NEW NIST PUBLICATION

June 12, 1989

NISTIR 89-3913

INTERLABORATORY COMPARISON

OF THE GUARDED HORIZONTAL

PIPE-TEST APPARATUS

Precision of ASTM Standard

Test Method C-335 Applied

to Mineral-Fiber Pipe

insulation

David R. Smith

National Institute of Standards and Technology

(formerly National Bureau of Standards)

U.S. Department of Commerce

Boulder, Colorado 80303-3328

April 1989

NISTIR 89-3913

INTERLABORATORY COMPARISON

OF THE GUARDED HORIZONTAL

PIPE-TEST APPARATUS

Precision of ASTM Standard

Test Method C-335 Applied

to Mineral-Fiber Pipe

Insulation

David R. Smith

Chemical Engineering Science Division

Center for Chemical Engineering

National Institute of Standards and Technology

Boulder, Colorado 80303-3328

April 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 v

LIST OF FIGURES vii

ABSTRACT 1

1. INTRODUCTION 2

2. COMPARISON OF THE GUARDED-HOT-PLATE AND

PIPE-TEST METHODS 3

a. The Guarded Hot Plate 3

b. The Horizontal Pipe-Test Apparatus 5

3 . SCOPE 8

4. PARTICIPANTS AND APPARATUSES 9

5. SPECIMEN CONDITIONING 10

6. THERMAL CONDUCTIVITY DATA 11

7. REFERENCE EQUATIONS AND DATA ANALYSIS 12

8. ESTIMATED PRECISION OF THE HPT METHOD 17

9. SUMMARY AND CONCLUSIONS 19

10. REFERENCES 21

TABLES 2 - 6 23-27

FIGURES 1 - 10 28-37

LIST OF TABLES

Table 1

.

Coding symbols used in figures to distinguish the

seven laboratories participating in the interlaboratory comparison, and sizes of their nominally 3-inch

pipe-test apparatuses 9

Table 2 . Inter laboratory comparison of apparent thermal conductivity of high-temperature mineral -fiber pipe

insulation measured on seven different horizontal pipe-test

apparatuses. Specimens had a nominal inner diameter of 89 mm

(3.5 in) and wall thickness of 51 mm (2 in). Measurements

were performed at the ambient atmospheric pressure of each

laboratory, 83 to 100 kPa (630 to 760 Torr), and at mean

temperatures from 318 to 652 K (113 to 1238°F). The nominal

density of the specimens is 90 kg/m3 (5.6 lbm/ft 3 ). Kcaic is

computed from eq (9). The standard deviation of the data set

from eq (9) for all specimens is 4.95 percent 23

Table 3. Interlaboratory comparison of apparent thermal conductivity of high-temperature mineral-fiber pipe

insulation measured on seven different horizontal pipe-test

apparatuses. Kcaic is computed from eq (10), obtained by

weighting each laboratory equally. The standard deviation of

the data set from eq (10) for all specimens is 5.08 percent 24

Table 4. Interlaboratory comparison of apparent thermal conductivity of high-temperature mineral-fiber pipe

insulation. This set of specimens is restricted to only

those which were conditioned by heating them to the highest

temperature of measurement before data was taken. Kcaic is

computed from eq (11). The standard deviation of the data

set from eq (11) for conditioned specimens is 4.34 percent 25

Table 5 . Interlaboratory comparison of apparent thermal conductivity of high-temperature mineral-fiber pipe

insulation. This set of specimens is restricted to only

those which were not conditioned by heating them to the highest temperature of measurement before data was taken. Kcaic

is computed from eq (12). The standard deviation of the data

set from eq (12) for nonconditioned specimens is 4.72

percent 26

v
Table 6. Apparent thermal conductivity of specimens of hightemperature mineral-fiber pipe insulation that were

not conditioned before they were measured. The last two

columns indicate deviations of these data from the leastsquares curve, eq (11), defined by specimens that, were

conditioned before they were measured. The standard deviation of the data set from eq (11) for conditioned specimens

is 5.40 percent 27

vi
LIST OF FIGURES

Figure 1 . Interlaboratory comparison of apparent thermal

conductivity of mineral -fiber pipe insulation

measured on the horizontal pipe-test apparatus. The nominal

density of the specimens is 90 kg/m 3 (5.6 lbm/ft 3 ) . Measurements were performed in air at ambient pressure. The solid

line is a plot of eq (9) for thermal conductivity as a function of temperature. Each point on this line represents the

thermal conductivity determined by the local thermal gradient

(vanishing temperature difference), at a point within the

specimen; the temperature at that point is given by the value

from the temperature axis. Each symbol represents the experimental conductivity obtained at (large) nonzero temperature

differences between the boundary surfaces at Tcoid and Thot

.

The value of conductivity at the symbol is the ratio of the

integral of the conductivity function between Tcoid and Thot

to the corresponding temperature difference. For this reason

the data points deviate from the curve when large temperature

differences are used. Specimens from laboratories 1, 2, 4,

and 6 were conditioned by heating specimens to the highest

temperatures of measurement before taking data. Filled triangles denote repeated measurements by laboratory 2 and

circled “plus" signs denote repeated measurements by laboratory 6 28

Figure 2. Deviations of apparent thermal conductivity of

mineralfiber pipe insulation, as measured by all

seven participants, from values calculated with eq (9),

thermal conductivity as a function of temperature. Each

experimental conductivity value is obtained at (large)

nonzero temperature differences between the boundary surfaces

at Tcoid and Thot . The integral of the conductivity

function is computed over the temperature interval from Tcoid

to Thot . We compute the ratio of this integral..., to the

corresponding temperature difference to obtain- the mean

conductivity over the interval from Tcoid to Thot. The

difference between the computed mean and the experimental

value is the deviation. Filled triangles denote repeated

measurements by laboratory 2; circled plus signs denote

repeated measurements by laboratory 6 . 29
Figure 3 . Interlaboratory comparison of apparent thermal

conductivity of mineral -fiber pipe insulation

measured on the horizontal pipe-test apparatus. Measurements

were performed in air at ambient pressure. The solid line is

a plot of eq (10) for thermal conductivity as a function of

temperature obtained by weighting each laboratory equally.

Specimens from laboratories 1, 2, 4, and 6 were conditioned

by heating specimens to the highest temperatures of measurement before taking data. Filled triangles denote repeated

measurements by laboratory 2 and circled “plus" signs denote

repeated measurements by laboratory 6. Please see the caption of figure 1 for an explanation of the difference between

the experimental points (symbols) and the fitted conductivity

function 30

Figure 4. Deviations of apparent thermal conductivity of

mineral -fiber pipe insulation, as measured by all

seven participants, from values calculated with eq (10),

obtained by weight-ing each laboratory equally. Filled

triangles denote repeated measurements by laboratory 2, and

circled plus signs denote repeated measurements by

laboratory 6. Please see caption of figure 2 for an

explanation of how the deviation is computed 31

Figure 5. Interlaboratory comparison of apparent thermal

conductivity of mineral -fiber pipe insulation mea

measured on the horizontal pipe-test apparatus. Measurements

were performed in air at ambient pressure. Specimens were

conditioned by heating them to the highest temperatures of

measurement before taking data. The solid line is a plot of

eq (11) for thermal conductivity as a function of temperature.

Please see the caption of figure 1 for an explanation of the

difference between the experimental points (symbols) and the

fitted conductivity function 32

Figure 6. Deviations of apparent thermal conductivity of

mineral -fiber pipe insulation, as measured after

conditioning, from values calculated with eq (11). Open

squares represent data from lab 4; downward-pointing triangles represent data from laboratory 6. Filled triangles are

repeated measurements by laboratory 6. As before, open circles represent data of laboratory 1, and upward-pointing triangles are data of laboratory 2. Please see caption of

figure 2 for an explanation of how the deviation is computed. ... 33

vi 1 1
Figure 7 . Apparent thermal conductivity of specimens of

mineral -fiber pipe insulation that were not

conditioned before they were measured. Measurements were

performed in air at ambient pressure and over the range of

mean temperatures from 319 to 531 K. The solid line is a

plot of eq(12) for thermal conductivity as a function of

temperature. Please see the caption of figure 1 for an

explanation of the difference between the experimental points

(symbols) and the fitted conductivity function 34

Figure 8. Deviations of apparent thermal conductivity of

mineral-fiber pipe insulation, not conditioned

before being measured, from values calculated with eq(12).

Please see caption of figure 2 for an explanation of how the

deviation is computed 35

Figure 9. Apparent thermal conductivity of specimens of

mineral -fiber pipe insulation that were not conditioned before they were measured. Measurements were performed in air at ambient pressure. The solid line is a plot

of eq (11), thermal conductivity as a function of temperature, for specimens that were conditioned before they were

measured. The position of the solid line was adjusted

vertically to minimize the rms deviation of this data from

the curve. Please see the caption of figure 1 for an

explanation of the difference between the experimental points

(symbols) and the fitted conductivity function 36

Figure 10. Deviations of apparent thermal conductivity of

mineral -f iber pipe insulation, not conditioned

before being measured, from values calculated with eq (11),

the relation for thermal conductivity of specimens that were

conditioned. Please see caption of figure 2 for an explanation of how the deviation is computed 37

INTERLABORATORY COMPARISON OF

THE GUARDED HORIZONTAL PIPE-TEST APPARATUS

Precision of

ASTM Standard Test Method C 335

Applied to Mineral-Fiber Pipe Insulation

David R. Smith

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

BOULDER, COLORADO 80303-3328

Apparent thermal conductivity of refractory pipe insulation from

the same production lot was measured by seven different laboratories. The purpose of this intercomparison was to assess the

precision and bias of the ASTM Test for Measurement of Steady-State

Heat-Transfer Properties of Horizontal Pipe Insulation (C 335).

Four laboratories submitted conductivity measurements for conditioned specimens. The test results for thermal conductivity of the

four conditioned specimens include the temperature range from 318

to 652 K and illustrate the interlaboratory reproducibility as well

as the temperature dependence of the conductivity . The standard

deviation of the data from each participating laboratory was measured by their deviation from a polynomial function fitted to all

data. For the 16 test results from the four laboratories that conditioned their specimens, the standard deviation was 4.3 percent.

