Reference

NBSIR 85-3221

NAT'L INST. OF STAND & TECH

AlllDb D3m3fl

An Assessment of the NBS 1-m

Guarded- Hot- Plate Limits

Brian G. Rennex

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Gaithersburg, MD 20899

August 1985

Prepared for: U.S. Department of Energy

LBuilding Energy

land Development

on, DC 20585

.U56

85-3221

1985

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NBSIR 85-3221

AN ASSESSMENT OF THE NBS 1-m

GUARDED-HOT-PLATE LIMITS

Brian G. Rennex

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Gaithersburg, MD 20899

August 1985

Prepared for: UoS. Department of Energy

Office of Building Energy

Research and Development

Washington, DC 20585

/9

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director

PREFACE

This report is one of a series documenting NBS research and analysis

efforts to support the Department of Energy /National Bureau of Standards'

Measurements Technology Program. The work reported in this document was sponsored by Department of Energy through DOE/ORO/NBS Interagency

Agreement No. DE-AI05-85OR21513, Task C-85/1, Guarded Hot Plate Assessment.

PRODUCT DISCLAIMER

Because of the nature of this report, to assess the limits of a particular

apparatus, there is an occasional use of a trade name or a manufacuturer's

name. This in no way represents an endorsement of a particular product or manufacturer.

11
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ABSTRACT

The report evaluates the National Bureau of Standards 1-meter Guarded Hot

Plate in terms of the range of values of operating parameters. The ranges

of operation are discussed according to three kinds of limiting factors.

The first is the limits of temperature over which the various apparatus

components can be used without damage. The second kind is the limits of

plate temperatures, specimen thickness, atmospheric pressure, and relative

humidity achievable with the existing control systems. The third kind is

any limits on the values of apparent thermal conductivity, thermal

resistance, or specimen thickness due to measurement error considerations.

The current operating range is documented by data of apparent thermal

conductivity versus specimen mean temperature and thickness. The current

temperature limits for the specimen mean temperature are -3°C to 55°C.

Minor improvement can extend this range to -30°C to 190°C. There are no

serious limits on thermal resistance or apparent thermal conductivity for

typical specimens. There is no pressure control, and to provide such

control would be a major expense. The thickness limits are 19 mm to 381 mm.

The current limits on relative humidity are from 2% to 35% at 24°C. The

upper limit can easily be extended. An estimate of apparatus uncertainty

is made over the ranges of specimen mean temperature, apparent thermal

conductivity, and thickness.

Keywords: apparent thermal conductivity, calibration, error analysis,

guarded hot plate, operating ranges, standard reference

material (SRM), thermal insulation, thermal resistance.

iii
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TABLE OF CONTENTS

Page

PREFACE (•*(«*e«e** 0 «*e*<ceeoeec<o 11- ABSTRACT 111

LIST OF FIGURES . v LIST OF TABLES , vii

LIST OF APPENDICES viii

ACKNOWLEDGMENTS ix

LIST OF SYMBOLS x

1. INTRODUCTION 1

X . I Objectives ...... .......c........ X X.2 Background X X.3 Scope. ........... ....... ...... 2

2. TEMPERATURE LIMITS OF APPARATUS COMPONENTS 2

2.

x Apparatus Description 2

2.2 Component MateriaXs Difficult to RepXace 2

2.3 Component MateriaXs Easy to Replace 3

3. PARAMETER CONTROL LIMITS ..... . . 6

3.

x Temperature Control ....... 6

3.2 Plate-Temperature Limits Due to Control Circuity. ... 6

3.3 Ambient Temperature Control 7

3.4 Thickness Constraints 7

3.5 Ambient Gas Pressure . 8

3.6 Relative Humidity Control . . 8

4. PARAMETER LIMITS DUE TO APPARATUS UNCERTAINTY CONSIDERATIONS 9

4.

x Introduction 9

4.2 Lower Limit for Apparent Thermal Conductivity 9

4.3 Upper Limit for Apparent Thermal Conductivity XX

4.4 Thickness Limit 13

4.5 Temperature Limits 15

4.6 Apparatus Uncertainty as a Function of kg and T^jj. . . . 15

5. APPARENT THERMAL CONDUCTIVITY DATA OVER THE CURRENT OPERATING

TEMPERATURE RANGE 16

6. SUMMARY OF PARAMETER LIMIT AND ESTIMATES OF COST IMPROVEMENTS 17

6.x Temperature Limits 17

6.2 Other Apparatus Limits 19

REFERENCES 21

APPENDICES

iv
LIST OF FIGURES

Page

Figure 1. Drawing of the NBS 1-m Guarded Hot Plate Showing

the Support System of the Hot and Cold Plate and

Showing the Rotatable Enclosure for Environmental

Control. 22

Figure 2. Temperature Control Circuit for the NBS 1-m

Guarded-Hot-Plate Apparatus 23

Figure 3. Resistance-Temperature Characteristics for

Temperature Control Thermistors 24

Figure 4, Control Circuit for the Guard Heaters for the NBS

1-m Guarded Hot Plate 25

Figure 5. View of the NBS 1-m Guarded-Hot-Plate Apparatus

Walls and Doors 26

Figure 6. Latch of the NBS 1-m Guarded-Hot-Plate Apparatus

Door-Lock Bar 27

Figure 7, Cross Section of the NBS 1-m Guarded-Hot-Plate

Apparatus Walls 28

Figure 8. Plot of Edge-Effect Coefficient "A” as a Function of

Specimen Thickness for the NBS 1-m Guarded Hot Plate,

Showing the Parametrical Dependence on the Ratio of

the Effective Surface Film Coefficient, hg, over the

Specimen Apparent Thermal Conductivity, kg 29

Figure 9, Plot of Edge-Effect Coefficient "B" as a Function of

Specimen Thickness for the NBS 1-m Guarded Hot Plate,

Showing the Parametrical Dependence on the Ratio of

the Effective Surface Film Coefficient, hg, over the

Specimen Apparent Thermal Conductivity, kg 30

Figure 10. The Edge-Effect Percent Uncertainty, Due to the A

Coefficient (0.25A) and the B Coefficient (B AX,

where AX = 0.036), as a Function of Specimen

Thickness, L, for the NBS 1-m Guarded Hot Plate 31

Figure 11. The Total Edge-Effect Percent Uncertainty, 0.25A + 0.036B, as a Function of Thickness, L, for the NBS

1-m Guarded Hot Plate 32

V
Figure 12. Relationship between temperature at edge of metering

section and the average temperature over the metering

section area as a function of specimen thermal

conductivity for the geometry indicated [3]. ...... 33

Figure 13. Correction Term, DD, for the NBS Guarded-Hot-Plate

Thickness Readout Based on an In Situ Measurement. . . . 34

Figure 14. Apparent Thermal Conductivity versus Specimen Mean

Temperature Points Showing the Ranges Measured on

the NBS 1-m Guarded Hot Plate. ............. 35

Figure 15. Apparent Thermal Conductivity versus Specimen Mean

Temperature for Insulation Materials .......... 36

Figure 16. Apparent Thermal Conductivity versus Specimen Thickness,

L, for Insulation Materials. ...... . 37

Figure 17. Temperature Limits for the NBS 1-m Guarded-Hot-Plate

Apparatus ...... ........... o...... 38

VI

LIST OF TABLES

Table 1.

Table 2.

Table 3.

Table 4.

Table 5.

Table 6.

Table 7.

Table 8.

Table 9.

Table 10.

Table 11.

Page

Relative Magnitudes of Contact Resistance and

the Thermal Resistance of a 25.4 mm Thick

Specimen for a Range of Specimen k-value. . . « . 39

Difference Between NBS 1-m Guarded Hot Plate

Thickness Readout and In Situ Thickness Readout . 40

Percentage Estimate of Uncertainties in the

Measured Apparent Thermal Conductivity for

the NBS Guarded Hot Plate 41

Total Apparatus Uncertainty for a Specimen

Thickness, L, of 23.4 mm, as a Function of

Specimen Mean Temperature, T^, and Specimen

Apparent Thermal Conductivity, kg . 42

Total Apparatus Uncertainty for a Specimen

Thickness, L, of 152.4 mm, as a Function of

Specimen Mean Temperature, T^, and Specimen

Apparent Thermal Conductivity, kg . 43

Total Apparatus Uncertainty for a Specimen

Thickness, L, of 304.8 mm, as a Function of

Specimen Mean Temperature, T^, and Specimen

Apparent Thermal Conductivity, kg ....... . 44

Total Apparatus Uncertainty for a Specimen

Thickness, L, of 381 mm, as a Function of

Specimen Mean Temperature, T^, and Specimen

Apparent Thermal Conductivity, kg 45

Apparent Thermal Conductivity as a Function of

Specimen Mean Temperature, T^^ 46

Apparent Thermal Conductivity as a Function of

Specimen Mean Temperature, T^^, Data Measured

on the NBS 1-m Guarded Hot Plate 47

Apparent Thermal Conductivity as a Function of

Specimen Thickness, L, Data Measured on the NBS

1-m Guarded Hot Plate, at a Mean Temperature of

23.9®C and a Temperature Difference of 27.8°C . . 48

Percent Difference Between the average k-value

of the Individual Layers in a Stacked Specimen

and the Actually Measured k-value of the

Stacked Specimen 49

vii
LIST OF APPENDICES

Page

Appendix 1 Copy of Reference [4] 1-1

Appendix 2 Positive Pressure Inside Chamber 2-1

Appendix 3 Vacuum Inside Chamber 3-1

Appendix 4 Calculation of Percentage Uncertainty in the

Measured Metered-Area Heater Power for a 152.4 mm Thick, Low k-value Insulation

Specimen [5] ....... 4-1

Appendix 5 Test Thickness Limitations Due to Edge Effect

Uncertainties 5-1

Appendix 6 Contact Resistance 6-1

viii
ACKNOWLEDGEMENTS

The author expresses appreciation to the Department of Energy whose

sponsorship made this effort possible. Programatic and technical

coordination was provided by Bill Gerken, Program Manager, Materials

Program, Building Systems Division, Office of Energy R & D, Department of

Energy, and Dr. David McElroy of the Oak Ridge National Laboratory. The

author wishes to thank William Stone, of Structures Division, CBT, NBS,

for the calculations in appendices 2 and 3, Brad Peavy, retired from the

Building Physics Division, CBT, NBS, for his help on the edge-effect

calculations and Carmen Gracia for her help in the preparation of this

document.

IX

LIST OF SYMBOLS

a radius of circular line-heat-source in the hot-plate metered area

A intercept of edge effect curve

h radius of metered area of the hot plate

B slope of edge effect curve

C maximum fiber axis from neutral axis for calculation of bending

stress

d area centroid distance from neutral axis for calculation of I

DD difference between DT and DF

DF thickness change with temperature referenced to a mean temperature

of 24°C as measured by the Farrand thickness transducers

DT thickness change with temperature referenced to a mean temperature

of 24°C as measured by the in-situ thickness transducer

e height of heater in hot plate

F(T) thickness , as measured by the Farrand thickness

transducers at temperature T

b surface film coefficient between the edge insulation and

the ambient

hg effective surface film coefficient including edge insulation

I composite moment of inertia for 1" strip

k apparent thermal conductivity

kg gas conductivity of air

kp plate thermal conductivity

kg specimen apparent thermal conductivity

L specimen thickness

Lg air-gap thickness

m hot-plate thickness

^MAX TM^xiiDum bending moment

^INT apparatus internal pressure

X
^total total force imparted to the GHP apparatus door due to the internal

pressure

Qm power produced by the metered-area heater

q heat flow per unit area

Q shear area moment

R thermal resistance

Red thermal resistance of edge insulation

Rfaeater metered-area heater resistance

Rr reaction forces for 1" strip analysis

Rm measured thermal resistance of stack

Ro thermal resistance that would result given perfect one-dimensional

heat flow across a specimen, as approximated by the sum of the

thermal resistance values of the component specimens in a stack

Rs shunt resistance

r contact resistance

Si reaction force which must be resisted by shear bars in the GHP

apparatus

T(T) thickness measured by the in-situ thickness transducer at a temperature T

T average air-gap temperature

Ta ambient temperature

cold-plate temperature

Th hot-plate temperature

m

mean temperature = (Tj^ + Tj.)/2

V maximum shear force

\ heater voltage

Vs shunt voltage

X = 2(T„ - - Te)

Y = (Ro - = A + BX

XI
0 extinction coefficient

AT temperature difference

Av voltage uncertainty

AX uncertainty in X

£ plate emittance

<T Stefan-Boltzmann constant

o’uit ultimate shear stress

ffg shear stress

Q optical depth

Subscripts

b bottom side of the two-sided apparatus

t top side of the two-sided apparatus

Xll

1 . INTRODUCTION

1.1 Objectives

Accurate measurement of the thermal resistance of insulation and building

materials is a matter of national interest. A viable national calibration

program must consist of accurate apparatuses, appropriate test methods, and

calibration specimens available over the needed ranges of test and material

parameters, such as temperature and apparent thermal conductivity. The

apparatuses are operated according to the test methods to provide these

calibration specimens. It is necessary to know the apparatus accuracy over

the entirety of the operating ranges over which the calibration specimens

are measured.

The objective of this report is to evaluate the operating capability of

the NBS 1-m Guarded -Hot-Plate (GHP) apparatus according to three kinds of

limiting factors. The first kind is the limits of temperature over which

the various apparatus components can be used without suffering damage. The

second kind is the limits of plate temperatures, specimen thickness,

atmospheric pressure, and relative humidity that can be achieved with the

existing control systems. The third kind is any limits on the values of

apparent thermal conductivity, thermal resistance, or specimen thickness

due to measurement error considerations.

1 . 2 Background

The issues related to the need for calibration test measurements over a wider range of test conditions were discussed in detail in previous

papers. Reference [1], published by an ASTM Working Group in 1978, gave

information on many candidate materials. In addition, it recommended (1) a search for new Standard Reference Materials (SRM's) and (2) the development

of a long-range priority scheme to provide these SRM's.

Reference [2] presented the rationale for a calibration program which would

minimize calibration errors by making available calibration points over the

entirety of the ranges of test parameters. It also assessed the need for

calibration points at various ranges of test parameters, and it

recommended a priority scheme for the development of new calibration

standards

.

This report gives parameter ranges of operation, and apparatus accuracies

over these ranges, for the 1-m GHP apparatus at NBS, Gaithersburg. This

device provides calibration specimens for thermal testing of insulation

materials. Its design was based on work by Hahn, Robinson and Flynn [3] at

NBS in the 1970's, and its construction by Hahn was completed in 1981. The

salient design feature was a line-heat source for the hot plate heaters. A

description of this apparatus is given in reference [4], and a detailed

error analysis is presented in reference [5]. This error analysis

indicated an upper limit for apparatus uncertainty of less than 0.5 percent

for thermal resistance measurement at 24°C.

1
1.3 Scope

The primary purpose of this report is to provide documentation on the

current operating capability of the 1-m NBS GHP apparatus. No changes have

been made to extend the operating range. However, brief discussions are

given to indicate the amount of effort that would be required to extend the

various ranges. This NBS internal report will be made available to parties

interested in NBS measurement capability, and it is intended to assist

other researchers in similar evaluations of their apparatuses.

