NAT'L INST OF STAND & TECH A111D7 22t>73fl

NIST Special Publication 260-173

Standard Reference Materials:

SRM 1450d, Fibrous-Glass Board, for

Thermal Conductivity from 280 K to 340 K

Robert R. Zarr Amanda C. Harris

John F. Roller Stefan D. Leigh

NiST RESEARCH LIBRARY

QC100 100 Bureau Drive

U57 atlthtrsburg, MD 20899-2800

NO. 260-173

2011

National Institute of Standards and Technology • U.S. Department of Commerce

NIST Special Publication 260-173

Standard Reference Materials:

SRM 1450d, Fibrous-Glass Board, for

Thermal Conductivity from 280 K to 340 K

Robert R. Zarr Amanda C. Harris John F. Roller Engineering Laboratory

Building Environment Division

Stefan D. Leigh

Information Technology Laboratory

Statistical Engineering Division

National Institute of Standards and Technology

Gaithersburg, MD 20899-8632

August 2011

U.S. Department of Commerce

Rebecca M. Blank, Acting Secretary

National Institute of Standards and Technology

Patrick D. Gallagher, Under Secretary of Commercefor Standards and Technology and Director
Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the

entities, materials, or equipment are necessarily the best available for the purpose.

National Institute of Standards and Technology Special Publication 260-173

Natl. Inst. Stand. Technol. Spec. Publ. 260-173, 128 pages (August 2011) CODEN: NSPUE2
Abstract

Thermal conductivity measurements at and near room temperature are presented as the basis for certified values of thermal conductivity for SRM 1450d, Fibrous Glass Board. The

measurements have been conducted in accordance with a randomized full factorial experi- mental design with two variables, bulk density and temperature, using the NIST 1016 mm

line-heat-source guarded-hot-plate apparatus. The thermal conductivity of the SRM speci- mens was measured over a range of bulk densities from 1 14 kg-mf

3 to 124 kg-irf3 and mean

temperatures from 280 K to 340 K. Uncertainties of the measurements, consistent in for- mat with current international guidelines, have been prepared. Statistical analyses of the physical properties from the SRM are presented and include variations between boards, as well as within board. Each unit of SRM 1450d is individually certified for bulk density, p, and batch certified for thermal conductivity with the following equation:

where X is the predicted thermal conductivity (W-rn -K" ) and Tm is the mean temperature (K)

valid over the temperature range of 280 K to 340 K. The expanded uncertainty for X values from the above equation is 1 % with a coverage factor of approximately k = 2.

calibration; bulk density; fibrous glass board; guarded-hot-plate apparatus; heat-flow- meter apparatus; standard reference material; SRM 1450d; thermal conductivity; thermal

insulation; uncertainty

Keywords

in
TABLE OF CONTENTS

Nomenclature 1

1 Introduction 4

2 Historical Background 6

2. 1 Early Program and Establishment of SRMs 1450 and 1450a 6

2.2 SRM 1450b 6

2.3 SRM 1450c 7

2.4 SRM 1450d 7

3 Terms and Definitions 8

3. 1 Reference Materials Definitions 8

3.2 Thermal Insulation Definitions 9

3.3 Uncertainty Definitions 10 4 Certification Project Design 12

4. 1 Project Definition and Scope for Intended Use 12

4.2 Material 12

4.2.1 Requirements 12

4.2.2 Fabrication 13

4.2.3 Fabrication Controls 13

4.2.4 Auxiliary Material Fabrication 14

4.3 Preparation 14

4.3.1 Inspection and Storage 14

4.3.2 General Sampling Procedure 14 4.4 Measurement Methods 15

4.4. 1 Bulk Density Study 1

5

4.4.2 Thermal Conductivity Measurements 15

5 Measurement Uncertainty 16

5.1 Combined Standard Uncertainty 16

5.2 Expanded Uncertainty 16

5.3 Type A and Type B Uncertainty Evaluations 17

5.4 Degrees of Freedom 17

5.5 Comments on Approach 17

6 Bulk Density Study 18

6. 1 Panel Mass Measurements 1

8

6.2 Dimensional Measurements 18

6.2.1 Lateral Panel Dimensions - Length and Width 19

6.2.2 Thickness 21

6.3 Homogeneity Assessment 22

6.3.1 Tabulated Results 22

6.3.2 Graphical Analyses 31

iv
6.3.3 Summary Statistics 38

6.3.4 Between- and Within-Panel Thickness Variations 38

6.3.5 Between-Panel Bulk Density Variations 40

6.3.6 Anomalous Panels (Outliers) 41

6.4 Establishing and Demonstrating Traceability 41

6.4.1 Mass 41

6.4.2 Length Dimensions 41

6.5 Bulk Density Uncertainty 41

7 Thermal Conductivity Measurements 43

7. 1 Experimental Design and Initial Model 43

7.1.1 Model Input Quantities - Bulk Density (p) and Temperature (T) 43

7.1.2 Other Quantities 43

7.2 Guarded-Hot-Plate Guard Insulation 44

7.3 Specimen Selection 45

7.4 Thermal Conductivity Apparatus 45

7.4. 1 Guarded-Hot-Plate Method 45

7.4.2 1 0 1 6 mm Guarded-Hot-Plate Apparatus 47

7.5 Establishing and Demonstrating Traceability 47

7.5.1 Specimen Heat Flow - Q 48

7.5.2 Temperature Difference - AT 49

7.5.3 Specimen Thickness - L 49

7.5.4 Meter Area -A 50

7.5.5 Influence (Secondary) Quantities 50

7.6- Identification of Uncertainty Sources 51

8 Data and Uncertainty Evaluation 53

8.1 Experimental Design Modification 53

8.2 Guarded-Hot-Plate Data 54

8.2. 1 Data Acquisition 54

8.2.2 Data Summary (Tabular Format) 54

8.2.3 Data Screening (Graphical Analysis) 56

8.2.4 Data Evaluation - Characterization 56

8.3 Final Model 58

8.4 Uncertainty in Experimental Thermal Conductivity (ktxp ) 58

8.4. 1 Uncertainty Budget 59

8.4.2 Confidence Limits (Working-Hotelling Bands) 60

8.4.3 Comments on Uncertainty Approach 61

8.4.4 Supplemental Thermal Conductivity Data 61

9 Certification 62

9. 1 Properties of Interest 62

9.2 Values and Uncertainties 62

9.3 Statement of Metrological Traceability 62

9.4 Instructions for Use 62

9.4.1 Storage 62

V
9.4.2 Preparation and Conditioning Before Measurement 63

9.4.3 Thermal Conductivity Measurement 63

9.4.4 Guidelines and Precautions 63

1 0 Acknowledgements 63

1 1 References 63 Annex 1 - Mass Plots 66 Annex 2 - Thickness Plots 84 Annex 3 - Bulk Density Uncertainty, Extensive Details 102 Annex 4 - Thermal Conductivity Uncertainty, Extensive Details 1 05 Annex 5 - Supplemental Thermal Conductivity Measurements 115

vi
LIST OF TABLES

Table 1 Thermal resistance and thermal conductivity of glass, silica, and polystyrene 5 Table 2 Chronology and certified property ranges of SRM 1450, Fibrous Glass Board 6 Table 3 Physical properties of SRM 1 450d units (450 panels) 23-30

Table 4 Summary statistics for the SRM 1450d production run (450 panels) 38

Table 5 Full factorial (3 X 3) experimental design 43

Table 6 Physical properties of guarded-hot-plate guard insulation 44

Table 7 Test specimens for (3><3) experimental design 45

Table 8 Calibration information for the NIST 1016 mm guarded-hot-plate apparatus 47

Table 9 Uncertainty sources for the NIST 1016 mm guarded-hot-plate apparatus 51 Table 10 Full factorial (3><5) experimental design 53 Table 1 1 Additional test specimens for (3 X 5) experimental design 53 Table 12 Required tolerance limits for acceptable steady-state test data 54

