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PUBLICATIONS

NISTIR 89-3919 fi' MICROPOROUS FUMED-SILICA

INSULATION AS A

STANDARD REFERENCE MATERIAL OF

THERMAL RESISTANCE AT

HIGH TEMPERATURE

David R. Smith

National Institute of Standards and Technology

U.S. Department of Commerce

Boulder, Colorado 80303-3328

August 1989

-QC

100

.056

89-3919

1989

C.2
NATIONAL INSTITUTE OF STANDARDS &

TECHNOLOGY

Research Information Center

Gaithersburg, h© 20899

DATE DUE

•

Demco. Inc. 3 3-293
NISTIR 89-3919

MICROPOROUS FUMED-SILICA

INSULATION AS A

STANDARD REFERENCE MATERIAL OF

THERMAL RESISTANCE AT

HIGH TEMPERATURE

David R. Smith

Chemical Engineering Science Division

Center for Chemical Engineering

National Engineering Laboratory

National Institute of Standards and Technology

Boulder, Colorado 80303-3328

August 1989

Sponsored, in part, by

U.S. Department of Energy

Oak Ridge National Laboratory

Oak Ridge, Tennessee 37830

U.S. DEPARTMENT OF COMMERCE, Robert A. Mosbacher, Secretary

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Acting Director

CONTENTS

Page

LIST OF TABLES iv

LIST OF FIGURES vi

ABSTRACT... xi

1. INTRODUCTION 1

2. DESCRIPTION OF MICROPOROUS FUMED SILICA 3

3. APPARATUS AND MEASUREMENTS 4

Time Required for Stability and Reproducibility 5

4. DEPENDENCE OF APPARENT CONDUCTIVITY ON TEMPERATURE

AND DENSITY 6

(A) Expected Dependence of Conductivity on Temperature

and Density 7

(B) Experimental Results 7

5. DEPENDENCE OF APPARENT THERMAL CONDUCTIVITY ON AMBIENT

AIR PRESSURE 9

(A) Constraints on the Ranges of Pressure Used in This

Work 9

(B) Expected Dependence on Ambient Air Pressure 10

(C) Measurements of Pressure 11

(D) Experimental Results 11

6. DEPENDENCE OF APPARENT CONDUCTIVITY ON PRESSURE AND

DENSITY 12

7. DEPENDENCE OF CONDUCTIVITY ON TEMPERATURE, DENSITY,

AND PRESSURE 13

8. COMPARISONS 18

9. REFERENCES 21

10. TABLES 1 - 5 22-31

11. FIGURES 1 - 22 32-53
LIST OF TABLES

Table 1. Apparent thermal conductivity of five pairs of microporous fumed-silica insulation boards with mean densities of (a) 348, Cb) 328, (c) 305, (d) 300, and (e) 315 kg/m^ , at

mean temperatures ranging from 318 to 723 K (45 to 450oC). One

hundred and seventy-eight measurements were performed in air at

ambient humidity and at pressures of approximately 83 kPa (625

Torr), by use of the high-temperature guarded hot plate at the

National Institute of Standards and Technology in Boulder, Colorado. Temperature differences through the specimens were chosen

to be about 10 percent of the value of the mean temperature within the specimens. The bias in values of Kmeas is estimated to be

1.5 percent at 330 K, and 2.5 percent at 720 K. The column labeled Kcaic gives values of apparent thermal conductivity calculated

from eq (3). The collective standard deviation of the 178 residuals between the data (Kdat ) and the fitted curve is 0.68 percent. Absolute (Kdev) and relative (Pdev) deviations compare

measured (Kdat ) to calculated (Kcaic ) values of thermal

conductivity 22

Table 2 . Apparent thermal conductivity of pair B14 of microporous

fumed-silica insulation boards measured at a mean specimen temperature of 318 K (45oG), and over the range of pressure

from 40 to 83 kPa (300 to 626 Torr), with the high-temperature

guarded hot plate. This pair has a mean density of 301 kg/m^

(19 lbm/ft3). Apparent conductivity was measured in air at ambient humidity. Temperature differences through the specimens were

chosen to be about 10 percent of the value of the mean absolute

temperature within the specimens. Absolute and relative deviations compare measured apparent conductivity to values of Kcaic

computed from eq (3) 28

Table 3. Apparent thermal conductivity of pair B8cd of microporous fumed-silica insulation boards measured at a mean

specimen temperature of 318 K (45^0, and over the range of pressure from 27 to 80 kPa (200 to 600 Torr)*, with the high-temperature guarded hot plate. This pair has a mean density of

348 kg/m3 (22 Ibm/ft^). Apparent conductivity was measured in

air at ambient humidity. Absolute and relative deviations compare

measured apparent conductivity to values of Kcaic computed from

eq ( 3 ) 29
Table 4. Apparent thermal conductivity of pair B34 of microporous

fumed-silica insulation boards measured at a mean

specimen temperature of 473 K (200oC), and over the range of

pressure from 40 to 83 kPa (300 to 626 Torr)

,

with the high-temprature guarded hot plate. This pair has a mean density of

315 kg/m3 (19.7 Ibm/ft^). Apparent conductivity was measured in

air at ambient humidity. Absolute and relative deviations compare

measured apparent conductivity to values of Kcalc computed from

eq ( 3 ) 30

Table 5. Apparent thermal conductivity of pair B8cd of microporous fumed-silica insulation boards measured at a mean

specimen temperature of 473 K (200oC), and over the range of

pressure from 27 to 84 kPa (200 to 630 Torr), with the high-temperature guarded hot plate. This pair has a mean density of

348 kg/m3 (22 Ibm/ft^). Apparent conductivity was measured in

air at ambient humidity. Absolute and relative deviations compare

measured apparent conductivity to values of Kcalc computed from

eq ( 3 ) 31

V
LIST OF FIGURES

Figure 1. Typical dependence of apparent thermal conductivity

of microporous fumed-silica insulation on ambient

air pressure. No theory exists to completely predict the sigmoidal shape modelling the dependence. The values along both

axes are arbitrary but representative. In this figure A is the

region of constant, low conductivity at low pressure; B-C-D is

the transitional region of rising conductivity at intermediate

pressures; E is the beginning of the plateau of approximately

constant, higher conductivity at higher pressures. The region

connecting the rising transitional region to the high-pressure

plateau (D-E) is the "knee." The low-pressure plateau of constant apparent conductivity is determined by radiative heat

transfer and by conduction in the solid material, which are

independent of pressure 32

Figure 2. Apparent thermal conductivity of pair B8cd of

microporous fumed-silica insulation at mean specimen temperatures ranging from 318 to 713 K (45 to 440^0, with

the NIST-B high-temperature guarded hot plate. This pair has a

mean density of 348 kg/m^ (22 Ibm/ft^ ) . Conductivity was measured in air at ambient humidity and at a pressure of 83 kPa.

The measurement bias in values of Kmeas is estimated to be 1.0

percent at 320 K, and 2.5 percent at 725 K. The solid curve

represents values of Kcaic obtained using eq (3) 33

Figure 3. Relative (percent) deviations of apparent thermal

conductivity of fumed-silica insulation pair B8cd

from values calculated with eq (3). The standard deviation of

the 45 residuals between the points and the curve is 0.70

percent 34

Figure 4. Apparent thermal conductivity of pair B23 of microporous fumed-silica insulation at mean specimen

temperatures ranging from 333 to 723 K (60 to 450oC). This

pair has a mean density of 328 kg/m^ (20 Ibm/ft^ ) . Conductivity was measured in air at ambient humidity and at a pressure

of 83 kPa. The solid curve represents values of Kcaic obtained

using eq ( 3 ) 35

Figure 5. Relative (percent) deviations of apparent thermal

conductivity of fumed-silica insulation pair B23

from values calculated with eq (3). The standard deviation of

the 22 residuals between the points and the curve is 0.35

percent 36
Fi^re 6. Apparent thermal conductivity of pair B12 of microporous fumed-silica insulation at mean specimen

temperatures ranging from 323 to 723 K (60 to 45QoC). This

pair has a mean density of 304 kg/m^ (19 lbm/ft3). Conductivity was measured in air at ambient humidity and at a pressure

of 83 kPa. The solid curve represents values of Kcaic obtained using eq (3) 37

Figure 7. Relative (percent) deviations of apparent thermal

conductivity of fumed-silica insulation pair B12

from values calculated with eq (3). The standard deviation of

the 42 residuals between the points and the curve is 0.58

percent 38

Figure 8. Apparent thermal conductivity of pair B14 of microporous fumed-silica insulation at mean specimen

temperatures ranging from 321 to 723 K (48 to 450^0

.

This

pair has a mean density of 301 kg/m^ (19 Ibm/ft^). Conductivity was measured in air at ambient humidity and at a pressure

of 83 kPa. The solid curve represents values of Kcaic obtained using eq (3) 39

Figure 9. Relative (percent) deviations of apparent thermal

conductivity of fumed-silica insulation pair B14

from values calculated with eq (3). The standard deviation of

the 38 residuals between the points and the curve is 0.30

percent 40

Figure 10. Apparent thermal conductivity of pair B34 of microporous fumed-silica insulation at mean specimen

temperatures ranging from 321 to 723 K (48 to 450 oC). This

pair has a mean density of 315 kg/m^ (20 Ibm/ft^ )

.

Conductivity was measured in air at ambient humidity and at a pressure

of 83 kPa. The solid curve represents values of Kcaic obtained using eq ( 3 ) 41

Figure 11. Relative (percent) deviations of apparent thermal

conductivity of fumed-silica insulation pair B34

from values calculated with eq (3). The standard deviation of

the 31 residuals between the points and the curve is 1.16

percent 42
Fi^re 12. Apparent thermal conductivity of pair B14, density

of 301 kg/m3 (19 lbm/ft3 )

,

at a mean specimen

temperature of 318 K (45oC) and at pressures ranging from 40 to

83 kPa. The solid curve represents values of Kcaic obtained

using eq ( 3 ) 43

Figure 13. Relative deviation, in percent, of measured apparent thermal conductivity of fumed-silica pair B14

at 318 K, from values calculated with eq (3), over the range of

pressures from 40 to 83 kPa . The standard deviation of the

residuals between the data and the curve is 0.62 percent 44

Figure 14. Apparent thermal conductivity of pair B8cd, density

of 348 kg/m3 (22 Ibm/ft^), at a mean specimen

temperature of 318 K (45oC) and at pressures ranging from 26 to

80 kPa. The solid curve represents values of Kcaic obtained

using eq ( 3 ) 45

Figure 15. Relative deviation, in percent, of measured apparent thermal conductivity of fumed-silica pair B8cd

at 318 K, from values calculated with eq (3), over the range of

pressures from 26 to 80 kPa. The standard deviation of the

residuals between the points and the curve is 1.22 percent 46

Figure 16. Apparent thermal conductivity of pair B34, density

of 315 kg/m3 (20 Ibm/ft^ )

,

at a mean specimen temperature of 473 K (200oC) and at pressures ranging from 37 to

83 kPa . The solid curve represents values of Kcaic obtained

using eq ( 3 ) 47

Figure 17. Relative deviation, in percent, of measured apparent thermal conductivity of fumed-silica pair B34

at 473 K, from values calculated from eq (3), over the range of

pressures from 37 to 83 kPa. The standard deviation of the

residuals between the points and the curve is 0.41 percent 48

Figure 18. Apparent thermal conductivity of pair B8cd, density

of 348 kg/m3 (22 Ibm/ft^), at a mean specimen temperature of 473 K (200^0 and at pressures ranging from 26 to

84 kPa. The solid curve represents values of Kcaic obtained

using eq ( 3 ) 49

viii
Figure 19. Relative deviation, in percent, of measured apparent thermal conductivity of fumed-silica pair B8cd

at 473 K, from values calculated from eq (3), over the range of

pressures from 26 to 84 kPa. The standard deviation of the

residuals between the data and the curve is 1.32 percent 50

Figure 20. Apparent thermal conductivity as a function of

density, for five measured pairs of fumed-silica

specimens, at temperatures of 300 to 800 K. Measurements were

performed with an ambient air pressure of 83 kPa. Open symbols

are values calculated from eq (3) for the densities of the

specimen pairs measured 51

Figure 21. Dependence of apparent thermal conductivity of

fumed-silica insulation on bulk density. Open

squares represent measurements at 297 K and at ambient pressure

of 101.3 kPa at NIST-G. Open circles represent points

calculated from the least-squares fit to actual data obtained

at NIST-B at 300 K and at ambient air pressure of 83.2 kPa.

Plus signs are data from NIST-B extrapolated upward to a pressure of 101.3 kPa by addition of 1.43 units 52

Figure 22. Dependence of apparent thermal conductivity of

fumed-silica insulation on temperature, as measured

at ambient air pressure of 83 kPa at NIST-B (open triangles)

and at ambient pressure of 101.3 kPa at NIST-G (filled square,

triangle and diamond) . Plus signs are data from NIST-B

extrapolated upward to a pressure of 101.3 kPa by addition of

1.43 units. Data from NIST-G are for a specimen with a density

of 330 kg/m^ . Data (open triangles) from NIST-B are for one

with a density of 328 kg/m^ (pair B23) and are identical to

data in figure 4 53

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f' 1..
Microporous Fumed-Silica Insulation

as a Standard Reference Material

of Thermal Resistance

David R. Smith

Chemical Engineering Science Division

National Engineering Laboratory

National Institute of Standards and Technology

Boulder, CO 80303-3328

Measurements of apparent thermal conductivity of microporous

fumed-silica insulation board, already certified as a Standard

Reference Material (SRM) of thermal resistance, are reported

here to extend the range of certification of this material to

higher temperatures and lower pressures. Apparent thermal conductivities of five different pairs of specimens ranging in

mean density from 300 to 348 kg/m^ were measured with a hightemperature guarded hot plate 25 cm in diameter. The measurements cover a range of mean specimen temperatures from 318 to

733 K (45 to 460OC), and of environmental air pressures from

26.7 to 83.5 kPa (200 to 626 Torr) . Detailed analyses are given, along with intercomparisons of previously published data.