2. TEMPERATURE LIMITS OF APPARATUS COMPONENTS

2.1 Apparatus Description

Reference [4] contains a brief description and a summary error analysis of

the 1-m GHP apparatus, and it is included as appendix 1, A more detailed

discussion of the error analysis is presented in reference [5], This

apparatus was designed to conform to the ASTM C 177-76 Test Method for the

absolute measurement of thermal resistance of insulation specimens [6],

Figure 1 is a drawing of the apparatus. The hot plate is maintained in

position between the two cold plates by a support system which in turn is

suspended within the ambient chamber (1.6 m on a side). The plates are 1 m

in diameter and are made of type 6061-T6 aluminum; the support system and

the metal parts of the ambient chamber are also made of aluminum. The

plates contain temperature sensors, heater wire, and epoxy; and they are

insulated with polystyrene. The ambient chamber walls contain

polyurethane,

2.2 Component Materials Difficult to Replace

This section documents the temperature limits to which the various nonmetal lie components of the apparatus can be subjected without damage.

Hot Plate Epoxv

An epoxy was used in the hot plate to keep thermocouple and heater leads in

grooves milled in the plate surfaces and to ensure a flat plate surface by

filling these grooves. The epoxy used was Eccobond 285 with catalyst #11,

produced by Emerson and Cummings, Inc.* The manufacturer recommended a safe lower temperature limit of -40°C, and a possible lower temperature

limit of -48®C, since below this limit the epoxy becomes brittle and can

crack. Because the epoxy is not used for mechanical support, it might be

possible to go to lower temperatures and tolerate any cracks that might

develop. Such cracks would not result in a measurable difference in test

results because they would comprise a very small percentage of the metered

area. Furthermore, the manufacturer does produce another catalyst (#24LV)

which can be safely used at cryogenic temperatures, and this could be used

to repair or replace the existing epoxy. The biggest risk at lower

*Because this report purports to specifically describe the existing

apparatus, there will be an occasional use of a manufacturer's name. This

in no way represents an endorsement of the various manufacturers.

2
temperatures is that the silver leads, which connect to the one heater in

the metered area and the two heaters in the guard area, might break due to

strain resulting from the epoxy cracking. The only way to know for sure

whether the lead would break would be to subject the actual hot plate to

temperatures below -40°C. If the wires were to break, it would be

necessary to disassemble the hot plate, mill out the old epoxy and leads,

and replace these with the new leads and the cryogenic epoxy. This epoxy

(#24LV) has an upper temperature limit that is 28°C lower than the existing

epoxy

.

The upper temperature limit of the existing epoxy (with catalyst #11) is

177°C for long-term use, according to the manufacturer. Oven tests between

85®C and 315®C were made on 34 specimens of a similar epoxy (using the same

resin and catalyst #9) which the manufacturer stated to have an upper

limit of use that is 24®C lower than that with the catalyst #11. These

oven tests indicated that the epoxy exhibited no changes up to 150°C for

tests as long as 16 hours. Between 150®C and 250°C the epoxy finish became

duller, and there was a progressive discoloration. According to the

manufacturer, the discoloration has no deleterious effect on mechanical

performance of the epoxy. Above 250°C the epoxy was damaged in that it

expanded, softened, and became extremely brittle when re-cooled to lower

temperatures. Finally, it crumbled at 300®C.

The conclusion of the experimental work is that the hot-plate epoxy could

be used at least up to temperatures of 250®C. However, a lower more

conservative value of 200®C is recommended to avoid any chance of

accidental increase to the unsafe higher temperature. This value of 200°C

is higher than the original NBS design temperature of 150°C or the

manufacturer's recommended upper limit of 177°C.

Cold-Plate Epoxv

The same epoxy, Eccobond 285 with catalyst #11, as that used in the hot

plate was also used in the cold plate, but for a different purpose. The

cold plate is type 6061-T6 aluminum and consists of a 6.4 mm thick cover

plate bonded with the epoxy to a 19.0 mm thick base plate. The base plate

contains milled grooves which form channels in a double-spiral

configuration. It is important that these channels remain leak-proof to

ensure a uniform temperature distribution over the cold-plate surface and

to prevent leaks from the cold plate itself. Cooling below -40®C could

result in leaks or even actual separation of the base and cover plates.

The same limit of 200°C as for the hot plate applies for the cold plate.

Any failure of the cold-plate epoxy would be more serious than in the case

of the hot plate. Since the hot plate is limited to use below 200°C, it is

unlikely that the cold plate would be used above 190°C, as the cold plate

is typically more than 10°C colder than the hot plate.

Plate Temperature Sensors

The two cold plates and the hot plate contain a single temperature sensor

each. These are Platinum Resistance Thermometers (PRT's), model number S1059-2, produced by the Minco Corporation. The manufacturer claims that

these devices can be used over a temperature range from -269®C to 220®C.

Their uncertainty value for 20 temperature cycles between plus and minus

200°C is 0.001 AT(°C).* Thus it is not expected that temperature cycling

between -40®C and 200®C would add a significant error contribution to the

* In this report the AT (°C) notation is used to indicate a temperature

difference as opposed to an absolute temperature.
plate temperature measurement. The low temperature limit is due to the

presence of helium gas in the encapsulated PRT device, and the high

temperature limit is due to the Teflon insulation for the lead wires. The

other temperature sensors in the hot plate are thermistors used for

temperature control. The upper limit for these, due to the Teflon

insulation, is 220°C.

The four PRT leads in the cold-plate are insulated from each other by Torr

Seal epoxy, manufactured by Varian Associates. This prevents any current

leakage that might result if the leads became wet. According to the

manufacturer, at temperatures above 120°C, the binder is driven out of the

epoxy, and it will crumble under stress. This would seem to limit the

operating temperature to 120°C, but it would be easy to remove the coldplate PRT's and protect them with higher-temperature epoxy.

If a PRT were damaged in a cold plate, it would be relatively easy to

replace because the PRT can be pulled out of its bore hole, which was

drilled from the edge of the cold plate to the center of the cold plate.

On the other hand, it would be necessary to disassemble the hot plate to

remove its PRT, which is located in the gap between the metered area and

the guard area. This would be a very time-consuming task.

It is not clear that it would be necessary to remove the hot-plate PRT to

replace the Torr Seal, for two reasons. First, moisture is normally driven

away from the hot plate, so there would be no current leakage because the

PRT leads could not get wet. The exception would be the case when the hotplate is below the ambient dew-point temperature. The relative humidity of

the ambient could be controlled, to avoid this case. The second reason is

that the hot-plate PRT is encased in a metallic holder. This means that

there is no requirement for structural integrity of the PRT-wire epoxy.

The epoxy's bulk would be expected to continue to provide protection from

moisture intrusion even with the binder removed.

A final argument in favor of attempting a high temperature for the hotplates is that, if moisture should collect at cold temperatures, it could

be driven off, simply by raising the hot-plate temperature.

Plate Warpage

The two components of the cold plates were epoxied together and then the

plate surfaces were machined. There is no reason to expect significant

warpage of these plates over the temperature range allowed by the

fabricating epoxy, -40°C to 200®C.

The hot plate was also designed to have very little warpage. It is made of

6061-T6 aluminum, and is constructed in such a way that there is a pressure

fit between the different parts of the hot plate. The inner and outer

parts of the metered area are separated by the metered-area heater. These

two parts were pressure fit, to expand and contract the same amount, with

temperature changes. The support between the metered area and the guard

region of the hot plate is accomplished with three stainless steel pins,

and the guard section itself is a single piece of aluminum. There is no

reason to expect significant warpage of the hot plate over the indicated

temperature range of -40°C to 200°C.

4
Ambient Chamber Wall Insulation

The ambient chamber is shown in figure 1. The purposes of this chamber are

(1) to support the plates so that they can be rotated and (2) to control

the temperature, gas composition, and relative humidity of the air

surrounding the GHP specimen. The chamber walls are composed of two sheets

of aluminum, 1-mm thick, around a 76-mm thick layer of molded polyurethane,

which is glued to the aluminum sheets. The polyurethane is not a limiting

factor on the low-temperature side, as it can be used at temperatures

below -40°C; but it is a limiting factor on the high-temperature side to

temperatures below 100°C. To be on the safe side, the ambient-chamber

temperature should not be allowed above 90°C.

This restriction would not result in upper-temperature limits for specimens

less than 150 mm in thickness, because the edge effects are negligible at

these thicknesses; hence, the ambient temperature need not to be maintained

equal to the mean temperature of the hot and cold plates.

To run at mean temperatures higher than 90®C, the following two methods

could be used. The first would be to put extra high-temperature insulation

on the inside walls. Assuming that the air temperature outside the ambient

temperature is 24°C and that 50 mm of typical insulation could be added,

the mean ambient temperature could be raised to approximately 134°C, before

the polyurethane insulation would reach 90°C. Another method would be to

put an insulated or water-cooled heater jacket around the edges of the

specimen. This would maintain a small layer of air at much higher

temperatures than the ambient chamber air, but the chamber walls would not

be subjected to these higher temperatures.

2.3 Component Materials Easy to Replace

Cold-Plate Polystyrene Insulation

Molded polystyrene having a thickness of 76 mm is used around both cold

plates. This material can be used at temperatures of -40°C or below, but

it is restricted on the high-temperature side to use below 85°C. The

purpose of this insulation is to enhance the uniformity of temperature over

the cold plate surface. It would be straightforward to replace the

polystyrene with another insulating material, such as high-density molded

glass-fiber board which can be used up to temperatures of 150®C or layers

of flexible Min-K material which can be used at temperatures much higher

than 200°C.

Teflon Tubing

Teflon plastic tubing is used to contain the thermistor, PRT, and

thermistor wires and hold them in place. Pieces of this tubing are in

direct contact with the cold plates and the hot plates. This tubing is

manufactured by Norton Plastics and Synthetics. The manufacturer did not

know the upper temperature limit for this tubing. Tests at NBS indicated

that the upper temperature limit for the tubing is 170°C, at which point

the tubing melts. Between 55°C and 170°C the tubing shrinks slightly in

length but not in diameter; this does not affect the tubing's function.

This tubing could be easily replaced.

5
3. PARAMETER CONTROL LIMITS

3.1 Temperature Control

The ranges of temperature, at which the cold plates, the hot plate, and the

ambient can be controlled, depend on the capabilities of the cold baths,

the power supplies, and feedback-control circuity, as well as the heating

and cooling loads. The cold-plate bath is a Tamson, model number TCZ-45,

produced by NESLAB Instruments, Inc. This circulating bath has the power

capability to go up to 230°C, but in practice it is limited to 80®C because

the heating unit must oppose the existing cooling unit. The cooling

capacity of this unit could be reduced, to allow the bath heater to reach a temperature of 200°C. However, the "Z” (force and suction) circulation

pump, cannot be used with foam-forming liquids such as oils, and, thus, the

bath is limited to temperatures below 110°C. The acquisition of a highertemperature pump for use with oil would permit the extension of the bath

circulator temperature capability to 230°C.

The cold-temperature limit is determined by the NESLAB PBC-2 portable bath

coolers which can cool the baths down to -30®C. Other baths such as the

NESLAB LT-50 low temperature bath circulator could lower the limit to

-50°C, or lower. The cooling fluid currently used is ethylene glycol.

This can be used up to temperatures of 110®C and down to temperatures of

-48°C. If colder temperatures were desired, a solution of methylene

chloride could be used down to -73®C.

The hot plate does not have any temperature limit within the range of -40°C

to 200°C, but the power output from the metered area of 0.1299 m^ is

limited to 40 W. This limits the temperature difference possible across

the various specimens.

3.2 Plate-Temperature Limits Due to Control Circuitry

The plate temperatures are controlled by the feedback control circuits

shown in figure 2. The amplifier labeled "A" does the fine temperature

control utilizing a thermistor in the plate as the feedback resistor. The

amplifier labeled "B" is used in conjunction with a computer-generated

digital signal to automatically bring the plates to the approximate desired

temperature. The power supply and resistance bank labeled ”C" is used, in

effect, to null the coarse control signal from "C", so that the "A"

amplifier can do the fine control. The current-summed output of these

three components is, in turn, the input to a summing amplifier, "D", the

output of which drives the plate-heater power supplies.

Thermistors are used for the feedback because they have a large resistancetemperature coefficient. The resistance of the plate-installed thermistors

changes by a factor of about 4000 between -50°C and 200®C (Figure 3). This

is an advantage for fine control at a particular temperature, but it

results in difficulties when the operating range is large. If the

thermistor resistance becomes too large, as the plate temperature

decreases, the "A" amplifier will saturate. For the existing circuit

components this occurs below -17°C for the hot and cold plates. It would

be straightforward to change a few circuit components in "A" and "B" by

less than a factor of 2, to control all plates down to temperatures of

-40°C

.

6
At higher temperatures the resistance-temperature coefficient of the

control thermistors decreases, resulting in a larger control band. This

can be compensated by reducing the input resistor value in "A" to increase

the amplifier gain or by changing the thermistors. It would be straightforward to change the cold-plate thermistors, but it would require a major

disassembly of the hot plate to change the hot-plate thermistors.

The control band of the hot plate is very small, 0.001 AT(®C). It could

increase by a factor of 10 to 100, before the control stability would

become a problem. Thus, it should be possible to control the hot plate up

to 100®C with minor circuit changes. The control between 100®C and 200®C

must be tried experimentally to be sure that the control stability is

adequate.

The two guard heaters in the hot plate are controlled by the circuits shown

in figure 4. Two thermistors, one on either side of the gap, are used to

control the inner guard heater, and another two thermistors, located

between the two guard heaters, are used to control the outer guard heater.

These thermistor pairs are used in a Wheatstone bridge to provide an input

to a differential amplifier. This input is a function of the resistance

difference, and hence the temperature difference, between the pair of

thermistors. Since both thermistors remain at the same temperature, there

is no problem with saturation. At temperatures above 100®C it may be

necessary to modify the amplifier to increase the gain as the sensitivity

to temperature change decreases, due to the decreasing resistancetemperature coefficient of the thermistors.

3.3 Ambient Chamber Temperature Control

The ambient chamber temperature control is accomplished with a heat

exchanger, a fan, and a heater. The current low-temperature limit is

determined by the cooling capacity of a single NESLAB PCB-2 cooling unit.

The lowest ambient temperature achieved was 2°C. Another cooling unit

could be added to attain an ambient temperature of -30°C. However, the

instrument used to control the ambient, a Versa-Therm #2155 temperature

controller made by the Cole-Parmer Instrument Company, is capable of

controlling only down to -20®C. This would have to be replaced.

The 500 W power supply for the heater is capable of maintaining the ambient

temperature at 128®C, based on a calculation of heat loss through the

existing ambient chamber walls to an outside temperature of 24®C. A

higher ambient temperature would require a larger power supply. Also the

existing heater and fan would need to be redesigned to ensure a uniform

temperature in all parts of the ambient chamber. A more stringent limit is

that the ambient controller is limited to 120®C. The alternative method

mentioned earlier would be to use an insulated heater jacket at the

specimen edges.

3.4 Thickness Constraints

Physical constraints determine the upper and lower thickness measurements.

The upper limit of 381 mm is the distance the cold plates can move from the

hot plate before the plates physically touch the ambient walls. The lower

limit of 19 mm is the thickness at which the hot-plate support structure

touches the cold-plate insulation. Smaller thicknesses could be achieved

with modification of either the cold-plate insulation or the hot-plate

support structure.

7
3.5 Ambient Gas Pressure

There was no attempt to include a control capability of the ambient

pressure in the original apparatus design. Pressurization control would

require that the ambient chamber be air-tight and that the structure be

strong enough to resist deformation. To satisfy the first requirement, it

would be necessary (1) to provide a feed-through interface for the wires

that enter the chamber and (2) to change the existing door gaskets to an 0-ring design. The capability of the structure to withstand pressurization

was estimated by considering the weakest part of the structure for both

positive and negative pressurization.