Table 1 3 Thermal conductivity data (sorted by Tm and pv ) 55 Table 14 Summary statistics for fixed- and recorded-value quantities 56

Table 15 Summary of linear profiles forX,exp versus ps (Fig. 14a) 58

Table 16 Summary of regression statistics for Xexp versus Tm (Fig. 14b) 58

Table A3-1 Uncertainty budget for height gage measurements 103 Table A4- 1 Summary of standard uncertainty components for u (Qm) 106 Table A4-2 Nominal settings for imbalance study (Yates order) 107 Table A4-3 Test results for imbalance study (Yates order) 107 Table A4-4 Parameter estimates and standard deviations for b\ and b2 in Eq. (A4-4) 108 Table A4-5 Estimates for uc (AQ) 108 Table A4-6 Combined standard uncertainty (A- = 1 ) for uc (Q) 1 09

Table A4: 7 Standard uncertainty components (k = 1) for T 110 Table A4-8 Standard uncertainty components (k — 1) for L 113 Table A4-9 Standard uncertainty components ( k = 1 ) for A 114 Table A4-10 Combined standard uncertainty (k = 1) for uc (A ) 114 Table A5- 1 Thermal conductivity data for specimen pair 1 84-369 1 1

5

vii
LIST OF FIGURES

Figure 1 Mass regain for Panel ID 438 after removal of panel from oven. Initial mass (m0) of

1.1060 kg was determined by linear extrapolation to time zero 19 Figure 2 a) Side view shows 610 mm height gage and right-angle fixture with insulation panel clamped between the aluminum jig plate and aluminum sheet, b) Front view shows panel

length measurements at locations l\, l2, h, U, h, and /6 (fixture and height gage are not shown). For a particular group of 50 panels, one panel was measured at all locations and

the other 49 panels were measured at locations l2 and /5 20

Figure 3 a) Front view shows 305 mm height gage and insulation panel (with workpiece) on granite surface plate, b) Top view shows an insulation panel and 8 thickness measurement locations (L/ - LH ) each in the geometric center of a 200 mm by 200 mm sub-area of the insula- tion panel. For a particular group of 50 panels, one panel was measured at all 8 locations and the other 49 panels were measured, in an alternating sequence, at the corner locations

(Z./, Lj, Li, L 7 ) and at the mid-center locations (L2 , L4 , L6 , L,s ) 21 Figure 4 Graphical analysis of panel mass (n = 450): (a) run sequence plot, (b) lag plot, (c) histo- gram, (d) normal probability plot (normality index). Summary statistics: mean =

1.1466 kg, standard deviation = 0.0250 kg, range = 0.1635 kg 32

Figure 5 Graphical analysis of panel length (n = 450): (a) run sequence plot, (b) lag plot, (c) histo- gram, (d) normal probability plot (normality index). Summary statistics: mean =

610.92 mm, standard deviation = 0.62 mm, range = 2.85 mm 33

Figure 6 Graphical analysis of panel width (n = 450): (a) run sequence plot, (b) lag plot, (c) histo- gram, (d) normal probability plot (normality index). Summary statistics: mean =

610.85 mm, standard deviation = 0.56 mm, range = 3.00 mm 34

Figure 7 Graphical analysis of panel area (n = 450): (a) run sequence plot, (b) lag plot, (c) histo- gram, (d) normal probability plot (normality index). Summary statistics: mean =

0.37318 m

2

, standard deviation = 0.00051 m

2

, range = 0.00243 m

2 35

Figure 8 Graphical analysis of panel thickness (n = 450): (a) run sequence plot, (b) lag plot, (c) his- togram, (d) normal probability plot (normality index). Summary statistics: mean =

25.88 mm, standard deviation = 0.18 mm, range = 1.74 mm 36

Figure 9 Graphical analysis of panel bulk density (n = 450): (a) run sequence plot, (b) lag plot, (c) histogram, (d) normal probability plot (normality index). Summary statistics: mean =

1 18.7 kg-m3

, standard deviation = 2.9 kg-m3

, range = 18.0 kg-m3 37

Figure 10 a) Graphical analysis of between-panel thickness variation represented by the means of the individual panel thickness measurements. Panels outside the control limits of three times

the standard deviation (±35, where s equals 0.18 mm from Table 4) are as follows: lowlimit, 039; high-limit 158, 159, 160, and 157. b) Graphical analysis of within-panel thick- ness variation represented by the standard deviations of the individual panel thickness measurements 39

Figure 1 1 Graphical analysis of between-panel bulk density variation. Panels outside the control limits of three times the standard deviation (±3s, where s equals 2.9 kg-m"3 from Table 4) are

as follows: low-limit, 055; high-limit 167 40

Figure 12 Guarded-hot-plate schematic, double-sided mode of operation - vertical heat flow 46

Figure 13 Electrical schematic for meter-plate power measurement 48

Figure 14 1450d: a) Graphical analysis of thermal conductivity versus bulk density. Error bars repre- sent expanded uncertainties of 0.86 %. b) Graphical analysis of thermal conductivity (with- out error bars for clarity) versus temperature 57

Figure 1 5 1450d: Graphical analysis of deviations (in %) for the fit given in Eq. (26) 59

Figure 16 1450d: 95 % Confidence Limits (Working-Hotelling Bands [29]) about the no-intercept

linear regression line ^exp on T. 60

Figure Ala Panel ID=l-25: Multiple mass observations (in kilograms) as a function of elapsed time (in seconds) for insulation panels 001 through 025. Linear fit for data (shown as solid line) was back-extrapolated to elapsed time zero (tQ ) to determine m0 for each insulation panel. 66

viii
Figure Alb Panel ID=26-50: Multiple mass observations (in kilograms) as a function of elapsed time

(in seconds) for insulation panels 025 through 050. Linear fit for data (shown as solid line) was back-extrapolated to elapsed time zero (/0) to determine m0 for each insulation panel. 67

Figure Ale Panel ID=5 1 -75: Multiple mass observations (in kilograms) as a function of elapsed time

(in seconds) for insulation panels 05 1 through 075. Linear fit for data (shown as solid line) was back-extrapolated to elapsed time zero (/0) to determine m0 for each insulation panel. 68

Figure Aid Panel ID=76-100: Multiple mass observations (in kilograms) as a function of elapsed time

(in seconds) for insulation panels 076 through 100. Linear fit for data (shown as solid line) was back-extrapolated to elapsed time zero (/0 ) to determine m0 for each insulation panel. 69

Figure Ale Panel ID=10 1-125: Multiple mass observations (in kilograms) as a function of elapsed time

(in seconds) for insulation panels 101 through 125. Linear fit for data (shown as solid line) was back-extrapolated to elapsed time zero (/0 ) to determine mQ for each insulation panel. 70

Figure Alf Panel ID=126-150: Multiple mass observations (in kilograms) as a function of elapsed time

(in seconds) for insulation panels 126 through 150. Linear fit for data (shown as solid line) was back-extrapolated to elapsed time zero (t0) to determine m0 for each insulation panel. 71 Figure Alg Panel ID=1 5 1-1 75: Multiple mass observations (in kilograms) as a function of elapsed time

(in seconds) for insulation panels 1 5 1 through 175. Linear fit for data (shown as solid line) was back-extrapolated to elapsed time zero (t0) to determine m0 for each insulation panel. 72

Figure Alh Panel ID=1 76-200: Multiple mass observations (in kilograms) as a function of elapsed time

(in seconds) for insulation panels 176 through 200. Linear fit for data (shown as solid line) was back-extrapolated to elapsed time zero (t0 ) to determine m0 for each insulation panel. 73

Figure Ali Panel ID=20 1-225: Multiple mass observations (in kilograms) as a function of elapsed time

(in seconds) for insulation panels 201 through 225. Linear fit for data (shown as solid line) was back-cxtrapolated to elapsed time zero (t0) to determine m0 for each insulation panel. 74