Apparent thermal conductivity is correlated with temperature,

pressure, and density; the correlation obtained represents all

the data within a standard deviation of 0.68 percent. This

microporous fumed silica (at an ambient pressure of 83 kPa and

a density of 300 kg/m3 ) has an apparent thermal conductivity of

19.8 mW/(m- K) at 300 K and is suitable for use as an SRM of

very low conductivity from 297 to 735 K (24 to 460OC). Adsorbed moisture within this material must be driven off by prolonged heating at llOoC before its conductivity is measured. Great

care in handling this material is necessary because of its

f ragility

.

Key words: apparent thermal conductivity; density; microporous

fumed silica; insulation board; pressure; Standard Reference

Material; temperature; thermal insulation; thermal resistance.

1. INTRODUCTION

The Office of Standard Reference Materials of the U'. S. National Institute of Standards and Technology (NIST) establishes Standard Reference Materials ( SRMs ) to improve reliability in measurement of physical properties. Specifically, SRMs of thermal resistance are used by government, academic, and industrial laboratories

to verify the correct operation of guarded hot plates (GHPs) and to

calibrate instruments such as heat-flow meters. These instruments

measure the rate of heat flow under given temperature differences

through specimens of thermal insulation of known thickness. From

such data, under steady conditions, one can obtain the thermal resistance (R-value) of the measured specimen as well as the apparent

thermal conductivity of homogeneous material. SRMs are also used

to indicate the accuracy of measurement of apparent conductivity of

thermally conducting materials over a range of parameters such as

temperature, bulk density, and environmental air pressure. The

Properties of Solids Group within the Chemical Engineering Science

Division of NIST in Boulder, Colorado (NIST-B), has participated

for about 25 years in establishing many different SRMs, including

SRMs of thermal resistance over a broad range of thermal conductivity, pressure, and temperature. The status of this effort has been

summarized by Bust [11-

During the mid-1970’s, the American Society for Testing and

Materials (ASTM) recognized the great need for SRMs of thermal

insulation. Consequently, a task-group was established under the

auspices of ASTM subcommittee C16.30 on thermal measurements.

Recommendations for establishing SRMs of thermal insulation were

published in 1978 [2].

No SRM of thermal resistance for use at temperatures above

330 K is now available from the Office of Standard Reference Materials of NIST in Gaithersburg, Maryland (NIST-G), in spite of the

very strong need for such SRMs. This work and another project now

under way will add two SRMs of very different apparent thermal conductivity, both being suitable for use both at ambient and at higher temperatures, to fill this need. One of these SRMs, microporous

fumed silica, is the subject of this report. The other, to be described in a separate publication [3], is a fibrous alumina-silica

insulation board. It will be certified over the same range of

temperature but will have an appreciably higher apparent thermal

conductivity (55 mW/(m- K) at 323 K (50oC)) than the one described

here. The two SRMs together will complement each other in range of

apparent conductivity and in ease of handling.

Many insulation materials commonly used in practice contain,

between their constituent particles and fibers, connected air

spaces with characteristic sizes much larger than the mean free

path of the air molecules occupying these spaces. The result is

that the thermal conductivity of the material may follow rather

closely the behavior of the thermal conductivity of air. Also, the

contribution of the gas component to the thermal conductivity of

1
these materials is very nearly independent of air pressure, as is

the total apparent thermal conductivity of the bulk material.

Unlike the apparent thermal conductivity of more commonly used

insulation materials, that of the microporous fumed-silica insulation studied here depends markedly on the barometric pressure of

the air surrounding the material and occupying its pores. This

effect is due to the extremely small size and random close packing

of the silica particles in this material. The random packing of

these particles produces very small, irregularly shaped, connected

pores having diameters, according to the manufacturer, of less than

about 100 nm. This characteristic size is approximately the same

as that of the mean free path of the occupying air molecules, which

is about 66 nm [4] at standard atmospheric pressure and 288 K

(15oC). As a result, (1) the contribution to the total apparent

thermal conductivity from that of the solid component is greatly

reduced because of the tortuosity of the conductive path through

the very fine, solid particles; (2) the contribution of the thermal

conductivity of the gas component to that of the bulk material is

greatly reduced by the- irregularity of the gas-conductive path

through the very fine pores of the solid; (3) the thermal conductivity of the gas component depends signif icantly on pressure, as

does the total apparent thermal conductivity of the bulk material.

The dependence of the apparent thermal conductivity of this

microporous insulation material on ambient gas pressure has a practical consequence of great importance: the geographic elevation of

the laboratory measuring the conductivity affects the value of

apparent conductivity obtained. Therefore it is not enough just to

know how the apparent conductivity depends on the temperature and

density of the specimen. The absolute barometric pressure of the

air filling the pores of this material must also be known in order

to predict accurately the apparent thermal conductivity to be

expected at the user’s laboratory.

Here we report measurements of apparent thermal conductivity

of five pairs of specimens of microporous fumed-silica insulation

board. These pairs were obtained as a selected subset of specimens

from the Heat Transfer Group of the Center for Building Technology

at NIST-G, which has certified this material as an SRM at room

temperature, based on measurements with their 1 -meter GHP. This

work at NIST-B has involved measurements of apparent thermal conductivity performed over a greater range of temperature and air

pressure than was possible with the 1-m apparatus at NIST-G.

Measured values were also correlated with the densities of the

specimens

.

The apparent thermal conductivity of this material lies in the

lower range of values seen for typical insulation materials. Its

conductivity is similar to that for closed-cell foam insulations of

great practical importance in consumer applications such as in

home-building and in home refrigerators and freezers. If care is

taken in handling this very fragile material, it will potentially

be of great use to those concerned with measuring apparent thermal

2
conductivity of foam insulations, with both guarded hot plates and

heat-flow meters. Such instruments are used for quality control by

manufacturers of thermal insulation and in developing new insulation products to conserve energy in domestic applications.

2. DESCRIPTION OF MICROPOROUS FUMED SILICA

This microporous fumed-silica insulation is produced as rigid

boards of bonded silica-aerogel composite made of very fine particles of synthetic amorphous silica, opacifier, fine ceramic fibers,

and a binder [5]. The size of the silica particles has been reported by the manufacturer to be approximately 10“® m. The fine

ceramic fibers increase the cohesiveness of the board, and the

binder cements the surfaces of the particles and fibers together

into a cellular structure by sintering when the boards are cured at

high temperatures (900oC). Ilmenite (Fe0-Ti02) is the opacifier

added to reduce radiative heat transmission through the board, to

make it suitable for use at high temperatures. The fractions of

silica particles, opacifier, and ceramic fiber stand approximately

in the ratios 60:35:5 by mass. All organic matter is burned out

in curing.

Microporous fumed-silica insulation board is very fragile and

must be handled with great care. The edges of the slabs are easily

chipped during installation and removal from the measurement apparatus. Boards having an edge dimension longer than about 30 cm are

easily damaged during handling and shipping unless great care is

taken to support them over a whole face and to protect them from

localized impacts. However, with proper cushioning of the specimens when they are packed for shipping, and with proper support of

the broad faces when they are installed in an apparatus, a careful

worker can probably measure them 20 or 30 times without significant

degradation of their surfaces due to chipping or breaking. Great

care will be necessary in handling these specimens.

Several evaluation lots of this insulation board were originally obtained by NIST-G [5]; the SRM candidate was selected from

these. A second lot of the selected material became SRM 1449 in

1988 [6]. The specimens as received were about 2.5 cm thick and 60

cm square. After apparent thermal conductivity was measured in the

1-m GHP at NIST-G, selected pairs of specimens were cut into 30-cm

squares and shipped to NIST-B. Specimens for which measurements of

apparent thermal conductivity are reported here had mean densities

of 301, 304, 315, 329 and 348 kg/m3 (18.8 to 21.7 lbm/ft3 )

.

3
3. APPARATUS AND MEASUREMENTS

The data for apparent thermal conductivity reported here were

obtained with the high-temperature GHP described by Hust, Filla,

Hurley, and Smith [7]. The outer diameter of this circular hotplate stack, and of the specimens measured, is 255 mm (10 in); the

diameter of the circular, concentric, metered main heater is 127 mm

(5 in )

.

The guarded hot plate is designed to measure heat transfer by

conduction, that is, by diffusive processes of heat transfer driven

by temperature gradients. Because of the density and microporosity

of this material, convective heat transfer is negligible at all

temperatures and pressures used in this study. Analysis of our

data in the following section suggests, however, that radiative

heat transfer in this material is not negligible, but neither does

it dominate. Near room temperature it contributes only a small

amount in comparison to conductive heat transfer. At the upper end

of the temperature range studied, thermal radiation becomes a

greater fraction of the total heat transfer, but still contributes

less than conduction does.

The insulation boards studied here are available in only one

thickness, nominally one inch. Our apparatus is unable to measure

two or more such thicknesses, and the fragility of this material

makes machining specimens down to smaller thicknesses impractical.

Therefore we cannot study the effect of specimen thickness and

thereby begin unambiguously to separate the magnitude of the radiative contribution from the diffusive heat transfer. However it

does appear that thermal conduction is the major contributor to the

total heat transfer. Because conductive and radiative heat transfer are both present, interactively, in this insulation material,

the term "thermal conductivity" alone is somewhat inaccurate and

misleading as a descriptor of the heat-transfer behavior of this

material over the temperature range studied. To call attention to

this fact, the term "apparent thermal conductivity" will be used in

the following text.

The microporous fumed-silica specimens were received as square

slabs nominally 12 in (30.5 cm) on a side. The measurement apparatus requires disks 255 mm in diameter, so disks were cut from the

square slabs by using a bandsaw set to a low cutting speed. The

material is very easily cut and the disk was not damaged during the

cutting. The annular material making up the rest of the square

sometimes splits during the cutting, however. Because the material

generates airborne dust during machining, prudence requires the use

of a dust mask by the person cutting this material. Although the

material from which the insulation is manufactured is not known to

be toxic. the dust is very fine and is borne by stray air currents

over distances of several meters.

4
We measured the thickness of each insulation board using a

digital electronic caliper with a precision of 0.03 mm (0.001 in).

Thickness was measured at eight locations equally spaced around the

perimeter of the disk and the measurements were averaged. The

standard deviation of the thickness measurements is 0.08 mm for a

nominal specimen thickness of 25 mm (relative standard deviation of

0 . 3 percent )

.

Using a steel ruler having a precision of 0.25 mm, we measured the diameter of each specimen along four different directions,

and averaged the results. The standard deviation of these four

diameters was 0.8 mm for a nominal diameter of 255 mm (relative

standard deviation of 0.3 percent).

The masses of the specimens were measured on a laboratory trip

balance with a sensitivity of 0.1 g for a typical mass of about

400 g (relative imprecision of 0.03 percent).

The density was determined from these measurements with a precision of +0.5 percent. The mass of each specimen decreased by

about 3 g from conditioning in an oven at SO^C before the thermal

conductivity was measured. These changes in mass due to the rigors

of conditioning and measurement amount to an uncertainty of about

0.8 percent in the density.

Time Required for Stability and Reproducibility

At the beginning of the measurement program the apparent conductivity was measured repeatedly to determine the minimum time

required to obtain stable and reproducible data. Under automatic

operation of the control system, conductivity at a mean specimen

temperature of 60^0 was measured at intervals averaging 7 h. The

values obtained approached a final, steady value of 21.12 mW/(m- K)

along an exponential-decay curve. The first value obtained was

22.16 mW/(m-K), at a time of 7 h into the series; the second value,

21.34 mW/(m-K), at 14 h, came within 1 percent of the final, stable

value. The third value, at 21 h, was within 0.5 percent (the

experimental reproducibility) of the stable value. Measurements

performed at mean specimen temperatures of 440^0 also required

about 14 to 18 hours to lie within experimental reproducibility of

the final, stable value. These observations led to the procedure

described next.

After the fumed-silica specimens were installed in the guarded-hot-plate stack they were dried by being heated to the highest

temperature of measurement (approximately 725 K, or 450^0) before

any values of apparent thermal conductivity were obtained. This

effectively removes almost all of the adsorbed moisture from the

specimens and gives stable values of apparent thermal conductivity

that are reproducible as long as the following measurements are

performed at temperatures less than the highest temperature. No

evidence of release of chemically bound water was detected.

5
For each measurement the temperature difference across a specimen was established at approximately one tenth of the absolute

mean temperature in the specimen. Temperature differences smaller

than this magnitude lead to systematic errors in apparent thermal

conductivity [7]. At temperatures above approximately 800 K, the

ceramic materials used in constructing the heater plates become

electrically conductive; this leads to leakage currents coupling

the thermocouples to the heater windings, and the alloys used in

the thermocouples and resistance thermometers begin to degrade.

For these reasons the highest temperature of the main heater plate

was limited to 773 K (SOO^C), so the highest mean temperature used

was about 733 K (460oC).

There is no evidence from the physical appearance of the specimens or in the apparent-conductivity data that phase changes occur

in the material below 500oC, the highest temperature to which the

specimens (that is, their sides adjacent to the hot main plate)

were exposed during measurements. There does seem to be some adsorption of moisture by the specimens; this must be driven off

before measurements become stable. We often found it necessary to

repeat measurements two or more times at the highest mean temperature until the values obtained did not vary by more than the experimental reproducibility (0.5 percent for this apparatus). This

required a period as long as 24 h to obtain a stable measurement.