For all test results from all seven participants, the standard deviation was 5 percent. This value is offered as the estimated precision of the horizontal pipe-test method. The accuracy of this pipetest method cannot be estimated from the data obtained in this

intercomparison

.

Key words: accuracy; apparent thermal conductivity ; bias; guarded

hot plate; high temperature; horizontal pipe; insulation; interlaboratory comparison; mineral fiber; precision; standard test method.

This work was supported in part by Oak Ridge National Laboratory

of the U.S. Department of Energy, through contract ORNL/IA-21428

.

1
1 . INTRODUCTION

A firm principle of measurement science is that a number for

the magnitude of a physical property such as thermal conductivity

conveys little information unless the precision and accuracy of the

numerical value are also given. The wise user seeks to know the

precision and accuracy of the value in order to understand the

confidence that he or she legitimately can give to the information.

Manufacturers of products such as thermal insulation, whose fitness

for intended use depends on specific physical properties, are

ethically and legally obligated to claim no more for the performance of their products than can be objectively demonstrated by

accepted standard test methods. Thus manufacturers also need to

know the precision and accuracy of numbers they want to use to

represent the performance of their products. Then they can honestly advertise all the benefits that their products are able to

deliver to the consumer, without subjecting themselves to legal

problems arising from misrepresentations.

Considerable progress has been made during the last twenty

years in improving equipment and techniques described by standard

ASTM test methods for measuring heat transfer in insulations,

especially those used in the building industries, at temperatures

near ambient. However there has been only limited knowledge available of the imprecision and bias of the ASTM test methods when they

are extended to higher temperatures. During the last few years a

concerted effort has been under way to evaluate the imprecision and

bias of the various ASTM test methods for measuring heat transport

through thermal insulations. The methods involving measurements at

temperatures several hundred kelvins above room temperature are

currently of particular interest.

Of the several instruments used to measure apparent thermal

conductivity of insulation materials, two are important because

they are independent of calibration materials and may be considered

to embody "absolute" methods. These two instruments are the guarded

hot plate ( GHP ) , for specimens in the shape of flat slabs, and the

horizontal pipe-test apparatus, for specimens in the shape of cylindrical shells. The laboratories of the U.S. National Institute

of Standards and Technology, at Gaithersburg , Maryland (NIST-G),

and at Boulder, Colorado (NIST-B), have played an active role in

helping to improve equipment, focussing on guarded hot plates [1-

4 ]

. Apparent thermal conductivity of two matched specimens can be

measured near room temperature with an accuracy of about 2 percent

[ 5 ] in a guarded hot plate complying with ASTM Standard Test Method

C 177 for "Steady-State Heat Flux Measurements and Thermal Transmission Properties by Means of the Guarded-Hot-Plate Apparatus" [ 6 ].

For measuring thermal conductivity of cylindrical pipe insulation the relevant ASTM test method is C 335, "Steady-State Heat

Transfer Properties of Horizontal Pipe Insulation" [ 7 ] , commonly

referred to as the "horizontal pipe-test" (HPT) method. The imprecision and bias of this test method have not yet been established,

and estimating these is the issue addressed by this report.

o
As a consequence of the incomplete knowledge of the imprecision and bias of the HPT method over the higher range of temperatures typically used in practice, seven interested members of ASTM

Subcommittee C-16.30 (Thermal Measurements') organized an interlaboratory comparison on this method in the fall of 1987. The objective was to measure specimens of homogeneous pipe insulation at mean

temperatures between ambient and about 673 K (400°C). Members of

the task group wanted to move quickly to learn the present state of

the quality of measurements with this method. To save time and to

reduce damage to the specimen, they decided not to pass around the

same specimen of pipe insulation for measurement, but rather to

measure concurrently specimens chosen from the same production lot.

The deadline for completion of the measurements was chosen to permit results to be presented in the spring of 1988 at the ASTM C16.30 meeting in Atlanta, Georgia.

2. COMPARISON OF THE GUARDED-HOT -PLATE AND PIPE-TEST METHODS

The recent experience in determining the imprecision and the

bias of the guarded hot plate is relevant to efforts to determine

them for the HPT method. The similarities and the differences between the two types of apparatus help us to understand the possible

causes of imprecision and bias in both instruments

.

a. The Guarded Hot Plate

To assess the imprecision and bias of high-temperature GHPs

,

an interlaboratory comparison of measurements of apparent thermal

conductivity was held in 1987 [8]. The study used GHPs designed

for high temperature to measure fibrous alumina-silica and calcium

silicate insulation boards as test specimens. This intercomparison

showed that, for mean specimen temperatures ranging from 313 to 773

K, considerably larger uncertainties exist in measurements made

with such GHPs than for room-temperature measurements. For the

fibrous alumina-silica specimens the greatest deviations of the

participants’ data from a least-squares fitted curve were +20 and

-12 percent, and the standard deviation was 7.4 percent. For

calcium silicate specimens the greatest deviations of the participants’ data from the fitted curve were +13 and -22 percent, and the

standard deviation was 8.0 percent. Thus for the GHP considered as

a standard ASTM instrument for measuring thermal conductivity at

high temperatures, the standard deviation of its data from a fitted

descriptor curve is almost 8 percent.

This was particularly surprising, because the GHP method is

considered to be an "absolute" test method for determining thermal

conductivity of insulations, because no calibration specimen is

used with this apparatus. The conductivity of the specimens is

simply calculated from several quantities obtained during the

experiment and from the geometry of the specimen.

3
The thermal conductivity of a specimen can be defined through

Fourier's law as the ratio of heat flux, q, to the magnitude [dT/dX]

of the thermal gradient (where square brackets denote the absolute

value )

:

k = q/[ dT/dX]. ( 1 )

The heat flux q is defined in terms of two physical quantities

measured for the metered area of the source of heat. These quantities are the rate of transport Q of thermal energy from the heater

through the adjacent area of specimen, and the corresponding crosssectional area A through which the energy is conducted. The ratio

of these, Q/A, defines the heat flux q through the metered area.

Two otter quantities (obtained during the course of the experiment

are the temperature difference AT along the direction of heat flow,

together with the corresponding thickness of specimen AX. However

the ratio of these, AT/AX, only approximates the thermal gradient

dT/dX required by Fourier's law. In practice, k is defined by a slight modification of relation (1), obtained by a single

integration

:

2

k ( T ) dT = (Q/A). AX, (2)

1

where AX is the spatial separation between the surfaces at temperatures Ti and T2 bounding the specimen. Of course this relation (2)

only implicitly specifies k.

The integral on the left side of this relation may be replaced

by an equivalent quantity, kmean- ( T2 -Ti ). Alternatively, the GHP is

often operated with temperature differences small enough that k(T)

may be estimated by a constant, kmean, over the applicable

temperature interval. In either case, relation (2) takes a form

which then explicitly defines the experimental thermal

conduct i vity

kmean = ( Q/A)*AX/( T2 “Tl ) . (3)

The correctness of the GHP method is determined in practice by

how nearly the apparatus approximates, within the metered area of

the specimen, uniform and unidirectional flow of heat through an

infinitely broad slab of material which has uniformly heated, parallel, planar surfaces and which is homogeneous along directions

4
parallel to the surfaces. The boundary temperatures at the surfaces of the specimens are maintained by heated for cooled) plates

whose temperatures are carefully controlled. If the specimens have

a constant thermal conductivity ( independent of temperature ) , the

thermal gradient dT/dX within the specimens is independent of

position along the direction of heat flow in the test area, and

then is exactly given by AT/AX. Any flow of heat into cr out of

the perimeter of the measured central area, or in other words, heat

flow that has a component along the normal to the axis of symmetry

within the metered area, leads to an erroneous value of thermal

conductivity

The existence of large differences among measurements carried

out by different laboratories using the GHP method [8] indicates

the possibility of uncompensated biases in measurement of the heat

flux or of the thermal gradient. One possible source of bias is

faulty thermal grounding, or tempering, of the leads of the thermocouples which measure the temperature difference from which the

thermal gradient is calculated. Most GHP devices are 20 to 25 cm

in diameter, with a consequent tempering path length of only 10 to

12 cm for the thermocouples measuring the thermal gradient at the

center of the specimen. One exception is the NIST-G 1-meter GHP

[ 1 , 3 ], whose diameter leads to a greater length of tempering of the

thermocouples used to measure the temperatures at the surfaces of

the specimens. Other exceptions are the two ( low-temperature and

high-temperature) GHPs at NIST-B [ 2 , 4 ], which use extra tempering

lugs to increase the effective length of thermal grounding of the

thermocouple leads as they exit the GHP stack.

b. The Horizontal Pipe-Test Apparatus

Using the same criteria applied above to the GHP method, the

ASTM C-335 HPT method for horizontal pipe insulation [7] could also

be considered to be an absolute test method, although it is not at

present so regarded. Like the guarded-hot-plate method, the C-335

HPT method is designed to simulate an ideal geometry of unidirectional heat flow. As with the GHP method, no calibration specimen

is necessary with the HPT apparatus, and the conductivity is also

calculated as the ratio of heat flux q to the (radial) thermal

gradient, dT/dr, both being obtained in the course of the

experiment

One important operational difference between the two methods

is that the GHP method uses relatively small temperature differences in measuring thermal conductivity , and uses an auxiliary

heater to vary the mean temperature of the specimen independently

of the magnitude of the temperature difference within it. In contrast, the HPT method relies on ambient (although controlled within

1°C) temperature to maintain the cold-side temperature of the specimen. It is not required that the HPT apparatus have an auxiliary

heater with which to vary the mean temperature. It is permissible

to vary the mean temperature by increasing the hot-side temperature,

with a large difference of temperature within the specimen.

5
With the HPT method, the cylindrical geometry of the physical

apparatus used in this test method also complicates matters slightto a cylindrical area 2 7t rL located at the radial position r

measured from the central line heater and occupying an interval L

The presence of the r factor in the left side makes the temperature

gradient dT/dr a function of position r even if k is constant.

This expression (4) must be integrated with respect to radial

position to obtain a result applicable to the finite differences in

where r2 and ri are the outer and inner radii of the cylindrical

insulation specimen.