Figure Alj Panel ID=226-250: Multiple mass observations (in kilograms) as a function of elapsed time

(in seconds) for insulation panels 226 through 250. Linear fit for data (shown as solid line) was back-extrapolated to elapsed time zero (/0) to determine m0 for each insulation panel. 75

Figure Alk Panel ID=251-275: Multiple mass observations (in kilograms) as a function of elapsed time

(in seconds) for insulation panels 25 1 through 275. Linear fit for data (shown as solid line) was back-extrapolated to elapsed time zero (/0) to determine m0 for each insulation panel. 76

Figure All Panel ID=276-300: Multiple mass observations (in kilograms) as a function of elapsed time

(in seconds) for insulation panels 276 through 300. Linear fit for data (shown as solid line) was back-extrapolated to elapsed time zero (r0 ) to determine m0 for each insulation panel. 77

Figure Aim Panel ID=30 1-325: Multiple mass observations (in kilograms) as a function of elapsed time

(in seconds) for insulation panels 301 through 325. Linear fit for data (shown as solid line) was back-extrapolated to elapsed time zero (/0) to determine m0 for each insulation panel. 78

Figure Aln Panel ID=326-350: Multiple mass observations (in kilograms) as a function of elapsed time

(in seconds) for insulation panels 326 through 350. Linear fit for data (shown as solid line) was back-extrapolated to elapsed time zero (/0 ) to determine m0 for each insulation panel. 79

Figure Alo Panel ID=35 1-375: Multiple mass observations (in kilograms) as a function of elapsed time

(in seconds) for insulation panels 351 through 375. Linear fit for data (shown as solid line) was back-extrapolated to elapsed time zero (/0) to determine m0 for each insulation panel.

ix
Figure Alp Panel ID=376-400: Multiple mass observations (in kilograms) as a function of elapsed time

(in seconds) for insulation panels 376 through 400. Linear fit for data (shown as solid line) was back-extrapolated to elapsed time zero (/0) to determine m0 for each insulation panel.

81 Figure Alq Panel ID=40 1-425: Multiple mass observations (in kilograms) as a function of elapsed time

(in seconds) for insulation panels 401 through 425. Linear fit for data (shown as solid line) was back-extrapolated to elapsed time zero (to) to determine m0 for each insulation panel. 82

Figure Air Panel ID=426-450: Multiple mass observations (in kilograms) as a function of elapsed time

(in seconds) for insulation panels 426 through 450. Linear fit for data (shown as solid line) was back-extrapolated to elapsed time zero (/0) to determine m0 for each insulation panel. 83

Figure A2a Panel ID=001-025: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 001 through 025. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame) 84

Figure A2b Panel ID=026-050: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 026 through 050. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame) 85

Figure A2c Panel ID=05 1-075: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 051 through 075. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame) 86

Figure A2d Panel ID=076-100: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 076 through 100. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame) 87

Figure A2e Panel ID=101-125: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 101 through 125. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame) 88

Figure A2f Panel ID=126-150: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 126 through 150. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame) 89

Figure A2g Panel ID= 151-1 75: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 151 through 175. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame) 90

Figure A2h Panel ID= 176-200: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 176 through 200. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame) 91 Figure A2i Panel ID=20 1-225: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 201 through 225. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame) 92

Figure A2j Panel ID=226-250: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 226 through 250. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame) 93

Figure A2k Panel ID=25 1-275: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 251 through 275. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame) 94

Figure A21 Panel ID=276-300: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 276 through 300. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame) 95

Figure A2m Panel ID=301-325: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 301 through 325. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame) 96

Figure A2n Panel ID=326-350: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 326 through 350. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame) 97

x
Figure A2o Panel ID=351-375: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 351 through 375. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame) 98

Figure A2p Panel ID=376-400: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 376 through 400. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame) 99

Figure A2q Panel ID=401-425: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 401 through 425. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame) 100

Figure A2r Panel ID=426-450: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 426 through 450. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame) 101 Figure A5a Re-measured thermal conductivity versus temperature for specimen pair 184-369. The

solid line represents the fitted model for certification data from Table 13. The dashed lines represent Miller-Lieberman 95 %- 95 % simultaneous tolerance intervals [35] 1 16

xi

Nomenclature

Symbol Description (Units) a regression coefficient in Eq. (10) (kg-s

1 )

cii regression coefficients in Eq. (2 1

)

A meter area (m ) As area of the specimen (panel) (m2

) bj regression coefficients in Eq. (A4-4)

Ci sensitivity coefficient for uncertainty analysis

d half-width of uniform rectangular distribution DMM digital multimeter

i index (dimensionless)

/ electrical direct current (A) ID identification (dimensionless) E modulus of elasticity (N-m 2

) / clamping pressure applied to specimen by cold plate (Pa) F clamping load applied to specimen by cold plate (N) k coverage factor for uncertainty (dimensionless) U linear dimensions (length, width) of insulation panel (mm)

h (mean) length dimension of insulation panel (mm)

h

' (mean) width dimension of insulation panel (mm)

L (in-situ) thickness of guarded-hot-plate test specimen (mm) Lavg average specimen thickness in Eq. (23) (m)

Li thickness dimensions of insulation panel (mm)

Lm mean thickness of insulation panel dimensions (mm) m reciprocal of Poisson's ratio (dimensionless) m (t) mass of the insulation panel as a function of time (kg) mo initial mass of the insulation panel in Eq. (10) (kg) ms mass of the specimen (panel) (kg) n number of independent observations (dimensionless) pa chamber air pressure (kPa) PRT platinum resistance thermometer Q heat flow rate through meter area of guarded-hot-plate test specimen (W)

Qe edge heat flow (W)

Qg

lateral (i.e., radial) heat flow rate across the guard gap (W)

Qm input power to meter-plate resistance heater in Eq. (24) (W)

Qmo input power to meter-plate resistance heater under balanced temperature conditions in Eq. (A4-3) (W)

l
q heat flow rate through a surface of unit area perpendicular to the direction of heat flow (W-nf2

) Yf radius of uniform loading applied to cold plate (m)

r, inner radius of guard plate (m)

r0 (outer) radius of meter plate (m)

rp

radius of (cold) plate (m) R thermal resistance (m2 KW~')

Rs electrical resistance of standard resistor (Q)

RH relative humidity of chamber air (%)

s standard deviation

sp standard deviation of process SPRT standard platinum resistance thermometer

t elapsed time in Eq. (10) (s)

to start time in Eq. (10) (s)

tc thickness of cold plate (m)

/-value estimate (e.g., slope) divided by standard uncertainty of estimate (dimensionless) T temperature (K) Ta chamber air temperature (K) Tc (average) cold-plate temperature (K)

Ti, hot-plate temperature (K) Tm mean specimen temperature (K) = (Th + Tc)/2 uc combined standard uncertainty (k = 1) uc>rei relative combined standard uncertainty {k= 1) (dimensionless)

iti standard uncertainty for quantity i us standard uncertainty for standard artifact U expanded uncertainty (k = 2)

Urei relative expanded uncertainty (k = 2) (dimensionless)

Vg voltage difference across guard gap thermopile (uV)

Vgo voltage difference across guard gap thermopile under balanced condition (uV)

Vm voltage difference across meter-plate resistance heater (V) Vs voltage difference across standard resistor (V)

Xj x-value for graphical analysis

xi-\ previous x-value for graphical analysis x arithmetic mean of x-values

X] imbalance input variable in Eq. (A4-4)

xi imbalance input variable in Eq. (A4-4) y response variable for imbalance study

2
(X illlCdl UlClllldl CXpdllMUll CUCIllLICIll ^IV ) A\ny CildilgC 111 1I1CICI -piaLC HCdLCi pUWCl ULIC IU UllUdldllCC HJ11U1L1U11 UCbLllUCU 111 Eq. (A4-3) (W)