The ambient chamber is much stronger for positive pressurization than for

negative pressurization because of the wall cross beams. These beams are on the outside of the walls; thus, they provide structural support to

prevent outward movements of the wall. Referring to figures 5a and 5b, for

each of the walls there are 12 aluminum square beams (26 mm x 26 mm) which

go from the center of the wall to the center of a side or to a comer. For

each of the four doors (two on each side), there are 10 such beams. These

beams provide considerably more support for pressurization than the weakest

part of the structure. The weakest structural parts are the bars which

lock the four doors closed (see Figure 6). The calculation in appendix 2,

made by Dr. William Stone of NBS, estimates that this bar would shear when

the inside pressure is 193 kPa (28 psi or 2 atmospheres) greater than the

outside pressure. These locking bars are on the outside of the structure,

so it would be feasible to add more of these to constrain the doors from

opening

,

The structure is much weaker to support vacuum. Figure 7 shows a crosssection of the walls, which consists of two aluminum sheets, 1 mm thick,

with 76 mm of molded polyurethane (32 kg/m*^) sandwiched between. The

polyurethane was bonded to the aluminum sheets. There is nothing in the

center of the door section (the weakest part) to constrain the wall from

bowing inward under negative pressurization. This sandwich structure will

eventually fail in a delamination shear mode as the bond between the outer

aluminum sheet and the polyurethane breaks. Or, the failure could occur

between successive layers of polyurethane near the outside aluminum sheet.

The calculation in appendix 3, made by Dr, William Stone of NBS, indicates

that this failure would occur for a pressure differential of 14.1 kPa (2.05

psi), or roughly one-seventh of an atmosphere.

A critical uncertainty in this calculation is that there was no

documentation of the adhesive used to bond the polyurethane to the aluminum

sheets. The assumption made was that this bond was at least as strong (in

the delamination shear mode) as the polyurethane itself. Even so, the

calculation shows that the structure could, at best, barely support a pressure of 86 percent of a standard atmosphere, which is greater than the

typical atmospheric pressure (80 percent) in Denver, Colorado,

3.6 Relative Humidity Control

The relative humidity (RH) within the ambient chamber can be controlled in

several ways. The first way takes advantage of the ambient temperature

control system, which consists of condensing coils, a fan, and a heater.

8
This system is capable of reducing the initial relative humidity of the

ambient chamber, 35 percent at 24°C which corresponds to the laboratory

environmental condition, down to 23 percent at 24°C. With this moisture

content, condensation will occur on surfaces within the ambient chamber,

which are at temperatures below 1®C. Thus, there is not any problem with

condensation as long as the cold plates are above 1®C.

In order to operate the cold plates or the ambient chamber at temperatures

below 0®C, it is desirable and sometimes necessary to reduce the moisture

content of the ambient air. This prevents the formation of ice on the

condensing coils, on the internal parts of the ambient chamber, on the

apparatus itself, and within the specimen. One way to reduce the moisture

content in the ambient chamber is to flush the ambient chamber with a gas

such as nitrogen or dry air. Using nitrogen, it was possible to reduce the

relative humidity to 2 percent at 24®C, A drawback is that the ambient

chamber is not very airtight, and thus it would be necessary to use

relatively large amounts of bottled gas to maintain the low relative

humidity condition. Another method to remove moisture from the ambient air

would be to use a desiccant within the chamber.

Moisture can be removed from the specimen, as opposed to the ambient air,

by baking until the specimens come to a constant weight. The specimen will

eventually condition to the humidity condition of the ambient chamber,

unless it is sealed. Currently, there is no humidifying equipment in the

ambient chamber. It would be a simple matter to purchase a humidifier for

the ambient chamber.

4. PARAMETER LIMITS DUE TO APPARATUS UNCERTAINTY CONSIDERATIONS

4.1 Introduction

The following sections discuss the apparatus uncertainty as operating

conditions are varied over their entire ranges. NBS researchers will use

this information to determine the operating limits which correspond to a desired measurement tolerance.

4.2 Lower Limit for Apparent Thermal Conductivity

The question of whether there is a lower limit on k-value is considered

first. The procedure will be to assume the lowest k-value that would be

expected for a GHP specimen, and to calculate the error for this low kvalue. A value of 0.0086 W/m*K is chosen for the lower limit of k-value.

This corresponds to a type of evacuated panel insulation material.

The first contribution to the error for a low k-value specimen is due to

the fact that the metered-area power is considerably smaller than for most

building insulation materials. As a result, any fixed systematic

uncertainty is a larger percentage of this smaller power. Appendix 4,

based on information in reference [5], contains a calculation of the

uncertainty expected for low k-value specimens. It shows that the most

important contribution to uncertainty in the measurement of the meter power

is due to the measurement of the voltage across the metered-area-heater

shunt resistor. For a 152 mm specimen with a temperature difference of

27.8 AT(^C) and for a k-value of 0.0086 W/m’K, the uncertainty due to

the shunt resistor is 0.03 percent. For a 305 mm specimen, the value would

be 0.06 percent and for a 381 mm specimen, the value would be 0.08 percent.

This error is negligible.
The other contribution to uncertainty [5] in the measurement of the

metered-area power is due to the uncertainty in the measurement of power

generated by thermistors located within the hot plate metered area, 0.4 mW,

and the uncertainty due to the measurement of the gap heat flow, 0.3 mW.

For the 152 mm specimen just described, the combined uncertainty of 0.7 mW

results in an uncertainty in power measurement of 0.2 percent. For the 305

mm specimen this is 0.36 percent, and for the 381 mm specimen the value

is 0.46 percent.

Thus there is a combined uncertainty in the measurement of the metered

heater power of approximately 0.5 percent for a worst-case specimen with a thickness of 381 mm and a k-value of 0.0086 W/m*K. For a more typical

thickness of 152 mm and the same k-value, the combined uncertainty in the

metered area power totals to 0.23 percent.

The conclusion is that the NBS 1-m GHP is not practically limited in its

operation with regard to low k-value, due to the heat-flow measurement.

The other factor that could limit the operating range for the NBS apparatus

in terras of low k-value is the edge effect. The edge effect is larger for

lower k-value specimens. One way to see this is to use the parameter

hg/kg, the ratio of the surface film coefficient to the specimen k-value.

The conductance to the edge of the specimen is proportional to the surface

film coefficient, and the conductance across the specimen is proportional

to the k-value. Thus, the larger the ratio of hg to kg, the greater the

edge effect.

The edge effect is defined in equation 1.

^ = (Rq -

The term is the thermal resistance that would result, given onedimensional heat flow across the specimen. It is approximated

experimentally by the sum of thermal resistance values of the components of

a thick stack. These component specimens are measured at small enough

thicknesses so that the edge heat flow is negligible. The term is the

actual measured thermal resistance of a thick stack of specimens which

includes some heat flow to or from the edge of the specimen. Equation 2

defines the A and B coefficients, shown in figures 8 and 9, and these

coefficients indicate the magnitude of the edge effect [3].

Y = A + B X (2)

The X term is a dimensionless temperature term which indicates the

unbalance, or difference, between the specimen mean temperature, T^^^, and

the ambient temperature, T^.

X = Tg)/(Tj^ - Tg) (3)

Tjj and T^ are the hot-plate and cold-plate temperatures. The T^j^ is

approximated experimentally as the average of Tj^ and T^.. As the ambient

temperature is varied above and below the mean temperature, the edge heat

flow changes, and the amount of this change is predicted by the magnitude

of the coefficients A and B in figures 8 and 9.

10
These figures are for the case of the NBS l-m GHP which has a metered-area

radius of 0.20326 m [4] and a guard radius of 0.508 m. Assuming there is

extra edge insulation around the specimen, a typical value of h is 0.57

W/K’m^, and a typical value for k is 0.03 W/m’K; these give a value of

18.9 m“^ for h/k. Figures 8 and 9 show the A and B coefficients as a function of h/k for values on either side of this typical value.

Inspection of the equations associated with the curves in these figures

shows that as the k-value decreases, the A and B curves asymptotically

approach a particular curve. The value of h/k that corresponds to the low

k-value of 0.0086 W/m*K is 66.3 m” . The figures show that the greater

value of h/k does not significantly change the thickness at which the edge

effect exceeds a particular tolerance level. This greater value of h/k does

result in an edge effect that is perhaps 30 percent larger, but, again,

this does not significantly change the maximum thickness for the apparatus.

To estimate the uncertainty in measured thermal resistance due to edge

effect, one must include the contributions of both the A and B terms.

As a working hypothesis, assume that A is predicted by the edge model

within +,25 percent of its value. To determine the B contribution, assume

a value of 0.036 for AX, which corresponds to (T^ - T^) = 27.8 AT(°C) and an uncertainty of 1 AT(°C) in (T^^^ - T^).

Assume an edge insulation resistance value, Rg(j» of 1.75 K* m /W. For

these parameter values, the contributions to uncertainty of the A and B

terms are shown in figure 10, and the sum of these is shown in figure 11.

These are shown for a range of specimen apparent thermal conductivity

values, kg, between 0.0577 and 0.00045 W/m*K,

Appendix 5 shows how the range of operation is affected by a lower k-value

assuming an edge error tolerance of 0.5 percent. A typical k-value of 0.033

W/m*K results in an upper limit on operating thickness of 350 mm, whereas a k-value of 0.0086 W/m*K results in an upper limit on thickness of 320 mm. This demonstrates that operation at a significantly lower value of apparent

thermal conductivity does not significantly change the thickness range of

the apparatus.

4.3 Upper Limit for Apparent Thermal Conductivity

The first factor that determines the upper limit in thermal conductivity

value is the line-source heater design used in the metered area of the hot

plate. This design and the corresponding temperature distribution over the

metered area are described in references [3] and [5]. Part of the

rationale for using this kind of heater is that, if the ratio of the gap

radius to the line-heater radius is equal to \/2^ the temperature measured

in the gap is approximately equal to the average temperature of the entire

metered area. Reference [3] performs the calculation of the error

associated with this approximation. This error is less than 0.01 percent

for the following condition:

/ m kg \ 1/2

V

2 " "P /

(4)

where m and L are the hot-plate and specimen thicknesses, and k are the specimen and the plate k-values. For the NBS apparatus,

s ^p

the term

11
on the left side of equation (4) is equal to 0.03, at specimen thickness

of 25 mm, when the specimen thermal conductivity is equal to 0.15 W/m*K.

Figure 12 from reference [3] shows that if kg were greater than 0.4 W/m’K,

the temperature error will be of the order of 0.1 percent. Above a value

of 0.6 W/m*K the error in the hot plate temperature exceeds 0.1 percent,

and the correction based on the use of more terms in the Bessel function

expansion would have to be made. The equation describing this correction

is given in reference [3], and such a correction would not require any

apparatus modification.

There is no restriction on k-value due to edge effect considerations, since

the edge effect becomes smaller as the k-value increases. The two factors

that are more important in practice, for restricting the thermal

conductivity of specimens, are the difficulty of obtaining large specimens

of high k-value material and the problem of contact resistance between the

specimen and the apparatus plate surface. The first problem is one of cost

and of difficulty of specimen fabrication. Typically, testing of specimens

with k-values above 1 W/m*K is performed on much smaller apparatuses. This

is acceptable because the higher-conductivity specimens are generally

much more uniform, and a smaller specimen can be representative of the

material. Also, the requirements of guarding are not as stringent because

the preferred path of heat flow is through the high conductivity specimen

itself

.

The second problem with high-k measurements is due to contact resistance

between the specimen and the apparatus plates. This extra thermal

resistance can lead to systematic errors in the measurement of the specimen

thermal resistance. Even if the plate temperature is known very

accurately, it is necessary to know the temperature of the specimen surface

in order to calculate the specimen thermal resistance. One way to

determine the actual specimen surface temperature is to place an appropriate number of thermocouples on the specimen surface. The personal

communication given in reference [7] indicated that such a procedure is

followed as a matter of course for specimens that have a thermal

conductivity greater than 0.1 W/m*K. To estimate the error that could

result if contact resistance were not taken into account, consider the

example of a 25.4 mm thick specimen with a thermal conductivity of

0,14 W/m’K which has an air gap on either side each with an average

thickness of 25.4 microns. The thermal resistance of this air gap can be

calculated by the expression R = ignoring thermal bridging

considerations and noting that any radiation contribution to the thermal

resistance for this order of magnitude of thickness is negligible (see

Appendix 6), The L term is the thickness of the air gap, 51 microns, and

k^ is the gas conductivity of air. Note that the convective heat transfer

mode is not operative for thicknesses of this small order of magnitude.

The R-value of this air gap is 2,0 x 10”^ K*m^/W, as compared with the Rvalue of the specimen itself, which is approximately 0.181 K*m^/W, Thus,

the contact resistance is approximately 1 percent of the specimen

resistance itself, in this example. The error could be of the same order of

magnitude if contact resistance were ignored.

Table 1 shows the error in thermal resistance, due to contact resistance,

as a function of specimen thermal conductivity. This table assumes an air

gap of 51 microns and a specimen thickness of 25.4 mm, and it demonstrates

that contact resistance quickly becomes a significant source of uncertainty

as the specimen k-value increases. The experimental problem is that the

12
actual contact resistance will depend on the distribution of the air gap

over the metered area; and this distribution is practically impossible to

measure. Calculation of the effective contact resistance would take into

account thermal bridging, since the contact resistance would vary over the

metered area. The calculation would also depend on the temperature

boundary conditions at the plate and specimen surfaces. Such a theoretical

approach would be impractical, if not impossible.

An empirical approach is recommended, using thermocouples or thermopiles to

measure the average temperature of the specimen surface. The number of

thermocouples required to measure this average will depend on statistical

criteria necessary to assure that the uncertainty in this average value is

within a pre-selected tolerance.

4.4 Thickness Limit

The most significant factor limiting the specimen thickness is the edge

effect, which is nonneg 1 igib le at thicknesses above 229 mm for the NBS

apparatus. A recent study of the edge effect indicated uncertainties of

0.5 percent at 283 mm, 1.0 percent at 345 mm, and 1.5 percent at 381 mm. Appendix 5 shows how these uncertainties were derived. These values depend

on the amount of change in the measured k-value as the ambient temperature

changes, and on the uncertainty in this ambient temperature. In this

estimate, the uncertainty in ambient temperature was 1®C. Thus, if the

other contributions to uncertainty were 0.5 percent and the tolerable

total uncertainty were 1 percent, then the apparatus would be limited to

measurements below the 285 mm.

Figures 8 and 9 show that if the ambient temperature cannot be controlled

at the specimen mean temperature, the edge effect increases considerably.

That is, the value of X is proportional to the difference between the

ambient temperature and the specimen mean temperature. If the slope, B,

were determined empirically, it would be possible to make an adjustment of

the measured thermal resistance value to the "true" value, corresponding to

X = 0. The uncertainty of such an adjustment would depend on the

uncertainty in the curve as well as the uncertainty in the value of X,

which in turn depends upon the uncertainty in the value of the ambient

temperature. Note that the specimen mean temperature will usually be

known much more accurately than the ambient temperature.

There is another possible source of error in thickness, when the mean

temperature is above or below 24°C. To understand this possibility, it is

necessary to examine the method of measuring and calibrating the specimen

thickness. The thickness measurement is described in detail in reference

[5]. Briefly, eight Farrand (produced by Farrand Industries, Inc.)

thickness transducers, four for each cold plate, give an average value for

the spacing between the hot plate and the two cold plates. The spatial

reference points for these Farrand transducers are mounted on invar rods

to minimize any change in position of these reference points. The average

spacing between the plates over the metered area is determined by a mapping

of the thickness using an in-situ thickness transducer; and this in-situ

measurement is used to calibrate the eight Farrand thickness transducers.