The factors ri , r2 , and L are constants during a given expertise temperatures Ti and T2 of the bounding surfaces is the conductthe integral of thermal conductivity which is obtained from the

conditions of the experiment (Q, ri , r2 and L), rather than the

thermal conductivity alone. This integral of k(T) over T is mathematically equivalent to a product of conductivity and temperature,

and may be used to define a "mean" conductivity by

ly. The heat flux q is the ratio of the rate heat of heat flow Q

along the axis of symmetry. The position r is that at which the

gradient, dT/dr, is evaluated. For this cylindrical geometry,

Fourier's law takes the form.

Q/2 ft rL = k- dT/dr. f 4)

T and r used in an actual experiment. This is easily done, and

results in the expression

( Q/2 Tl L ) In ( r2 / ri ) k(T)dT, (5)

Jl

iment. The integral of the thermal conductivity function between

ivity-related quantity proportional to the heater power Q. It is

( 6 )

which is generally not the same as k(Tmean) [11].

6
The correctness of the HPT method is determined by how nearly

the HPT apparatus approximates purely radial flow of heat, from a

uniform source of heat at the center of symmetry, through an infinitely long cylinder of material which has concentric cylindrical

surfaces and which is homogeneous along directions parallel to the

surfaces. The boundary temperature at the inner surface of the

specimen is maintained by a cylindrical heated pipe, whose temperature is carefully controlled. However, in contrast to the case of

the GHP, the temperature at the outer (cooler) surface of the insulation is not maintained by a temperature-controlled surface, but

rather by the ambient, laboratory temperature. Even though the

laboratory temperature may be controlled, the temperature of the

specimen surface is not as tightly controlled as it would be by a

cooled surface in thermal contact with it. Also, because of the

cylindrical geometry, which causes the heat flux lines to diverge

from the linear center of symmetry, the temperature gradient within

the specimen must always be a function of position from the central

heater, in contrast to the situation with the GHP method. This is

true even if the conductivity is independent of position along the

direction of heat flow.

Any flow of heat along the direction parallel to the cylindrical symmetry axis, into or out of the boundaries of the measurement

length, or in other words, heat flow that has a component parallel

to the axis of symmetry, would lead to an erroneous value of thermal conductivity . The temperatures defining the thermal gradient

are measured by thermocouple leads introduced along a cylindrical

isothermal surface. A greater length of thermal grounding of the

leads, typically 30 to 45 cm, is possible in comparison to the

length available with the disk-shaped heater plates in the GHP.

This is so because of the commonly encountered combined length (60

to 90 cm) of the test and guard regions within the cylindrical HPT

apparatus

Only the GHP method has found wide acceptance in the U.S. as

the prime method for measuring thermal conductivity of insulating

materials. One major factor is that the GHP method uses specimens

in the shape of flat slabs, which is the most common geometry for

insulation materials. Although each GHP apparatus has a definite

limit on the maximum thickness of specimen whose conductivity it

can measure accurately, specimens of any thickness less than that

maximum may be measured. The cylindrical geometry of the HPT

method is on the other hand somewhat restrictive because a given

apparatus can measure only specimens of radius matching that of the

cylindrical inner surface, even though any size of outer surface

may be used. Manufacture of homogeneous insulation specimens of

cylindrical shape is somewhat more difficult than that of flat-slab

specimens

To date no systematic comparison has been carried out to link

results on identical materials measured with both the guarded hot

plate and the HPT methods. Such a comparison would be a valuable

test of the accuracy and bias of both methods, in light of the

existing uncertainty in measurements with high-temperature GHPs

7
One study by Kimball [9] of a large HPT apparatus compared

calculated steady-state thermal conductance (rate of heat flow per

unit area, per kelvin) with experimental measurements, for nominal

3-inch polyurethane foam insulation, used on 18-inch pipelines in

the Arctic. He reported measuring conductance through the insulation with an exterior temperature of -56.7°C (~70°F) and an interior (pipe) temperature of +710C (+160°F). The experimental thermal

conductance was 6 percent higher than the theoretical. This discrepancy was explained by heat leak from the interior along the

central boundary joining the two abutting sections making up the

complete specimen. A measurement of the conductance at 7.2°C

(45°F) under transient conditions agreed within 4 percent with the

corresponding calculated value.

The only previous interlaboratory comparison of the test method for horizontal pipe insulation took place over a period of more

than seven years and was reported by Hoi 1 ingsworth [10] in 1977.

Ten laboratories took part in this comparison, which covered a

range of mean specimen temperatures from about 323 to 423 K; the

highest pipe-heater temperature used was about 533 K (260°C).

Hollingsworth concluded that the test error was approximately 3

percent . However, both the HPT method and the insulations tested

with it are frequently used at mean temperatures much higher than

the upper limit of 423 K of the 1977 intercomparison.

3 . SCOPE

This report analyzes apparent thermal conductivity of hightemperature pipe insulation measured by seven testing laboratories

using guarded horizontal pipe-test apparatuses. Their instruments

comply with ASTM test method C 335 for "Steady-State Heat Transfer

Properties of Horizontal Pipe Insulation." The specimens measured

were homogeneous mineral-fiber insulation designed for use at temperatures up to 600 K or more. Four of the testing laboratories

submitted data for "conditioned" specimens, over the range of mean

temperatures from 318 to 652 K. The results presented here apply

specifically only to homogeneous specimens, to measurements within

the cited range of temperatures, and to guarded, horizontal pipetest apparatus. Extension of these results to inhomogeneous specimens, to calibrated rather than guarded apparatus, to vertically

oriented apparatus, or to temperatures outside the cited range , is

inappropriate

.

Only one nominal density of pipe insulation was measured.

Furthermore, visual inspection shows that the pipe insulation

material has relatively large pores, with dimensions of up to

tenths of a millimeter. Only for an insulation material for which

all pores have dimensions of less than micrometers ( "microporous"

)

would pressure dependence be a factor in its thermal conductivity.

This implies that intercomparisons of the thermal conductivity data

reported here do not have to be corrected for the elevation above

sea level of the different participating laboratories.

8
4. PARTICIPANTS AND APPARATUSES

The chairman of the task group , who took part in the intercomparison, carefully selected some specimens from one supplier and

distributed them to the other six participating laboratories.

After the thermal conductivity was measured the seven participants

submitted their data directly to me for analysis.

The names of the seven laboratories participating in the

intercomparison are given here in alphabetic order to identify the

sources of the data presented. Listing these names does not in any

way imply endorsement of the organizations, or of their products or

services, either by NIST in particular, or by the U.S. government.

The seven participants were:

California Bureau of Home Furnishings and. Thermal Insulation

CertainTeed Corporation, Blue Bell, Pennsylvania

Dynatech Scientific, Inc. (now Holometrix ),' -Cambridge , Mass.

Fiberglas Canada, Inc. , Sarnia, Ontario, CANADA'

Manville Corporation, Denver, Colorado

Owens-Corning Fiberglas, Granville, Ohio

PABCO, Fruita, Colorado

Random numbers and symbols were assigned, to : the -data sets from

the participants and used throughout the ' figures .'in .this report.

The symbols chosen are listed in table 1 ; along with the characteristics of the horizontal HPT apparatus used -by* the participants.

All apparatuses were "guarded" rather' than "calibrated" HPT apparatuses, and all had nominal diameters ' of ' 3 . in ' (actual diameters of

3.5 in , or 89 mm ) .

’

Table 1

Coding symbols used in figure's to * <distinguish the

seven laboratories participating * in the interlaboratory

comparison

apparatus

, and sizes of their nominally 3 -inch pipe-test

Lab Lab Metered Length Guard Length

Code — Symbol — ( cm) (in) ( cm) (in)

1 0 91.4 36 30.5 12

2 A 61.0 24 15.2 6

3 91.4 36 30.5 12

4 V 61.0 24 7.6 3

5 O 91.4 36 30.5 12

6 + 61.0 24 15.2 6

7 X 61.0 24 10.2 4

9
5. SPECIMEN CONDITIONING

When the test results were submitted and presented at the Atlanta meeting of ASTM C 16.30 in the spring of 1988, it was realised from the order in which the data had been submitted that an

important item had been overlooked. Five participants had measured

the thermal conductivities of their specimens with mean temperature

increasing from one measurement to the next. However, the specimens may change slightly as the temperature increases during the

sequence of measurements leading to the highest temperature of

measurement. For example, some binder begins to burn out of the

insulation when it is heated to temperatures above about 400 K;

other physical changes , such as loss of adsorbed water, followed at

still higher temperatures by loss of water of crystallisation , can

take place to some degree, depending on the composition of the

insulation material and on the highest temperature to which the

specimen is subjected. Such changes, although minor in their overall effect, still lead to variation in the physical properties of

the specimen under study. Except for loss of adsorbed moisture

from the surfaces of the pores, these changes are irreversible and

permanent. Each increase in mean temperature alters rhe specimen;

therefore successive measurements on the "same" specimen are

actually being performed on slightly different specimens.

On the other hand, we can hope that the specimens of insulation material as received from the manufacturer have already been

uniformly conditioned by the manufacturing process. Thus even in

the presence of physical changes caused by heating to the

temperatures used in this study, all specimens have identical

histories during comparative measurements of conductivity up to the

lowest maximum temperature employed by the group of participants.

If heating the specimens causes physical changes affecting the

thermal conduct ivity , then only specimens heated to temperatures

greater than the maximum of another participant are different from

that participant’s specimen. Of course, the specimen heated to the

group’s maximum of temperature becomes unique.

Even if we accept this view, after the maximum temperature is

reached the properties of a particular specimen depend on what that

maximum was; no further loss of binder or of water of crystallization should take place unless the maximum temperature is later

exceeded. Measurements of conductivity thereafter should be reproducible, but they will be different from those initially obtained

in the first excursion from low temperatures to the maximum. Thus

we still conclude that, if we want to know what the conductivity of

the material is, we should use only the data obtained after the

specimen has reached its maximum temperature.

To obtain stable and reproducible results, specimens of hightemperature pipe insulation should first be conditioned, or stabilized, by heating to the highest temperature of measurement when

this lies more than about 80 K above room temperature. Also, the

conditioning temperature should be the same for all laboratories in

10
the intercomparison . Only then are the different specimens stable

and suitable for use in an interlaboratory comparison. However one

other difficulty is that not all laboratories could reach the same

highest temperature, and the highest temperature that all could

reach was not determined before the intercomparison began. For

these reasons, slight variations in the heat-transfer properties of

the material were unavoidable. These variations, which are actually material variability, may appear disguised as interlaboratory

variation in the data submitted by the participants.