AT temperature difference across specimen (K) = (7), — Tc ) average temperature difference in Eq. (23) (K) ATmp temperature difference in Eq. (25) (K) = (Tf, — 20 °C)

8 plate emittance (dimensionless) X thermal conductivity (W m '-K

1 ) Xa or ka apparent thermal conductivity ( W-rn'-K 1 ) ^-exp experimental thermal conductivity in Eq. (22) and Eq. (23) (W-rn'-K"

1 ) P bulk density (kg-m 3

) Ps bulk density of specimen panel in Eq. (1) (kg-m"

3 )

Additional subscripts

1 top cold plate/specimen 2 bottom cold plate/specimen

A Type A standard uncertainty evaluation B Type B standard uncertainty evaluation

Additional superscript denotes sample mean

3
1 Introduction

Thermal insulation Standard Reference Materials" (SRMs) 1 are issued by the National

Institute of Standards and Technology (NIST) for materials with certified value assign- ments for thermal resistance and thermal conductivity. SRMs are provided by NIST as primary tools to assist user communities in achieving measurement quality assurance and

metrological traceability. These materials are used by industry, academia, and govern- ment to verify or improve the accuracy of specific measurements and to advance the

state-of-the-art knowledge. Thermal insulation SRMs, in particular, are utilized in stan- dard test methods for the purposes of checking guarded-hot-plate apparatus [1], calibrat- ing heat-flow-meter apparatus [2], and, when necessary, for checking or calibrating hot- box apparatus [3]. These SRMs also assist insulation manufacturers in the United States

in complying with federal requirements for labeling and advertising of home insulation

(also known as the U.S. Federal Trade Commission "R-value Rule" [4]). Value assignments for thermal insulation SRMs are developed with the guarded-hot-plate method [1]. The method is considered an absolute measurement procedure because the re- sulting thermal transmission properties are determined directly from basic measurements of

length, area, temperature, and electrical power. Essentially, the method establishes steadystate heat flow through flat homogeneous slabs - the surfaces of which are in contact with

adjoining parallel boundaries (i.e., plates) maintained at constant temperatures. By accurately monitoring the plate separation and knowing the geometric shape factor for the heat flow, the

steady-state heat transmission properties of the test specimen are determined using the Fourier heat conduction equation. Influence quantities such as plate clamping pressure, plate emittance, and ambient air temperature, among others, are controlled; while other quantities such as ambient air pressure are monitored during the measurement process. In principle, the method can be used over a wide range of insulating materials, mean temperatures, and temperature differences. For a material lot, the thermal resistance and thermal conductivity of a thermal insulation SRM are generally characterized as functions of bulk density and mean temperature. The

characterization is typically accomplished by batch certification. A statistically sound

sampling scheme is used to select specific specimens from the material lot for testing in the guarded-hot-plate apparatus. The analysis of the thermal conductivity data of the sample sub-lot is used for certification of the SRM lot. Consequently, the uncertainty statement for a thermal insulation SRM contains a component of uncertainty (usually small) due to the material lot variability. It should be noted that a thermal insulation SRM unit issued to a customer has not been measured directly in a NIST guarded-hotplate apparatus. The advantage of the batch approach is realized by characterizing a large quantity of units that are economical and available on demand. In practice, thermal insulation SRM lots are prepared with a sufficient number of units to meet anticipated de- mand for a period of ten years.

' The term "Standard Reference Material" and the diamond-shaped logo which contains the term "SUM,"

are registered with the United States Patent and Trademark Office.
Standard Reference Material 1450d, like previous 1450 lots, is a semi-rigid, high-density, molded fibrous-glass board that was fabricated from a single production run by a commercial manufacturer of molded fibrous-glass products. The Standard Reference Material 1450 Series is one of several certified thermal insulation reference materials issued by NIST. These related thermal insulation SRMs have been categorized by the NIST

Standard Reference Materials Program (SRMP) in Table 203.17 - Thermal Resistance and Thermal Conductivity Properties of Glass, Silica, and Polystyrene (solid forms) [5] reproduced in Table 1

.

Table 1 . Thermal resistance and thermal conductivity of glass, silica, and polystyrene Designation Description Temperature range (K) 1449 Fumed silica board 297.1 1450d Fibrous glass board 280 to 340

1452 Fibrous glass blanket 297.1 (100 to 330) 1453 Expanded polystyrene board 285 to 310

1459 Fumed silica board 297.1

NIST Special Publication 260-173, which is part of the "NIST Special Publication 260

Series," provides supplemental documentation for the 1450d Certificate and covers the following subject matter:

. historical background of the SRM 1450 Series; standard terminology for reference materials, thermal insulation materials, and measurement uncertainty; project plan for certification including the fabrication and procurement of the material lot; measurement methods for the bulk density and thermal conductivity evaluations; uncertainty analysis; and,

certification.

5
2 Historical Background

Table 2 summarizes the production chronology of SRM 1450, Fibrous Glass Board. The SRM approach for thermal insulating reference materials was recommended by a working group under ASTM Subcommittee CI 6.30 on Thermal Measurement as part of a lar- ger task to establish a national accreditation program for thermal insulation [6]. In re- sponse, NIST (formerly the National Bureau of Standards

2

) established SRM 1450 and, subsequently, 1450a using previously obtained materials.

Table 2. Chronology and certified property ranges of SRM 1450, Fibrous Glass Board SRM designation Date issued Bulk density (kgrn 3

) Temperature

(K) 1450 26 May 1978 100 to 180 255 to 330

1450a 12 Feb. 1979 60 to 140 255 to 330

1450b (I) 21 May 1982 110 to 150 260 to 330

1450b (II) 20 May 1985 110 to 150 100 to 330

1450c 05 Mar. 1997 150 to 165 280 to 340

1450d 11 July 2011 114 to 124 280 to 340

2.1 Early Program and Establishment of SRMs 1450 and 1450a The National Bureau of Standards (NBS) had actually formally initiated a thermal insula- tion reference material program in 1958 [7], which provided individual (calibration) measurements of high-density molded fibrous glass insulation board. From 1958 to 1978, NBS provided over 300 pairs [8] of "calibrated reference specimens1

' selected from

four lots of fibrous-glass board, designated by the year of their acquisition (1958, 1959,

1961, and 1970) using the NBS 200 mm guarded-hot-plate apparatus. In 1978, the re- maining boards in these internal lots were used to initiate SRMs 1450 and 1450a [8]. 2.2 SRM 1450b Due to limited stockpiles, 1450 and 1450a were rapidly depleted and two additional lots were acquired in 1980 and 1981 for the development of SRM 1450b. The thermal characterization of SRM 1450b was jointly carried out by the NBS Center for Building Tech- nology in Gaithersburg, Maryland and by the NBS Center for Chemical Engineering in Boulder, Colorado [9]. Standard Reference Material 1450b was initially issued with as- signed certified values at a moderate temperature range and informational values below

255 K (Table 2, 1450b(I)). After conducting additional low-temperature measurements, NBS re-issued 1450b(II) with assigned certified values from 100 K to 330 K [9] (Table 2).

2 In 1901, Congress established the National Bureau of Standards (NBS) to support industry, commerce,

scientific institutions, and all branches of government. In 1988, as part of the Omnibus Trade and Competitiveness Act, the name was changed to the National Institute of Standards and Technology (NIST) to

reflect a broader mission for the agency. For historical accuracy, this report will use, where appropriate, NBS for events prior to 1988.

6
2.3 SRM 1450c

In 1995, the NIST Standard Reference Materials Program (SRMP) requested that the Building and Fire Research Laboratory initiate a research program to replenish 1450b

with a new SRM lot, designated 1450c. Because 1450b had been characterized in the

early 1980s, a questionnaire to re-assess requirements for a new SRM was disseminated

to the user community. Based on the responses, NIST procured a new material lot of molded fibrous-glass insulation boards [10] having a nominal bulk density of 160 kg-m"

3

. In contrast to previous 1450 lots, the procedures for acquisition, testing, and production of 1450c were modified as follows. A single production run of molded fibrous-glass boards was acquired (in contrast

to multiple production runs for previous versions of 1450), thereby reducing the density range for the SRM lot (Table 2). Under guidance from the NIST Statistical Engineering Division, a balanced ex- perimental design was developed and implemented for batch certification of the material lot [10]. Additional measurements and statistical analyses were carried out to assess not only the between-board but also within-board variability for thickness and bulk

density.