Then measurements of apparent conductivity below that temperature

were stable and reproducible.

4. DEPENDENCE OF APPARENT CONDUCTIVITY ON TEMPERATURE AND DENSITY

The object of this work is to obtain the dependence of apparent thermal conductivity on three independent physical variables:

temperature, density, and ambient air pressure. The complete apparent-conductivity function describing these relationships therefore occupies a four-dimensional space. Consequently it was much

more convenient to study and to present the data in smaller subsets

of lower numbers of variables. We shall therefore first treat

apparent thermal conductivity as a function of temperature and

density with ambient pressure constant. Then we shall study the

apparent conductivity as a function of pressure, with the temperature and density held constant. These separate treatments will

allow us to justify the mathematical form of the final correlation

chosen to represent the dependence of apparent thermal conductivity

on all three independent variables.

To determine the dependence on temperature and density, the

apparent thermal conductivity of each pair of specimens was measured at mean temperatures from about 318 to 733 K (45 to 460oC)

with air at ambient humidity and pressure (83 kPa, or 625 Torr in

Boulder) in the environmental chamber surrounding the measurement

stack. Absolute temperatures and temperature differences were

stabilized and measured with a precision of 0.02 percent. The precision of measurements of apparent thermal conductivity with this

apparatus has been estimated as 0.5 percent at 330 K, and 0.7 per6
cent, at 720 K [7]. Measurements of apparent conductivity have a

repeatability of about 0.75 percent. The bias of measurements obtained with this apparatus is estimated to be 1.0 percent for mean

specimen temperatures near 320 K; this is based on recent measurements of a specimen of SRM 1450b performed over the range of temperatures from 315 to 370 K. The bias of measurements of apparent

thermal conductivity is estimated to rise to no more than 2.5 percent at 725 K, as estimated from an analysis of propagation of

errors based on sensitivity measurements performed on the GHP

apparatus [7]

.

The five pairs of specimens of microporous fumed-silica insulation boards used in this study were identified by in-house codes

as (a) B-08c and B-08d, (b) B-132 and B-133, (c) B-101 and B-102,

(d) B-101 and B-104, and (e) B-073 and B-074. Because no member of

a pair was measured individually, it will be simpler to refer to

these pairs by the last digits of the individual identification

codes of their two members. Thus the five pairs measured will be

identified throughout this report respectively as (a) B8cd, (b)

B23, (c) B12, (d) B14, and (e) B34.

(A) Expected Dependence of Conductivity on Temperature and Density

A simple phenomenological relation based on the following

reasoning was chosen to represent the data. Any thermally insulating material in a gaseous atmosphere is composed of finely divided

solid material permeated with the environmental gas. The thermal

conductivities of gases and nonmetallic solids at ambient and higher temperatures have an approximately linear dependence on temperature. Black-body radiation depends on the fourth power of temperature of the emitting body, so heat transfer between two adjacent

surfaces depends, to a very good approximation, on the product of

the third power of the mean, temperature with the temperature difference. The density of insulation material has two effects:

transmission of thermal radiation decreases, and solid conduction

increases, as the bulk density of the material increases. However,

the increase in apparent thermal conductivity with density is less

than proportional to the change in density. These considerations

suggested the simple form of the dependence on density and temperature in the relation used here to represent the apparent-conductivity data.

(B) Experimental Results

In an environment of air at ambient humidity and at local ambient pressure of 82.5 to 83.4 kPa (619 to 626 Torr)

,

178 measurements of apparent thermal conductivity were made on five pairs of

specimens with densities ranging from 301 to 348 kg/m^ , Diameters'

of the specimens were 255 mm and thicknesses were 25.4 mm (1 in).

Measurements covered the range of temperature from 318 to 733 K (45

to 460oC). The behaviors (apparent conductivity as a function of

temperature) of all five pairs of specimens were qualitatively very

similar.

7
The correlation of apparent thermal conductivity with temperature and density was represented by an expression of the form,

k = Ao + Ai D + A2- T + A3- T3 /D, (1)

where k is apparent thermal conductivity , T is absolute temperature, and D is density. The second term reflects the expected

increase of apparent conductivity with bulk density of the material, and the inverse dependence on density in the fourth term reflects the expected decrease in radiative heat transport through

the material as the density increases.

A correlation of this form was obtained using the thermal conductivity integral (TCI) method [8], with a weighted least-squares

routine fitting both temperature and density simultaneously. The

dependence on density was found from the statistical parameters of

the fit to be small over this range of density, but significant.

The apparent thermal conductivity as a function of temperature

had som'e curvature, but it was not strong. During these measurements, the temperature gradients imposed on the specimens were

determined by the rule that the temperature difference should be

about 10 percent of the absolute mean temperature. At all temperatures, such a temperature difference covers a small range over

which the apparent-conductivity function is very nearly linear.

Thus it would not be necessary to use the TCI method to fit the

data for these specimens with acceptable accuracy. The TCI method

should be used whenever measurements are made (1) with large differences in the boundary temperatures of the specimen and (2) with

appreciable curvature in the apparent-conductivity function over

the included range of temperature. Still, we use the TCI method as

a matter of course, whether or not the data seem to have enough

curvature to require the method. This ensures that the mathematics

of our fitting procedure introduces no additional errors due to

nonlinearity in the fitted function.

The standard deviation of the residuals between the curve given by eq ( 1 ) and the 178 data p^

deviations of the residuals for

were

:

(a) B8cd

,

45 residuals

,

(b) B23, 22 residuals

,

(c) B12, 42 residuals

,

(d) B14, 38 residuals

,

(e) B34, 31 residuals

,

ints was 0.68 percent. Standard

the individual pairs of specimens

0.70 percent

;

0 . 35 percent

;

0 . 58 percent

;

0 . 30 percent

;

1.16 percent

.

8
These values of standard deviations, which measure the goodness of

the fit, compare very favorably with the value of the experimental

reproducibility, 0.8 percent, for the GHP apparatus used. The dependence of apparent conductivity on temperature and density for

this material is very well represented by a curve of the form of eq

( 1 ).

The densities of the specimens used in this work can be uncertain by about 1 percent due to adsorption and desorption of moisture during the measurements. The densities also vary slightly with

mean specimen temperature, due to thermal expansion, but not enough

to affect the dependence of apparent conductivity on density arrived at in this report. It was deduced from the numerical coefficients of the fit to eq (1), using values of temperature and density

typical of the measurements reported here, that a change (or uncertainty) of 1 percent in density results in a change (inaccuracy) in

values of apparent conductivity of no more than 0.2 percent. This

is well within the experimental reproducibility. The uncertainty

in temperature has a negligible impact on the accuracy of measurements of apparent thermal conductivity.

6. DEPENDENCE OF APPARENT CONDUCTIVITY ON AMBIENT AIR PRESSURE

(A) Constraints on the Ranges of Pressure Used in This Work

To study the effects of ambient air pressure, the apparent

thermal conductivity was measured under several different conditions of air pressure and bulk density. We chose a range of air

pressures that would also permit us to compare data taken at our

local ambient pressure with complementary data obtained on the 1-m

guarded hot plate at NIST-G. The elevation of our laboratory is

approximately 1650 m above sea level, and the local ambient air

pressure is typically about 84 kPa (625 Torr)

;

the elevation of the

laboratory at NIST-G is close to sea level, with a mean ambient air

pressure of about 100 kPa (750 Torr).

Due to the large size and rectangular geometry of the environmental chamber containing the 1-m GHP at NIST-G, there are severe

constraints on the allowed variation of air pressure within the

chamber. A moderate difference between pressure within the chamber

and the outside atmospheric pressure would damage its structure.

As a result, data on the NIST Certificate for SRM 1449 (fumedsilica board) are tabulated only over the range from 97 to 102 kPa.

9
Within the environmental chamber surrounding the 25-cm GHP at

NIST-B, air pressures at the specimens can be obtained over the

range from local ambient, 84 kPa, down to pressures of less than

about 1 Pa. However in this chamber an opposite constraint applies: air pressures greater than local ambient could be obtained

only with difficulty and some danger. Due to the large horizontal

cross section of the vacuum chamber, an internal lifting force of

about 9 kN (1 ton) would be exerted on the roof on the chamber if

it were pressurized to 101 kPa (1 atm). The energy stored within

the large volume of pressurized air would not be negligible (about

10 kJ)

.

(B) Expected Dependence on Ambient Air Pressure

Over a wide range of environmental air pressure, the dependence of apparent thermal conductivity on pressure for commonly used

insulation materials is qualitatively well understood. The curve

for the dependence of apparent conductivity on pressure typically

has a sigmoidal shape (figure 1; the values along both axes are

arbitrary but representative). There is a region of constant, low

conductivity at low pressure (A)

,

a transitional region of rising

conductivity at intermediate pressures (BCD), and a plateau of

approximately constant, higher conductivity at higher pressures

(E). The region connecting the rising transitional region to the

high-pressure plateau (DE) is called the "knee." The low-pressure

plateau of constant apparent conductivity is determined by radiative heat transfer and by conduction in the solid material, which

are independent of pressure. The contribution from conduction in

the gas within the pores of the bulk specimen determines the position and shape of the high-temperature plateau. There is no theory

that completely describes the empirical pressure dependence depicted in figure 1 over the whole range of pressure; many different

mathematical functions can be chosen to model the behavior approximately . For the three pairs of boards used to study the dependence of

apparent thermal conductivity on environmental air pressure, and at

the four conditions of temperature and density used, the dependence

of apparent conductivity on pressure was strong and clearly did not

correspond to the high-pressure plateau. Instead, the conductivitypressure relation for this material, for each condition of temperature and density, seemed to occupy only a narrow region of the

transitional region below the knee (CD, figure 1), and appeared to

be most simply described by a segment of a parabola.

10
(C) Measurements of Pressure

For the studies of dependence of apparent thermal conductivity

on pressure discussed in this section, air pressure was measured

with a Bourdon-tube pressure gauge with an imprecision of about

0.13 kPa (1 Torr) ; the relative imprecision is about 0.3 percent at

the lowest pressures, and approaches 0.1 percent at the highest

pressures used. The inaccuracy of the measurements of pressure is

about 1 percent.

The ambient air pressures used in this work could vary by 0.5

percent (typical) to 1 percent (maximum observed) during the course

of measurements, due to changes in barometric pressure. From the

numerical coefficients of the fitted curve giving the dependence of

apparent conductivity on pressure, using coefficients for pair B14

and values of temperature and pressure typical of the measurements

reported here, we deduced that a change (or uncertainty) of one

percent in pressure results in a change (inaccuracy) in values of

apparent conductivity of about 0.3 percent. This is well within

the experimental reproducibility of values of apparent thermal

conduct ivity

.

(D) Experimental Results

We measured the apparent thermal conductivity of three different pairs of specimens, representing three different bulk densities, over a range of air pressures of approximately 27 to 84 kPa

(200 to 626 Torr). In particular, 20 values of apparent conductivity for specimen pair B14, with a mean density of about 301 kg/m^

,

were measured at a mean specimen temperature of 318 K. Nineteen

values for pair B34, with a mean density of about 315 kg/m^ , were

measured at a mean specimen temperature of 473 K. Finally, pair

B8cd, with a mean density of about 348 kg/m^ , was measured both at

318 K (21 values) and at 473 K (22 values). A total of 82 measurements was made. Data for apparent thermal conductivity k as a

function of ambient air pressure for all four pairs, individually

as well as collectively, were well represented by a relation of the

form

k(P) = Bo + Bi - P + B2- P2 , ( 2 )

where P is ambient air pressure surrounding the specimens. The

sign of Bi is positive, and that of B2 is negative. All three

coefficients are significant. The standard deviations of the resid-'

uals for the data for the four individual pairs of specimens ranged

from 0.16 to 0.25 percent. Clearly a relation of the form of eq

(2) describes well the dependence of apparent thermal conductivity

on pressure.

11
6. DEPENDENCE OF APPARENT CONDUCTIVITY ON PRESSURE AND DENSITY

Specimen pairs B14 and B8cd were measured at 318 K. When the

data for pressure dependence of apparent conductivity for these two

pairs of two different densities were plotted together, the combined data for the two pairs were also well represented by a relation

of the form of eq ( 2 ). The standard deviation of the 41 residuals

between the data and the single fitted function was 0.66 percent.

The dependence of apparent thermal conductivity on density for

these two pairs is not large enough to be seen above the limits of

experimental reproducibility.

Specimen pairs B34 and B8cd were measured at 473 K. When the

data for the pressure dependence of apparent conductivity for these

two pairs of different densities were plotted together, the combined data for the two pairs were also well represented by a relation

of the form of eq (2). The standard deviation of the 41 residuals

between the data and the single fitted function was only 0.37 percent. The dependence on density for these two pairs is also not

large enough to be seen above the limits of experimental reproducibility . The k(P) curve for the two pairs of specimens at 318 K and the

corresponding curve for the two pairs at 473 K were very similar in

shape. This suggested that both sets of data might be accurately

represented by a single function. The two sets of data were superimposed by the following technique.

The apparent-conductivity data for the two pairs at 318 K were

adjusted by adding a constant to each conductivity datum. Then a

curve of the form of eq (2) was fitted to the data for all four

pairs, to all of which a temperature of 473 K effectively now applies. Trial and error found a constant additive term of 1.70

mW/(m* K) that gave the best fit between the curve and the data for

the four pairs. For this fit the standard deviation of the 82

residuals between the curve and the data was only 0.50 percent.