Five laboratories had measured thermal conductivity before

stabilizing their specimens at the highest temperature. These

participants agreed, as time allowed, to remeasure their specimens

before the C-16.30 Tucson meeting in the fall of 1988. Two laboratories were able to submit data for their repeated measurements.

All data submitted by the participants in the intercomparison are

presented here for review. Because of differences in conditioning

of the test specimens, several different points of view will be

used to critically examine the conductivity measurements in order

to estimate the imprecision and the bias of the horizontal pipetest method as presently standardized by ASTM method C 335.

6. THERMAL CONDUCTIVITY DATA

The thermal conductivity data submitted by the participants on

the standardized forms provided to them were compiled into tabular

files for analysis by computer. One participant submitted data

directly in SI units; the remaining data, submitted in engineering

units, were converted to SI units for uniformity and ease of

comparison

Table 2 contains all the test data for the pipe insulation

used in this intercomparison (in the column headed Kdat ). In particular, in table 2 the first four lines of data for laboratories 2

and 4, and ail the data for laboratories 3, 5 and 7 are for nonconditioned specimens (data taken with temperature increased

between measurements). Because the fourth line of data for

laboratory 4 is for the maximum temperature of measurement, it is

effectively a conditioning point; thus the last line for laboratory

4, and the fourth line, are for a conditioned specimen. All the

data for laboratories 1 and 6, and the last four lines of data for

laboratory 2 are also for conditioned specimens. The complete data

set is plotted in figure 1, with seven different symbols used to

distinguish the data from the seven participants . As is conventional, the points are plotted in figure 1 at a value of

temperature equal to the mean of the two boundary temperatures

However the experimental values of thermal conductivity (Kdat ) are

averages of the conductivity over the complete temperature interval

and are therefore to be associated with that specific interval.

11
7. REFERENCE EQUATIONS AND DATA ANALYSIS

It is now widely appreciated that several factors contribute

to the total transfer of heat from one boundary surface to the

other in most insulations. The main contribution is usually conductive, due to diffusive flow of heat driven by a temperature

gradient , or spatial rate of change of temperature, through the

solids and surrounaing gas. However another important component is

radiative heat transfer, for which the radiated energy flux per

unit time is driven not by a spatial gradient but by the difference

between the fourth powers of the temperatures at the bounding

surfaces

:

qrad = B- ( Th 4 - Tc 4

) , (7)

where B is a combination of several constants . The quantity in

parentheses can be algebraically factored into several terms, one

of which is the. difference (Th-Tc) between the boundary temneraures . Thus this relation can be cast into the form of Fourier’s

law of conduction involving the usual approximation AT/AX to the

temperature gradient: one then obtains an effective "radiative"

conductivity . Equation (6) can be transformed into an algebraically

identical form:

qrad = [B- ( Th 2 + Tc 2 )

• ( Th +Tc ) • AX] AT/AX , (8)

where AT is the temperature difference (Th-Tc), and the quantity in

square brackets is the "radiative" conductivity parameter, obtained

at the cost of introducing into it a dependence on specimen thickness AX. An additional result of interest is that this "radiative

conductivity" varies approximately as Tmean 3

, where Tmean is the

arithmetic mean of Th and Tc

.

Fourier’s law of conduction, which relates the conductive heat

transfer to the thermal gradient, only approximately models the

total heat transfer within an insulation. The total transfer of

heat between two different isotherms within an insulation material

depends partly on the difference of the temperatures if radiative

transport of heat is appreciable. This radiative heat transfer

term may be added to the conductive term under the (only approximately valid) assumption that they represent non-interactive and

parallel, or linearly additive, modes of heat transfer. The resultant total heat transfer, which is predominantly, but not purely,

conductive, is called the "apparent" thermal conductivity to

distinguish it from a true conductivity driven only by a thermal

gradient. For brevity, the term "thermal conductivity " will be

used in the following text and figures.

12
In the analyses below, the "thermal conductivity integral"

method [11,12] was used in fitting thermal conductivity functions

to experimental data. That is, a specific polynomial for the thermal conductivity as a function of temperature was assumed, and then

integrated, and the polynomial function was fitted to the data by

means of a least-squares fit to obtain the numerical values of the

coefficients in the assumed relation. The deviations shown in the

tables and in the deviation plots were also calculated by the

integral method. This was done to remove any potential inconsistency caused by the presence of both large and small temperature

differences in the data set. The use of large temperature

differences is inherent in ASTM method C 335 for measurements of

pipe insulation at mean temperatures well above room temperature.

When we fitted functional curves to the experimental conductivity data, weighted least-squares fits were used; the weighting was

chosen to minimize the sum of the squares of the relative deviations, rather than the sum of squares of absolute deviations. This

is considered preferable because when measuring thermal conductivity, experimentalists tend to keep the relative (percentage) errors

constant

The seven participants' complete set of data for the thermal

conductivity of pipe insulation extends over the range of mean

temperatures from 318 to 652 K (table 2). These data include

measurements for both conditioned and nonconditioned specimens.

The variation of conductivity with temperature for the complete

data set can be represented by the correlation

k = 16.734 + 0.04180 T + 0.17954*10-6 T3 , (9)

where k is in mW/(m- K) and T is in K; this relation is plotted as

the solid line in figure 1. The presence of the term in T3 represents an expected contribution from "radiative" conductivity . The

coefficients in eq(9) were obtained from a weighted least- squares

fit of the data, for specimens having a mean density of 91 kg/m3 . The standard deviation of density about the mean is 4.55 percent.

Because of the position of the solid line below the high-temperature data in figure 1, the curve appears to be an incorrect fit.

This is however an artifact of experiments performed to measure

thermal conductivity at large temperature differences of materials

whose conductivity is a nonlinear function of temperature. This

situation is normal in measurements with the HPT method, which uses

very large temperature differences. Use of the "thermalconductivity integral" method reflects this state of affairs and

correctly illustrates the relations between the individual data

points and the thermal conductivity function. Here the functional

13
curve is concave upward. As a consequence, any given data point,

which is closely related to the integral of the conductivity

function over the interval between the boundary temperatures, is

displaced upward [11, 12].

The deviations of the individual data points from the curve

representing eq ( 9 ) are plotted in figure 2 and listed in the last

two columns of table 2 as absolute deviations (Dev) and as relative, or percentage, deviations (Kdev). Measurements on conditioned specimens by laboratories 2 and 4 (triangles) are indicated in

figures 1 and 2 by the filled triangles, and repeated measurements

by laboratory 6 (plus signs) are given by plus signs within

circles. As discussed in references 11 and 12, experimental data

(Kdat ) are actually averages of the thermal conductivity over the

interval from Tlow (or Ti ) to Thigh ( T2 ) . Numbers in the Kcaic

column of table 2 were obtained by the thermal -conductivity

integral method, and represent likewise the temperature-averaged

mean of the conductivity function, eq(9), over the interval from

Tl ow to Th i g h . For the complete set of data the greatest positive deviation

from the fitted curve is 8.3 percent, and the greatest negative

deviation is -9.8 percent. The standard deviation of the measurements from the curve is 5.0 percent.

One participant questioned whether this method of fitting is

fair, as three laboratories each submitted only four data points,

while one submitted eight data points. In fact, the contribution

from each participant is weighted by the number of data points

taken. This has the consequence that the sets of data from laboratories 1, 3, and 5 are each given only 50% of the weight of the set

from laboratory 6. All other laboratories (submitting four, five,

or six data points) are also given only a fraction of the weight of

the one providing eight points. In the matter of weighting data

points equally as opposed to weighting laboratories equally, I

agree that the point should be explicitly addressed, rather than

defaulting to an unexamined assumption. Both ways were tried.

A new fit was performed over the same set of data, with

weightings chosen to give each laboratory equal weight, based on

"one man, one vote," rather than the choice of "one data point, one

vote" that led to eq(9). The results of this fit yielded the

correlation

k - 18.134 + 0.036504 T + 0.18478*10-6 T3 (10)

with k and T defined as before. This functional relation is

plotted in figure 3. The deviations of the data points from this

curve are plotted in figure 4 and listed in the last two columns of

table 3. For this curve for equally weighted laboratories the

14
greatest positive deviation of the defining set of data is +8.5

percent and the greatest negative deviation is -9.2 percent, compared to deviations of +8.3 and -9.8 percent from the curve given

by eq(9) for equally weighted data . The standard deviation here is

5.1 percent, as opposed to 5.0 percent for the equally weighted

data. Thus for both methods of weighting data, the results are

closely similar: greatest deviations of about +8.5 and -9.5

percent, and a standard deviation of 5 percent.

To estimate the precision of measurements performed by the HPT

method, let us examine the set of data from only those

participants that measured their specimens after conditioning

(heating the specimens first to the highest temperature of

measurement and then performing measurements. These data are from

participants identified by code numbers 1, 2, 4 and 8 and are

listed in table 4; the data are plotted in figure 5, encoded by

symbols distinguishing the laboratories responsible for the data.

The data from laboratory 2 are repeated measurements; data from

laboratory 6 include both original data, which according to the

submitted data sheet are valid, as well as additional data

submitted in response to the call for repeated measurements.

Laboratories 3,5 and 7, which had not submitted data for

conditioned specimens, were apparently not able to perform repeated

measurments . Thus there were four laboratories providing data on

conditioned specimens.

By means of a least-squares fit a correlation of the same form

as that of eq(9) was obtained. This correlation for the data from

conditioned specimens is given by

k = 10.449 + 0.066314 T + 0.140223*10-6 T3 , (11)

with k and T defined as before. This correlation is plotted as the

solid line in figure 5. The data used to obtain this correlation

cover the range in temperature from 318 to 652 K. Deviations of

the individual data points from eq(10) are plotted in figure 6 and

are listed in the last two columns of table 4.

The greatest positive and negative deviations of data points

from the correlation (11) are both 6.4 percent; the total set of

data fits the curve within a standard deviation of 4.3 percent.