As long as there is no bowing or warping deformation of the plate, any

change in thickness due to thermal expansion of the plates or the plate

support system is indicated by the eight Farrand thickness transducers. As

long as the plate spacings are calibrated at the same temperature

13
conditions at which the specimen is measured, this plate deformation

contribution to the error will be less than 51 microns, or 2 mils*.

Measurement difficulties arise at lower and higher temperatures (than

24°C). It is not practical to calibrate the plate spacings (1) at low

temperatures, because of ice formation in the interior of the ambient

chamber and (2) at high temperatures, because of safety considerations and

the difficulty of maintaining these high temperatures when the ambient

chamber is open and the plates are exposed to the room temperature. A

study was performed to measure the difference between (1) the thickness

indicated by an in situ thickness transducer, located between the plates at

their centers, and (2) the thickness indicated by the Farrand thickness

transducers — as the mean temperature was varied between 0°C and 57®C.

One would expect the plate spacings to change due to thermal expansion of

the plate structure; the purpose of the study was to see if the change

indicated by the Farrand thickness transducers corresponded to the change

indicated by the in-situ thickness transducers.

Table 2 and figure 13 show the results of this study; the reference point,

at which DD = 0, is at the mean temperature of 24°C. The DT term refers

to the change in thickness as the mean temperature changes, as measured by

the in-situ thickness transducer. The DF term refers to the change in

thickness with the same change in mean temperature, as measured by the

Farrand thickness transducers. The subscripts t and b refer to the top

side and the bottom side of the two-sided apparatus. The DD term refers to

the difference between DT and DF. This DD is a measure of the error in

thickness that would result if plate deformation were ignored.

The points in figure 13 were taken in three sets. The slope of the average

line is 0.22 mils/K, and the scatter of the points about the average line

is ~ 1 mil. The difference between the two thickness readouts is systematic

and repeatable. The in-situ detector is more reliable, because it is

possible to calibrate it over the entire temperature range. The effective

coefficient of thermal expansion of this aluminum in-situ detector was

empirically determined, and the measured value agreed with the handbook

value of 25 x 10“^ m/m*K, within 1 percent. This coefficient was used to

correct the in situ readings for thermal expansion.

The curve in figure 13 can be used to correct the readings of the Farrand

thickness transducers. It should be possible to have a 20 percent

confidence in the slope of this line with further repeats. For a 25.4 mm

thick specimen, a thickness error of 1 mil corresponds to a percentage

error of 0.1 percent. Thus, an error of ~ 1.0 percent would result over

the temperature range indicated in the figure, if the plate deformation

were not taken into account.

* The units of mils, or milli-inches are used since the size of the

measured effect is ~1 mil. The metric values can be obtained by noting

that there are 25.4 microns in a mil.

14
4.5 Temperature Limits

The three platinum resistance thermometers (pete's) which measure the plate

temperatures are capable of a temperature range from ”269°C to 220°C.

These were calibrated at NBS over a temperature range of 0®C to 50°C, with

a calibration bath uncertainty of 0.005 AT(®C). Before NBS 1-m GHP data

for temperature points outside this calibrated range can be published, it

will be necessary to calibrate the plate PRT's over the wider range of - 40®C to 200°C. This would be easy for the two cold-plate PRT's because

they are easily removed. It would require about a man-month of highly

skilled technical labor for the hot-plate PRT, because the hot plate would

have to be disassembled. A preferable and a feasible procedure would be

to use the two cold-plate PRT"s to perform an in-situ calibration of the

hot-plate PRT.

The PRT manufacturer was contacted to obtain an order of magnitude for the

uncertainty that would pertain if the PRT"s would be used outside the

calibrated range from 0®C to 50®C [91. The manufacturer's estimate was

that the extrapolation uncertainty would increase linearly from zero at

50°C to ~0.250®C at 200°C, and the same slope could be used to estimate

the uncertainty between 0®C and -50°C. For a temperature difference of 28

AT(°C), this method of estimation results in an additional uncertainty in

kg of 0.35 percent at T = -30®C, 0.55 percent at 120®C, and 1.55 percent

at 180°C.

Reference [5] discusses other contributions to the uncertainty of the

average temperature over the surface of the metered area of the plates. An

amount equal to 0.002 AT(°C) was due to uncertainties in the measurement of

the PRT resistance. The largest amount, 0.015 ,ilT(®C), was due to the

difficulty in ascertaining by an independent in situ measurement that the

surface temperature is constant over the metered area. This is important

because the PRT measures the temperature in one location, and the accuracy

with which this value at one location represents the average over the

entire metered area must be considered. Neither of these two contributions

will change when the temperature range is extended from -50°C to 200®C.

4.6 Apparatus Uncertainty as a Function of kg and T^j^

Table 3 from reference [5] shows a summary of apparatus uncertainties as a function of specimen thickness, L, for the case of compressible specimens

at a mean specimen temperature of 24°C and a plate temperature difference

of 27.8®C. This table will serve as the basis for the estimate of

uncertainties as the specimen apparent thermal conductivity, kg, and the

specimen mean temperature, T^^, are varied over the following ranges;

kc = 0.0086 to 0.30 W/m*K o \ = -30 to 180°C

The total uncertainties are shown in tables 4 to 7 for L-values of 25.4,

152.4, 304.8, and 381 mm. The additional uncertainty contributions (to

Table 3) are due to contact resistance (see Section 4.3, Appendix 5, and

Table 1), the thickness calibration uncertainty as the temperature varies

away from 24°C (see Section 4.4 and Figure 11), the temperature

extrapolation error as the sensor temperature varies from the calibrated

range of 0°C to 50®C (see Section 4.5), and the edge effect (see Sections

15
4.2 and 4.4, Appendix 4, and Figure 10). The effects of these four factors

on the numbers in tables 4 to 7 will be discussed next.

The first factor, the contact-resistance estimate> is the same for all

temperatures and was based on an assumption for the specimen-plate air gap

which is reasonable but which would be difficult to verify. It also

applies only to rigid specimens. That is, this factor would not apply for

specimens of compressible material such as low-density, glass-fiber

material. Assuming the specimens are not compressible, it is a significant

term, even for typical insulation materials, "0.3 percent, for L = 25.4 mm,

but it is not significant at greater thicknesses because it is inversely

proportional to the thickness. This term could be largely eliminated if

the specimen surface temperature were independently measured. In this

case, the specimen thickness would also have to be measured independently.

The second factor is due to plate deformation as the ambient and plate

temperatures vary above and below 24®C. This error estimate is based on the

rather conservative estimate that the slope of the curve in figure 13 is

known only to within i50 percent. It is quite significant at L = 25.4 mm,

having values of 0.5 percent at T^ = -30°C and 0.9 percent at T^ = 120°C.

It too varies inversely with thickness, and is not as significant at large

thicknesses

.

The third factor is the estimate of extrapolation uncertainty due to the

fact that the PRT's were calibrated only between 0°C and 50°C. This term

can be as large as 0.5 percent, but it can be eliminated with further

calibration.

The fourth factor is due to the edge effect. It is significant only for

thicknesses above 200 mm, and it is slightly more significant for lower

values of k_.

In summary, tables 4 to 7 can be used to determine the current limits on

operating values for thickness, temperature, and thermal conductivity that

correspond to a given tolerance. For example, if this tolerance were +.1 percent, one would determine the acceptable range of kg by noting the range

of values of T^^^ and L for which the table values are less than or equal to

1 percent.

5. APPARENT THERMAL CONDUCTIVITY DATA OVER THE

CURRENT OPERATING TEMPERATURE RANGE

Figures 14 and 15 show the ranges of apparent thermal conductivity and

specimen mean temperature over which the NBS 1-m GHP has been operated; and

tables 8 and 9 contain the data used in these figures. The plate

temperature difference was -27.8 AT(®C). Figure 15 shows a smaller kg

range for typical insulation materials, while figure 14 shows a wider kg

range. One indication of the measurement uncertainties at temperature

extremes is the agreement between the data points and a curve that has been

shown to be typical of a particular material. For example, for the glassfiber material of density equal to 114 kg/m^, a straight line should fit

the data within better than 0.1 percent between 0®C and 40®C [10]. Thus

the variation of -1 percent about a straight-line fit for the high-density

glass-fiber material is an indication of the consistency of the data.

16
It is possible, however, that an error in slope could exist, such as that

described in section 4.4 and shown in figure 13. Such a systematic error

would not show up on a kg vs T plot, and must be discovered by independent

investigation of any systematic errors that might exist in the parameters

that determine the calculated value of kg.

Another feature of interest is that the polyisocyanurate data do not fit a straight line when a portion of the specimen is below 0°C. This is

probably because condensation of the fluorocarbon gas on the insulation

cell walls results in a higher gas conductivity within the cells that make

up this material. Also, at these lower temperatures the measured kg-value

was not as repeatable as at higher temperatures, presumably because the

amount of condensation of the fluorcarbon gas depends on the past

temperature history of the specimens [1].

The data for the Min-K material fits a quadratic expression within +.1 percent over the temperature range 0°C to 55®C. The NBS measured value of

0.0254 W/m*K at 24°C is between the two values quoted in a recent report

[2l, 0.020 and 0.030 W/m*K, and it is within 4 percent of the value of

0.0262 W/m*K quoted in reference [1]. Since the kg-value of Min-K varies

with atmospheric pressure, this parameter is included in table 9.

Figure 16 and table 10 show the variation in measured k-value as the

specimen thickness increases. The data for specimen A is based on curve

fits of data for a low-density, glass-fiber material. The k-value was

plotted versus specimen density for a number of specimens [11], and the

values in the figure represent the average curve value for a density of 9.6

kg/m"^ at three thicknesses. This data confirmed the thickness effect in

this material. Specimen B was a glass-fiber material of density equal to

19.2 kg/m"^. No thickness effect is expected at this high density, and the

scatter represents the variability from specimen to specimen — as four

25.4 mm specimens were stacked to greater thicknesses.

Specimen C consisted of stacks of extruded polystyrene specimens, each of a thickness approximately equal to 51 mm. If a constant value is used to fit

this **kg vs L" data up to the maximum thickness, the standard deviation is

0.4 percent. Part of this value is due to the variation in the k-value of

the layers of the stacked specimen. To remove this contribution to the

scatter, the individual layers were measured. Table 11 presents data of

the percent difference between the average k-value of the individual layers

in a stacked specimen and the actually measured k-value of the stacked

specimen. This percent difference is an indication of the uncertainty in

the measured k-value as a function of thickness. For thicknesses below 154

mm the average values are within 0.3 percent of the measured values; for

larger thicknesses (205 to 381 mm), the comparison was within 0.6 percent.

6. SUMMARY OF PARAMETER LIMITS AND ESTIMATES OF COSTS OF IMPROVEMENTS

6.1 Temperature Limits

The temperature limits are given in figure 17. A solid line indicates the

current range for a particular factor; a dotted line indicates a possible

extension of the range. The following discussion proceeds from the most

restrictive to the least restrictive factor. Methods to increase the range

are mentioned, along with an estimate of implementation costs. These costs

17
are categorized

the estimate is

Cold Plate

Low limit

Next low limit

Next low limit

High limit

Next high limit

Next high limit

Next high limit

Next high limit

Next high limit

Hot Plate

Low limit

Next low limit

High limit

as "low" when the estimate is less than $1K, "medium" when

between $1K and $10K, and "high" if greater than $10K.

= -17°C Due to amplifier saturation in the plate

temperature-control circuits. This circuit

could be easily upgraded at a low cost by

changing circuit components.

= -30°C Due to the cold-plate bath cooling capacity. A

replacement bath that would achieve -50°C

could be purchased at a low cost.

= -40°C Due to the epoxy used to construct the cold

plate. This is not extendable.

= 50°C Due to 1 imited capacity of the cold-plate

heater power supply to oppose the existing

cooling unit. This is extendable with the

purchase of a power supply at a low cost.

= 85®C Due to the cold-plate insulation. This could

be easily replaced at a medium cost.

= 100°C Due to a possible loss of sensitivity in the

plate-temperature control circuits. This is

because of low values of the temperatureresistance coefficient of the plate

thermistors. This circuit could be upgraded at

a medium cost by changing circuit components.

= 110°C Due to the circulating pump in the cold-plate

bath. This could be replaced at a medium cost.

= 120°C Due to the PRT-wire epoxy. This could be

easily replaced at a low cost.

= 180°C Due to the epoxy used to construct the cold

plates. This is not extendable.

= -17°C Due to amplifier saturation in the plate

temperature-control circuits. This circuit

could be upgraded at a low cost by changing

circuit components.

= -48°C Due to the epoxy used to keep thermocouples and

heater leads in place. This is not extendable.

= 100®C Due to a possible loss of sensitivity in the

plate-temperature control circuits.* This

results from the low values of the temperatureresistance coefficient of the plate

thermistors. This circuit could be upgraded at

18
a medium cost by changing circuit components

and testing the performance.

Next high limit = 170°C Due to Teflon tubing around the thermistor,

PRT, and thermistor wires. This could be

easily replaced at a low cost.

Next high limit = 200°C Due to the hot-plate epoxy. This is not

extendable.

Ambient Temperature

Low limit = 2®C Due to the cooling capacity of the cold bath.

A low-cost purchase of another bath would

extend the limit to -30®C.

Next low limit = -20®C Due to the ambient temperature controller.

This could be easily replaced at a medium cost.

High limit = 90®C Due to the polyurethane in the ambient chamber

walls. This could be extended at a medium cost

to 120®C (the high-temperature limit of the

ambient controller), with extra insulation

inside the ambient chamber. To extend to

190®C, an insulated heater jacket would have to

be designed, constructed, and tested — at a high cost.

6.2 Other Apparatus Limits

Thickness

Low limit = 19 mm

High limit = 381 mm

Thermal Resistance and Apparent Thermal Conductivity

The discussion in chapter 4 concluded that any practical insulation

specimen could be tested in the apparatus. In this sense, there are no

limits on these parameters.

AmbiPTit Gas Pressure

There is no current control capability of the ambient gas pressure. At a very high cost, it might be possible to achieve a low limit of 80 percent

of 1 atmosphere and high limit of 3 atmospheres.

19
Relative Humidity

Lov limit = 23 percent at 24°C

Next low limit = 2 percent at 24°C

High limit = 35 percent at 24®C

Using the existing condensing coils.

Using nitrogen or dry air.

Due to the existing RH control in

the laboratory room. This could be

increased to a higher value with a low-cost humidifier.

20
REFERENCES

1. ASTM Subcommittee C16.30, "Reference Materials for Insulation

Measurement Comparisons," Thermal Transmission Measurements of

Insulation, ASTM STP 660, R. P. Tye, Ed,, American Society for Testing

and Materials, 1978, pp, 7-29.

2. Rennex, B. G,, "An Assessment of Needs for New Thermal Reference

Materials," National Bureau of Standards Interagency Report NBSIR 82-

2538 (Washington, D.C., NBS, 1985).

3. Hahn, M. H., Robinson, H. E., and Flynn, D. R., "Robinson Line-HeatSource Guarded-Hot-Plate Apparatus," Heat Transmission Measurements in

Thermal Insulations, ASTM STP 544, American Society for Testing and

Materials, 1974, pp. 167-192.