The significance of this fact is that all four pressure relations for apparent thermal conductivity for two different temperatures and three different densities can be described by a function

having a fixed shape. The position of the conductivity-pressure

relation for one temperature is then determined from the position

of the conductivity-pressure relation at another temperature by

only the difference in apparent conductivities at the two different

temperatures. In contrast to the situation with the measurements

of apparent conductivity as a function of temperature, the data for

apparent conductivity as a function of pressure is not sensitive to

the density of the specimens used, so these data may be adjusted

slightly as needed when combined with the conductivity-temperature

data

.

12
7. DEPENDENCE OF CONDUCTIVITY ON TEMPERATURE, DENSITY, AND PRESSURE

The relation between apparent thermal conductivity and pressure given by eq (2) can now be additively combined with the relation among apparent conductivity, density, and temperature given by

eq (1) to obtain the correlation for apparent thermal conductivity

of microporous fumed silica. As a function of all three independent variables, temperature, density and pressure, the apparent

thermal conductivity k is

k(T,D,P) = 5.11 + 0.1478-P - 3.6996- 10-4. P2 + 1 . 2064- 10" 2 . D

+ 2. 34402- 10-3. T + 5 . 8703- 10-6. T3 /D, (3)

where k is in units of mW/(m-K), D is density in kg/m3 , P is pressure in kPa, and T is temperature in K. The coefficients are

determined by a total of 260 (178 + 82) measurements of apparent

conductivity. The first three terms on the right side of this

relation are consistent with eq (2) for the dependence of apparent

conductivity on pressure; the first and last three terms are consistent with eq (1) for the dependence of apparent conductivity on

temperature and density.

In eq (3) the constant term (5.11) was predicted from the combination of the fits to eqs (1) and (2) to be 5.18. However, while

this value gave a nearly optimum fit for the conductivity-temperature data, it yielded residuals approaching 2 percent in magnitude

for the conductivity-pressure data. The value of 5.11 was found by

trial and error to give fits with approximately equal residuals,

less than 2 percent, for both sets of data for apparent conductivity. This is not appreciably different from the predicted value.

Table l(a-e) lists the 178 measurements of apparent thermal

conductivity as a function of temperature and density, with pressure held constant at near 83 kPa. Data for each pair are listed

on separate pages, with the density of the pair given at the top of

the last column on each page. Also given are the values for apparent thermal conductivity calculated (Kcaic) from the least-squares

fitted curve, eq (3), as well as both absolute (Kdev) and relative

(Pdev) deviations of the data from the curve. The apparent-conductivity data for each of the five individual pairs (at fixed

density) are also plotted as a function of temperature in figures 2

through 11. Each odd-numbered figure illustrates the relative deviation, in percent, of' the data from the calculated values, for the

even-numbered preceding figure.

13
While calculating the fit, we allowed for the slight decrease

in specimen density, from the nominal value listed in the table,

accompanying increases in temperature. This variation in density

is due to effects of thermal expansion of the thickness and area of

the specimen. It slightly affects the values listed as kcaic.

Likewise the values for the measured apparent conductivity, kdat

,

were also corrected for the effects of thermal expansion.

The collective value of the relative standard deviation of the

residuals between eq (3) and all five sets of temperature data combined with all four sets of pressure data was 0.68 percent. This

is only slightly greater than the separate values for apparent conductivity as a function of temperature or for apparent conductivity

as a function of pressure. The extremal deviations of the data

from eq (3) were within ±2.2 percent. We consider the fact that

one dependent variable is fitted here to three independent variables, with the experimental imprecision being 0.8 percent. In this

light, for a relation in three variables as simple as eq (6), the

standard deviation seems to be acceptably small; the extremal deviations are a little larger than desired but are judged not inconsistent with the combined effects of the standard deviation (0.68

percent), the total number of data fitted (260), and the value of

experimental imprecision (0.8 percent).

For all five pairs of this microporous fumed-silica insulation,

the apparent thermal conductivity is approximately 20 mW/(m- K) at

300 K and 83 kPa. This is substantially lower than the thermal

conductivity of dry air, which is approximately 25.6 mW/(m- K) at

300 K and 101.3 kPa [9]. Although the lower ambient air pressure

is responsible for part of the reduced conductivity, it does not

explain the total difference. The microporous structure of the

material seems to reduce the apparent conductivity of this insulation to a value below that of free air, despite the presence of

conduction through the solid matrix of silica particles, in parallel with (and additive to) conduction through the permeating gas

(air). This is probably due to the greatly reduced mean free path

of the air molecules within the very small pores of the solid

structure

.

The curvature of the solid line in each even-numbered figure,

2 through 10, is correlated with the T3 /D term in eq (1), which,

being nonlinear, grows larger relative to the other two terms with

increasing temperature. This T3 /D term is related to the contribution of radiative heat transfer to the total heat transfer through

the material. At 297 K the magnitude of this term is about 0.5

mW/(m- K) out of a total apparent conductivity of about 20 mW/(m- K),

or about 2.5 percent of the total. At 700 K the magnitude of the

T3 term is about 6.7 mW/(m- K) out of a total of 27 mW/(m- K), or 25

percent of the total. Thus in this range of temperature, the radiative contribution to the total heat transfer is becoming appreciable, but conductive heat transfer still dominates.

14
To illustrate the goodness of fit between the data for apparent conductivity as a function of pressure and eq (3), plots of

apparent thermal conductivity are provided as a function of pressure for each of the pairs and conditions from which the pressure

dependence was derived. Figures 12 and 14 give the apparent conductivity data for pairs B14 and B8cd at fixed temperatures of 318

K, and figures 13 and 15 are the corresponding deviation plots.

Similar information for pairs B34 and B8cd at fixed temperatures of

473 K are given in figures 16 through 19. The data for the individual pairs are all listed in tables 2 through 5.

The correlations of apparent thermal conductivity with temperature for all five pairs compose a family of five curves, each

for a given density. It is useful to illustrate the explicit

dependence of the k(T,D) relation on density, giving a family of

curves at constant temperature. However, it was inconvenient to

use the original data for apparent conductivity as a function of

density, because the actual data cannot be grouped precisely into

coherent isotherms. To illustrate the density dependence, eq (1)

was used to calculate the apparent conductivity arbitrarily at

temperatures of 300 to 800 K, at intervals of 100 K, and at the

five densities describing the actual five pairs of measured specimens. The points corresponding to these conditions are shown in

figure 20. Deviation plots are not given here because the points

used are calculated; however the points have an experimental basis

through the data upon which eq (1) is based.

For this material the rate of change of apparent thermal conductivity with density, holding temperature constant, is given

mathematically by the first partial derivative of the right side of

eq (3) with respect to the variable D, holding terms in temperature and pressure constant. Carrying out this operation gives

3k/dD = Ai + A3- T3/D2

= 0.012064 - 5.8703- 10-6. T3/D2 , ( 4 )

so that the variation of apparent conductivity with change in density depends both on the temperature and on the density itself. In

particular, as T increases with D fixed, the magnitude of the second (negative) term grows, so the slope decreases with increasing

temperature (at constant density). As D increases with T fixed,

the magnitude of the second term is reduced, so the slope increases,

with increasing density (at constant temperature).

15
We evaluate this expression for temperatures of (a) 300 K,

(b) 600 K, and (c) 800 K, and compare the results with the curves

of figure 20. At these three temperatures, and at a density of 300

kg/m3 (the lowest value measured here), the rates of change of apparent conductivity (in units of mW/(m-K) ) with density (in kg/m^

)

are respectively (a) 10 . 3 - 10 “ 3, (b) -2.0-10“3, and (c) -21.3- 10"3.

At a density of 348 kg/m3 (the highest value measured here),

these rates of change are respectively (a) 10.7- 10~3, (b) 1.6- 10”3,

and (c) -12.8- 10~3. From these calculated values, or equivalently,

from figure 20, it is seen that (a) the curve for 300 K has a

small, approximately constant positive slope; (b) the curve for 600

K has a slope near zero; and (c) the curve for 800 K has a negative

slope, of magnitude greater than that for 300 K, and decreasing in

magnitude as density increases. The range of density covered here

is not great enough for figure 20 to show unambiguously that the

curvature is upward for all five curves, that is, that the slope

increases as density increases. But this effect is shown by the

numerical values cited here for each temperature.

Returning to ©q (4) for the rat© of change of apparent conductivity with density at constant pressure, we compute the rate of

change of apparent conductivity with density for a temperature of

318 K and a mean density of 324 kg/m^ (mean of 300 and 348 kg/m3

,

the densities of pairs B14 and B8cd). The value obtained is

10.3- 10“ 3 for apparent conductivity in mW/(m- K) and density in

kg/m3 )

.

For a temperature of 348 K and a mean density of 332 kg/m3

(mean of 315 and 348 kg/m3 , the densities of pairs B34 and B8cd),

the rate of change of apparent conductivity with density is

9.8- 10“ 3. The difference between the two values is not greatly

significant for our purpose here; the average is about 10- 10“

3

mW/ ( m- K ) . The slopes of the six different lines in figure 20 have a

physical origin. For a given mean temperature within a thermal

insulation, there is an optimum density that minimizes the apparent

thermal conductivity. At densities lower than this optimum value,

apparent conductivity rises because radiative heat transfer is not

efficiently blocked; at densities higher than the optimum, conductivity rises due to the increased fraction of material that is

solid, leading to greater conductive heat transfer. Thus the

curves for 300 and 400 K show that the optimum density is less than

295 kg/m3 , while the curves for 700 and 800 K indicate that the

optimum density is greater than 350 kg/m3 . For temperatures of 500

to 600 K the range of densities included on the graph is near the

optimum value. The small numerical values of the nonzero slopes

show that, for all curves from 300 to 750 K, the minimum in the

relation between apparent conductivity and density is very broad.

Therefore the optimum density is imprecisely located, but on the

other hand the apparent thermal conductivity is not very sensitive

to departures from the optimum density.

16
Because k(P) as given by eq (2) depends quadratical ly on P,

the rate of change of k with pressure is pressure-dependent. The

coefficient Bi in eq ( 3 ) was positive, and B2 negative, so the

slope of k versus P is positive but decreases as pressure increases. The rate of change of apparent conductivity with pressure, or

slope of the k(P) function plotted in figure 12 (or 14, 16 or 18),

is given by the mathematical first derivative of k(P). The derivative of the right side of eq (2) takes the form

dk/dP = Bi +2- B2- P. (5)

For pair B14, as an example, this relation takes the form

dk/dP = 0.17436 - 1 . 12246- 10" 3 . P, (5')

for k in mW/(m- K) and P in kPa. At sea level, where Psi is about

101 kPa, the rate of change of apparent conductivity with pressure,

dk/dP from eq (5’), takes the value 0.0606 for pair B14 (with a

density of 300 kg/m3 ) . At the elevation of our laboratory at Boulder, where the pressure is Pb = 83.5 kPa, the rate of change of

conductivity with pressure is 0.0806. But because these slopes are

different (k depends nonlinearly on P) , neither of them is valid

for extrapolating values of k obtained at one ambient pressure to a

different range of pressure. Rather, the k(P) relation itself,

eq (3), should be used to estimate the apparent conductivity to be

expected at a given ambient pressure.

17
8. COMPARISONS

The microporous f umed-silica insulation board studied here

comes from the same lot that has already been measured [6] and

certified [10] by Ebberts , Somers, and Zarr at NIST-G, for use as

an SRM of low apparent thermal conductivity. All but three published measurements were performed at a mean specimen temperature

of 297 K (24oC) and at a pressure of 101.33 kPa (760 Torr), on

specimens having densities ranging from 310 to 333 kg/m^

.

The certificate [10] for SRM 1449 (fumed silica) furnishes

both tabular data, and an algebraic formula (coefficients as given

here have been modified to give apparent conductivity for heat flow

in milliwatts )

,

kG(297 K) = 6.9943 -f 0,021375- D + 0.070723- P, (6)

relating apparent thermal conductivity kc in mW/(m-K), density D in

kg/m3 , and ambient air pressure P in kPa (subscript G on k denoting

"as determined at NIST-G" )

.

This correlation is valid only for a

temperature of 297 K. The specimens on which eq (6) is based covered a somewhat smaller range of density (300 to 330 kg/m^ ) and

were measured over a considerably smaller range of pressure (97 to

102 kPa) than the measurements reported here; the certification

data and accompanying table imply that these limits define the

range of applicability of eq (6).

The coefficient of density, 21.375- 10~3, in eq (6) gives the

rate of change of apparent thermal conductivity with density at

constant temperature (297 K) and pressure. It was obtained for a

fit of apparent conductivity to both density and pressure as independent variables. This coefficient is about twice the value

we found, 10- 10~3. The paper describing the certification work [6]

gave a value of 19.92- 10~3 for the density coefficient in a simplified correlation of apparent conductivity with density alone. A

still earlier paper [5] listed a value of 30.76- 10~3 for this coefficient, for a separate lot of material from the same manufacturer,

before the effect of moisture content was known. Thus there is

evidence that the value for the density coefficient is sensitive to

moisture content and lot of manufacture, as well as to the number

of variables handled in fitting the correlation. The differences

between these numbers also depend on the effects of combined

experimental imprecision in developing an empirical correlation

among several independent parameters (apparent thermal conductivity

with temperature, pressure, and density).