This standard deviation is considerably smaller than the standard

deviation of the results from the interlaboratory comparison for

the high-temperature GHPs [ 8 ], which covered a slightly greater

temperature range (297 to 773 KK including the range used in this

study. This comparison yielded standard deviations of 7.4 and 8

percent for the two materials studied, and maximum deviations of

almost +20 percent. Although we must not push the comparison

between the GHP and the HPT methods too far, as there were only

15
seven participants in each of the two interlaboratory comparisons,

comparisons between the precisions of the two methods might be made

cautiously

.

Having fitted only the data for conditioned specimens, obtaining eqill), we now fit the set of data for noncondit ioned specimens

and compare the two sets. Table 5 lists the data for these nonconditionea specimens, which are plotted in figure 7. A weighted

least-squares fit to the data for nonconditioned specimens gave the

correlation

k - 42.980 - 0.05409 T + 0.34209*10-6 T3 , (12)

with k and T defined as before. This correlation is plotted as the

solid line in figure 7.

The last two columns of table 5 show the deviations from the

least-squares fit to these data, and the relative deviations are

plotted in figure 8. The point of interest is that these data for

nonconditioned specimens exhibit extremal deviations from the

fitted curve of +6.9 and -7.5 percent. This is somewhat larger

that the corresponding deviations of data for conditioned specimens

from their fitted curve, as would be expected if the effect of

conditioning is real. The standard deviation from the fitted curve

for nonconditioned specimens is 4.7 percent, as opposed to 4.3

percent for the conditioned specimens.

The internal self -consistency of data for conditioned specimens seems to be better than that for nonconditioned specimens. We

might conclude that conditioning makes a difference, but with

reservations--there are only four sets of data for conditioned

specimens and only five sets for nonconditioned specimens. The

sizes of the two statistical samples are too small for us to be

sure that the effect of conditioning is real.

The standard deviation of the complete set of thermal

conductivity data, including measurements on both conditioned and

nonconditioned specimens, is about 5 percent. The precision of the

HPT method was estimated to be about 4.3 percent, so the effect of

not conditioning the specimens seems to be about 1 percent.

Another instructive exercise is to compare the data for the

nonconditioned specimens with the fitted curve for conditioned

specimens; this curve is given analytically by eq (11). This was

done by preserving the shape of the curve for conditioned specimens

and simply raising it up or down parallel to the conductivity axis.

16
That is, we found a constant multiplier equal to 0.98, such that

the rms deviations from this curve were minimized for data for nonconditioned specimens. The least-squares fit for this procedure is

shown by the solid curve in figure 9 and the deviations are plotted

in figure 10. The numerical values for this fit are given in table

6. The extremal deviations of the data for noncondit ioned specimens were + 9-7 percent, and the standard deviation of the fit is

5 . 4 percent

This situation for a subset of the data appears paradoxical at

first, with a standard deviation of 5.4 percent for the subset of

nonconditioned specimens, compared with a standard deviation of

only 4.95 for the set of all data, from the curve described by

eq(9). This standard deviation of 5.4 percent may be understood to

measure the internal consistency of data for purely nonconditioned

specimens. The internal consistency of data for conditioned

specimens, the complementary subset of data, is measured by a

standard deviation of only 4.3 percent, which is less than the

standard deviation of 4.95 for the complete set. The standard

deviation for conditioned specimens is about 1 percent greater than

that for nonconditioned specimens. Remembering that we deal here

with a small statistical sample, we may again cautiously conclude

that conditioning may make a difference of about 1 percent.

8. ESTIMATED PRECISION OF THE HPT METHOD

In measurement theory imprecision in a series of measurements

of a physical quantity indicates the closeness of approach of the

individual values to the mean value. Precision says nothing about

how the mean value compares to the "true" value. Scatter of the

measurements around the mean value is caused by random influences,

which by definition have unpredictable magnitude and sign, and will

tend to cancel out each other if a large enough number of measurements is made. The mean value of a large enough group of measurements of the same physical quantity tends to become free of the

effects of the random influences.

By contrast, accuracy of a physical quantity indicates the

closeness of approach of the mean of a series of measurements to

the "true" value. Inaccuracy is caused by nonrandom, or systematic

errors of measurement, which have not been corrected during the

process of measurement because they are not known to the person

performing the processes of measurement and analysis. These

systematic errors, if present, might be disclosed by performing

measurements of the same physical quantity on the same material but

in a different type of apparatus, preferably based on a different

principle of measurement. One could postulate that the true value

is reached in the limit of a very large number of measurements,

performed under very different conditions. If a large enough population of measurements has been obtained from many different types

of apparatus that measure the same quantity, such that errors made

in measurements based on one type of apparatus are offset by errors

17
in measurements from very different apparatuses, then the mean

value of this large set of measurements may approach the "true"

value. Accuracy of a set of measurements performed on one apparatus is then indicated by the difference between the mean value for

the apparatus and the global mean for all apparatuses, that

estimates the true value.

The present interlaboratory comparison of the ~ HPT method

involves instruments of the same type, so there may be inherent in

this method some biases that have not been revealed by these

measurements. We do not know of any comparative measurements of

the same pipe insulation material on an apparatus of a different

type. For the HPT method there is neither a theoretical value nor

a standard reference material against which to compare the experimental results. Therefore the "true" value of the material measured here is unknown. An estimate of accuracy of the horizontal

pipe-test method cannot be made at this time.

The precision of measurements with the HPT method is indicated by the scatter of measurement data around the group mean.

One estimate of the group mean of the thermal conductivity is given

by the fitted curve, eq (11), for conditioned specimens measured by

four different laboratories. An estimate of the scatter of the

data around the mean for the four laboratories is given by the

standard deviation of the data (4.3 percent) from the fitted curve.

A larger statistical sample for basing an estimate of accuracy is

available: the complete set of data including both conditioned and

nonconditioned specimens. For this set the standard deviation, or

scatter of data about the mean, is about 5 percent. Preferring to

be conservative by basing the estimate on the largest possible set

of data and by choosing the looser of the two possible estimates, I

estimate the precision of the HPT method to be 5 percent over the

range of temperature from 318 to 530 K. This is based on measurements performed with only one type of apparatus, the guarded-end

HPT apparatus, and only one type of insulation material. Caution

should be exercised in generalizing these results to another type

of HPT apparatus.

Because the participants in this interlaboratory comparison

did not measure the same specimen, but rather measured different

specimens (obtained from the same supplier, to reduce variability),

some of the scatter of the measurements about the mean, or imprecision, may be due to material variability in the heat-transfer

properties of the different specimens used.

18
9. SUMMARY AND CONCLUSIONS

Measurements of thermal conductivity have been presented for a

mineral-fiber pipe insulation material at mean temperatures from

318 to 652 K. Two methods of fitting the data were used: weighting

individual data points equally, and weighting individual laboratories equally. There seems to be no significant difference in the

closeness of the fits for the two different methods of weighting.

Of seven participating laboratories, four responded with data

on specimens that were conditioned by heat first to the highest

temperature of measurement, so that physical changes in the

specimen had already occurred before data was taken. This conditioning was an issue that led to submission of additional measurements by the participants. Results from these laboratories,

compared with measurements from those that did not do so, have suggested that conditioning the specimens before performing measurements may have a detectable effect on the measured thermal

conductivity . The small number of participants makes it statistically difficult to draw firm conclusions on this point.

Reference equations are obtained which describe the dependence

of the thermal conductivity on temperature for the refractory pipe

insulation material, and are illustrated in the figures. Figures 1

and 2 compare results from all seven participants. Figures 3 and 4

make a similar comparison, with equal weighting for each participant. Figures 5 and 6 give the thermal conductivity of conditioned

specimens. Figures 7 through 10 allow comparisons to be made with

specimens that were not so conditioned. All the odd-numbered

figures illustrate the fact that data points from measurements of

thermal conductivity with large temperature differences do not

coincide with the thermal conductivity function at the same temperature. This shows the necessity of using the thermal conductivity

integral method [11,12] to obtain the heat transport to be expected

under large differences in temperature between boundaries.

The reference equations are used to analyze the precision of

interlaboratory measurements made by the seven laboratories that

participated in the round robin. The precision of measurement of

thermal conductivity by the horizontal pipe-test method is estimated to be about 5 percent as measured by the standard deviation of

measurements about the group mean for the participants. This

estimate is almost independent of the effects of conditioning. An

estimate of the accuracy of measurements performed with the HPT

apparatus cannot be made at this time.

19
The comparison of the guarded-hot-plate method with the pipetest method in Section 2 of this report suggest qualitatively that

there may be fewer uncorrected biases in measurements made with the

HPT apparatus than with the GHP at high temperatures . In contrast

to the comparative method, which intrinsically depends on one or

two reference materials in order to determine the conductivity of

the specimen under study, both the HPT and the GHP involve

"absolute" methods of measurement that are in principle independent

of calibration standards. This interlaboratory comparison of the

HPT method demonstrated that for a population of seven laboratories

using both conditioned and nonconditioned specimens, the standard

deviation of the data from the group mean was about 4.5 percent

over a range of mean specimen temperatures up to 652 K. Using only

conditioned specimens over the same range of mean temperatures,

four participants achieved a standard deviation from the group mean

of only 4.3 percent. This is signif icantly better than the

standard deviation of almost 8 percent resulting for the interlaboratory comparison of the GHP method at high temperatures.

Although there is at present no standard reference material for

cross-checking measurements made with the HPT apparatus, current

evidence suggest that results of measurements with the HPT are on

the average at least as good as those made with the GHP, both

apparatuses being in principle "absolute" methods. With both

instruments, care in experimental design and technique is

indispensable in obtaining trustworthy data.

A very desirable next step would be to perform an interlab-

'oratory test comparing the horizontal pipe-test apparatus and the

guarded hot plate, on the same specimens. Because of the great

difference in geometry inherent in these two measurement methods,

it would be almost impossible to use identical specimens on the two

different types of apparatus. However the use of loose-fill

insulation materials, properly conditioned by standardized

procedures, could permit the comparison of results from these two

different types of apparatus. To compare measurements from these

apparatuses is highly desirable, since the GHP apparatus when used

at temperatures significantly higher than ambient seems to fall

short of expectations. The limited information from two interlaboratory comparisons, each involving only seven laboratories, suggests that the HPT apparatus is more reliable at high temperatures

than is the GHP. Yet the HPT method is limited to materials with

cylindrical geometry, and cannot be used to measure a large fraction of the types of commercial insulation materials, in flat or

block geometry, of great economic importance in residential

building construction.