4. Rennex, B, G. and Powell, F. J,, "The NBS Line-Heat-Source Guarded Hot

Plate for Thick Materials," ASHRAE SP38, Thermal Performance of the

Exterior Envelopes of Buildings - II, 657-672, (1983)

5. Rennex, B, G., "Error Analysis for the NBS 1016 mm Guarded Hot Plate,"

Journal of Thermal Insulation, Vol. 7, pp. 18-51 (July 1982).

6. 1984 Annual Book of ASTM Standards . Vol 04,06, ANSI/ASTM C 177-76,

"Standard Test Method for STEADY-STATE THERMAL TRANSMISSION PROPERTIES

BY MEANS OF THE GUARDED HOT PLATE," American Society for Testing and

Materials, 1916 Race Street, Philadelphia, PA 19103, pp, 20-53.

7. Personal communication from Andre Desjarlais of Dynatech R&D

Corporation - Their policy, when measuring thermal resistance of

higher k-value specimens, to minimize errors due to contact resistance

is to place thermocouples on the specimen surfaces for k-values

greater than 0.10 W/m*K, 1985.

8. Rennex, B. G. , "Thermal Parameters as a Function of Thickness in LowDensity Insulation," Journal of Thermal Insulation, Vol. 3, pp. 37-61

(July 1985).

9. Personal communication from Dana Schurr of MINCO Products, Inc.,

Minneapolis, Minnesota, 1985.

10. Siu, M, C. I,, J, G, Hust, National Bureau of Standards, Certificate

of Standard Reference Material 1450b, Thermal Resistance - Fibrous

Glass Board, May 21, 1982,

11. Rennex, B. G., "Low-Density Thermal Insulation Calibrated Transfer

Samples — a Description and a Discussion of the Material

Variability," National Bureau of Standards Interagency Report NBSIR

82-2538 (Washington, DC, NBS, 1982).

21
Figure 1 - Drawing of the NBS 1016 ram Guarded Hot Plate Showing

the Support System of the Hot and Cold Plates and

Showing the Rotatable Enclosure for Environmental

Control,

22
J I

Figure 2 Temperature Control Circuit for the

NBS 1-m Guarded Hot Plate Apparatus.

23
RESISTANCE

RATIO

“50 0 50 100 150 200 250 300

TEMPERATURE °C

Figure 3 - Resistance-Temperature Characteristics for

Temperature Control Thermistors

24
+6.2V

Figure A - Control Circuit for the Guard Heaters

for the NBS 1-m Guarded Hot Plate.

25
Figure 5 - View of the NBS 1-m Guarded Hot Plate Apparatus

walls and doors.

26
Figure 6 - Latch of the NBS 1-tn Guarded Hot Plate

Apparatus Door-Lock Bar,

27
Altimimnn

1

1 mm

76 mm

1 ram 1

Figure 7 - Cross Section of the NBS 1-m Guarded Hot Plate

Apparatus Walls.

28
600*0 oo<3-

J

C

A

y

W E m •H

0)u c y

c.

(j

y CP u

x: c y H y X =13 4J o C c m 0) y )-< fO E C- y

“H

y > O o o

(Uc- iH

t/D C5

y

O

X “H o y 9i J-l 43 c 0) c o E y

"H TO •H o w y o o y TO T-l m c P- U-i 3 <43 Oi y

x: o

(0u

u

w 6C E

CC

C 1—1 •H 1-1 3 fc. < c £ X y

uz

y

TO

O c 0i <43 • m i <v y CO CM E *H 4-1 3 X u TO CP "H «i 3 Vi-j P. y >s

U-i 1 > 4-1 y 4-1 •H *H o o 4-J > u a: y iH 1 y 4-1 4J ’V ctJ y U y <43 3

ID T3 C3 Tj

U-J

u c o u- TO y 0 o w 3 X u CN 1 4-1 <U f-H GC E <43 TO -o 1 o E

bJ

y o y

dJ •H

X

JZ P3y

H

u z TO Pi

y

U-i 0) c o X y y

4J

X

y o 4.) y TO m o u> D. 1^ o c a

p- >4-1

O < I GO

(Uu3

GC •H

Pu oo <

29
CM o 00 VC CM o 00 VO '3' CM

es CN pH o o O o • • • • • • • • • • • O o o C o O o o o o o oo

<ro

lO

cnoo

fnom

csi ooCNomoc

tc

30

Figure 9-

Plot

of

the

Edge-Effect

Coefficient

*'B"

asa

Function

of

Specimen

Thickness,

L,

for

the

NBS

1-m

Guarded-Hot-Plate,

Showing

the

Parametrical

Dependence

on

the

Ratio

of

the

Effective

Surface

Film

Coefficient, h,

over

the

Specimen

Apparent

Thermal

Conductivity, k, ^
=

57

W/m oo<•

31

Figure

10-

The

Edge-Effect

Percent

Uncertainty,

Due

to

the A

Coefficient

(0»25A)

and

the B

Coefficient

(BAX,

where

AX=

0,036),

asa

Function

of

Specimen

Thickness,

L,

for

the

NBS

1-m

Guarded-Hot-Plate.
(%) X3UTB3aaoun 3uaoaaa aoajgs-aSpa

32

Figure

11

-

The

Total

Edge-Effect

Percent

Uncertainty,

0.25A +

0.036B,

as

a

Function

of

Thickness,

L,

for

the

NBS

1-m

Guarded-Hot-Plate

,
Figure 12 - Percentage difference between temperature at edge of

metering section and the average temperature over the

metering section area as a function of specimen thermal

conductivity for the following parameters: b/a ^\/2

2b/m ” 16, and, e/m = 0,5,

33
6

5

4

3

2

1

0

•1

•2

3

4

5

•6

60

Figure 13 - Correction Term, DD, for the NBS GuardedHot-Plate Thickness Readout Based on an In-Situ Measurement.

34
Apparent

Thermal

Conductivity

(W/m*K)

0.14

0.12

0.10

0.08

0.06

0.04

0.02

Polyisocyanurate

(40 kg/m^)

0 I I 1 I L

-10 0 10 20 30 40

Specimen Mean Temperature ( C)

Figure 14 - Apparent Thermal Conductivity versus Specimen

Mean Temperature Points Showing the Ranges

Measured on the NBS 1-m Guarded Hot Plate.

35
0.05 sro

o

fn CN O o • • o o

m

LH

o

m

in

-ao>3-

m

cn

o

cn

m

evi

O

CN

in

in

o

in

I

o

I

CJ o

o

Vi3

u

COV4

0)a

B

(Uc

CO<u S

c

(Ueu

(Ua

w

()i,®/W) i^3TAT:ionpuo3 3ueaBddv

36

Figure

15

-

Apparent

Thermal

Conductivity

versus

Specimen

Mean

Temperature

for

Insulation

Materials,
Apparent

Thermal

Conductivity

(W/m*K)

L (in)

0 2 4 6 8 10 12 14 16

Figure 16 - Apparent Thermal Conductivity versus Specimen

Thickness, L, for Insulation Materials.

37

o

Apparent

Thermal

Conductivity

Btu-ln/(ft

-hr-°F)
100 -50 0 50 100 150 200

1 1 1 1

Polyurethane Insulation in VJalls

1 1 1

”T—

1

1 1

1

Ambient Temp. Controller

1 1

1

1

Cold Bath

1 1

1 1

Teflon Tubing

_|

L.

H.P. Epoxy

1

1

H.P. Circuits

- 1 1

1

1 1

PRT-wire Epoxy

1

—

j

1

C.P. Insulation

1

1

C.P. Epoxy

1

h

C.P, Bath

1 -1 -

1

1 -]

C.P. Circuit

1 1

1

1 1

1 1 1 1 1

100 -50 0 50 100 150 200

AMBIENT

TEMPERATURE

HOT

PLATE

COLD

PLATES

TEMPERATURE ( C)

Figure 17 - Temperature Limits for the NBS 1-m GuardedHot-Plate Apparatus,

38
TABLE 1 - Relative Magnitudes of Contact Resistance, r, and the Thermal

Resistance of a 25.4 mm Thick Specimen for a Range of Specimen

k-value

.

k-value (W/m*K) R-value (m^’K/W) Percent

0,02 1.27 0.153$

0.04 0.635 0,306$

0.06 0.423 0.459$

0.08 0.318 0.610$

0.10 0.254 0.764$

0.12 0.212 0.915$

0.14 0.181 1.072$

0.16 0.159 1 .220$

0.18 0.141 1.376$

0.20 0.127 1 .528$

0.22 0.116 1 .672$

0.24 0.106 1 .830$

0.26 0.0977 1.986$

0.28 0.0907 2.139$

0.30 0.0847 2.290$

39
Table 2 - Difference Between NBS 1-m GHP Thickness

Readout and In Situ Thickness Readout.

OB T

(°C)

DF^

(mils)

DT^

(mils)

DDt

(mils)

DFb

(mils) (mils)

DDb

(mils)

Average

(mils)

23.899 27.714

38.007 30.611 -4.9 -8.2 -3.3 -12.8 -13.5 -0.7 -2.0

56.976 31.133 -12.8 -18.7 -5.9 -19.0 -25.7 -6.7 -6.3

0.101 28.333 8.6 12.1 3.5 20.8 28.0 7.2 5.4

26.698 27.532

15.148 30.099 5.7 7.7 2.0 8.1 12 3.9 2.95

37.954 28.031 -3.3 -4.7 -1.4 -7.7 -11.1 -3.4 -2.4

50.183 27.260 -8.1 -11.8 -3.7 -17.4 -23.7 -6.3 -5.0

26.492 27.988

5.087 28.173 9.5 12.6 3.1 21.8 26.6 4.8 3.95

15.194 30.686 2.5 2.7 0.2 11.5 15.7 4.2 2.2

38.125 27.623 -5.8 -8.1 -2.3 -5.1 -8.7 -3.6 -2.95

51.169 25.733 -9.5 -14.8 -5.3 -12.3 -19.2 -6.9 -6.1

DF^ = F^.(T) - F^(24°C)

DT^ = T^(T) - T|.(24°C)

DDt = DTt - DFt

The same for the bottom side of the two-sided apparatus, indicated by the

subscript b.

40
Table 3 . Percentage Estimate of Uncertainties in the Measured Apparent

Thermal Conductivity for the NBS Guarded Hot Plate*

Quantitative

Thickness

Value 25 mm

(1 inch)

75 mm

(3 Inches)

150 mm

(6 inches)

300 mm

(12 inches)

Percent Uncertainty

Area

(12 ym or 0.5 mil

in radius

0.01 0.01 0.01 0.01

Thickness

(25 ym or 1.0 mil)

0.1 0,03 0.02 0.01

Meter Power 0,04 0,04 0.04 0.04

Meter Resistive

Device (0.4 mW)

0,00 0.01 0.02 0.04

Gap Heat Flow

(0.3 mW, or 0,5 yV

in gap voltage)

0.00 0.01 0.02 0.03

Edge Heat Flow 0,00 0.00 0.00 0.50

Hot , cold-plate

Temperature

Difference (44 mR)

0.16 0.16 0,16 0.16

TOTAL 0.31 0.26 0.27 0.79

* These values are for compressible, low-density, glass-fiber insulation

measured in the two-sided mode with a plate temperature difference of

28 K. Uncertainty values of less than 0*01 percent are reported as zero.

41
n Table 4 - Total Apparatus Uncertainty for a Specimen Thickness,

L, of 25.4 mm, as a Function of Specimen Mean Temperature,

^s

and Specimen Apparent Thermal Conductivity

Mean Temperature

, kg.

(W/m-C) -30°C 0°C 24°C 50°C 120°C 180°C

0.0086 1 .23 0.68 0.38 0.78 2.81 3.62

0.024 1 .34 0.79 0.49 0.89 2.14 2.93

0.033 1 .41 0.86 0.56 0.96 2.21 3.00

0.046 1.51 0.96 0.66 1.06 2.31 3.10

0.15 2.30 1.75 1 .45 1.85 3.10 3.89

0.30 3.45 2.90 2.60 3.00 4.25 5.04

This is for a temperature difference across the specimen of

27.8®C and for two-sided operation of the NBS 1-m Guarded

Hot Plate.

42
Table 5 - Total Apparatus Uncertainty for a Specimen Thickness,

L, of 152.4 mm, as a Function of Specimen Mean Temperature,

Tjjj, and Specimen Apparent Thermal Conductivity, kg.

kg Mean Temperature

(W/m-C) -30°C 0°C 24°C 50°C 120°C 180®C

0.0086 0.71 0.41 0.28 0.33 0.98 2.08

0.024 0.73 0.43 0.30 0.35 1 .00 2.10

0.033 0.74 0.44 0.31 0,36 1.01 2.11

0.046 0.76 0.46 0.33 0.38 1.03 2.13

0.15 0.89 0.59 0.46 0.51 1.16 2.26

This is for a temperature difference across the specimen of

27.8°C and for two-sided operation of the NBS 1-m Guarded

Hot Plate.

43
Table 6 - Total Apparatus Uncertainty* for a Specimen Thickness,

L, of 304.8mm, as a Function of Specimen Mean Temperature,

Tjjj, and Specimen Apparent Thermal Conductivity, kg.

k^ Mean Temperature

s (W/m*C) -30°C 0°C 24°C 50°C 120°C 180°C

0.0086 1 .07 0.79 0.68 0.71 1.31 2.36

0.024 0.97 0.69 0.58 0.61 1.21 2.26

0.033 0.92 0.64 0.53 0.56 1 .16 2.21

0.046 0.89 0.61 0.50 0.53 1.13 2.18

This is for a temperature difference across the specimen of

2?.8°C and for two-sided operation of the NBS 1-m Guarded

Hot Plate.

44
Table 7 - Total Apparatus Uncertainty for a Specimen Thickness,

L,of 381 mm, as a Function of Specimen Mean Temperature,

Tjjj, and Specimen Apparent Thermal Conductivity,

k„ Mean Temperature

% r\ ^ (W/m-K) -30°C 0°C 24°C 50°C 120°C 00 00

0

0.0086 1.55 1 .28 1,17 1 .20 1.78 2,82

0.024 1 .41 1.14 1.03 1.06 1 .64 2.68

0.033 1.30 1.03 0.92 0.95 1.53 2.57

0,046 1.27 1 .00 0.89 0.92 1 ,50 2.54

This is for a temperature difference across the specimen of

27.8°C and for two-sided operation of the NBS 1-m Guarded

Hot Plate,

A5
Table 8 - Data of Apparent Thermal Conductivity as a Function of

Specimen Mean Temperature, Tjjj.

Material Density (kg/m^) Tjjj (°C) k-value (W/m*K)

Wood 415 37.5 0.12448

23.9 0.11133

10.0 0.09320

Polystyrene 17 37.4 0.04481

24.1 0.04286

-6.3 0.03808

Glass-fiber 13 37.8 0.04012

15.6 0.03587

4.4 0.03378

-8.8 0.03136

Polyisocyanurate 40 37.7 0.02571

30.0 0.02516

23.9 0.02448

15.5 0.02287

4.5 0.02234

-8.7 0.02391

46
Table 9 - Apparent Thermal Conductivity as a Function

of Specimen Mean Temperature » Tjjj, Data Measured

on the NBS 1~m GHP Apparatus.