18
The correlation of apparent conductivity with density obtained here may be compared with a set of 15 data points obtained at

NIST-G for specimens at 297 K and having densities ranging from 304

to 325 kg/m3 . This set is published in reference [6] as open

squares in a figure, and also in a table. We show these same data,

replotted here in figure 20 as open squares. The data plotted in

our figure 20 from our correlation for specimens of five different

densities and at 300 K are also replotted in figure 21, as open

circles. The five circles lie well below the 15 squares for data

from NIST-G. However, we must remember that these data (circles)

apply to specimens measured at 83.2 kPa. Using either eq (2) or eq

(3), we find that, for fixed density and temperature, the effect of

increasing ambient air pressure from 83.2 kPa (NIST-B) to 101.3 kPa

(NIST-G) is to increase the apparent conductivity by an additive

contribution of 1.43 mW/(m-K). The five open circles in figure 21

have therefore been corrected for the influence of ambient air

pressure by being moved upward 1.43 mW/(m- K) and replotted as

"plus" signs. Now the disagreement is only about 0.5 mW/(m-K).

The corrected NIST-B data deviate from the NIST-G data by a relative difference of about +2 percent.

To compare the correlation of apparent conductivity with temperature obtained here with results obtained at NIST-G, we choose

one specimen, B23, with a density (328 kg/m^ )

,

very nearly equal to

that of a specimen described in reference [6] which had a density

of 330 kg/m3 . Comparison may be made only after correcting our

data for the effect of ambient air pressure on the apparent conductivity. Figure 22 shows the original data obtained here for

pair B23, previously shown in figure 3. The single set of data

from NIST-G for dependence of apparent conductivity on temperature

was obtained at three different temperatures. The measurements

listed in Table 4 of reference [6] are

These 6 data from NIST-G are plotted in figure 22 as a filled

square, triangle, and diamond, along with data obtained here for

pair B23 (open triangles). The filled symbols lie well above the

open triangles. The same correction must be applied to the data to

correct for the effect of ambient air pressure. The same term used

previously with the density correlation, 1.43 mW/(m- K) , was added

to the NIST-B data, obtaining the numbers shown in figure 22 aS

plus signs. The agreement between the data for NIST-G and NIST-B

is now very good. The filled triangle and diamond agree with the

corrected data within experimental scatter; the filled square may

be about 1 percent lower than the trend line.

Mean Temperature

K

Apparent thermal conductivity

mW/(m- K)

283

297

311

21.06

21.31

21.51

19
At the elevation of the NIST-B laboratory in Boulder, Colorado, 1650 m (5400 ft), the mean atmospheric pressure is approximately 83.2 kPa , with normal fluctuations, due to local weather, of

+0.9 kPa . Table 2 gives the dependence of apparent conductivity on

varying ambient air pressure for pair B14, at approximately 318 K.

From the first row we find, for an air pressure of 83.4 kPa (626

Torr), near the maximum pressure used, that kdat = 20.07 mW/(m-K),

and kcaic =19.87. By extrapolating eq (3) to a condition of mean

atmospheric pressure at sea level, or 101.3 kPa , the apparent

thermal conductivity at T = 297 K is estimated to be ksl = 21.11

mW/(m-K). This value is higher than the value kcaic = 19.87 for

our elevation of 1650 m, by 1.24 mW/(m. K). We found earlier that

the curve for dependence of conductivity on pressure has the same

shape, within experimental error, independent of density and temperature . The Certificate for SRM 1449 states that values of measured

apparent conductivity (on the NIST-G GHP) should agree with Certificate values within 1.5 percent, where apparent conductivity is

measured at 297 K and within the range of pressure from 97 to 102

kPa. The NIST-B GHP has a claimed accuracy of 1 percent. The

combined inaccuracies of measurements by the two laboratories could

be as great as 2.5 percent, especially since values from each

laboratory are estimated here at conditions somewhat outside the

range of validity of the correlation for that lab. The agreement

between the two laboratories is judged acceptable, considering the

combined experimental uncertainties.

Another similar insulation material of low apparent conductivity, made of microporous fumed silica and having a nominal density

of about 310 kg/m3 , was studied by Tye [ 12 ]. He measured specimens

from four different lots and found very small variations in conductivity between the lots. His results reproduced those of the

manufacturer within 4 percent up to temperatures higher than 450® C.

For these reasons he recommended in 1970 that it be considered as a

possible SRM. Its apparent conductivity ranged from 26.5 to 48.5

mW/(m- K) at temperatures from 25 to 650oC. These values are somewhat higher than the apparent conductivities found here for this

material made by a different manufacturer, but are in fair agreement with them. It is known that materials of similar densities

but from different manufacturers will yield different apparent

thermal conductivities [ 5 ].

20
9. REFERENCES

[1] Hust, J.G. "Status of Thermal Conductivity Standard Reference

Materials at the National Bureau of Standards", THERMAL CONDUCTIVITY 18: Proceedings of the 18th International Conference on Thermal

Conductivity, Ashworth, T. and Smith, David R. , Eds.; pp. 327-338

(Plenum, New York, 1985).

[2] ASTM Subcommittee C16.30. "Reference Materials for Insulation

Measurement Comparisons", Thermal Transmission Measurements of Insulation, ASTM STP 660, Tye, R.P., Ed.; pp. 7-29 (ASTM, Philadelphia, 1978 )

.

[3] Smith, David R. , "Fibrous Alumina-Silica Insulation Board as a

Standard Reference Material of Thermal Resistance", to be

published

.

[4] F.W. Sears and G.L. Salinger, Thermodynamics, p. 290 (AddisonWesley, Reading, Massachusetts, 1975).

[5] Rennex, B.G., Somers, T.A., Faison, T.K., and Zarr, R.R.,

"Evaluation of Fumed-Silica Insulation for a Thermal Conductivity

Standard Reference Material", Insulation Materials, Testing and

Applications, ASTM STP 1030 (ASTM, Philadelphia, 1989).

[6] Zarr, R.R., Somers, T.A. and Ebberts, D.F. "Room-Temperature

Thermal Conductivity of Fumed-Silica Insulation for a Standard Reference Material", NBSIR 88-3847, (U.S. National Institute of Standards and Technology, June 1988).

[7] Hust, J.G., Filla, B.J., Hurley, J.A. and Smith, D.R. "An

Automated High Temperature Guarded-Hot-Plate Apparatus for Measuring Thermal Conductivity of Insulation Between 300 and 750 K"

,

NBSIR 88-3089 (U.S. National Institute of Standards and Technology,

May 1988).

[8] Hust, J.G., and Lankford, A.B. "Comments on the Measurement of

Thermal Conductivity and Presentation of a Thermal Conductivity

Integral Method", Int. J. of Thermophysics, 3/1 . 67-76 (1982).

[9] F. Kreith and W. Black, Basic Heat Transfer, Appendix G,

p. 520 (Harper & Row, New York, 1980).

[10] "National Institute of Standards and Technology Certificate,

Standard Reference Material 1449, Thermal Resistance - Fumed Silica

Board", NIST, Gaithersburg, MD, 1989.

[11] Tye, R.P. "The Thermal Conductivity of MINK-2000 Thermal Insulation in Different Environments to High Temperatures", Proc . of

9th Conference on Thermal Conductivity, CONF-691002, pp. 341-351

(U.S. Atomic Energy Commission, Div. of Technical Information,

March 1970 ) .

21
Table 1. Apparent thermal conductivity of five pairs of microporous fumed-silica insulation boards with mean densities of (a) 348, (b) 328, (c) 305, (d) 300, and (e) 315 kg/m^ , at

mean temperatures ranging from 318 to 723 K (45 to 450^0) . One

hundred and seventy-eight measurements were performed in air at

ambient humidity and at pressures of approximately 83 kPa (625

torr), using the high-temperature guarded hot plate at the

National Institute of Standards and Technology in Boulder, Colorado. Temperature differences through the specimens were chosen

to be about 10 percent of the value of the mean temperature within the specimens. The bias in values of Kmeas is estimated to be

1.5 percent at 330 K, and 2.5 percent at 720 K. The column labeled Kcaic gives values of apparent thermal conductivity calculated

from eq (3). The collective standard deviation of the 178 residuals between the data (Kdat ) and the fitted curve is 0.68 percent. Absolute (Kdev) and relative (Pdev) deviations compare

measured (Kdat) to calculated (Kcaic) values of thermal

conductivity

.

22
Table la. Apparent thermal conductivity of pair B8cd as a function of temperature.

Run Thii gh T 1 ow Tmeon Pr<sss Kdat Kcc1 1 c Kdev Pdev

No. (K) (K) (K) (kPa) mW/(>.K) (Pet)

059 653,.181 592. 922 623..052 82.,51 24,,76 24. 53 0.,23 0.,94

060 708,.283 638. 063 673..173 82..51 25,.86 25. 73 0.,13 0..50

061 708,.098 638. 001 673.,050 82.,51 25..86 25. 73 0.,13 0,.50

062 708,.211 638. 084 673.,148 82.,51 25,.98 25. 73 0.,25 0,.96

065 708,.134 638.,194 673.,164 82.,51 26,.06 25. 73 0, 33 1 ,.27

066 748,.370 678. 234 713. 302 82,.51 27,.20 26. 82 0.,38 1 ,,41

067 748,.087 678. 163 713..125 82.,51 27..20 26. 81 0,.39 1 ,.46

070 748..109 678. 070 713,.090 82.,51 27..18 26. 81 0..37 1 ,.39

071 707,.944 638. 027 672..986 82.,51 25,.91 25. 73 0.,18 0,.69

072 652..692 593. 131 622..912 82..51 24..72 24. 53 0,,19 0,.78

073 602,.810 543.,148 572..979 82..51 23..60 23. 50 0., 10 0,.43

077 548.,148 498.,143 523.,146 82.,51 22,.87 22. 62 0,.25 1 .10

078 522.,940 473. 073 498,,007 82.,51 22,,46 22. 22 0..24 1 .08

079 498..049 448.,121 473.,085 82,,51 21 ,.95 21 . 87 0,.09 0 .40

080 468..026 428. 111 448..069 82..51 21 ,.54 21 . 54 0,,00 0 .02

081 443. 079 403. 121 423..100 82.,51 21 ..16 21 . 24 -0,.08 -0 .37

082 418.,084 378. 122 398..103 82.,51 20 ,91 20. 96 -0,,06 -0 .28

083 338.,120 308. 127 323..124 82..51 20.,30 20. 29 0,.01 0 .04

084 338..153 308. 170 323..162 82.,51 20,,33 20. 29 0.,03 0 .15

085 368..278 328. 207 348..243 82.,51 20,.55 20. 50 0,.05 0,.26

086 393. 210 353. 153 373..182 82..51 20,.88 20. 72 0,, 16 0,.79

090 333..235 303. 190 318. 213 83..04 20.,19 20. 30 -0,, 1

1

-0 .53

091 333..153 303. 151 318. 152 83.,04 20..20 20. 30 -0,. 1

1

-0 .53

096 363..151 333. 149 348. 150 83. 04 20,,57 20. 54 0. 03 0,.16

097 366..176 329. 588 347. 882 83.,04 20..64 20. 54 0.,10 0,.49

098 363. 143 333. 154 348. 149 83.,04 20,,52 20. 54 -0.,02 -0 .09

099 338. 295 308. 220 323. 258 83. 04 20.,34 20. 34 0.,00 0,.00

100 341 . 215 305. 226 323. 221 83. 04 20..40 20. 34 0.,06 0,.31

101 338. 157 308. 163 323. 160 83. 04 20..35 20. 34 0. 01 0,.05

102 368. 159 328. 087 348. 123 83. 04 20..67 20. 54 0,.13 0,,63

103 371 . 177 325. 177 348. 177 83. 04 20. 62 20. 54 0.,08 0,,39

104 368. 126 328. 068 348. 097 83. 04 20..55 20. 54 0. 00 0,,02

105 393. 239 353. 141 373. 190 83. 04 20..90 20. 76 0., 14 0,,66

106 396. 167 350. 155 373. 161 83. 04 20..77 20. 77 0.,01 0..04

109 418. 170 378. 151 398. 161 82. 64 21 . 12 20. 98 0.,15 0,.70

110 420. 167 376. 171 398. 169 82. 64 21 ..10 20. 98 0..12 0.,59

1 1

1

418. 122 378. 129 398. 126 82. 64 21 . 13 20. 98 0. 16 0.,74

112 448. 272 398. 141 423. 207 82. 64 21 . 43 21 . 25 0.,18 0,.84

113 451 . 177 395. 150 423. 164 82. 64 21 . 38 21 . 25 0.,13 0..61

114 448. 135 398. 146 423. 141 82. 64 21 . 36 21 . 25 0. 1

1

0..52

116 473. 168 423. 1 1

1

448. 140 82. 64 21 . 72 21 . 55 0. 17 0..78

117 476. 190 420. 145 448. 168 82. 64 21 . 68 21 . 55 0. 12 0.,58

118 473. 107 423. 128 448. 118 82. 64 21 . 68 21 . 55 0. 13 0..59

119 498. 244 448. 134 473. 189 82. 64 22. 07 21 . 88 0. 19 0. 87

120 503. 243 443. 235 473. 239 82. 64 22. 00 21 . 88 • 0. 12 0. 55

STANDARD DEVIATION - 0.70

Dens i ty

(kg/m^)

34-8

23
Table 1b. Apparent thermal conductivity of pair B23 as a function of temperature.

Run

No

.