20
10. REFERENCES [1]

. Siu, M.C.I. and Bulik, C. "National Bureau of Standards

Line-Heat-Source Guarded-Hot-Plate Apparatus", Rev. Sci. Instrum.

52/11, 1709-1716 (1981). [2]

. Smith, David R., Hust, J.G. and Van Poolen, Lambert J. "A

Guarded-Hot-Plate Apparatus for Measuring Effective Thermal

Conductivity of Insulations Between 80 K and 360 K" , NBSIR 81-1657

(U.S. National Bureau of Standards, January 1982).

[3]

. Rennex. Brian. "Error Analysis for the National Bureau of

Standards 1016 mm Guarded Hot Plate", NBSIR 83-2674 (U.S. National

Bureau of Standards, February 1983).

[4]

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

Automated High-Temperature Guarded-Hot-Plate Apparatus for

Measuring Apparent Thermal Conductivity" , NBSIR 88-3089 (U.S.

National Bureau of Standards, May 1988).

[5]

. Hust, J. G. and Pelanne, C. M. "Round Robins on the Apparent

Thermal Conductivity of Low-Density Glass Fiber Insulations Using

Guarded Hot Plate and Heat Flow Meter Apparatus', NBSIR 85-3026

(U.S. National Bureau of Standards, 1985)

f 6]

ASTM Standard Test Method C 177 for "STEADY-STATE HEAT

FLUX MEASUREMENTS AND THERMAL TRANSMISSION PROPERTIES BY MEANS OF

THE GUARDED-HOT-PLATE APPARATUS", ANNUAL BOOK OF ASTM* STANDARDS,

Vol. 04.06, pp. 21-36 (ASTM, Philadelphia, 1986).

[7]

. ASTM Standard Test Method C 335 for "STEADY-STATE HEAT TRANSFER PROPERTIES OF HORIZONTAL PIPE INSULATION", ANNUAL BOOK OF ASTM

STANDARDS, Vol. 04.06, pp. 83-96 (ASTM, Philadelphia, 1986).

[8]

. Kimball, L.R. "Thermal Conductance of Pipe Insulation--A

Large-Scale Test Apparatus", Heat Transmission Measurements in

Thermal Insulations, ASTM STP 544, pp. 135-146, (ASTM,

Philadelphia, 1974).

[9]

. Hollingsworth, M. Jr. "An Interlaboratory Comparison of the

ASTM C 335 Pipe Insulation Test", Thermal Transmission Measurements

of Insulation, ASTM STP 660, R.P. Tye, Ed., pp. 50-59, (ASTM,

Philadelphia, 1978).

[10]

. Hust, Jerome G. and Smith, David R. "Round-Robin Measurements

of the Apparent Thermal Conductivity of Two Refractory Insulation

Materials, Using High-Temperature Guarded-Hot-Plate Apparatus",

NBSIR 88-3087 (U.S. National Bureau of Standards, April 1988).

21
[ 11

]

. Hust, J. G. and Lankford, A. B. "Comments on the Measurement

of Thermal Conductivity and Presentation of a Thermal Conductivity

Integral Method", International Journal of Thermophysics, 3/1, 67-

77, [12] (1982).

. ASTM Standard Test Method C 1045 for "CALCULATING THERMAL

TRANSMISSION PROPERTIES FROM STEADY-STATE HEAT FLUX MEASUREMENTS",

ANNUAL BOOK OF ASTM STANDARDS, Vol . 04.06, pp. 689-696 (ASTM,

Philadelphia, 1986).

22
Table 2. Inter I aboratory comparison of apparent thermal conductivity of

high—temperature mineral-fiber pipe insulation measured on seven different horizontal pipe— test apparatuses. The nominal density of the

specimens is 90 kg/m 3 (5.6 lb /ft 3

. Specimens had a nominal inner diameter

of 89 mm (3.5 in), and a wall thickness of 51 mm (2 in). Measurements were performed at the ambient atmospheric pressure of each laboratory, 83 to 100

kPa (630 to 760 Torr), and at mean temperatures from 318 to 652 K (113 to

1238°F). Kcalc is computed from eq

set: from eq (9) for a 1 1 specimens is

Lab Dens i ty Th igh T

ow De IT No. (kg/m3

) (C) (C) (C)

1 100 .91 942 .928 360 .983 581 .944

1 100 .91 854 .483 349 .039 505 .444

1 100 .91 687 .094 328 .261 358 .833

1 100 .91 503 .706 309 .650 194 .056

2 86 .98 379 .261 302 .150 77 .111

2 86 .98 419 .206 306 .150 113 .056

2 86 .98 523 .706 313 .817 209 .889

2 86 .98 632 .928 323 .928 309 .000

2 85 .60 624 .706 321 .706 303 .000

2 85 .60 526 .094 310 .983 215 .111

2 85 .60 422 .706 304 .817 117 .889

2 85 .60 379 .372 302 .428 76 .944

3 94 .35 339 .261 299 .039 40 .222

3 94 .35 451 .483 306 .483 145 .000

3 94 .35 590 .928 318 .706 272 .222

3 94 .35 728 .150 334 .817 393 .333

4 92..26 439..706 303,.761 135 .944

4 92.,26 529..761 311 .039 218 .722

4 92..26 628..483 320..650 307 .833

4 92..26 726..539 332.,928 393,.611

4 92.,26 493.,039 308.,428 184.,61

5 90..13 404. 283 297.,822 106.,461

5 90. 13 429. 311 302. 256 127. 056

5 90. 13 502. 089 306. 483 195. 606

5 90. 13 551 . 383 312. 694 238.,689

6 90. 50 549. 561 310. 639 238. 922

6 90. 50 438. 889 303. 800 135. 089

6 90. 50 348. 761 298. 617 50. 144

6 88. 23 727. 850 329. 840 398. 010

6 88. 23 533. 100 309. 600 223. 500

6 88. 23 338. 580 296. 950 41 . 630

7 90. 50 375. 650 300. 261 75. 389

7 90. 50 438. 761 303. 872 134. 889

7 90. 50 493. 539 308. 428 185. 1 1

7 90. 50 559. 761 314. 428 245. 333

7 90. 50 679. 150 327. 150 352. 000

(9). The standard deviation of the data

4.95 percent.

Tave Kca 1 c Kdat Dev Kdev

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

651 .956 103.649 100 .294 -3 .36 -3 .24

601 .761 87.912 84 .010 -3 .90 -4 .44

507 .678 64.382 62 .828 -1 .55 -2 .41

406 .678 46.497 45 .536 -0 .96 -2 .07

340 .706 38.167 38 .907 0 .74 1 .94

362 .678 40.667 40 .924 0 .26 0 .63

418 .761 48.251 49 .426 1 .18 2 .44

478 .428 58.444 61 .531 3 .09 5 .28

473 .206 57.489 61 .819 4 .33 7 .53

418 .539 48.262 51 .156 2 .89 6 .00

363 .761 40 . 808 42 .510 1 .70 4 .17

340 .900 38.187 39 .483 1 .30 3 .39

319 .150 35.934 38 .907 2 .97 8 .27

378 .983 42.706 44 .671 1 .96 4 .60

454 .817 54.150 56 .199 2 .05 3 .78

531 .483 69.596 73 .491 3 .90 5 .60

371 .733 41 .804 40 .492 -1 .31 -3 .14

420 .400 48.550 47 .553 -1 .00 -2 .05

474..567 57.779 57..496 -0 .28 -0 .49

529 .733 69.250 68..303 -0 .95 -1 .37

400,.733 45.652 44..527 -1 ,.12 -2..46

351 .,053 39.354 36.,601 -2.,75 -7..00

365.,783 41 .076 37. 466 -3,,61 -8..79

404.,286 46.192 41 . 645 -4..55 -9..84

432.,039 50.377 45. 680 -4..70 -9. 32

430. 100 50.099 50. 147 0. 05 0. 10

371 . 344 41.754 39. 772 -1 . 98 -4. 75

323. 689 36.390 35. 305 -1 . 09 -2. 98

528. 845 69.156 73. 549 4. 39 6. 35

421 . 350 48.722 52. 193 3. 47 7. 12

317. 765 35.802 38. 345 2. 54 7. 10

337. 956 37.877 38. 042 0. 17 0. 44

371 . 317 41 .750 41 . 933 0. 18 0. 44

400. 983 45.688 46. 256 0. 57 1 . 24

437. 094 51.179 52. 308 1 . 13 2. 21

503. 150 63.434 65. 421 1 . 99 3. 13

Standard Dev i at i on = 4. 95

23
Table 3. Inter I aboratory comparison of apparent thermal conductivity of

high-temperature m i ne ra I— f i be r pipe insulation measured on seven different horizontal pipe-test apparatuses. Kcalc is computed from eq (10),

obtained by weighting each laboratory equally. The standard deviation of

the data set from eq (10) for all specimens is 5.08 percent.