Material Density (kg/m^) Tn, (°C) k-value (W/m*K) Pressure

Glass-fiber 12 37o8 0.04681

23.9 0.04265

0.1 0.03638

Glass-fiber 15 37.9 0.04382

23.9 0.04019

0.0 0.03473

ExpandedPolystyrene 25 37.7 0.03730

23.9 0.03558

10.0 0.03375

0.0 0.03247

High-density

Glass-fiber 114 37.7 0.03363

23.9 0.03195

10.0 0.02992

0.2 0.02941

Min-K 320 55.0 0.02663 29.612

38.9 0.02588 29.454

23.9 0.02541 29.437

-0.4 0,02462 29.574

Polyisocyanurate 40 46.6 0.02718

37.7 0.02571

15.5 0.02287

4.5 0.02234

-8.7 0.02391

A7
Table 10 - Apparent Thermal Conductivity as a Function

of Specimen Thickness, L, Data Measured on the

NBS 1-m GHP Apparatus for a Mean Temperature

of 23.9°C and a Temperature Difference of

27.8°C

.

Bulk

Material Density Thickness k-value

( kg/m^) (mm) (in) (W/m*K)

Glass-fiber 9.6 152. 6 0.04752

76.2 3 0.04721

25.0 1 0.04554

Glass-fiber 19.2 101 .6 4 0.03773

76.2 3 0.03766

50.8 2 0.03778

25.4 1 0.03749

Extruded

Polystyrene 32 381 .0 15 0.02929

342.9 13.5 0.02917

304.8 12 0.02905

254.0 10 0.02884

203.2 8 0.02911

152.4 6 0.02901

101 .6 4 0.02890

50.8 2 0.02873

48
Table 11 - Data of the Percent Difference Between the Average

k-value of the Individual Layers in a Stacked Specimen

and the Actually Measured k-value of the Stacked

Specimen.

Thickness

(mm) (in)

102 4 0.2$

154 6 0 , 3 %

205 8 0,6$

257 10 -0.5$

309 12 0.2$

345 13e5 0.6$

381 15 0.6$

49

Appendix 1

Copy of referenc

THE NBS LINE-HEAT-SOURCE GUARDED HOT PLATE FOR THICK MATERIALS

Prank J. Povell

Brian C« Rennex

ABSTRACT

The use of thicker thermal Insulation material with greater thermal resistance resulted in a need for the National Bureau of Standards to produce a new apparatus for absolute measurement

of the thermal resistance of thick Insulation samples to be used as transfer standards. These

standards are used to calibrate or verifj^ heat-flowneter (ASTM C-518) or guarded-hot-plate

(ASTM C-177) equipment.

This paper gives the background and description of the line-source heater In the hot

plate and discusses the need to measure thick samples. The actually constructed apparatus Is described, with emphasis given to innovative features. The data-acquisition system is discussed and data are presented. Finally, a summary of the error analysis is presented, indicating an overall absolute uncertainty of less than ^ 1% in the measured thermal

conductivity. ~

The hot plate is made of aluminum and has a 40-in. (1-m) diameter and a 16-in. (406 mm)

measuring diameter, and contains circular line-source electric resistance heaters. The plates

are housed in an environmental chamber that can be rotated for vertical or horizontal measurements on a pair of specimens up to l5-1n. (380-mm) thick. The range of material thermal

conductivity that can be measured is 0.14 to 2.1 Btu»in/hr •ft2.®F (0.02 to 0.30 W/m«K). The

hot plate can be controlled over the temperature range of -4 to 302*F (-20 to 150“C) and the

cold plates cover a range from -40 to 212“F (-40 to i00"C).

INTRODUCTION

The purpose of this paper is to briefly describe the 40-in, (1016-inn) National Bureau of

Standards (NBS) guarded-hot-plate (GHP) apparatus in terms of its actual construction, its

data acquisition capability, and its absolute accuracy. Earlier papers have presented a detailed analysis of the temperature distribution expected with the line-source heaterl and a detailed error analysis.

2

The guarded-hot-plate apparatus is used worldwide to determine thermal conductivity and

thermal resistance of thermal insulation and building materials. The first apparatus at NBS was designed in 1909 and construction was completed in 1912.3 The test method has been

standardized in several countries^t5.6 and the International Standards Organization (ISO),

technical committee 163, thermal insulation, is in the process of producing an international

standard method of test.

Many guarded-hot-plate apparatuses are made by uniformly distributing an electric

resistance heater winding over a square or rectangular laminated metal hot plate. This

construction has several disadvantages: (1) construction and repair are complicated and

difficult, (2) differential thermal expansion can cause warpage of the plate, resulting in

inaccurate measurement of specimen thickness and nonuniform thermal contact between the

specimen and the plate, (3) repeated thermal cycling can lead to permanent plate deformation.

Frank J. Powell and Brian G. Rennex, National Bureau of Standards, Washington, DC 20234.
(4) the location of the qap thermopile for one-sided tests Is problematical, and (5) square

corners make nathenaticai analysis difficult.

Ideas to overcome these difficulties were presented by Robinson In 1964.^ These ideas

Involved the use of a circular metal hot plate containing a line-source electric resistance

heater. Analysis was given to show that the circular line-source heater could be located at Such a radius that the temperature at the outside edge of the meter area (on the meter side

of the gap) would be equal to the average temperature of the entire meter areas. Thus, plate

Surface temperature measurements would not be necessary.

In 1971, under the sponsorship of MBS, Hahn completed an in-depth analysis of these'ideas

and examined several design options. 8 The concept, mathematical analysis, and proposed

design- features were published in Ref. 2. The development of a prototype line-source

apparatus? and its description and results of measurements were reportedlO before undertaking

the design and construction of the 40- in. (1016 mm) apparatus under discussion here.

Many guarded-hot-plate apparatuses were designed to accommodate test samples of 1 or 2-in.

(25 or 50-mn) thicknesses. Such equipment was satisfactory, provided the value of thermal

resistance obtained for a 1-in. (25-mm) thick sample could be used to calculate the value of

ther-.al resistance for thicker materials by linear extrapolation. With the use of greater

thicknesses of insulation to reduce building heating and cooling energy consumption, it became

necessary to know more precisely the thermal resistance of thick insulations (up to 12-in.

[300 tnn] thick products are available). In the case of low-density fiberglass insulation,

there were indications that linear extrapolation from a 1-in. (25-mn) thick sample could ^

in error. The thermal testing community and manufacturing industry required thick specimens

to calibrate their guarded-hot-plate and heat flowmeter apparatuses. Furthennore, the test methods of the American Society for Testing and Materials (ASTM) required calibration with

transfer standards traceable to a national standards laboratory, and the Federal Trade

Commission promulgated a rule requiring that advertised thermal resistance values be derived

from a "representative thickness" of the material. Representative thickness was defined as the thickness of material whose measured thermal resistance can be extrapolated linearly to

obtain a thermal resistance at a greater thickness that is within ^2% of the measured value of

the thick material

.

This paper presents a technical description of the as-built NBS line-source, 40-in.

(1016-rm) diameter guarded-hot-plate apparatus, with emphasis given to innovative features.

Sample results and data that indicate that the absolute uncertainty of measured thermal resistance values is +11 are given. The development of the equipment was jointly sponsored by the

National Bureau of Standards and the Department of Energy and was supported by a research

associate from the Mineral Insulation Manufacturers Association.

PRINCIPLE OF MEASUREMENT

The principle of measurement of a guarded-hot-plate is illustrated in Fig. 1. Electric power

is supplied to the meter heater and guard heaters to maintain constant and equal temperatures

of each of these plates. The guard and meter sections of the hot plate are separated by an air gap. Differential thermocouples are connected across the air gap to indicate whether heat

is flowing radially across the gap. The electric power to the guard heaters is controlled to maintain net gap heat flow as nearly as possible to zero. The cold plates are controlled to produce a constant, uniform surface temperature. Under these steady conditions heat flows

unidirectionally from the meter plate to the cold plates. A layer of thermal insulation

surrounds the peripheral 'edges of the specimens. If none of the heat produced by the meter

plate is lost to the guard heater (or gained from the guard plate) or transferred from or to

the environment surrounding the plates, the following steady-state relationship can be used

to determine the total thermal resistance of both specimens (assuming the heater power, Q, is

split evenly between the two sides):

. n - MT, - T,) (Q/2)

( 1 )

where

R total sample thermal resistance of thickness f in. (ra), ft2.hr»*F/Btu (m2/K«U) A metered area, in. 2 (m2)

Tfj • average temperature over the meter section of the hot plate, *F (K)

2
Tc “ average cold plate temperature, *F (K) g

» electrical energy consumed by the meter plate to maintain its temperature, W

By definition, the apparent thermal conductivity, X, is

X • L/R (2)

It is possible to operate the hot-plate apparatus with one of the cooled plates maintained

at the same temperature as the hot plate. In this case, a single specimen is measured instead

of a pair of specimens. This brief explanation of the principle of measurement was given to

enable to reader to see the various sources of measurement uncertainty suwaariied later,.

DESCRIPTION OF APPARATUS

Hot Plate

The hot plate is circular and has a uniform thickness of 0.635 in. (16,13 mm). It is made of

type 6061-T6 aluminum. Fig. 2. The center part is a solid diameter 11.299 in, (287,0 nn). A

commercially available nichrome ribbon heater (-4 mil [0,1 mm] thick and 160 mil [4 tm wide])

encased in plastic surrounds the edge of the center. The circular ribbon heater is referred

to as a line-heat-source hot-plate design. The section surrounding the center part has an inside diameter of 11.299 in. (287,0 nm) and an outside diameter of 15,970 in, (405.6 mm).

These two inner sections comprise the heated, metered area of the hot plate. When fabricated,

the center part was cooled to liquid nitrogen temperature and placed inside the outer section

(held at room temperature), with the nichrome heater between, forming a shrink-fit assembly.

Three equally spaced pins (120 mil [3 nin] diameter stainless-steel) are used to support the

meter-area part within the guard ring as shown in Fig. 2. The guard ring has an inner diameter

of 16,040 in. (407.4 mm) and an outer diameter of 40.000 in, (1016 mm). The gap between the

guard and meter-area parts is 35 mil (0.9 rm) wide. There are two circular heaters or each

side of the guard surface at diameters of 20,658 in, (524.7 iim) and 31,584 in, (6: .1 wn).

These are located in circular grooves, cut into the guard surface, and are embe". in epoxy.

Several holes (160 mil [4 rm] in diameter) penetrate the guard ring from its ol:-* eoge to the

gap to permit access for thermistor, heater leads, platinum resistance thermomeicr, and

thermocouple wires. The plate thickness of 0.635 in, (16,13 ttm) was selected as a balance

between a desired large thickness with great structural rigidity and a small thickness with

less heat capacity. The plate surfaces are black anodized to achieve a normal, visible

emittance value of 0.89^0.01.

The gap shape was chosen to allow maximum gap volume and a greater thermal resistance

across the gap, without having too large a plate-surface gap separation with its accompanying

potential for a larger uncertainty in meter-area value. The measured flatness of the meterarea is ;! mil (25 \tn) across its diameter.

The design mathematical analysis, and experimental results related to the line heat source

are discussed in Refs 1 and 2, For a 1-in. (25-Rm) thick sample with a heat flowrate per unit

area of - 28 Btu/hr»ft2 (90 W/m2) and a hot-to-cold-plate temperature difference of 50®F

(28 K), the measured temperature difference between that of the hot plate surface at the linesource-heater location and that of the plate center was 180 mF (60 mK). Thus, the results

given in Ref 1 indicate the plate temperature is quite uniform. In addition, the temperature

at the outside edge of the meter section (at a radius of 7.985 in. [202.8 mm]) was equal to

the average temperature over the entire meter area, within the limits of the measurement

accuracy (~ 27 mF or 15 mK). This result justifies the use of a platinum resistance thermometer

at the edge of the meter section (inside the gap on the meter side) to determine the average

absolute temperature of the meter area.

Cold Plates

The construction of the liquid (ethylene glycol) cooled cold plates is shown In Fig. 3. Each

aluminum plate Is 1 in. (25.4 mm) thick and consists of a 0.25 in. (6.4 mm) thick cover plate

bonded with epoxy to a 0.75 in, (19,0 im) thick base plate. The base plate contains milled

grooves 0.375 in. (9.5 mm) deep and 0.375 in, (9.5 mm) wide arranged in a double-spiral configuration. This arrangement allows leak-tight counterflow channels in which the incoming

coolant passes next to outgoing coolant for a more uniform temperature distribution over the

cold-plate surface. A 0. 125-in. (3.2-mm) diameter hole was bored from the side to within

2.5 in. (63 mm) of the plate center to provide access for a platinum resistance thermometer.

3 .
which 1s used tc measure the absolute temperature of the cold plates. The backs and edges of

the cold plates are insulated with 4 In. (102 tnm) thick expanded polystyrene.

Supporting Structure

Figures 4 and 5 show how the three plates are supported by four stainless-steel rods of 2-1n.

(51-mn) diameter. The rods are mounted in an airtight insulated chamber for environnental

control

.

.The hot plate is rigidly and permanently mounted on the four support rods. Each cold

plate Is supported at its center, and, at the point of support, has a load cell to measure the

force that the sample exerts on the plate. This support has a ball joint so that the plate can

tilt to conform to a nonparallel rigid sample. The cold plates are constrained in the radial

direction by steel cables attached to four spring loaded bearings mounted on the hotplate

Support rods. This construction ensures that the plates remain aligned when the whole of the

apparatus is rotated 180* in either direction.

Environmental Chamber

The environmental chamber is cube-shaped and 5.2 ft (1.6 m) on an inner side (see Fig. 4 ). The

inside and outside surfaces are of sheet aluminum, and the core consists of 3 In. (75 mm)

thick expanded polystyrene insulation. Rigidity is provided by 2-in. (50-nm) square box-beam

members. The plate-support rods are secured at the top only, to hang within the chamber.

Axles extending froin the center of two opposite sides are mounted on gimbals, allowing 180*

rotation of the entire apparatus. Full access to the plates is allowed by doors on both the

front and back of the chamber. The temperature within the chamber is maintained at the desired

value (^ 2*F or 1 K) using a platinum resistance thermometer and a feedback circuit to control

a heater that loads a constant cooling heat exchanger. The present operating range is 0 to 150'F (273 to 340 K).

Thickness Measurement

The thickness, L, in Eq 2 is the average, over the meter area, of the spacing between the hot

and cold plates. The basic calibration methodl involves measuring the hot-to-cold spacings

at the outside edges of the cold plates at four equally spaced positions. The four spacings

are correlated with a “known meter-area plate separation," which is determined with a direct measurement of the thickness in the center of the plates, using an independent set of

temporarily mounted thickness transducers accurate to within 0.3 rails (7 ym).

The outside cold-plate positions are measured using four permanently mounted thickness

transducers on each plate. These thickness transducers measure any change in position relative

to the initial reference point. The calibration must be done for each plate orientation and

for compressible and rigid samples.

These four permanently mounted thickness transducers are mounted on Invar bars to minimize

error resulting from ambient temperature variation and measure the average spacing with a repeatability of 0.2 mils (5 wm). Thus, the thickness can be measured continuously during a test as temperature testing conditions change, an improvement over the procedure of measuring

thicknesses only at the beginning and end of each test.

Plate Temperature Control

The plate temperatures are controlled with feedback circuits. Thermistors are used in these

circuits because of their large change in resistance with temperature. A thermistor Is located

in each of the hot and cold plates. In addition, pairs of thermistors are used to control the

temperatures between the gap and the outer guard. (The “gap" readout, however, is accomplished

with a thermopile.) For the NBS/GHP apparatus the hot-plate temperature can be controlled to within a range of 2 mF (1 itiK), the cold plate temperatures to within 12 mF (6 mK), and the

average temperature difference across the gap to within 2 mF (1 mK). A microprocessor is used

in conjunction with the feedback circuit to automatically bring the plate temperatures to a desired value. The use of thermistor control circuits makes it possible to achieve

steady-state test conditions within 3 hours for low-density, 6-in. (150-tiri) thick samples.