Th i gh

(K)

T 1 ow

(K)

Tmeon

(K)

Press

(kPa)

Kdat Kca 1 c mW/(m.K)

Kdev Pdev

(Pet)

Dens i ty

(kg/ml)

256 758. 120 688. 183 723. 152 83. 17 27. 18 27. 29 -0. 1

1

-0. 40 328

258 733. 087 663. 257 698. 172 83. 17 26.,48 26. 55 -0, 07 -0. 26

259 710. 971 635. 124 673. 048 83. 17 25,,74 25. 86 -0. 12 -0. 45

260 708. 132 638. 140 673. 136 83. 17 25,,77 25. 86 -0. 08 -0. 33

261 683. 061 613. 263 648. 162 83. 17 25.,10 25. 21 -0. 1

1

-0. 44

262 656. 124 590. 154 623. 139 83. 17 24,.53 24. 60 -0. 08 -0. 32

263 653. 132 593. 178 623. 155 83. 17 24 ,54 24. 60 -0. 06 -0. 24

264 628. 057 568. 103 598. 080 83. 17 23,.94 24. 04 -0. 10 -0. 42

265 606. 044 540. 117 573. 081 83. 17 23 . 44 23,,52 -0. 08 -0. 35

266 603.,123 543. 136 573.,130 83. 17 23 .50 23,,52 -0. 02 -0.,09

267 578. 067 518..144 548.,106 83.,17 22 .97 23 .04 -0,.07 -0,.29

269 548.. 108 498,.119 523,.114 83.,17 22 .55 22 .59 -0.,04 -0,.17

271 526.,172 470,.002 498..087 83.,17 22 .29 22 .19 0..10 0,. 44

272 501 .077 445,.054 473,,066 83..17 21 .89 21 .81 0,.07 0 .34

273 498..122 448,.041 473,.082 83..17 21 .92 21 .81 0 . 1 1 0 .52

274 473 ,262 423 .156 448 .209 83,, 17 21 .61 21 .47 0 .14 0 .65

275 446 .115 400,.147 423 .131 83,.17 21 .20 21 .16 0 .04 0 .20

276 443 .132 403 .126 423 .129 83,.17 21 .26 21 .15 0 .10 0 .49

279 398 .173 348 .188 373 . 181 83 .17 20 .65 20 .62 0 .04 0 .17

281 368 . 143 328 .155 348 .149 83 .17 20 .37 20 .38 -0 .02 -0 .09

283 356 .152 310 .757 333 .455 83 .17 20 .25 20 .26 0 .00 -0 .02

204 353 .153 313 .157 333 .155 83 .17 20 .25 20 .25 0 .00 0 .00

St ondo rd Dev i at i on «= 0 .35

I

24
Table 1c. Apparent thermal conductivity of pair B12 os a function of temperature.

Run Thi gh Tlow Tmean Pre 83 Kdat Kca1 1 c Kdev Pdev

No. (K) (K) (K) (kPa) mW/( m.K) (Pc:t)

502 498. 183 448,.071 473..127 83. 17 21 . 87 21 . 67 0. 20 0. 94

303 498. 274 448..069 473..172 83. 17 21 . 88 21 . 67 0. 21 0. 98

305 548. 184 508.,095 528,.140 83. 17 22.,65 22. 60 0. 05 0. 24

306 603. 323 542,.847 573,.085 83. 17 23. 47 23. 50 -0. 03 -0. 12

310 758. 098 688..084 723 .091 83. 17 27.,37 27. 54 -0. 17 -0. 63

311 728. 113 658 ,150 693 .132 83. 17 26.,41 26. 60 -0. 18 -0. 69

312 730. 173 655 .069 692 .621 83. 17 26..56 26. 58 -0. 02 -0. 07

313 728., 119 638,.098 683 .109 83. 17 26..23 26. 31 -0. 07 -0. 28

314 708.,163 638,.201 673 .182 83. 17 26,.06 26. 01 0..06 0. 22

315 733.,259 663,.169 698 .214 83. 17 26,,87 26. 75 0..12 0. 46

316 758..324 688 .206 723 .265 83. 17 27.,56 27. 55 0,.01 0. 04

317 760..159 686 .055 723 .107 83. 17 27,.57 27. 55 0..02 0. 09

318 751 , 047 675 .142 713 .095 83. 17 27,.15 27. 22 -0,.07 -0. 26

319 748..105 678 .189 713 .147 83. 17 27,.23 27. 22 0,,01 0. 05

320 735..004 661 .088 698 .046 83. 17 26 .76 26. 75 0,.01 0. 04

321 733,,113 663 .125 698 .119 83. 17 26,.81 26. 75 0 .06 0. 24

322 710.,142 636 .144 673 .143 83. 17 26 .09 26. 01 0..09 0.,33

323 708,,130 638 .178 673 .154 83. 17 26 .09 26. 01 0..08 0.,33

324 683. 069 613 .537 648 .303 83. 17 25 .41 25. 31 0 .09 0,,36

325 655..996 590 .102 623 .049 83. 17 24 .71 24. 66 0 .05 0..22

326 653,.108 593 .162 623 .135 83. 17 24 .82 24. 66 0 .17 0.,67

327 633..075 573 .113 603 .094 83. 17 24 .19 24. 17 0 .01 0..06

328 608.,024 538 .134 573 .079 83. 17 23 .57 23. 50 0 .07 0.,28

329 606.,123 540 .129 573 .126 83. 17 23 .60 23. 50 0 .10 0..41

330 603,.156. 543 .146 573 .151 83. 17 23 .63 23. 50 0 .13 0,.57

331 578..048 518 .115 548 .082 83. 17 23 .00 22. 98 0 .02 0,.09

332 551 ,.044 495 .115 523 .080 83. 17 22 .56 22.,51 0 .05 0.,24

333 548,,190 498 .153 523 .172 83. 17 22 .68 22. 51 0 .17 0,.77

334 523..088 473 .143 498 .116 83. 17 22 .12 22.,07 0 .05 0 ,22

335 501 ,,054 445 .128 473 .091 83. 17 21 .80 21 . 67 0 .13 0,.58

336 498..121 448 .132 473 .127 83. 17 21 .86 21 . 67 0 .19 0 .88

337 473,,095 423 .152 448 .124 83. 17 21 .43 21 .,30 0 .12 0 .58

338 445,.083 400 .185 422 .634 83. 17 21 .07 20.,96 0 . 1

1

0 .52

339 443,,291 403 .166 423 .229 83. 17 21 .24 20,,97 0 .27 1 ,.27

340 423,.085 373 .136 398 .111 83. 17 20 .84 20.,67 0 .17 0 .82

341 393,.049 353 .137 373 .093 83. 17 20 .47 20..39 0 .07 0 .37

342 376,.093 330 .125 353 .109 83. 17 20 .39 20..19 0 .20 0 .98

343 373,.126 333 .136 353 .131 83. 17 20 .35 20..19 0 .16 0 .80

344 353,.113 313 .181 333 .147 83. 17 20 .20 20,,01 0 .19 0 .96

345 348,.113 318 .139 333 .126 83. 17 20 . 13 20.,01 0 .12 0 .62

346 343 .134 313 .165 328 .150 83. 17 20 . 1

1

19.,97 0 .15 0 .74

347 338,.143 308 .157 323 .150 83. 17 20 .09 19,,92 0 .17 0 .83

<Stan dard Dev i at i on * 0 .58

Dene i ty

(kg/m*)

305

25
Table Id. Apparent thermal conductivity of pair B14 as a function of temperoture.

Run Th i gh Tlow Tmean Pre ss Kdat Kcc1 1 c Kdev Pdev

No. (K) (K) (K) (kPa) mW/( m.K) (Pc:t)

401 443.256 403. 184 423. 220 83. 57 21 . 00 20. 98 0. 02 0. 09

402 441 .168 405. 093 423. 131 83. 57 20. 93 20. 98 -0. 05 -0. 25

403 443.168 403. 099 423. 134 83. 57 20. 95 20. 98 -0. 03 -0. 12

404 445.166 401 . 159 423. 163 83. 57 20. 95 20. 98 -0. 03 -0. 14

405 603.281 543. 078 573. 180 83. 57 23. 60 23. 53 0. 07 0. 29

406 708.294 637. 800 673. 047 83. 57 25. 96 26. 06 -0. 10 -0. 40

409 758.146 688. 102 723. 124 83. 57 27. 71 27. 62 0. 09 0. 33

410 737.959 658. 086 698. 023 83. 57 26. 78 26. 82 -0. 04 -0. 14

41 1 735.060 661 . 128 698. 094 83. 57 26. 86 26. 82 0. 04 0. 14

412 733.157 663. 205 698. 181 83. 57 26. 86 26. 82 0. 04 0. 16

413 713.031 633. 139 673. 085 83. 57 26. 06 26. 07 -0. 01 -0. 04

414 71 1 .104 635. 156 673. 130 83. 57 26. 07 26. 07 0. 00 0. 02

415 708.141 638. 187 673. 164 83. 57 26. 09 26. 06 0. 02 0. 08

416 706.160 640. 261 673. 211 83. 57 26. 06 26. 06 0..00 -0. 01

417 681 .099 615. 150 648. 125 83.,71 25.,36 25..37 -0,,01 -0. 03

418 653.024 593. 135 623.,080 83,,71 24,,65 24,,71 -0..06 -0. 26

419 653.150 593. 229 623..190 83,,71 24,,63 24,.72 -0,.09 -0..37

420 653.151 593.,201 623,,176 83,,71 24,,69 24,.72 -0..03 -0..12

421 628.057 568.,134 598,.096 83,.71 24,.00 24 .11 -0.. 1

1

-0,,45

422 605.207 541 .,133 573,.170 83,.71 23,.52 23 .55 -0,.02 -0,,10

423 603.127 543,.159 573,.143 83,.71 23 .52 23 .55 -0 .02 -0 .10

424 601 .125 545,.221 573 .173 83 .71 23 .53 23 .54 -0 .01 -0 .05

425 578.078 518,.148 548 . 113 83 .71 22 .96 23 .02 -0 .06 -0 .27

426 550.107 496 .166 523 .137 83 .71 22 .43 22 .54 -0 . 1

1

-0 .50

427 548.151 498 .170 523 .161 83 .71 22 .51 22 .54 -0 .03 -0 .15

428 546.152 500 .169 523 .161 83 .71 22 .55 22 .54 0 .01 0 .04

429 523.120 473 .165 498 .143 83 .71 21 .99 22 .10 -0 . 1

1

-0 .50

430 500.134 446 .159 473 .147 83 .71 21 .65 21 .70 -0 .05 -0 .22

431 498.134 448 .130 473 .132 83 .71 21 .65 21 .70 -0 .05 -0 .21

432 496.097 450 .108 473 .103 83 .71 21 .62 21 .70 -0 .07 -0 .35

433 391 .242 355 .150 373 .196 83 .71 20 .38 20 .41 -0 .03 -0 .17

434 393.187 353 .153 373 .170 83 .71 20 .31 20 .41 -0 .10 ~0 .48

435 395.141 351 .120 373 .131 83 .71 20 .36 20 .41 -0 .05 -0 .23

436 418.205 378 .168 398 .187 83 .71 20 .69 20 .69 0 .01 0 .03

438 341 . 115 306 .888 324 .002 83 .71 19 .79 19 .95 -0 .16 -0 .79

439 339.181 307 .182 323 .182 83 .71 19 .81 19 .94 -0 .13 -0 .66

440 340.177 306 .394 323 .286 83 .71 19 .90 19 .94 -0 .04 -0 .21

441 337.172 305 .412 321 .292 83 .71 19 .89 19 .92 -0 .04 —

c

.18

Standord Deviation * 0.30

Dens i ty

(kg/m»)

300

26
Table 1e. Apporent thermol conductivity of poir B34 os a function of temperoture

.

Run ThIi gh Thow Tmean Pr(ess Kdot Kcia 1 c Kdev Pdev

No

.

(K) (K) (K) (kPo) mW/(m.K) (Pet)

503 758 .300 687 .931 723..116 83,,04 27.,76 27.,40 0. 35 1 .,30

504 773,.111 692 .596 732,.854 83..04 28.,07 27. 72 0. 36 1 ,,28

505 771 ,.047 694 .546 732,.797 83,.04 28,,10 27.,71 0. 38 1 ,,37

506 768 .085 697 .949 733..017 83,.04 28,,13 27. 72 0.,41 1 ,,47

507 706 .264 540 .143 623,.204 83,.04 24..91 24. 68 0. 22 0..90

508 708,.213 638 .115 673..164 83.,04 26..21 25. 91 0, 29 1 ,. 14

509 710,.143 636 .099 673..121 83.,04 26,.19 25. 91 0..27 1 ,.06

510 678 .082 618 .152 648.. 117 83,.04 25..42 25.,24 0..18 0,.73

512 653..166 593 .21

1

623 .189 83,,04 24,.89 24. 61 0.,28 1 .,13

513 651 ,.106 595 .169 623 .138 83,.04 24..89 24.,61 0. 28 1 ,.13

514 628,.121 568 .216 598,.169 83,.04 24,,25 24, 03 0,,22 0,.90

515 605,.155 541 .203 573..179 83,.04 23.,62 23.,50 0,.13 0,,54

516 498,,252 448 .158 473..205 83,,44 21 ,.81 21 .,76 0..05 0,.23

517 578,,376 518 .169 548.,273 83,.04 23 .24 23.,00 0, 24 1 ,.05

518 548..098 498 .124 523,,111 83..04 22,.60 22.,53 0..07 0.,31

519 523,.086 473 . 116 498,,101 83,,04 22,.17 22., 1

1

0,,06 0..28

539 471 ..239 425 .202 448,,221 83,,04 21 ,.50 21 .,37 0..14 0,.64

541 333,,203 304 .985 319.,094 83,.04 20,,16 20. 00 0.,16 0..81

542 338.,107 308 .111 323..109 83,,04 20,,18 20, 03 0.,15 0..75

543 340,,083 306 .837 323,.460 83.,04 20..17 20.,03 0.,14 0..70

544 343.,273 313 .273 328,,273 83.,04 20,,16 20. 07 0, 09 0,,44

545 346. 222 310 .223 328, 223 83..04 20.,36 20. 07 0,,29 1 ,,44

546 353.,195 313,.179 333.,187 83.,04 20.,41 20..12 0. 30 1 ,48

547 355. 243 311 ,.665 333.,454 83,,04 20.,45 20.,12 0,,34 1 ,.67

548 367.,983 328,.002 347..993 83,.04 20.,57 20.,24 0.,33 1 ,,61

549 366. 118 330,.051 348. 085 83,,04 20. 69 20. 25 0.,45 2.,21

551 402. 406 363,.342 382. 874 83. 04 20. 83 20. 58 0.,25 1 ..19

552 404. 422 360,,877 382. 650 83.,04 20, 84 20. 58 0. 26 1 ,.25

553 416. 088 380,.081 398.,085 83.,04 20,.90 20. 75 0.,15 0,,72

556 418. 235 378,,193 398.,214 83. 04 21 ., 12 20. 75 0. 37 1 ,.77

557 446. 232 402.,098 424. 165 83.,44 21 . 30 21 . 08 0. 22 1 ,,05

STANDARD DEVIATION « 1.16

Dens i ty

(kg/m»)

315

27
Table 2. Apparent thermal conductivity of pair B14 of microporous

fumed-silica insulation boards measured at a mean specimen temperature of 318 K (45°C), and over the range of pressure

from 40 to 83 kPa (300 to 626 torr)

,

with the high-temperature

guarded hot plate. This pair has a mean density of 301 kg/m^

(19 lbm/ft3 )

.