2.4 SRM 1450d

The initial planning and research phase for 1450d began in 2007. Technical information and requirements were collected from SRM customers and from an ASTM CI 6.30 Reference Materials Task Group. After an extensive search for suitable materials, NIST ac- quired and evaluated [11] two commercial replacement candidates. Based on this evaluation, NIST procured, in 2009, 450 insulation panels from one vendor for the production of SRM 1450d. The basic approach utilized for the production and certification of 1450c,

outlined in Sec. 2.3, has been implemented for SRM 1450d.

7
3 Terms and Definitions

3.1 Reference Materials Definitions

Section 3.1 provides a list of NIST-adopted and NIST-developed definitions [12] for the production, certification, and use of NIST SRMs.

Reference Material (RM): material, sufficiently homogeneous and stable with respect to one or more specified properties, which has been established to be fit for its intended use

in a measurement process (ISO Guide 30: 1992(E)/Amd. 1:2008 [13]). NOTE 1 RM is a generic term. NOTE 2 Properties can be quantitative or qualitative, e.g. identity of substances or species. NOTE 3 Uses may include the calibration of a measurement system, assessment of a measurement procedure, assigning values to other materials, and quality control. NOTE 4 A single RM cannot be used for both calibration and validation of results in the same measurement procedure. NOTE 5 VIM3 has an analogous definition (ISO/IEC Guide 99:2007, 5.13), but restricts the term "measurement" to apply to quantitative values and not to qualitative properties. However, Note 3 of ISO/IEC Guide 99:2007, 5.13, specifically includes the concept of qualitative attributes, called "nominal properties". Certified Reference Material (CRM): Reference material characterized by a metrologically valid procedure for one or more specified properties, accompanied by a certificate that provides the value of the specified property, its associated uncertainty, and a state- ment of metrological traceability (ISO Guide 30:1992(E)/Amd.l:2008 [13]). NOTE 1 The concept of value includes qualitative attributes such as identity or sequence.

Uncertainties for such attributes may be expressed as probabilities. NOTE 2 Metrologically valid procedures for the production and certification of reference

materials are given in, among others, ISO Guides 34 and 35. NOTE 3 ISO Guide 3 1 gives guidance on the contents of certificates. NOTE 4 VIM has an analogous definition (ISO/IEC Guide 99:2007, 5.14). NIST Standard Reference Material® (SRM): A CRM issued by NIST that also meets

additional NIST-specified certification criteria. NIST SRMs are issued with Certificates of Analysis or Certificates that report the results of their characterizations and provide

information regarding the appropriate use(s) of the material [12]. NOTE 1 An SRM is prepared and used for three main purposes: (1) to help develop accurate methods of analysis; (2) to calibrate measurement systems used to facilitate ex- change of goods, institute quality control, determine performance characteristics, or measure a property at the state-of-the-art limit; and (3) to ensure the long-term ade- quacy and integrity of measurement quality assurance programs. NOTE 2 The terms "Standard Reference Material" and the diamond-shaped logo which contains the term "SRM," are registered with the United States Patent and Trademark

Office. NIST Certified Value: A value reported on an SRM certificate or certificate of analysis

for which NIST has the highest confidence in its accuracy in that all known or suspected

sources of bias have been fully investigated or accounted for by NIST [12].

3 International Vocabulary of Metrology (VIM).

8
NIST Information Value: A NIST Information Value is considered to be a value that will be of interest and use to the SRM/RM user, but insufficient information is available

to assess the uncertainty associated with the value [12].

3.2 Thermal Insulation Definitions

Section 3.2 provides a list of terms, symbols, definitions, and units pertaining to properties and measurements of thermal insulating materials. apparent thermal conductivity, Xa or ka: a thermal conductivity assigned to a material

that exhibits thermal transmission by several modes of heat transfer resulting in property

variation with specimen thickness, or surface emittance [14]. NOTE 1 Thermal conductivity and resistivity are normally considered to be intrinsic or specific properties of materials and, as such, should be independent of thickness. When nonconductive modes of heat transfer are present within the specimen (radiation, free convection) this may not be the case. To indicate the possible presence of

these phenomena (for example, thickness effect) the modifier "apparent" is used, as

in apparent thermal conductivity. NOTE 2 Test data using the "apparent" modifier must be quoted only for the conditions of

the measurement. Values of thermal conductance and thermal resistance calculated from apparent thermal conductivity or resistivity, are valid only for the same conditions. density, p: the mass per unit volume of material. (SI units: kg-m"3

) [14]. NOTE 1 The metered section density, p,„, or the specimen density, ps where metered section area density cannot be obtained, are to be reported as the average of the two pieces (excerpted from Ref. [1]). The equation for specimen density is the following:

where: ms = mass of the specimen (kg), As = area of the specimen (m2

), and L = specimen thickness (m). heat flow; heat flow rate, Q: the quantity of heat transferred to or from a system in unit time (W) [14]. NOTE 1 see heat flux for the areal dependence. NOTE 2 This definition is different than that given in some textbooks, which may use Q or q to represent heat flow rate. The ISO definition uses O. heat flux, q: the heat flow rate through a surface of unit area perpendicular to the direc- tion of heat flow (W-m"2

) [14]. fibrous glass: a synthetic vitreous fiber insulation made by melting predominantly silica sand and other inorganic materials, and then physically forming the melt into fibers [14]. thermal conductivity, X: the time rate of steady state heat flow through a unit area of a homogeneous material induced by a unit temperature gradient in a direction perpendicular to that unit area (SI units: (W/m2 )/(K/m) = W-nf'-K" 1 ) (excerpted from Ref. [14]).

9
NOTE 1 Thermal conductivity testing is usually done in one of two apparatus/specimen geometries: flat-slab specimens with parallel heat flux lines, or cylindrical specimens

with radial heat flux lines. The operational definition of thermal conductivity for

flat-slab specimens is given as follows:

' - QL

(2) AAT

where: Q = heat flow rate, A = area through which Q passes, and L = thickness of the flat-slab specimen across which the temperature difference AT

exists The AT/L ratio approximates the temperature gradient. thermal resistance, R: the quantity determined by the temperature difference, at steady

state, between two defined surfaces of a material or construction that induces a unit heat flow rate through a unit area.

R -~-k < 3 > q X A resistance (R) associated with a material shall be specified as a material R. A resis- tance (R) associated with a system or construction shall be specified as a system R. (R in SI units : K/(W/m2

) = K-nr-W" 1 (excerpted from Ref. [14]). NOTE 1 Thermal resistance and thermal conductance are multiplicative reciprocals. thermal transmission properties: those properties of a material or system that define

the ability of a material or system to transfer heat such as thermal resistance and thermal

conductivity, among others (excerpted from Ref. [1]). semi-rigid board insulation: qualitative property associated with the degree of supple- ness (i.e., flexibility), particularly related to the geometrical dimensions and bulk density of the board.

3.3 Uncertainty Definitions

Section 3.3 provides a list of international definitions for the expression of uncertainty in measurement [15]. combined standard uncertainty, uc

: standard uncertainty of the result of a measurement when that result is obtained from the values of a number of other quantities, equal to the

positive square root of a sum of terms, the terms being the variances or covariances of

these other quantities weighted according to how the measurement result varies with changes in these quantities. coverage factor, k: numerical factor used as a multiplier of the combined standard uncertainty in order to obtain an expanded uncertainty. NOTE 1 A coverage factor, k, is typically in the range 2 to 3.