The steady-state value of apparent thermal conductivity is achieved in the constant hotplate temperature mode, rather than a constant meter-area-heater power mode. This factor is important for the reduction of test times. Note that because the control range of the hot-plate

4 .
temperature and the corresponding control range of the neter pov/er Is very small, the accuracy

of the final steady-state value of the apparent thermal conductivity is not compromised by

using the constant-temperature mode,

DATA ACQUISITION AND D0CU^t:NTATI0N

Automatic Data Acquisition

The control of plate temperatures and data acquisition Is accomplished with a microprocessor.

The selected plate temperatures are entered, and the computer reads temperatures as measured

„with platinum resistance thermometers. These values and a control algorithm are used to

bring the temperatures to the desired values. Raw data consist of readings of a number of

voltages. *A scanner selects the voltage to be read by a digital voltmeter. When a complete

scan Is made of all the required voltages, the information Is transmitted to a desk

. calculator-computer and stored on a cassette tape.

The desk calculator also produces plots of the Important data as a function of time, such

as plate temperatures or hot-plate power, Figs. 6-10. Note that the steady-state values on these figures lie within a narrow band (for example, 0.05% for the apparent thermal conductivity, x). This short-term scatter Is mostly due to the power change required by the meterarea heater to maintain the hot plate at a constant temperature. The hot plate Is In turn

responding to the short-term changes In the cold-plate baths, ultimately causing most of the

short-term scatter In X. However, the mean value of x over several hours Is known much

better than within the 0.055 band (drifts in mean value of -0.015 can be detected). Stated

differently, the short-term scatter contributes a negligible amount to the uncertainty In x, as long as the steady-state interval Is several hours long. Rather, It is the data drifts

over a period of about one day or more, as well as the systematic errors, that contribute

significantly to the uncertainty in X. The time plots are Invaluable for ascertaining that

the test is in steady state, meaning that there Is no monotonic change over time In the measured

mean value of X.

Sample Report

A sample of reported data, shown In Fig. 11, illustrates the standard data that are transmitted

to a user when an insulation standard is measured at the National Bureau of Standards. This

includes information on sample Identification and on test conditions that should be reproduced

by the user laboratory undertaking equipment verification or calibration.

SUW!^ARY OF ERROR ANALYSIS

Method of Suming Individual Uncertainties

The apparent thermal conductivity and the thermal resistance of an Insulation sample are calculated quantities based on several measured parameters. Each of these measured parameters

has an associated uncertainty. In turn, this uncertainty has a random and a systematic part.

It is possible to estimate the uncertainty of each parameter by an independent test. For

example, the apparatus thickness readout can be compared with a thickness gauge placed between

the plates. It Is less straightforward to estimate the overall uncertainty of the calculated

quantity, because there Is usually not sufficient information on the breakdown between the

random and systematic parts of the uncertainty for each individual parameter. In principle.

It is possible to gather this Information, but In practice it would be too time consuming.

A more simple and practical approach was used In this error analysis. The individual

parameters, such as the thickness or temperature distribution over the meter area, were measured

with an independent detector under test conditions. A comparison of the apparatus readout with

these independent measured values made possible the estimate of the upper bound on the total

uncertainty for each parameter. Since there Is not sufficient Information to assure that the

measured values are randomly distributed about a “true" mean value, the upper bounds for each

individual parameter are simply summed to arrive at the overall uncertainty. This approach

differs from an alternative approach In which the uncertainties are treated as standard deviations that are then added In quadrature, i.e., the total uncertainty Is the square root of the

sum of the squares of the Individual uncertainties. The method of simple addition results in

a somewhat larger estimate of the overall uncertainty (by as much as 305) as compared with the

method to sum in quadrature), but It eliminates the need to make an Inordinate number of checkup measurements to assure that there are no outlier values. This more conservative approach 1$

thought by the authors to be appropriate for use by a national Insulation standards laboratory.

5 .
The following philosophy was used with regard to the estimate of upper bounds. Even If

an unce''tainty might have been expected to be smaller, based on theoretical considerations and

manufacturer specifications, the uncertainty value actually used was that of the detector

making the independent check. For example, the plate temperature might very well be known

within 10 or 20 mF (5 or 10 mk). The uncertainty value actually used—44 mF (22 mK)—was associated with the thermopile used independently to check the plate temperature.

It is possible to estimate the overall random uncertainty, as the range of values of

repeated measurements on the same sample with the same apparatus. This range within a period

of several months for the NBS 40-1n. (1016-rm) GHP apparatus at a thickness of 4 In. (100 nui) was within 0.11.

Generally speaking, the data on a single test are of two parts. The transient part at the

beginning of the test shows an increasing or decreasing curve. When there is no monotonic

trend, the steady-state condition has been achieved. There is still a scatter of data points,

due mostly to the cycling of the bath temperatures. The scatter band is about 2 mF (1 mK) for

the hot-plate temperature, 12 mF (6 mK) for the cold-plate temperatures, and 1 mW for the power.

The scatter in the calculated X-value is about 0.011 for a two-sided, 1 in. (25 mm) sample

and 0.031 for a two-sided, 6-in. (150-mm) sample. The mean x-value is known even better. The scatter in the data points, after the steady-state condition has been attained, is negligible

compared to the estimated systematic errors In x.

Individual Contributions to the Apparatus Uncertainty

Table 1 shows the contributions to uncertainty for the individual measured parameters such as the thickness or heat flow; the overall uncertainty values are also shown for various thicknesses. The methods of estimating these uncertainties are discussed in detail in Ref 10. This summary of uncertainties is for the case of compressible insulation samples at a mean

t&nperature of 75®F (297 K) and a pi ate-temperature difference of 50“F (27 K). Note that at

a thickness of 1 in. (25 nri) , the temperature and thickness uncertainties are largest. At

6 in. (150 nm), the temperature is the only large uncertainty. At 12 in. (300 nm) the edge

uncertainty is dominant. The gap-voltage uncertainty was kept small, even at 12 in. (300 rtm)

,

by using an 18-stage gap thermopile, low-thermal wiring, and a highly accurate voltmeter.

The overall uncertainty value is about 0.31 up to a 6-in. (150 ram) thickness. At 12 in.

(300 nm), it should be possible to decrease the uncertainty with further edge studies.

CONCLUSIONS

A description of the as-built NBS line-source guarded-hot-plate apparatus capable of measuring

the thermal resistance of specimens of thermal insulation and building materials up to 15 in.

(380 tm) thick is presented. The apparatus conforms to ASTM Standard C-177-76 , "Standard Test Method for Steady-State Thermal Transmission Properties by means of the Guaroed Hot Plate."

Experience with the apparatus and the results of uncertainty analyses justifies the conclusion

that the NBS apparatus is a viable means for measuring absolute values of thermal resistance

to an uncertainty of ^ 11.

REFERENCES

1. B. Rennex, Error Analysis for the NBS 1016 mm Guarded Hot Plate , National Bureau of

Standards Report NB5iK-b3-i;6/4 (Wasm'ngton: nBS, 1983).

2. M, H. Hahn, H. E. Robinson, and D. R. Flynn, "Robinson Line-Heat-Source Guarded-Hot-Plate

Apparatus," Special Technical Publication 544 (Philadelphia: American Society for

Testing and Materials, 1974), p. 167-192.

3. Paul R. Achenbach, Building Research at the National Bureau of Standards Through 1968 , NBS Building Science Senes, bSS 0 (Washington: NBS, 19/U), p. ll.

4. American Society for Testing and Materials, 19S2 Annual Book of ASTM Standards , (Philadelphia: American Society for Testing and Materials, 198^), Part Id, p. 20-53.

5. British Standards Institute. Methods for Determining Thermal Properties . B.S. 874 (London:

British Standards Institute^

6. Bestimung der Wameleitfahigkeit mit der'Plattengerat, DIN 52612 (Berlin: Deutsch

Normenausschuss)

.

6 .
7.

R. P. Tye, Nature 204 (1964)

8. M. H. Hahn, “The Line Heat Source Guarded Hot Plate for Measuring the Thernal Conductivity

of Building and Insulating Materials" Ph.D. dissertation. Catholic University of Anerica,

1971.

9. F. J. Powell and M. C. I. Siu, “Development of the Robinson Line-Heat-Source Guarded-HotPlate Apparatus for Measurement of Thermal Conductivity, Proceedings of XIV International

Congress of Refrigeration (Moscow: International Institute of Refrigeration, 1975),

10.

M, C. I. Siu and C. Bulik, National Bureau of Standards Line Heat Source Guarded Hot Plate

Apparatus. Review of Scientific Instruments 52:11 (Nov. 1981) p. 1709-1716.

7 .
TABLE 1

Percentage Estinate of Uncertainties In the Measured Apparent

Thermal Conductivity for the MBS Guarded Hot Plate

Quantitative

Thickness

Value 1 in.

(25 mm)

3 in.

(75 mm)

6 in. (150 tm)

12 in.

(300 mm)

Uncertainty, 5

Area

(0.5 mil or 12 iffl In radius)

0.01 0.01 0.01 0.01

Thickness

(1.0 mil or 25 un)

0.1 0.03 0.02 0.01

Meter power 0.04 0.04 0.04 0.04

Meter resistive

Device (0.4 mW)

0.00 0.01 0.02 0.04

Gap heat flow

(0.3 mW, or 0.5 uV

in gap voltage)

0.00 0.01 0.02 0.03

Edge heat flow 0.00 0.00 0.00 0.50

Hot, cold-plate

temperature

difference

(79 m®F or 44 mk)

0.16 0.16 0.16 0.16

TOTAL 0.31 0.26 0.27 0.79

* These values are for compressible, low-density, fiberglass Insulation measured

in the two-sided mode with a plate temperature difference of 50“F (28 K).

Uncertainty values of less than 0.015 are reported as zero.

8
LIST OF FIGURES

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

1. Principle of measurenwnt

2. Hot plate

3. Cold plate

4. Drawing showing rotatable support system for hot and cold plates

5i Photo of support systems for hot and cold plates

Hot plate temperature

7. Cold plate temperature

8. Meter-area power

9. Gap voltage

10. Apparent thermal conductivity

11. Sample report

9 .
Figure

1

Principle

of

Measurement

for

a

Guarded

Hot

Plate

aaruviQdwiL miawv

3afUV5GdK31 1M318WV

10

COLD

PLATE
Figure 2 Hot Plate Construction for the NBS 1016inn) Guarded Hot Plate

A • RIBBON HEATER

B-CAP

C - GUARD HEATERS

0 • SUPPORT PIH
Figure 3

Cold

Plate

Construction

for

the

NBS

1016nnn

Guarded

Hot

Plate

MILLED

ALUMINUM

BOTTOM

PART
Figure 4 Drawing of the NBS 1016tnm Guarded Hot Flate Shoving the

Support System of the Hot and Cold Plates and Shoving the

Rotatable Enclosure for Environmental Control

13 .
Figure 5 Photo of Plates and Support System for the 1016Ban

NBS Guarded Hot Plate

14
HOT

PLATE

TEMP

(c)

FIGURE 6 Typical Data for the Hot-Plate Teaperature as a Function of Time for the NBS 1016nnn Guarded Hot Plate

DATA OH HOT PLATE TEMP FROM 07/09 1981 AT 19:27:11 TO 07/10 1981 AT 08s57sSl

ELAPSED TIME. FROM FIRST TO LAST READING IS 13.50 HOURS

STATISTICAL DATA

HEAH 37.7761

niH

HAX

RANGE

HUMBER OF PTS

First record*

37.7753

37.7777

.0824 AS 7. OF MEAN

163

1 Last record* 163

.006 ::

time (HOURS)

15.
UPPER

COLD

PLATE

(c)

FIGURE 7. Typical Data for the Cold-Plate Temperature as a Functiovr

of Time for the NB5 1016mm Guarded Hot Plate

DPTfl ON UPPER COLD PLATE FROM 07^09 1981 AT 19:27:11 TO 07X10.1981 AT 08:57:11

ELAPSED TINE FROM FIRST TO LAST READING IS 13.50 HOURS

mean

STATISTICAL DATA

10.0018

MIN

MAX

range

NUMBER OF PTS

First record*

10.0001

10.0044

.0042

1€3

1 Last record*

AS 5s OF MEAN

163

.042 Ss

TIME (HOURS)

16 .
POWER

(Watts)

FIGURE 8. Typical Data for the Center Hot Plate Power as a Function

of Time for the NBS 1016sm Guarcied Hot Plate

RTfl ON POUEft FROM 07^09 1981 ftT 19l27:il TO 07^10 1981 AT 08;57:il

.LAPSED T1T1E FROM FIRST TO LAST READING IS 13.50 HOURS

STATISTICAL DATA

1EAN 4.8024

niN

MAX

RANGE

NUMBER OF PIS

First record* 1

.5990

.8035

.0045

183

Last record*

AS 5j OF MEAN

183

.097 %

TIME (HOURS)

17.
GRP

VOLTRGE

(u

Volts)

FICITRZ 9 Typical Data for the Gap Voltage as a Function of Time

for the NBS 1016cm Guarded Hot Plate

DftTfl ON CAP VOLTftCE FROM 97^23 1981 «T 17:09:07 TO 07^29 1981 0T 08:40:07

ELRPSED TIME FROM FIRST TO LAST READING IS 15.52 HOURS

STATISTICAL BATA

AERN .012388

AIN -.280000

r.p.y. .480000

HUnBER OF PTS 134

First record* 1 Last record* 134

0)

tsc.o

e

o

u

a

Wi«

0)E

e«

w

«

9

DO«

JSe

«>»V

.o

PRT TEST

18
t

FIGURE 10. Typical Data for the Apparent Thermal Conductivity

as a Function of Time for the NBS 1016nsi Guarded

Hot Place

DflTfl ON K CRdj. Cond.> FROM 07/^09 1981 «T I9;27sil TO 07^10 S981 «T 08:57ni

ELftPSED TINE FROM FIRST TO LAST RERLINC IS 13.50 HOURS

STfiTISTICRL DRTfl

HERN .048830

niN

. nfl}<

RRNCE

NUMBER OF PTS

- First record*

.048594

.048849

.000055

183

1 Last record*

RS % OF HERN

183

.114 k

E

•<

time (HOURS)

19.
Figure 11 Sample Test Report for NBS 1016mm Guarded Hot Plate

Test Results

Apparatus: NBS •KJHP-IOOO

Table 1 Test No.