Apparent conductivity was measured in air at ambient humidity. Temperature differences through the specimens were

chosen to be about 10 percent of the value of the mean absolute

temperature within the specimens. Absolute and relative deviations compare measured apparent conductivity to values of Kcaic

computed from eq (3).

Run Thi gh T 1 ow Tm<>an P ress Kdot Kca1 1 c Kdev Pdev

No

.

(K) (K) (H0 (kPa) mw/( m . K

)

(Pet)

442 331 . 151 305,.119 318. 135 83., 44 20. 07 19. 87 0. 20 0. 99

443 333.,152 304 .224 318. 688 83., 44 20. 05 19 . 88 0. 17 0. 85

444 334. 130 304 .259 319. 195 83.. 44 19. 97 19 . 88 0. 09 0. 45

445 331 ., 143 305 .150 318. 147 83.,04 19 , 91 19 . 84 0. 07 0. 37

446

* 331 . 095 305 .076 318. 086 79.,97 19 . 63 19. 57 0. 06 0. 29

447 332. 209 304 .294 318. 252 73..31 19.,10 18. 96 0.,13 0. 71

448 333..133 304 .090 318. 612 73..31 19 , 05 18. 97 0.,09 0. 46

449 334., 140 304 .205 319. 173 73..31 19,,09 18. 97 0..12 0. 62

450 335. 229 304 .469 319. 849 66,.64 18.,45 18. 34 0.. 1

1

0. 60

451 332.. 142 304 . 149 318. 146 59,.98 17. 81 17. 65 0,,16 0.,91

452 331 ..164 305 .155 318. 160 53..32 17,,08 16. 95 0.,14 0..81

453 332..147 304 .151 318.,149 53 .32 17,.06 16. 95 0,. 1 1 0..67

454 331 . 167 305 .178 318.,173 53 .32 17,.02 16. 95 0,.07 0,.42

455 332,. 141 304 . 142 318.,142 46 .65 16,.28 16. 21 0,.07 0..42

456 331 . 121 305 .109 318., 115 46 .65 16,.25 16. 21 0,.04 0,.24

457 332.,185 304 .187 318. 186 39 .99 15,.44 15. 44 0 .01 0. 05

458 333..123 303 .818 318.,471 39 ,99 15,.38 15. 44 -0 .06 -0..40

459 332.. 142 304 .138 318.,140 39 .99 15,.40 15. 44 -0 .04 -0,.26

460 331 ..152 305 .167 318,.160 59 .98 17 .77 17. 65 0 .12 0,.66

461 332..125 304 .120 318,.123 59 .98 17 ,80 17. 65 0 .15 0,,85

Standard Deviation = 0.62

Dens i t y (kg/m^)

301

28
Table 3. Apparent thermal conductivity of pair B8cd of microporous fumed-silica insulation boards measured at a mean

specimen temperature of 318 K (45oC), and over the range of pressure from 27 to 80 kPa (200 to 600 torr), with the high-temperature guarded hot plate. This pair has a mean density of

348 kg/m3 (22 Ibra/ft^ )

.

Apparent conductivity was measured in

air at ambient humidity. Absolute and relative deviations compare

measured apparent conductivity to values of Kcaic computed from

eq ( 3 )

.

Run Thi gh T 1 ow Tmeon Pr«i99 Kdot Kco1 1 c Kdev Pdev

No

.

(K) . (K) (K) (kPo) mW/( m . K) (Pet)

149 333. 199 303..114 318. 157 47. 05 16. 50 16. 73 -0. 23 -1 . 39

150 335. 160 301 .,180 318. 170 39.,99 15.,76 15. 91 -0. 16 -0. 98

151 333. 145 303,,135 318. 1 40 39.,99 15.,71 15. 91 -0. 20 -1 . 25

152 335. 153 301 ..179 318. 166 39..99 15.,75 15. 91 -0.,17 -1 . 04

153 333. 140 303..139 318. 140 39..99 15. 67 15. 91 -0. 24 -1 . 52

154 335. 147 301 ,.160 318. 154 39..99 15..74 15. 91 -0.,18 -1 ., 1

1

155 333. 139 303.,122 318. 131 39,.99 15,.68 15. 91 -0,,23 -1 .,43

156 335. 144 301 ,.188 318. 166 53.,32 17..29 17. 42 -0.,13 -0.,76

157 333. 141 303..139 318. 140 33..32 14. 82 15. 1

1

-0,,29 -1 , 89

158 335. 159 301 ,,181 318. 170 26..66 13,,97 14. 27 -0..30 -2,,13

159 333. 127 303..098 318., 113 66,.64 18,.56 18. 80 -0.,24 -1 ..30

160 335. 154 301 ..181 318.,168 66..64 18.,61 18. 80 -0..19 -1 ,.00

161 333. 141 303..091 318.,116 66,.64 18,.56 18. 80 -0,.24 -1 ,.26

162 335. 155 301 ,,163 318.,159 66.. 1

1

18..64 18. 75 -0,. 1

1

-0,.59

163 333. 139 303..094 318., 117 73,.04 19,.24 19. 42 -0..17 -0,.88

164 335. 158 301 .,179 318.,169 59..98 18,.00 18. 13 -0..13 -0 .72

165 333. 139 303..087 318.,113 59,.98 17,.93 18. 13 -0,.20 -1 .12

166 335. 159 301 .,158 318.,159 79..97 19..86 20. 05 -0,.19 -0,.96

167 333. 199 303.,115 318.,157 79,.97 19,.88 20. 05 -0,.17 -0 .84

168 335. 161 301 ..177 318.,169 79,.97 19..93 20. 05 -0,. 1

1

-0 .57

169 333. 147 303..138 318.,143 79 .97 19, oo oo 20. 05 -0,.17 -0 .83

Standord Deviation » 1.22

Dens i ty

(kg/m^)

348

29
Table 4. Apparent thermal conductivity of pair B34 of microporous

fumed-silica insulation boards measured at a mean

specimen temperature of 473 K (200oC), and over the range of

pressure from 40 to 83 kPa (300 to 626 torr), with the high-temprature guarded hot plate. This pair has a mean density of

315 kg/m^ (19.7 lbm/ft3 )

.

Apparent conductivity was measured in

air at ambient humidity. Absolute and relative deviations compare

measured apparent conductivity to values of Kcalc computed from

eq ( 3 )

.

Run Thi gh T I ow Tmean Pr<!8S Kdat Kca 1 c Kdev Pdev

No. (H0 (H:) (K0 (kPo) mW/( m . K

)

(Pc:t)

516 498. 252 448. 158 473. 205 83. 44 21 . 81 21 . 76 0. 05 0. 23

520 501 . 086 445. 137 473. 112 83. 44 21 . 75 21 . 76 -0. 01 -0. 03

521 498. 116 448. 086 473. 101 73. 31 20. 91 20. 85 0. 07 0. 32

522 496. 134 450. 131 473. 133 73. 31 20. 95 20. 85 0. 10 0. 50

523 498. 177 448. 172 473.,175 66. 64 20. 28 20. 21 0. 07 0. 36

524 500.,161 446 . 139 473. 150 66. 64 20,.31 20. 21 0. 10 0. 50

526 498.,294 448. 226 473. 260 59. 98 19..63 19. 54 0. 09 0. 46

527 501 , 048 445.,019 473.,034 59.,98 19..62 19. 53 0. 08 0. 42

528 498. 088 448. 029 473..059 53..32 18,.90 18. 83 0. 07 0. 38

529 495,,101 451 .. 108 473..105 53..32 18..91 18. 83 0,.09 0,.46

530 498.,139 448,.137 473..138 53..32 18,.95 18. 83 0 .12 0,,62

531 500,.070 446 ,066 473,,068 53,.32 18 .82 18. 83 0 .00 -0..02

532 498..136 448 .133 473,.135 46 .65 18,.10 18. 09 0 .01 0,.05

533 496,. 192 450 .190 473 ,191 39,.99 17 .34 17. 32 0 .03 0..14

534 498 .037 448 .035 473 .036 39 .99 17 .32 17. 32 0 .00 0 .00

535 500 .204 446 .339 473 .272 59 .98 19 .58 19. 54 0 .04 0 .20

536 497 .984 448 .002 472 .993 79 .97 21 .62 21 . 45 0 .17 0 .80

537 496 .110 450 .121 473 .116 79 .97 21 .59 21 . 45 0 . 14 0 .64

538 498 .395 448 .268 473 .332 79 .97 21 .53 21 . 46 0 .07 0 .33

539 498 .395 448 .268 473 .332 37 .99 17 .07 17. 08 -0 .01 -0 .06

STANDARD DEVIATION =0.41

Density

(kg/m^)

315

30
Table 5. Apparent thermal conductivity of pair B8cd of microporous fumed-silica insulation boards measured at a mean

specimen temperature of 473 K (200oC), and over the range of

pressure from 27 to 84 kPa (200 to 630 torr), with the high-temperature guarded hot plate. This pair has a mean density of

348 kg/m3 (22 lbm/ft3). Apparent conductivity was measured in

air at ambient humidity. Absolute and relative deviations compare

measured apparent conductivity to values of Kcalc computed from

eq ( 3 ) .

Run Thii qh Tl<DW Tmelan Pr<!3S Kdat Kcc1 1 c Kdev Pdev

No. (K) (t<) (K) (kPa) mW/( m.K) (P'ct

)

123 498.,156 447 .973 473. 065 39.,99 17,,36 17. 52 -0.,16 -0 .94

124 498..179 448 .010 473. 095 26,,66 15..73 15. 88 -0.,16 -0 .98

125 501 .,171 445 . 119 473. 145 26,.66 15,,70 15. 88 -0.,18 -1 . 1 4

126 498.,143 448 . 149 473. 146 26.,66 15.,70 15. 88 -0.,18 -1 . 1 4

127 498.,146 448 .155 473. 151 26,.66 15..71 15. 88 -0..18 -1 . 1 1

128 498. 143 448 .152 473. 148 26., 66 15,, 69 15. 88 -0, 20 -1 . 23

129 498.,145 448 .099 473. 122 26,.66 15.,71 15. 88 -0..17 -1 .09

130 498. 147 448 .142 473. 145 33,,32 16..53 16. 72 -0..19 -1 . 14

131 498. 140 448 .125 473. 133 46.,65 18..06 18. 30 -0,,24 -1 .29

132 498. 142 448 .144 473. 143 53.,32 18..76 19. 03 -0,,28 -1 .45

133 501 . 169 445 .186 473. 178 53,.32 18,.80 19. 04 -0,.23 -1 .22

134 498. 137 448 .126 473. 132 53,,32 18,.73 19. 03 -0,,31 -1 .61

135 501 . 156 445 .154 473. 155 59,.98 19..44 19. 74 -0..30 -1 .52

137 501 . 181 445 .161 473. 171 66,,64 20.,24 20. 41 -0.,18 -0 .87

138 498. 133 448 .123 473. 128 73,.31 20.,77 21 . 05 -0,.29 -1 .36

139 501 . 166 445 .192 473. 179 73,,31 20.,76 21 . 05 -0. 29 -1 .40

140 498. 142 448..140 473. 141 73,,31 20.,76 21 . 05 -0..30 -1 .41

141 501 . 167 445,.170 473. 169 79,,97 21 ..36 21 . 66 -0..30 -1 .40

142 498. 135 448,.139 473. 137 79,,97 21 ,.33 21 . 66 -0.,33 -1 .53

143 501 . 162 445,.179 473. 171 79, 57 21 . 33 21 . 63 -0, 29 -1 .36

144 498. 131 448,.132 473. 132 79, 57 21 . 32 21 . 62 -0. 30 -1 .39

145 501 . 170 445,.129 473. 150 83. 71 21 , 65 21 . 99 -0,,34 -1 .55

Standard Deviation = 1.32

Density

(kg/m^)

34-8

31
RPPflRENT

THERMAL

CONDUCTIVITY

PRESSURE, kPa

Figure 1. Typical dependence of apparent thermal conductivity

of microporous fumed-silica insulation on ambient air

pressure. No theory exists to completely predict the sigmoidal

shape modelling the dependence. The values along both axes are

arbitrary but representative. In this figure A is the region of

constant, low conductivity at low pressure; B-C-D is the transitional region of rising conductivity at intermediate pressures; E

is the beginning of the plateau of approximately constant, higher

conductivity at higher pressures. The region connecting the rising transitional region to the high-pressure plateau (D-E) is the

'‘knee" . The low-pressure plateau of constant apparent conductivity is determined by radiative heat transfer and by conduction in

the solid material, which are independent of pressure.