10
expanded uncertainty, U: quantity defining an interval about the result of a measure- ment that may be expected to encompass a large fraction of the distribution of values that could be reasonably attributed the measurand. standard uncertainty, «,-: uncertainty of the result of a measurement expressed as stan- dard deviation. Type A evaluation (of uncertainty): method of evaluation of uncertainty by the statisti- cal analysis of series of observations Type B evaluation (of uncertainty): method of evaluation of uncertainty by means other than the statistical analysis of series of observations

11
4 Certification Project Design

Section 4 provides a summary of the overall project plan starting with the project defini- tion and the intended scope for SRM 1450d. A brief description for the reference material including requirements, fabrication, and manufacturer controls is presented. The material preparation including inspection, storage, and conditioning as part of the general

sampling plan is described. Lastly, the choice of measurement methods for the homogeneity analysis, certification measurements, and corresponding uncertainty evaluation are described.

4.1 Project Definition and Scope for Intended Use

The certification project is defined as follows. "The preparation of thermal insulation SRM 1450d for thermal resistance and

thermal conductivity measurements with expanded uncertainties (k = 2) associated

with the certified values ofless than or equal to 2 % over a mean temperature range

of 280 K to 340 K." Standard Reference Material 1450d is intended for use as a proven check for the guardedhot-plate apparatus (or other absolute thermal conductivity apparatus) and for calibration of a heat-flow-meter apparatus over the temperatures 280 K to 340 K. This report cannot exclude the use of SRM 1450d for other purposes, but the user is cautioned that other purposes are not necessarily covered by the 1450d Certificate or by this report. Additional usage issues are covered in Sec. 9.4.4 and in the 1450d Certificate (under Instruc- tions For Handling, Storage, And Use).

4.2 Material

4.2.1 Requirements

The material requirements were based on recommendations from current SRM customers and members of the ASTM CI 6.30 Reference Materials Task Group and were defined as follows: - material type: molded fibrous-glass insulation board - nominal bulk density: 128 kg-nf3 - nominal thickness: 25 mm

- finished panel size: 610 mm x 610 mm

- number of panels: 450 (minimum) from the same production run The material is a semi-rigid thermal insulation board fabricated in square panels having

finished dimensions (610 mm by 610 mm by 25 mm) that are intended for the test equip- ment covered in the Scope (Sec. 4.1). The nominal bulk density (128 kg-m"3 ) for the material lot is consistent with the bulk densities of previous 1450 lots (Table 2). The number of panels needed was dictated by the number of units to be produced (based on a

10 year SRM inventory) plus the number of panels needed for the homogeneity study and

the thermal characterization of the candidate SRM.

12
4.2.2 Fabrication The material lot was fabricated by Quiet Core Incorporated

4 over a three-day period and

delivered to NIST in April 2009. The details of the fabrication process are proprietary, but the basic progression of steps is as follows. The raw material consists of rolls of un- cured fibrous-glass insulation having two different densities. Raw material from the two

rolls is cut and assembled by building up multiple layers between two metal platens. The

layered assembly is subsequently molded into board form under pressure and heat. The

glass fiber lay for the assembly is characteristically parallel to the long dimensions of the sheet (i.e., perpendicular to the direction of heat flow in application). After removal from

the mold, the sheet is cooled and die-cut into six panels each having a nominal finished

size of 610 mm by 610 mm.

The technical information for the physical properties of the finished material lot is summarized below: - production run time period: - bulk density: - approximate mold size : - number of molded sheets: - number of panels per sheet: - number of panels: - nominal panel size: - panel color: - raw material fiber diameter

4.2.3 Fabrication Controls The manufacturer implemented the following fabrication controls for production of the material lot. - Prior to fabrication, four of the incoming uncured rolls of material having the same nominal density were selected at random and the gram mass per unit area sampled at six pre-determined locations. The gram mass average ( x ) and range were computed and checked against required nominal values and range limits for acceptance. - During the fabrication process, the molded sheets were monitored regularly at 1 h

intervals by control charting (x, range chart) measured data for the thickness, gram mass, and density.

o The control limits for the thickness average and range were determined for a subgroup of four measurements taken from each panel location within a sheet

(6 panels x 4 measurements per panel = 24 measurements per sheet). The

control limits for the thickness average and range were compared against a specified thickness of 25.4 mm and range of 0.8 mm, respectively.

3 days

128 kg-m"3 ± 10%

1245 mm x 1930 mm

75

6450 (= 75 x 6) 610 mm x 610 mm x 25.4 mm

amber

9.3 um (average); 9 urn to 1 1 urn (range)

The full description of the procedures used in this paper requires the identification of certain commercial

products and their suppliers. The inclusion of such information should in no way be construed as indicat- ing that such products or suppliers are endorsed by NIST or are recommended by NIST or that they are necessarily the best materials or suppliers for the purposes described.

13
o The control limits for the gram mass and density were determined for each of

the panels measured. The control limits for the density average and range were compared against the specified density of 128 kg-m"3 and tolerance of ±10%.

During the fabrication process, the individual sheets were also inspected visually

for any obvious material defects. After the cutting process, the panels were

stacked in order of manufacture and crated for protection.

4.2.4 Auxiliary Material Fabrication The manufacturer fabricated, from the same lot of raw material, 25 sheets of additional material having the same nominal density and finished dimensions of 1200 mm by

1200 mm by 25.4 mm. These large sheets were from the same production run, but were

not part of the 1450d material lot. These large sheets were utilized by NIST, as described

in Sec. 7.2, for testing the 1450d material lot in a 1016 mm diameter guarded-hot-plate

apparatus.

4.3 Preparation

Section 4.3 describes the inspection of the material lot and subsequent conditioning treat- ment for the homogeneity study.

4.3.1 Inspection and Storage

The insulation panels were visually inspected for damage after delivery. After inspection, each panel was identified with a permanent 3 -digit number assigned from 001 to 450 (hereafter, Panel ID) in preparation for the 100 % sampling requirement. The material lot was stored for several months in laboratory workspace at ambient conditions.

4.3.2 General Sampling Procedure

For 1 00 % sampling of the material lot, the panels were divided into 9 separate groups of 50 randomly selected panels (panel randomization sequence 1). Each group of 50 panels was processed through a three-day measurement procedure outlined below. - Day 1 - Conditioning at 100 °C for 20 h

o Condition 1: One group of 50 panels was removed from laboratory storage and placed collectively in a convection oven and heat treated in air at 100 °C

for 20 h (overnight). - Day 2 - Mass measurements

o Over a time period of 3 h to 4 h, each panel was removed individually from

the oven and weighed repeatedly to establish a mass time history.

o Condition 2: After weighing, the group of 50 panels was placed collectively

in laboratory ambient conditions at 23 °C for about 17 h (overnight). - Day 3 - Dimensional measurements

o Over a time period of 3 h to 4 h, the length dimensions of each panel were

measured by Operator 1. The measurements were conducted in a different randomization sequence order (panel randomization sequence 2). o Over an overlapping time period of 3 h to 4 h, the thickness dimensions of

each panel were measured by Operator 2.

14
The entire measurement process for all 9 groups of 50 panels (450 panels in total) re- quired 30 days. The detailed protocols and measurement results for the panel mass and

dimensions are presented in Sec. 6.

4.4 Measurement Methods

Section 4.4 describes the primary (definitive) methods for sampling the bulk density and

for thermal characterization of the material lot.

4.4.1 Bulk Density Study

The bulk density, as defined in ASTM Test Method C 177 [1] (Terms and Definitions), was determined for each individual finished panel (610 mm by 610 mm by 25 mm) from

established gravimetric and dimensional measurement procedures that are documented in Sec. 6. The major objective of the bulk density study is to assess the material variability of the material lot (i.e., variability between insulation panels), thereby providing quantitative information for the following: - quantitative ranking of the material lot by bulk density; - the upper and lower bulk density limits of the material lot; and, - detection of any anomalous thermal insulation panels for possible exclusion.