Specln>en Identification no. Plate orientation during test Horizontal

Direction of heat flow Vertical (up)

Test Configuration

Cold Plate #1

Sample

Hot Plate

Sample

Cold Plate 02

Test thickness (average) 152.35

Thermal resistance a) (ffi2.K)/W 3.2554

Cold plate tfl temperature b) -c 10.00

Hot plate temperature b) •c 37.78

Cold plate 02 temperature b) •c 37.78

Specimen (mean) temperature •c 23.89

Ambient temperature •c 24

Ambient humidity % rh 30

Meter area 0.1299

Power input to meter area W 1.108

Edge insulation thermal resistance c) (t?.K)/W

«) Last digit Included for rounding

b) Emlsslvity of the surface at room temperature: 0»9

c) Nominal R-value of insulation around plates

The thermal resistance value in the above table was determined for that

portion of the specimen within the laeter area (central 406.4-an diameter

region) of the NBS -GKP-1000. The uncertainty In this thermal resistance

value is estimated to be not more than + 3/4 percent; this uncertainty

Includes apparatus systematic error and apparatus repeatability*

20 .
Appendix 2 POSITIVE PRESSURE INSIDE CHAMBER

31.5”

/

63"

Definitions

P^ ^ = Total force imparted total . - to door from internal

pressure

= • 01.5) (63)

= Reaction force which

must be resisted by

shear bars

Assume: Shear bar material 6061-T6 Aluminum

ult

= 38 psi

1. Pin shear criterion:

S = a -A = 38 (.75)(.5) = 14.25K shear

^MAY ult

2. Clevis shear:

S = 38 (.5) (.625) (2) = 23.75K shear

^MAX

tension

= 38 (.5)(.75)(2) 28 . 5K Tension

2-1
Pin Shear Controls and S 1A.25K

MAX

Moment Equilibrium about Hinge A - A:

^ ^A-A

” ^ ^total (^-^) - 2 (31o5) = 0

MAX

^otal = 57K

Max Internal Pressure

total

INT (31.5)(63)

= 28 psi** (above atmospheric pressure)

**Note: Leakage due to bending in the panel will probably

limit this to a lower value.

2-2
Appendix 3 - VACUUM INSIDE CHAMBER

Edge Reactions

For the purposes of this analysis,

the following assumptions can be made:

1. The door is simply supported along

its edges as shown.

2, Although some 2-way panel action

will occur in the proximity of

the left hinge, we assume that

a conservative estimate of the

door's resistance to load can be

calculated by considering a 1”

vertical strip, simply supported

at its ends and subjected to a pressure loading equal to the

difference between atmospheric

pressure and the internal pressure.

~ 14.7 Ib/in'^ (atmospheric pressure)

/ Jr

'1 1 '

1 ' f '

- 1[tilt >

p INT

. Zi' strip

63"

Vertical Force Equilibrium requires

2 F = 0 : 2R^ + -63 - 14.7 • (63) = 0

y F IN 1

Rf 2 (1^-7 ^int^

(EQ 1)

3-1
Maximum Bending Moment occurs at center span

W = = 'iNT <f>0 (EQ 2)

14.7

1 ^ 1 \I

^ ^ \ax

4 T Tt

INT

R

F

k

63/2

Substituting (EQ 1)

.63 63>

^SlAX ^ 2

^ ^INT^ ^ 2

^

+ (Pint " (f> <f>

= 14586 - 992.25 P

INT

Calculate Section Properties

0.0394"

I ~ Ad' Aluminum

MAX

(urethane shear)

MAX

(aluminum)

1(0.0394)(1.5) (2)

0.1773 in^

0.217 MPa

31.44 psi

30 Ksi

(standard alum, plate)

Check Flexural Strength of Composite

^ ^ ^ ^ (14586 - 992.25 P^^^^) (1.5) ^ 3

® ^ 0.1773

Minimum P = 14586 (1.5) - 30,000 (.1773)

1.5 (992.25)

^INT

~ 11.126 absolute psi

MIN

i.e. max. vacuum = 14.7 ~ 11.126 = 3.57 psi

3-2
Check Max Urethane Shear

a

s VQ

IB

31.44 psi 1 1

2 A

for rectangular sections

A

V

(1)(3.079) = 3.079

(U.7 - (f)

0 = 31.44

s I

( 14.7 - (f)

^ 3.079

14.7 - 3.079 (31.44) (|) (-^) =

^INT

~ 12.65 psi min. (absolute)

this controls

The chamber rating is therefore:

12.65 < < 42 absolute

or -2,05 < < 28 (relative change WRT atmospheric)

3-3

Appendix 4

Calculation of Percentage Uncertainty

in the Measured Metered-Area Heater Power

for a 152.4 mm Thick, Low k-Value Insulation Specimen [53

The term, Qjjj, is the power produced by the meter heater. A known standard

shunt resistor, Rg, of approximately 0.1® , that is maintained in an oil

bath, is used to determine the current. Voltage taps across the meter

heater lead wires in the center of the gap are used to measure the voltage

corresponding to the power that flows one-dimensional ly from the hot plate

to the cold plates.

0

- theater _^s (4-1) “ ' «s Rg = 0.1000700 ® ± 5 ppm at 25.0°C (4-2)

An additional uncertainty of 20 ppm is included since the resistor is in a

bath at 28°C. The uncertainty of 25 ppm corresponds to a 0.0025 percent

uncertainty, which is negligible compared with other uncertainties.

If the heater voltage taps were not in the center of the gap, there would

be an error in the measurement of The 28 gauge nichrome wire has

a resistcince value of 42 ®/305 m (1000 ft). Assuming (conservatively) that

the taps might be misplaced by half the gap width of 6 mm (0.23 in), then

the error in Rheater is 8 * 10~^fi. This is negligible when compared with

the value of Rheater approximately 56 ®.

As a worst-case example, the following calculation is for a thick two-sided

specimen with a k-value that is at the low extreme of what would be

expected (k^ = 0.0086 W/m*K). The following equation expresses the

metered-area heater power required to maintain a temperature difference,

4-1
AT, of 27.8°C across the 152.4 mm thick specimen, for the NBS 1-m GHP. The

metered-area is 0.1299 m^.

Qjn = (2 kg AT A)/L (4-3)

= 0.408 W

Given that the metered-area heater resistance, Rj^, is “560 and the shunt

resistance, Rg, is -0.1 the shunt voltage is calculated as follows:

V5 = R3

= 8.5 mV

Thus Vjj = 4.7 V.

These order-of-magnitude estimates are necessary to calculate the

percentage errors in and Vg. As an example, for the 10 V range

of the digital voltmeter and for a 90-day period, the manufacturer’s

specifications give the following formula to calculate the voltage

uncertainty, Av.

3 Av = V + 2 counts x count value) (4-5)

100

This is for a 6-digit readout and an average over 10 power line cycles.

The count value is somewhat larger than the minimum detectable signal and

has a value of 10 yV. If V = 4.7V, Av = .0000004 = 0.00004 percent. This

is obviously negligible compared to other voltage errors.

The more significant contribution to uncertainty results from the reading

of the shunt voltage, Vg, on the 0.1 V scale. Vg = 8.5 mV, which is a

worst-case value. The manufacturer's uncertainty formula for this range

is:

3 AV = ^ ^*100

'^ ^ counts X 0.1 yV) (4-6)

= 2.7 yV

-2-^ = 0.0003 = 0.03? (M)

V

s 4-2
This Av uncertainty is the only contributor to the uncertainty in Qjjj that

is not negligible, and it is mostly due to the "24 counts".

4-3
/iBW ^ tJi 'ifkli^h^tMu
Appendix 5

Test Thickness Limitations Due to

Edge Effect Uncertainties

Figures 8 and 9 show the A and B edge effect coefficients for the NBS 1-m

GHP apparatus parameters. These are a metered-are radius

equal to 200 mm and a guard-area radius equal to 400 mm. The A and B

coefficients Indicate the magnitude of the edge effect as is shown in

equations (1), (2) and (3) in the text. Each curve shows the dependence of

A and B on specimen thickness, L. The set of curves demonstrates

parametric dependence on the parameter h^/kg. Here, h^ is the effective

surface film coefficient between the specimen edge and the ambient, and kg

is the specimen apparent thermal conductivity.

The effective surface film coefficient, hg, is calculated in terms of the

thermal resistance of edge insulation, and the surface film

coefficient between this edge Insulation and the ambient, h.

he = (Red + 1/h)*'' (5-1)

A typical value for Rg^j is 1.75 m^*K/W and for h is 5.67 W/m^*K. Then, hg

is equal to 0.52 W/m^*K.

Typical values of hg/kg are 11.3 m“^ for a low-density, glass-fiber

material (kg = 0.046 W/m*K), 15.8 m”^ for a high-density glass-fiber

material (kg r 0.033 W/m*K), and 21.7 m“^ for an extruded polystyrene

material (kg = 0.024 W/m*K). For the low extreme value for kg of 0.0086

W/m*K, hg/kg is equal to 60.5 m“\

Figure 8 shows A(X) for various values of h_/k„. The term A is the 9

5-1
Intercept value, Y(0), when X = 0, or equivalently when the ambient

temperature equals the mean temperature (refer to Equation (2)). There are

two approaches to estimate edge error. One is to consider A the

uncertainty. Another is to rely on the edge-effect model to adjust to the

value of Y at which Y = 0, which implies a knowledge of R^, the onedimensional or "true" thermal resistance of the thick specimen. For the

sake of brevity, the first approach is adopted here.

For a typical specimen, with kg = 0.046 W/m*K and h^/kg = 11.3 and for

a tolerance of 0.2$, the error curve in figure 8 exceeds the tolerance at a

thickness of -325 mm. Whereas, for kg = 0.0086 W/m*K and hg/kg = 60.5 m“^,

the curve exceeds the same tolerance at a thickness of -310 mm. Thus, a

decrease in kg by a factor of 5 to the extreme low value 0.0086 W/m*K, does

not result in a significant decrease in the thickness operating range.

At the maximum operating thickness of 381 mm, the A value is -0.5$ for kg =

0.046 W/m’K, and 0.8$ for kg = 0.0086 W/m*K. Again, please note that the

uncertainty would be smaller if the model were used to adjust the measured

k-value. For example, if there were a 25$ confidence in the model

predictions, these values of 0.5$ and 0.8$ would be smaller by a factor of

4.

Figure 9 shows the curves of B(L) for various values of h^/kg (refer to

equations (1), (2) and (3)). The B term is the slope of the edge effect

term, Y, plotted as a function of the dimensionless ambient temperature

unbalance, X. This slope is easy to determine empirically, by measuring

change in the thermal resistance as the ambient temperature is varied.
Then, to estimate the uncertainty in R-value due to B, multiply the

empirically determined value of B times the uncertainty in X, AX. If (Tjj -

Tq) r 27.8°C and if the uncertainty in (Tjjj - T^) is 1°C, then AX - 0.036.

The term, BaX, gives the uncertainty in the measured R-value.

For the two k-values used in the discussion of the A term, = 0.046 W/m*K

and kg = 0.0086 W/m*K, the values of BAX are equal to 0.2$ at thicknesses

of -295 mm and -282 mm. The same conclusion holds, as for the case of A,

that a decrease in k-value to the low extreme expected in practice, does

not affect the thickness operating range significantly.

The reason for this conclusion is that the curves of A(L) and B(L) are

highly unlinear. They are essentially zero until L“200 mm. Between L =

200 mm and L = 300 mm, the slope increases rapidly, and above 300 mm it is

approximately constant. As a result, small changes in the curve, such as

those due to the parametrical dependence on hg/kg, do not significantly

affect the operating thickness threshold.

5-3
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is'.. ='-i<i... "Six*, .j-"’ m^;
Appendix 6

Contact Resistance

Contact resistance is the resistance to heat flow resulting from the air

gaps between a specimen and the apparatus platese

To estimate the error that could result if contact resistance were not

taken into account, consider a 25.4 mm thick specimen with an air gap of

25.4 microns on each side. The heat transferred through the gap

considering conductive and radiative heat transfer is given by the

following equation [8].

q = kg ^ + 4<y T^ AT (6-1)

Lg 2/c - 0.9343 + 3/4

where kg is the thermal conductivity of air (0.0259 W/m’K), C is the

plate emittance (0.9), T is approximately equal to the average air-gap

temperature, AT is the temperature difference across the air gap, and is

the optical depth. It is defined as:

( 6- 2 ) where 0 is the extinction coefficient and L is the air-gap thickness.

O

Since both 0 (for air) and Lg are small, the value of is negligible.

The gap average temperature, T, is different on the hot-plate and coldplate sides. The T value of the hot-plate air gap, 35°C (308,15 K), is

used because the radiation heat transfer contribution is slightly larger.

6-1
In general, the thermal resistance is defined as R= T/ q. Using this

and equation (5-1), the contact resistance, r, is the following,

r = 1 (6-3)

k^/Lg + [(4 (tT^)/(2/^ - 0.9343)]

The relative values of the two terms in the denominator are the following.

= 5.7024 W/m^'K (6-4)

2/£ - 0.9343

k^/L„ = 510.59 W/m^-K (6-5)

“ s From equation (6-3) the contact resistance is the following.

r = 1 = 0.00194 m*K/W (6-6)

510.59 + 5.7024

Thus, the radiation contribution to the thermal resistance is very small

(approximately 1%).

The ratio of r to the thermal resistance of a 25.4 mm specimen is used to

indicate the order of magnitude of error due to contact resistance. Table

1 shows the percent value of this ratio for a range of k-values from 0,02

to 0,30 W/m*K,

6-2
i-*c u.l DEP’T. Of COkAA. 1. PUBLICATION OR 2. PeTorming O'gar.. Repor; Nc. 1. Puplicatior Date BIBLfOGRAF»HIC DATA

REPORT NO.

&^EET (See insvvctior.s NBSIR-85/3221 AUGUST 1985 . title and Subtitle

An Assessment of the NBS 1-m Guarded-Hot—Plate Limits

S. AUTHOR(S)

Brian Rennex

i. PERF^OR^inG ORGANIZATION nf >oint O'" ©O^e'" lAori NES. »ee trttrucUor> t)

rational bureau of standards

defartnent of commerce

WASHINGTON. D.C. 202S4

7. Contr*ct/G'snt Nc. t)E-Al05-850R21513

Task C85'':

I. Typ* of Repon A Pe'-iotf Covered

Final

S, SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Sireei. City. Sioie, ZIP)

Department of Energy

Oaic Ridge Operations Office

le. Supplementary notes

Document ©escribes e comoute' pr©fr«m; SP-I8E, F|PS Software Summary, is attached.

li. abstract (A 20D-w©ro ©r less focu>ol swmmory of most Significant information. If bocumeru induces c Significant

bitiiogDpny or iitercuire survey. menUon it here; The report evaluates the National Bureau of Standards 1-meter Guarded Bot Plate in

terms of the range of values of operating parameters. Tne ranges of operation are discussed according to three kinds of limiting factors. The first is the limits of

temperature over which the various apparatus components can be used without suffering' damage. Tne second kind is the limits of plate temperatures, specimen thickness,

atmospheric pressure, and relative humiditT achievable with the existing control systems. Tne third kind is any limits on the values of apparent thermal conductivity,

thermal resistance, or specimen thickness due to measurement error considerations.

The current operating range is documented by date of apparent thermal conductivity

versus specimen mean temperature and thickness. Tne current temperature limits for

the specimen mean temperature are -3°C to 55°C. Kinor Improvements can extend this

range to -30°C tc 190°C. There are no serious limits on thermal resistance or apparent thermal conductivity for typical specimens. There is no pressure control, and to

provide such control would be a major expense. The thickness limits are 19inm and 381

ram. The current limits on relative humidity are from 21 to 35J at 24®C. The upper

limit can easily be extended. An estimate of apparatus uncertainty is made over the

ranges of specimen mean temperature, apparent thermal conductivity, and thickness.

12. KEY WORDS fSi« to twelve entries; alphabetical order; capitalize only proper names. anC separate key words by semicolons)

epparent thermal conductivity; calibration; error analysis; guarded hot plate;

operating ranges; standard reference material (SRM) ; thermal insulation; thermalresistance.

13. availability

(X I Unlimited

[ I For Official Dletribotion. Do Not Releake to NTIS

1 I Order F rorr, Supermtendent of Documenti, U.S. Governmani Printing Off ice, 14 aihington. D.C. 20402.

f^l Order From National Technical Information Service (NTIS), Springfield. VA. 22161 ^ ^

14. NO. OF

PRINTED PAGES

15. Price

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