32
RPPRRENT

THERMRL

CONDUCTIVITY,

mW/(m.K)

MEAN TEMPERATURE, K

Figure 2. Apparent thermal conductivity of pair B8cd of microporous fumed-silica insulation at mean specimen temperatures ranging from 318 to 713 K (45 to 440<>C), with the NIST-B

high-temperature guarded hot plate. This pair has a mean density

of 348 kg/m^ (22 lbm/ft3 )

.

Conductivity was measured in air at

ambient humidity and at a pressure of 83 kPa. The measurement

bias in values of Kmeas is estimated to be 1.0 percent at 320 K,

and 2.5 percent at 725 K. The solid curve represents values of

Kcaic obtained using eq (3).

33
lUUlX.-X

,

J/X

,

obs

caLc

coLc

MEAN TEMPERATURE, K

Figure

culated

between

3. Relative (percent) deviations of thermal conductivity

of fumed-silica insulation pair B8cd from values calwith eq (3). The standard deviation of the 45 residuals

the points and the curve is 0.70 percent.

34
APPARENT

THERHAL

CONDUCTIVITY

23 I f1

t £

£

MEAN TEMPERATURE, K

Figure 4. Apparent thermal conductivity of pair B23 of microporous fumed-silica insulation at mean specimen temperatures ranging from 333 to 723 K (60 to 450oC). This pair has

a mean density of 328 kg/m^ (20 lbm/ft3 )

.

Conductivity was measured in air at ambient humidity and at a pressure of 83 kPa. The

solid curve represents values of Kcaic obtained using eq (3).

35
100(\,-\

I

]/x

,

obs

coLc

coLc

MERN TEMPERRTURE, K

Figure 5. Relative (percent) deviations of thermal conductivity

of fumed-silica insulation pair B23 from values calculated with eq (3). The standard deviation of the residuals

between the points and the curve is 0.35 percent.

36
APPARENT

THERMAL

CONDUCTIVITY

MEAN TEMPERATURE, K

Figure 6. Apparent thermal conductivity of pair B12 of microporous fumed-silica insulation at mean specimen temperatures ranging from 323 to 723 K (50 to 450oC). This pair has

a mean density of 304 kg/m^ (19 lbm/ft3 )

.

Conductivity was measured in air at ambient humidity and at a pressure of 83 kPa. The

solid curve represents values of Kcaic obtained using eq (3).

37
obs

coLc

coLc

MERN TEMPERRTURE, K

Figure 7. Relative (percent) deviations of thermal conductivity

of fumed-silica insulation pair B12 from values calculated with eq (3). The standard deviation of the residuals

between the points and the curve is 0.58 percent.

38
RPPRRENT

THERMAL

CONDUCTIVITY

28

V

300 350 400 450 500 550 600 650 700 750

MEAN TEMPERRTURE, K

Figure 8. Apparent thermal conductivity of pair B14 of microporous fumed-silica insulation at mean specimen temperatures ranging from 321 to 723 K (48 to 450oC). This pair has

a mean density of 301 kg/m^ (19 lbm/ft3). Conductivity was measured at ambient humidity and at a pressure of 83 kPa. The solid

curve represents values of Kcaic, obtained using eq (3).

39
100(

X

^

-X

,

)/x

,

obs

coLc

coLc

MEAN TEMPERATURE, K

Figure 9. Relative (percent) deviations of thermal conductivity

of fumed-silica insulation pair B14 from values calculated with eq (3). The standard deviation of the residuals

between the points and the curve is 0.30 percent.

40
RPPRRENT

THERMAL

CONDUCTIVITY

MERN TEMPERATURE, K

Figure 10. Apparent thermal conductivity of pair B34 of microporous fumed-silica insulation at mean specimen temperatures ranging from 321 to 723 K (48 to 450oC). This pair has

a mean density of 315 kg/m^ (20 lbm/ft3 )

.

Conductivity was measured at ambient humidity and at a pressure of 83 kPa. The soli

curve represents values of Kcaic, obtained using eq (3).

41
100(x,“x

,

]/x

,

obs

coLc

caLc

flERN TEMPERATURE, K

Figure 11. Relative (percent) deviations of thermal conductivity

of fumed-silica insulation pair B34 from values calculated with eq (3). The standard deviation of the residuals

between the points and the curve is 1.16 percent.

42
flPPRRENT

THERMAL

CONDUCTIVITY

e E

E

PRESSURE^ kPa

Figure 12. Apparent thermal conductivity of pair B14, density of

301 kg/m3 (19 Ibrn/ft^ ) , at a mean specimen temperature of 318 K (45<>C) and at pressures ranging from 40 to 83 kPa.

The solid curve represents values of Kcaic obtained using eq (3).

43
1

G.8

0.6

0.4

0.2

0

- 0.2

- 0.4

' - 0.6

35 40 45 50 55 60 65 70 75 80 85

PRESSURE, kPa

Figure 13. Relative deviation, in percent, of measured apparent

thermal conductivity of fumed-silica pair B14 at

318 K, from values calculated with eq (3), over the range of

pressures from 40 to 83 kPa. The standard deviation of the

residuals between the points and the curve is 0.62 percent.

" 1

' 1

'

1

, , . : .... 1

:

0

-

- 0

o 0 .

o

o 0

- o

o -

o 0

o o .

- 0 .

. 0 ,

- 0

-

. o -

- o

-

- o

-

•

. . 1 . , . t, i i ^ > .1 ,

1 - ' 1 1 , , . , 1 , ' 1 ‘
RPPRRENT

THERMRL

CONDUCTIVITY

13

, I , ,

1^^

25 30 35 40 45 50 55 60

PRESSURE^ kPo

65 70 75 80

Figure 14. Apparent thermal conductivity of pair B8cd, density

of 348 kg/m3 (22 Ibm/ft^ ) , at a mean specimen temperature of 318 K (45oC) and at pressures ranging from 26 to 80 kPa.

The solid curve represents values of Kcai c obtained using eq (3).

45
lUUl\,-\

,

J/X

,

obs

coLc

caLc

- 0.50

_ n '7C U • / w'

-1

-] .25

- 1.50

- 1.75

- 2,25 *

' ‘ ^ ^ ^ 1 - ^ 1 I ' : : I . . ' . I . . . . I . . . I . . ! . . . ! . . I 25 30 35 40 45 50 55 60 65 70 75 80

PRESSURE, kPa

Figure 15. Relative deviation, in percent, of measured apparent

thermal conductivity of fumed-silica pair B8cd at

318 K, from values calculated with eq (3), over the range of

pressures from 26 to 80 kPa. The standard deviation of the

residuals between the points and the curve is 1.22 percent.

o

o

o

o

o

o

o

o o

o

o

o

o

o

o

o

o

, , . , I . , J i I i i I

46
APPARENT

THERNAL

CONDUCTIVITY

35 40 45 50 55 60 65 70 75 80 85

PRESSURE, kPa

Figure 16. Apparent thermal conductivity of pair B34, density of

315 kg/m3 (20 Ibm/ft^ ) , at a mean specimen temperature of 473 K (200oC) and at pressures ranging from 37 to 83 kPa.

The solid curve represents values of Kcaic obtained using eq (3).

47
100( X

,

,

]/\

I

obs

coLc

cgLc

0.3

0.7

0.5

0.5

0 .^

0.3

0.2

0.1

0.0

- 0.1

35 ^0 ^5 50 55 60 65 70 75 80 85

PRESSURE, kPa

Figure 17. Relative deviation, in percent, of measured apparent

thermal conductivity of fumed-silica pair B34 at

473 K, from values calculated from eq (3), over the range of

pressures from 37 to 83 kPa. The standard deviation of the

residuals between the points and the curve is 0.41 percent.

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

48
flPPRRENT

THERMRL

CONDUCTIVITY

PRESSURE, kPa

Figure 18. Apparent thermal conductivity of pair B8cd, density

of 348 kg/m3 (22 Ibm/ft^ ) , at a mean specimen temperature of 473 K (200oC) and at pressures ranging from 26 to 84

kPa. The solid curve represents values of Kcalc obtained using

eq (3).

49
1Q0(

\

,

]/\

,

obs

cal.c

cgLc

- 0.8

- 0.9 -

-

1

- 1 1

-

1

2 -

3

-

-1

5 -

- 1.6

- 1.7

20 30 40 50 60 70

PRESSURE^ kPo

80 90

WiSMTo 19. Relative deviation, in percent, of measured apparent

thermal conductivity of fumed-silica pair B8cd at

473 K, from values calculated from eq (3), over the range of

pressures from 26 to 84 kPa. The standard deviation of the

residuals between the points and the curve is 1.32 percent.

50
nPPFIRENT

THERMAL

CONDUCTIVITY

DENSITY, kg/m^

Figure 20. Apparent thermal conductivity as a function of density for five measured pairs of fumed-silica specimens,

at temperatures of 300 to 800 K. Measurements were performed

with an ambient air pressure of 83 kPa . Open symbols are values

calculated from eq (3) for the densities of the specimen pairs

measured

.

51
APPARENT

THERMAL

CONUUU

1

V1

Y,

mN/(m.K)

DENSITY, kg/m^

Figure 21. Dependence of apparent thermal conductivity of fumedsilica insulation on bulk density. Open squares represent measurements at 297 K and at ambient pressure of 101.3 kPa

at NIST-G. Open circles represent points calculated from the

least-squares fit to actual data obtained at NIST-B at 300 K and

at ambient air pressure of 83.2 kPa. Plus signs are data from

NIST-B extrapolated upward to a pressure of 101.3 kPa by addition

of 1.43 units.

52
flPPRRENT

THERMRL

CONDUCTIVITY,

mW/(m.K)

MEAN TEMPERATURE, K

Figure 22. Dependence of apparent thermal conductivity of fumedsilica insulation on temperature, as measured at

ambient air pressure of 83 kPa at NIST-B (open triangles) and at

ambient pressure of 101.3 kPa at NIST-G (filled square, triangle

and diamond). Plus signs are data from NIST-B extrapolated upward to a pressure of 101.3 kPa by addition of 1.43 units. Data

from NIST-G are for a specimen with a density of 330 kg/m^

.

Data (open triangles) from NIST-B are for one with a density of

328 kg/m3 (pair B23) and are identical to data in figure 4.

53

us GOVERNMENT PRfNTiNG OFFICE 1989-Jacket 676-528/5119 Region 8

1 NBS-114A (REV. 2-80

U.S. DEPT. OP COMM. 1 . BIBLIOGRAPHIC DATA

SHEET (See instructions)

4. TITLE AND SUBTITLE

PUBLICATION

REPORT NO.

OR 2. Performing Organ. Report No. 3.

NISTIR 89-3919

PubI ication Date

August 1989

MICROPOROUS FUMED-SILICA INSULATION AS A STANDARD REFERENCE MATERIAL OF THERMAL

RESISTANCE

5. AUTHOR(S)

DAVID R. SMITH

6. PERFORMING ORGANIZATION (If joint or other than MBS. see instructions)

National Institute of Standards and Technology

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State, ZIP)

U.S. Department of Energy

Oak Ridge National Laboratory

Oak Ridge, Tennessee 37830

10. SUPPLEMENTARY NOTES

Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200- word or less factual summary of most significant information. If document includes a si gn i fi cant

bi bl iography or literature survey, mention it here)

Measurements of apparent thermal conductivity of microporous fumedsilica insulation board, already certified as a Standard Reference

Material (SRM) of thermal resistance, are reported here to extend the

range of certification of this material to higher temperatures and

lower pressures. Apparent thermal conductivities of five different

pairs of specimens ranging in mean density from 300 to 348 kg/m^ were

measured with a high-temperature guarded hot plate 25 cm in diameter.

The measurements cover a range of mean specimen temperatures from 318

to 733 K (45 to 460° C), and of environmental air pressures from 26.7

to 83.5 kPa (200 to 626 Torr) . Detailed analyses are given, along

with intercomparisons of previously published data. Apparent thermal

conductivity is correlated with temperature, pressure, and density;

the correlation obtained represents all the data within a standard

deviation of 0.68 percent. This microporous fumed silica (at an ambient pressure of 83 kPa and a density of 300 kg/m3 ) has an apparent

thermal conductivity of 19.8 mW/(m- K) at 300 K and is suitable for

use as an SRM of very low conductivity from 297 to 735 K (24 to

460«>C). Adsorbed moisture within this material must be driven off by

prolonged heating at 110° C before its conductivity is measured. Great

care in handling this material is necessary because of its fragility.

I

k

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semi colon s) apparent thermal conductivity; density; insulation board; microporous

fumed silica; pressure; Standard Reference Material; temperature;

thermal insulation; thermal resistance.

13. AVAILABILITY 14. NO. OF

PRINTED PAGES

[^] Uni imited

1 1 For Official Distribution. Do Not Release to NTIS 68

1 1 Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402. 15. Price

[y~l Order From National Technical Information Service (NTIS), Springfield, VA. 22161

USCOMM-DC 6043-P80
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