4.4.2 Thermal Conductivity Measurements

The steady-state thermal transmission measurements (i.e., thermal conductivity) were de- termined in accordance with ASTM Test Method C 177 [1] using the NIST 1016 mm

guarded-hot-plate apparatus [16]. In contrast to the 100 % sampling process for the ho- mogeneity study, the thermal conductivity of 1450d was batch certified. Sub-sampling of

the insulation material lot was based on the demonstrated approach taken for the devel- opment of the previous version, SRM 1450c [10]. The 1450d lot was sub-sampled at three levels of bulk density (low, mid, and high). Quantitative values for these rankings were defined using the results of the homogeneity study (Sec. 6). Detailed procedures of

the guarded-hot-plate test method, apparatus, corresponding uncertainty, and thermal

characterization are documented in Sec. 7.

15
5 Measurement Uncertainty

Section 5 summarizes relevant equations for the determination and expression of measure- ment uncertainty in accordance with current international guidelines for the expression of measurement uncertainty in the Guide to the Expression of Uncertainty in Measurement

[15], also known as the "GUM."

5.1 Combined Standard Uncertainty

The combined standard uncertainty of a measurement result, uc (y) is expressed as the positive square root of the combined variance ir.(y)

Equation (4) is commonly referred to as the "law of propagation of uncertainly" or the "root-sum-of-squares." A sensitivity coefficient (c/) is equal to the partial derivative of an

input quantity (dfldXi) evaluated for the input quantity equal to an input estimate (X, = x,). The corresponding term, u (x,), (shorthand expression «,) is the standard uncertainty associ- ated with the input estimate x;

. The relative combined standard uncertainty is defined as follows (where y * 0):

5.2 Expanded Uncertainty The expanded uncertainty, U, is obtained by multiplying the combined standard uncertainty, uc (y), by a coverage factor, k, when an additional level of uncertainty is required

that provides an interval about the measurement result (similar to a confidence interval):

The value of k is chosen based on the desired level of confidence to be associated with the

interval defined by U and typically ranges from 2 to 3. Under a wide variety of circumstances, a coverage factor of k = 2 defines an interval having a level of confidence of ap- proximately 95 % and k = 3 defines an interval having a level of confidence greater than 99 %. At NIST, a coverage factor consistent with international practice of k = 2 is used, by

convention [15]. The relative expanded uncertainty is defined as follows (where y 0):

(4)

U = kuc (y) (6)

(7)

16
5.3 Type A and Type B Uncertainty Evaluations Each u (Xj) in Eq. (4) is evaluated as either a Type A or a Type B standard uncertainty. Evaluation examples are provided in Ref. [15]. Type A standard uncertainties are evaluated by statistical means. The evaluation of uncertainty by means other than a statistical analysis of a series of observations is termed a Type B evaluation. Type B evaluations are usually based on scientific judgment and may include measurement data from another ex- periment, experience, a calibration certificate, manufacturer specification, or other means

[15]. A common example of a Type A evaluation entails repeated observations. Consider an in- put quantity Xj determined from n independent observations obtained under the same conditions. In this case, the input estimate x, is the arithmetic mean determined from

The standard uncertainty, it associated with x, is the estimated standard deviation of the sample mean (where s is the standard deviation of n observations):

u(xi ) = s(Xi ) = ^= (9)

It is emphasized that the designations "A" and "B" apply to the two methods of evaluation, not the type of error. In other words, the designations "A" and "B" should not be associ- ated with the traditional terms "random" or "systematic." Categorizing the evaluation of

uncertainties as Type A or Type B is a matter of convenience, since both are based on

probability distributions

5 and are combined equivalently.

5.4 Degrees of Freedom

For Type A evaluations, the degrees of freedom, v, is equal to n - 1 for the simple case given in Eq. (8). For the case when uc is the sum of two or more variance components, an

effective degrees of freedom can be obtained from the Welch-Satterthwaite formula as described in Ref. [15]. For certain Type B evaluations, v may be assumed to be infinity. As

described later in Annex 3 and Annex 4, Type B evaluations are often the dominant components of uncertainty.

5.5 Comments on Approach

A general approach taken in this report is to consider conservative (i.e., maximum) esti- mates for the standard contributory uncertainties.

5 Note that the probability distribution for a Type B evaluation, in contrast to a Type A evaluation, is as- sumed based on the judgment of the experimenter.

17
6 Bulk Density Study

Section 6 describes the measurements of mass and linear dimensions for the determination of bulk density of an insulation panel. Graphical analyses and tabulated results for mass, panel area, thickness, and bulk density for all 450 specimens are presented.

6.1 Panel Mass Measurements

The mass measurement of the insulation panel is based on the gravimetric method. The

measurement station consisted of the following equipment: a) digital weighing balance

(32.1 kg range, 0.0001 kg resolution); b) foot switch for manual event activation; and,

c) RS-232 serial interface for the balance and a desktop computer. Each sample of 50 insulation panels was placed collectively in a large convection oven at 100 °C and conditioned overnight for approximately 20 h. The panels were removed

from the oven, one by one, and weighed as a function of time. The start time (to) was

synchronized with removal by activation of the foot switch. The mass data (in kilo- grams) were acquired from the digital balance every 20 s for 180 s (3 min) using a computer program. When placed in ambient conditions, the insulation panel (re-) gains mass

immediately due to the difference in relative humidity between the 100 °C environment and ambient air. By measuring the panel mass at equal time intervals and establishing a mass history, the initial mass (mo) for each panel at time zero (to) is determined by regres- sion analysis, thus correcting for the small mass change with time. The mass data at time (t) were fitted to Eq. (10) using three different computer analysis programs, cross-checked for complete consistency of results.

m(t) = m0 +at (10)

Annex 1 provides a graphical analysis of the mass measurements for all 450 insulation panels and summarizes regression values for mo for each panel. Figure 1 illustrates the typical mass regain data for an insulation panel (438). The indi- vidual observations, shown as diamond symbols, are plotted with error bars representing an expanded uncertainty (k = 2) of 0.00012 kg. The linear fit for the data is shown as a

solid line. The initial mass (mo) of 1.1060 kg was determined by linear backextrapolation (dashed line extension in Fig. 1) to time to. The mass regain for an insula- tion panel over the time interval of 1 80 s was typically about 0. 1 %.

6.2 Dimensional Measurements

The dimensional measurements are derived from one-dimensional length measurements

using precision electronic height gages referenced to a surface plate datum. The height gages were placed on, and referenced to, a granite surface plate having linear dimensions of 1.2 m by 1.8 m and a unilateral flatness tolerance of 0.018 mm. Each height gage util- ized a touch signal probe that provided a consistent contact force with the artifact. The

length value (in millimeters) was transferred to a desktop computer with a USB (Universal Serial Bus) interface cable and recorded in an electronic spreadsheet template. The

length, width, and thickness measurements of each group of 50 insulation panels were

18
1.1080

1.1055 1 1 1 1 0 20 40 60 80 100 120 140 160 180 200 Elapsed time, s

Figure 1. Mass regain for Panel ID 438 after removal of panel from oven. Initial mass (m() ) of 1.1060 kg was determined by linear extrapolation to time zero.

performed at the same time by two operators under ambient conditions of approximately 23 °C and 35 % relative humidity.

6.2.1 Lateral Panel Dimensions - Length and Width

Figure 2 illustrates the essential details for measurement of the panel lateral dimensions

(length and width). The measurement station consists of the following instrumentation:

a. granite surface plate ( 1 .2 m by 1.8 m, unilateral flatness tolerance of 0.0 1 8 mm);

b. electronic height gage with digital readout (635 mm range, 0.01 mm resolution);

c. bi-directional touch probe (3 mm diameter carbide ball contact point, 0.4 N

measuring force); and,

d. SPC (statistical process control) data output cable with converter tool to USB

(Universal Serial Bus) communication cable for connection to a desktop computer. The insulation panel was placed on edge, in the vertical position, on the granite surface

plate and clamped securely between an aluminum sheet and a right-angle support fixture

(Fig. 2a). The fixture consisted of an aluminum jig plate (13 mm thick by 560 mm

560 mm) fastened to two precision ground right angles (200 mm by 125 mm). The right angles were precision ground square to within 0.051 mm (per 150 mm) and parallel to within 0.006 mm (per 150 mm). The touch probe measurements were carried out with a round high-grade gage block as the workpiece (in contact with the insulation panel).

