

is shown by the horizontal dashed line. In the

neighborhood of the Curie point, the Lorenz function obtained using the

conductivity and resistivity values given by the dashed parts of Figure 2 shows an upturn, for both parts of the curve in Figure 3* The

upturns probably represent too-large values of k, or p, or both, obtained in the near region of the Curie point as a result of the con- siderable temperature difference from end to end of a measuring span in

this region.

As inferred from intersections of the various curves from lower

and higher temperatures, the approximate apparent values of the Curie

temperature of the electroformed nickel specimen are 376 0 C from the

thermal conductivity data, 376° C from the electrical resistivity data,

and 378° C from the thermoelectric power data. These values compare

with the value J58° C given for nickel by Bozorth [6],

1 aftahr.
- 7

-

6. REFERENCES

[1] T. W. Watson and H. E. Robinson, Thermal conductivity of some commercial iron-nickel alloys, ASME Jour, of Heat Transfer

(November 1961) p. 403-408.

[2] M. S. Van Dusen and S. M. Shelton, Apparatus for measuring thermal conductivity of metals up to 600 C, J. Research NBS , 12 , 429 (1934) RP668.

[ 3 ] W. F. Roeser, Temperature, Its Measurement and Control in Science

and Industry, p. 1312 (Reinhold Publishing Corp. , New York, N. Y.

1941).

[4] G. K. White and S. B. Woods, Electrical and thermal resistivity

of the transition elements at low temperature, Phil. Trans. Roy.

Soc. 251A, 273 (1959).

[5] American Institute of Physics Handbook, p. 4-8, 9 (McGraw-Hill

Book Co., Inc., 1963, Second Edition).

[6] R. M. Bozorth, Ferromagnetism, p. 270 (Van Nostrand, 1951).
TABLE 1

Chemical Composition -

Percent

Ni* Co Cu Fe A1

99.85 0.11 0.026 0.006 0.001

Si Ti Mg Cr Mn

< 0.004 < 0.002 < 0.001 < 0.001 < 0.0005

A general qualitative examination did not

reveal the presence of other elements.

* By difference
TABLE 2

Thermal Conductivity and Electrical Resistivity

of a Sample of Electroformed Nickel

Temperature , t

°C - 162 - 150 - 100 - 50

0

50

100

150

200

250

300

350

400

450

500

Thermal

Conductivity, k

W/cm deg

1.078

1.058

0.981

0.918

0.863

0.819

0.780

0.744

0.708

0.672

. O .636

. (0.600) .

0.588

0.600

0.611

0.620

Electrical

Resistivity, p

Ufl cm

2.08

2.42

3.88

5.47

7.24

9.24

11.50

14.09

17.05

20.43

24.27

. (28.64) .

• 32.34 .

. 34.10

. 35.86

. 37.26

Lorenz f kp

Function T

V

2 / deg2

2.02 x

10~ 8

2.08

2.20

2.25

2.29

2.34

2.41

. 2.48

2.55

2.63

2.69

2.76

2.83

2.83

2.83

540 2.85

53.0

COOLANT

APPARATUS FOR MEASURING THE THERMAL

CONDUCTIVITY OF METALS

Figure 1
THERMAL

CONDUCTIVITY,

W/cm

deg

ELECTRICAL

RESISTIVITY

microhm

cm

ELECTROFORMED NICKEL

-200 -100 0 100 200 300 400 500 600

TEMPERATURE, °C

FIGURE 2. THERMAL CONDUCTIVITY AND ELECTRICAL RESISTIVITY OF ELECTROFORMED NICKEL VERSUS TEMPERATURE
ELECTROFORMED NICKEL

TEMPERATURE, °C

FIGURE 3. THERMOELECTRIC POWER OF ELECTROFORMED NICKEL RELATIVE TO A CHROMEL P THERMOCOUPLE WIRE, AND LORENZ FUNCTION (kp/T)

,

VERSUS TEMPERATURE

LORENZ

FUNCTION,

VVdeg