Lab Den si ty Th igh T 1

<©w De IT Tave Kca 1 c Kdat Dev Kdev

No. (kg/m3

) (C) (C) (C) (C) mW/(m.K)

1

e>'W' e * (Pet)

1 100 .91 942 .928 360 .983 581 .944 651 .956 103 .387 100 .294 -3 .09 -2 .99

1 100 .91 854 .483 349 .039 505 .444 601 .761 87 .518 84 .010 -3 .51 -4 .01

1 100 .91 687 .094 328 .261 358 .833 507 .678 63 .914 62 .828 -1 .09 -1 .70

1 100 .91 503 .706 309 .650 194 .056 406 .678 46 .165 45 .536 -0 .63 -1 .36

2 86 .98 379 .261 302 .150 77 .111 340 .706 38 .023 38 .907 0 .88 2 .33

2 86 .98 419 .206 306 .150 113 .056 362 .678 40 .452 40 .924 0 .47 1 .17

2 86 .98 523 .706 313 .817 209 .889 418 .761 47 .892 49 .426 1 .53 3 .20

2 86 .98 632 .928 323 .928 309 .000 478 .428 57 .994 61 .531 3 .54 6 .10

2 85 .60 624 .706 321 .706 303 .000 473 .206 57 .045 61 .819 4 .77 8 .37

2 85 .60 526 .094 310 .983 215 .111 418 .539 47 .905 51 .156 3 .25 6 .79

2 85 .60 422 .706 304 .817 117 .889 363 .761 40 .590 42 .510 1 .92 4 .73

2 85 .60 379 .372 302 .428 76 .944 340 .900 38 .042 39 .483 1 .44 3 .79

3 94 .35 339 .261 299 .039 40 .222 319 .150 35 .865 38 .907 3 .04 8 .48

3 94 .35 451 .483 306 .483 145 .000 378 .983 42 .445 44 .671 2 .23 5 .25

3 94 .35 590 .928 318 .706 272 .222 454 .817 53 .728 56 .199 2 .47 4 .60

3 94 .35 728 .150 334 .817 393 .333 531 .483 69 .125 73 .491 4 .37 6 .32

4 92 .26 439 .706 303 .761 135 .944 371 .733 41 .563 40 .492 -1 .07 -2 .58

4 92 .26 529 .761 311 .039 218 .722 420 .400 48 .189 47 .553 -0 .64 -1 .32

4 92 .26 628 .483 320 .650 307 .833 474 .567 57 .334 57 .496 0 .16 0 .28

4 92 .26 726 .539 332 .928 393 .61

1

529 .733 68 .781 68 .303 -0 .48 -0 .69

4 92 .26 493 .039 308 .428 184..61

1

400 .733 45..334 44 .527 -0 .81 -1 .78

5 90 .13 404 .283 297..822 106..461 351 .053 39..177 36..601 -2 .58 -6 .57

5 90 .13 429 .311 302 .256 127..056 365 .783 40 .853 37 .466 -3..39 -8 .29

5 90 .13 502 .089 306 .483 195.,606 404 .286 45. 867 41 ,.645 -4.,22 -9 .20

5 90 .13 551 .383 312..694 238.,689 432 .039 49..994 45..680 -4.,31 -8 .63

6 90..50 549 .561 310.,639 238. 922 430.. 100 49..720 50.. 147 0. 43 0 .86

6 90..50 438 .889 303. 800 135. 089 371 .. 344 41 . 515 39.,772 -1 . 74 -4 .20

6 90..50 348..761 298..617 50. 144 323..689 36.,304 35.,305 -1 . 00 -2..75

6 88..22 727..850 329. 840 398. 010 528..845 68. 689 73. 560 4. 87 7..09

6 88.,22 533..100 309. 600 223. 500 421 .,350 48. 360 52. 210 3. 85 7..96

6 88.,22 338..580 296. 950 41 . 630 317.,765 35. 738 38. 360 2. 62 7..34

7 90..50 375.,650 300. 261 75. 389 337. 956 37. 742 38. 042 0. 30 0. 80

7 90. 50 438.,761 303. 872 134. 889 371 . 317 41 . 51 1 41 . 933 ' 0. 42 1 .,02

7 90. 50 493.,539 308. 428 185. 1 1 1 400.,983 45. 370 46. 256 0. 89 1 . 95

7 90. 50 559. 761 314. 428 245. 333 437. 094 50. 786 52. 308 1 . 52 3. 00

7 90. 50 679. 150 327. 150 352. 000 503. 150 62. 968 65. 421 2. 45 3. 90

Standard Deviation = 5.08

24
Table 4. Inter I aboratory comparison of apparent thermal conductivity of

h igh— temperature mineral— f iber pipe insulation. This set of specimens is restricted to only those which were conditioned by heating them to

the highest temperature of measurement before data was taken. Kcalc is computed from eg (11). The standard deviation of the data set from eq (11) for

conditioned specimens is 4.34 percent.

Lab Den s i ty Th i gh T

ow Del T Tave Kca 1 c Kdat Dev Kdev

No. (kg/m 3

) (C) (C) (C) (C) mW/(>.K) mW/( m.K) (Pet)

1 100 .91 942 .928 360 .983 581 . 944 651 .956 100. 280 100. 294 0 .01 0 .01

1 100 .91 854 .483 349 .039 505. 444 601 .761 86. 299 84. 010 -2 .29 -2 .65

1 100 .91 687 .094 328 .261 358. 833 507 .678 64. 754 62. 828 -1 .93 -2 .98

1 100 .91 503 .706 309 .650 194. 056 406 .678 47. 386 45. 536 -1 .85 -3 .90

2 85 .60 624 .706 321 .706 303. 000 473 .206 58. 210 61 . 819 3 .61 6 .20

2 85 .60 526 .094 310 .983 215. 1 1

418 .539 49. 164 51 . 156 1 .99 4 .05

2 85 .60 422 .706 304 .817 117. 889 363 .761 41 . 498 42. 510 1 .01 2 .44

2 85 .60 379 .372 302 .428 76. 944 340 .900 38. 681 39. 483 0 .80 2 .07

4 92 .26 726 .539 332 .928 393. 611 529 .733 69. 299 68. 303 -1 .00 -1 .44

4 92 .26 493 .039 308 .428 184. 61

400 .733 46. 526 44. 527 -2 .00 -4 .30

6 90 .50 549 .561 310 .639 238. 922 430 .100 50. 988 50. 147 -0,.84 -1 .65

6 90 .50 438 .889 303 .800 135. 089 371 .344 42. 492 39. 772 -2,.72 -6 .40

6 90 .50 348 .761 298 .617 50. 144 323 .689 36. 698 35. 305 -1 ,.39 -3 .80

6 88 .23 727 .850 329 .840 398. 010 528 .845 69. 195 73. 549 4 .35 6 .29

6 88 .23 533 .100 309 .600 223. 500 421 .350 49. 618 52. 193 2,,58 5,.19

6 88,.23 338 .580 296 .950 41 . 630 317 .765 36. 040 38. 345 2..31 6,.40

Standard Deviation = 4.34

25
Table 5. Inter 1 aboratory

high-temperature

imens is restricted to only

to the highest temperatures

computed from eg (12). The

for noncond i t i oned specimens

comparison of apparent thermal conductivity of

mineral-fiber pipe insulation. This set of specthose which were not conditioned by heating them

of measurement before data was taken. Kcalc is

standard deviation of the data set from eq (12)

is 4.72 percent.

Lab

No.

Dens i ty

(kg/m 5

)

Th i gh

(C)

Tlow

(C)

DelT

(C)

Tave

(C)

Kca 1 c mW/(m.K)Kdat

mW/(m . K)

Dev Kdev

(Ret)

2 86.98 379.261 302 . 1 50 77.111 340.706 38.252 38.907 0.65 1 .71

2 86.98 419.206 306.150 113.056 362.678 40.077 40.924 0.85 2.12

2 86.98 523.706 313.817 209.889 418.761 47.026 49.426 2.40 5.10

2 86.98 632.928 323.928 309.000 478.428 58.468 61 .531 3.06 5.24

3 94.35 339.261 299.039 40 . 222 319.150 36.880 38.907 2.03 5.50

3 94.35 451 .483 306.483 1 45 . 000 378.983 41.781 44.671 2.89 6.92

3 94.35 590.928 318.706 272.222 454.817 53 . 444 56.199 2.76 5.16

3 94.35 728.150 334.817 393.333 531.483 72.620 73.491 0.87 1 .20

4 92.26 439.706 303.761 135.944 371.733 41 .031 40.492 -0.54 -1 .31

4 92.26 529.761 311.039 218.722 420.400 47.376 47.553 0.18 0.37

4 92.26 628.483 320.650 307.833 474.567 57.716 57.496 -0.22 -0.38

4 92.26 726.539 332.928 393.611 529.733 72.195 68.303 -3.89 -5.39

5 90.13 404.283 297.822 106.461 351 .053 39.130 36.601 -2.53 -6.46

5 90.13 429.311 302.256 127.056 365.783 40.440 37.466 -2.97 -7.35

5 90.13 502.089 306.483 195.606 404.286 45.038 41.645 -3.39 -7.53

5 90.13 551.383 312.694 238.689 432.039 49.301 45.680 -3.62 -7.35

7 90.50 375.650 300.261 75.389 337.956 38.067 38.042 -0.02 -0.06

7 90.50 438.761 303.872 134.889 371.317 40.985 41 .933 0.95 2.31

7 90.50 493.539 308.428 185.111 400.983 44.519 46.256 1 .74 3.90

7 90.50 559.761 314.428 245.333 437.094 50.152 52.308 2.16 4.30

7 90.50 679.150 327.150 352.000 503.150 64.668 65.421 0.75 1 .16

Standard Deviation = 4.72

26
Table 6. Apparent thermal conductivity of specimens of h igh— temperature

mineral-fiber pipe insulation that were not conditioned before

they were measured. The last two columns indicate deviations of these data

from the least-squares curve, eq (11), defined by specimens that were conditioned before they were measured. The standard deviation of the data set

from eq (11) for conditioned specimens is 5.40 percent.

Lab

No.

Dens i ty

(kg/m3

)

Thigh

(C)

Tlow

(C)

DelT

(C)

Tave

(C)

Kcalc Kdat

mW/(m.K) mW/(m.K)

Dev Kdev

(Pet)

2 86.98 379.261 302.150 77.111 340.706 37.881 38.907 1 .03 2.71

2 86.98 419.206 306.150 113.056 362.678 40.519 40.924 0.41 1 .00

2 86.98 523.706 313.817 209.889 418.761 48.173 49.426 1 .25 2.60

2 86.98 632.928 323.928 309.000 478.428 57.942 61 .531 3.59 6.19

3 94.35 339.261 299.039 40 . 222 319.150 35.461 38.907 3.45 9.72

3 94.35 451.483 306.483 145.000 378.983 42.617 44.671 2.05 4.82

3 94.35 590.928 318.706 272.222 454.817 53.877 56.199 2.32 4.31

3 94.35 728.150 334.817 393.333 531.483 68.226 73.491 5.26 7.72

4 92.26 439.706 303.761 135.944 371 .733 41.687 40.492 -1 .20 -2.87

4 92.26 529.761 311.039 218.722 420.400 48.455 47.553 -0.90 -1 .86

4 92.26 628 . 483 320.650 307.833 474.567 57.305 57.496 0.19 0.33

4 92.26 726.539 332.928 393.61

529.733 67.904 68.303 0.40 0.59

5 90.13 404.283 297.822 106.461 351.053 39.131 36.601 -2.53 -6.46

5 90.13 429.31

302.256 127.056 365.783 40.934 37.466 -3.47 -8.47

5 90.13 502.089 306.483 195.606 404.286 46.119 41.645 -4.47 -9.70

5 90.13 551 .383 312.694 238.689 432.039 50.238 45.680 -4.56 -9.07

7 90.50 375.650 300.261 75.389 337.956 37.568 38.042 0.47 1 .26

7 90.50 438.761 303.872 134.889 371 .317 41.633 41.933 0.30 0.72

7 90.50 493.539 308.428 185.111 400.983 45.625 46.256 0.63 1 .38

7 90.50 559.761 314.428 245.333 437.094 51.018 52.308 1 .29 2.53

7 90.50 679.150 327.150 352.000 503.150 62.576 65.421 2.85 4.55

Standa rd Dev i at i on *5.40

27
O LflB 1 O LflB 5 A LflB 2 + LflB 6

LflB 3 X LflB 7 7 LflB i

MEAN TEMPERATURE, K

Figure 1. I nte r I aboratory comparison of apparent thermal conductivity of

mineral-fiber pipe insulation measured on the horizontal pipetest apparatus. The nominal density of the specimens is 90 kg/m^ (5.6

lb /ft^). Measurements were performed in air at ambient pressure. The

solid line is a plot of eq (9), thermal conductivity as a function of

temperature. Each point on this line represents the thermal conductivi ty

determined by the local thermal grodient (vanishing temperature difference), at o point within the specimen; the temperature at that point is

given by the value from the temperature axis. Each symbol represents the

experimental conductivity obtained at (large) non-zero temperature differences between the boundary surfaces at Tcold and Thot . The value of

conductivity at the symbol is the ratio of the integral of the conductivity function between Tcold and Thot to the corresponding temperature

difference. For this reason the data points deviate from the curve when

large temperature differences are used. Specimens from laboratories 1, 2,

4 and 6 were conditioned by heating specimens to the highest temperatures

of measurement before taking data. Filled triangles denote repeated measurements by laboratory 2 and circled "plus" signs denote repeat measurements by laboratory 6.

28
10

o

_>oo \o

o

u—

o

u

X

JDO

7.5

5

2.5

0

-2.5

-5

-7.5

-10

300 350 400 450 500 550 600 650 700

MEAN TEMPERATURE, K

Figure 2. Deviations of apporent thermal conductivity of m i nera I— f i ber

pip® insulation, as measured by all seven participants, from

values calculated with eq (9), thermal conductivity as a function of

temperature. Each experimental conductivity value is obtained at (large)

nonzero temperoture differences between the boundary surfaces at Tcold

and Thot . The integral of the conductivity function is computed over the

temperature interval from Tcold to Thot. We compute the ratio of this

integral to the corresponding temperature difference to obtain the mean

conductivity over the interval from Tcold to Thot. The difference between

the computed mean and the experimental vo I ue is the deviation. Filled

triangles denote repeated measurements by laboratory 2, and circled plus

signs denote repeated measurements by laboratory 6.

29
O LAB 1 O LAB 5 A LAB 2 + LAB 6 LAB 3 X LAB 7 V LAB 4

MERN TEMPERRTURE, K

Figure 3. Inter I aborotory comparison of apparent thermal conductivity of

mineral-fiber pipe insulation meosured on the horizontal pipetest apparatus. Measurements were performed in air at ambient pressure.

The solid line is a plot of eq (10), for thermal conductivity as a function

of temperature, obtained by weighting each I aborotory equally. Specimens

from laboratories 1, 2, 4, and 6 were conditioned by heating specimens

to the highest temperatures of measurement before taking data. Filled triangles denote repeated measurements by laboratory 2 and circled plus signs

denote repeoted measurements by laboratory 6. Please see the caption of

figure 1 for on explanation of the difference between the experimental

points (symbols) and the fitted conductivity function.

30
10

7.5

o 2.5

in -Oo O -2.5

o

-5

-7.5

-10

•

' 1

' 1 1

e

A

1 1 1 1

1 1 1 1

1

1 1

' 1

" ©

A

© •

A -

A - A

A X

X

-

A

X

X o X + 7

-

7

o V

7 0

+ 7

0

+ O

o

-

o O

! 0

1 .... 1 .

. 1 • 1 300 350 400 450 500 550 600

MEAN TEMPERATURE, K

650 700

Figure 4. Deviations of apparent thermal conductivity of m i ne ra I -f i be

- pipe insulation, as measured by all seven participants, from

values calculated with eg (10) obtained by weighting each laboratory equally- Filled triangles denote repeated measurements by laboratory 2, and

circled plus signs denote repeat measurements by laboratory 6. Please see caption of figure 2 for an explanation of how the deviation is computed.

31
HERN TEMPERATURE, K

Figure 5. Inter I aboratory comparison of apparent thermal conductivity

of m i ne ra I -f i be r pipe insulation measured on the horizontal pipetest apparatus. Measurements were performed in air at ambient pressure.

Specimens were conditioned by heating them to the highest temperatures of

measurement before taking data. The solid line is a plot of eq (11) for

thermal conductivity as a function of temperature. Please see the caption

of figure 1 for an explanation of the difference between the experimental

points (symbols) and the fitted conductivity function.

32
8

u

o

u

UJ -DO

6

4

2

0

-2

-4

-6

-8

300 350 400 450 500 550 600 650 700

MEAN TEMPERATURE, K

Figure 6. Deviation of apparent thermal conductivity of mineral-fiber pipe — insulation, as measured after conditioning, from values calculated with eq (11). Open squares represent data from laboratory 4; downwardpointing triangles represent data from laboratory 6. Filled triangles are repeoted measurements by laboratory 6. As before, open circles represent

data of laboratory 1, and upwa rd— po i nt i ng triangles are data of laboratory

2. Please see caption of figure 2 for an explanation of how the deviation

is computed.

33
Figure 7. Apparent thermol conductivity of specimens of m i ne ra I— f i be r pipe

insulation that were not conditioned before they were measured.

Measurements were performed in air at ambient pressure and over the range

of mean temperatures from 318 to 531 K. The solid line is a plot of eq (12)

for thermal conductivity as a function of temperature. Please see the

caption of figure 1 for an explanation of the difference between the experimental points (symbols) and the fitted conductivity function.

34
O LflB 2

A LflB 3

LflB A V LflB 5

O LflB 7

u

—

o

o

U

_>o

u

/<

I CO -Oo O

300 325 350 375 400 425 450 475 500 525 550

MEAN TEMPERATURE, K

Figure 8. Deviations of apparent thermal conductivity of m i ne ra I -f i be

pip* insulation, not conditioned before being measured, from

values calculated with eq (12). Please see caption of figure 2 for an explanation of how the deviation is computed.

35
MEAN TEMPERATURE, K

Figure 9. Apparent thermal conductivity of specimens of m i ne ra I -f i be

r

pipe insulation that were not conditioned before they were measured. Measurements were performed in air at ambient pressure. The

The solid line is a plot of eq (11), thermal conductivity as a function

of temperature, for specimens that were conditioned before they were measured. The position of the solid line was adjusted vertically to

minimize the rms deviation of this data from the curve. Please see the

caption of figure 1 for an explanation of the difference between the

experimental points (symbols) and the fitted conductivity function.

36
3"|D3

0"]O3

sqo

O LRB 2

A LftB 3

LRB i

V LRB 5

O LRB 7

10

7.5

5

2.5

0

O -2.5 O

-5

-7.5

-10

300 325 350 375 400 425 450 475 500 525 550

MEAN TEMPERATURE, K

Figure 10. Deviations of apparent the rma I conductivity of mineral-fiber —— — pipe insulation, not conditioned before being measured, from

values calculated with eq (11), the relation for thermal conductivity

of specimens that were conditioned. Please see caption of figure 2 for an explonotion of how the deviation is computed.

37
NBS-114A (REV. 2-80

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR 2 REPORT NO.

NISTIR 89-3913 1

. Performing Organ. Report No.l 3. Publ ication Date

April 1989

4. TITLE AND SUBTITLE

INTERLABORATORY comparison of the guarded horizontal pipe-test apparatus

Precision of ASTM Standard Test Method C-335 Applied to Mineral-Fiber Pipe Insulation

5. AUTHOR(S)

David R. Smith

6. PERFORMING ORGANIZATION (If joint or other than

National Institute of Standards and

NXXKW^BMKEXMXWXXTXKBXKBX

NBS. see in stru ction s) Technology

7. Contract/Grant No.

DEPARTMENT OF COMMERCE

Gai thersburg, MD 20899

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

g 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 significant

bibliography or literature survey, mention it here)

Apparent thermal conductivity of refractory pipe insulation from the same production

lot was measured by seven different laboratories. The purpose of this intercomparison

was to assess the precision and bias of the ASTM Test for Measurement of Steady-State

Heat-Transfer Properties of Horizontal Pipe Insultation (C 335). Four laboratories

submitted conductivity measurements for conditioned specimens. The test results for

thermal conductivity of the four conditioned specimens include the temperature range

from 318 to 652 K and illustrate the interlaboratory reproducibility as well as the

temperature dependence of the conductivity. The standard deviation of the data from

each participating laboratory was measured by their deviation from a polynomial function fitted to all data. For the 16 test results from the four laboratories that

conditioned their specimens, the standard deviation was 4.3 percent. For all test

results from all seven participants, the standard deviation was 5 percent. This

value is offered as the estimated precision of the horizontal pipe-test method. The

accuracy of this pipe-test method cannot be estimated from the data obtained in this

in tercomparison.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) accuracy; apparent thermal conductivity; bias; guarded hot plate; high temperature;

horizontal pipe; insulation; interlaboratory comparison; mineral fiber; precision;

standard text method

13.

AVAILABILITY

j)t^] Unl imited

For Official Distribution. Do Not Release to NTIS

Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

14. NO. OF

PRINTED PAGES

48

15. Price

PCX'1 Order From National Technical Information Service (NTIS), Springfield, VA. 22161

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