19
1) Height gage

2) Touch probe

3) SPC output

4) Workpiece 4

5) Insulation panel

6) Granite surface plate

7) Right-angle fixture

h h

i i i

b)

Figure 2. a) Side view shows 610 mm height gage and right-angle fixture with insulation panel clamped

between the aluminum jig plate and aluminum sheet, b) Front view shows panel length measurements at locations l\, A, 1-$, /4 , A, and /6 (fixture and height gage are not shown). For a particular group of 50 panels, one panel was measured at all locations and the other 49 panels were measured at locations l2 and /5

.

Linear dimensions l\, h, and I3 were obtained by moving the height gage and measuring

at the three locations. The panel was subsequently undamped, rotated 90° clockwise, and re-clamped to measure linear dimensions U, I5, and k- Preliminary tests indicated

that data acquired from two middle locations, h and I5, were sufficient for the accurate determination of bulk density. As a check, however, one panel from each group was se- lected, at random, for measurements at all locations (h, I2, h, h, h, and h). After completion of the mass measurements (Sec. 6.1), the group of 50 panels was placed

collectively in a laboratory ambient of 23 °C and conditioned overnight for about 1 7 h. Prior to dimensional measurements, a zero reference plane for the workpiece with respect

to the surface datum, was established. The measurement process was checked at the be- ginning and end using a 609.6 mm gage standard consisting of two 304.8 mm gage

blocks wrung together. During the measurement process, the zero reference plane was

re-established, as necessary. For 49 panels, the linear dimensions h and I5 were obtained. For one panel, selected at random from each group, the linear dimension measurements were conducted at h, l2 , h, U, h, and k. For nine panels, one from each group of 50 (Panel ID: 048, 1 10, 173, 298, 336, 348, 350, 392, and 408), the area of the panel As was computed using Eq. (11).

20
The areas (As ) of the other panels were computed using Eq. (12). As =l2 xl5 (12)

6.2.2 Thickness

Figure 3 illustrates the essential details for measurement of the panel thickness dimensions. The measurement station consists of the following equipment and instrumentation:

a. granite surface plate (1.2 m by 1.8 m, unilateral flatness tolerance of 0.018 mm);

b. electronic height gage with digital readout (330 mm range, 0.01 mm resolution);

c. bi-directional touch probe (3 mm diameter carbide ball contact point, 0.4 N measuring force); and,

d. SPC (statistical process control) data output cable with converter tool to USB

(Universal Serial Bus) communication cable for connection to a desktop computer.

1

[I 3

-

1) Height gage

2) Touch probe

3) SPC output

4) Workpiece

5) Insulation panel 200 mm

6) Granite surface plate

200 mm < >

Li

L4 L3

a) b)

Figure 3. a) Front view shows 305 mm height gage and insulation panel (with workpiece) on granite sur- face plate, b) Top view shows an insulation panel and 8 thickness measurement locations (L/ - L8) each in the geometric center of a 200 mm by 200 mm sub-area of the insulation panel. For a particular group of 50

panels, one panel was measured at all 8 locations and the other 49 panels were measured, in an alternating sequence, at the corner locations (L h L ? , L5, L 7 ) and at the mid-center locations (L2, L4, L6, LH ).

The insulation panel was placed, in the horizontal position, on the granite surface plate

(Fig. 3a) and a modest load (approximately 43 N, not shown in Fig. 3a) was applied to the top of the panel. The panel thickness was measured at 8 locations {L\, L2, L3, £4, £5, ^6, £7, and Lg as shown in Fig. 3b); each location representing the geometric center of a 200 mm

by 200 mm sub-area. The touch probe measurements were carried out with a round highgrade gage block as the workpiece in contact with the insulation panel (Fig. 3a).

21
The linear dimensions L\, L2 , L4 , L5 , L6 , Lli and L8 were obtained by fixing the location of the height gage (in contrast to the lateral dimensional measurements where the height gage was moved from location to location) and re-positioning the panel for each measurement. Preliminary tests indicated that the data acquired from four locations were

sufficient for an accurate determination of the bulk density. For each group, approximately one-half of the panels were measured at the corners (L\, L3, L5, and L-j) and, for the other half, at the mid-centers {Li, L4, and Ls)- The measurement pattern was alter- nated from panel to panel. The thickness measurements were conducted by a second operator at the same time that the lateral panel dimensions (Sec. 6.2.1) were collected. Prior to dimensional measurements, a zero reference plane for the workpiece with respect to the surface datum, was

established. The measurement process was checked at the beginning and end using a 25.4 mm (1 in.) gage block standard. During the measurement process, the zero refer- ence plane was re-established, as necessary. For 49 panels, the linear dimensions at the corners (L\, Li, L5, and Li) and at the mid-centers (L2, L4, Ls, and L%) were obtained. For one panel, selected at random from the group, the linear dimension measurements were

conducted at L\, L2, Li, L4, L5, Le, Lj, and L%. For nine panels, one from each group of 50 (Panel ID: 048, 1 10, 173, 298, 336, 348, 350,

392, and 408), the mean thickness of the panel was computed using Eq. (13). The thick- nesses of the other panels were computed using either Eq. (14) or Eq. (15).

Annex 2 provides a graphical analysis of the thickness measurements for all 450 insulation panels.

6.3 Homogeneity Assessment

6.3.1 Tabulated Results The following data were collected over a 30 day period. - 4050 mass measurements (9 points per panel x 450 panels) 936 lateral panel dimensions (2 per panel x 441 panels + 6 per panel x 9 panels) - 1836 thickness dimensions (4 per panel x 441 panels + 8 per panel x 9 panels) Table 3 summarizes mass (mo), length (/2 ), width (/5 ), area (As), thickness (Lm), and bulk

density (p) for the 450 panels. The bulk density for each panel was determined using

Eq. (1) and the values presented in Table 3 were rounded to the nearest whole number for

certification purposes.

(13)

(14)

(15)

22
Table 3. Physical properties of SRM 1450d units (450 panels)

Panel ID Mass

(kg) Length (mm)

Width (mm)Area (m2

) Thickness (mm)

Bulk density (kg-m 3 ) 001 1.12414 61 1.24 610.08 0.37291 25.93 116 002 1.13986 611.1

611.77 0.37386 25.94 118 003 1.11269 610.96 610.07 0.37273 25.68 116 004 1.18653 61 1.04 611.53 0.37367 25.81 123 005 1.17210 61 1.10 610.21 0.37290 25.83 122 006 1.13738 610.67 611.33 0.37332 25.63 119 007 1.16968 610.11 611.11 0.37284 25.95 121 008 1.15530 611.82 61 1.07 0.37386 25.85 120 009 1.18189 610.19 610.51 0.37253 25.74 123 010 1.15906 611.96 610.53 0.37362 25.71 121 Oil 1.16495 610.10 610.80 0.37265 25.78 121 012 1.16937 611.55 610.50 0.37335 25.60 122 013 1.14597 610.37 610.54 0.37266 26.10 118 014 1.12582 611.42 610.63 0.37335 25.95 116 015 1.11244 610.25 610.75 0.37271 25.83 116 016 1.18237 61 1.47 611.21 0.37374 25.88 122 017 1.12531 610.15 611.20 0.37292 25.88 1 17 018 1.12734 61 1.72 611.15 0.37385 25.70 117 019 1.18564 610.86 610.00 0.37262 26.02 122 020 1.12829 610.88 611.76 0.37371 25.95 116

021 1.17589 610.66 610.20 0.37262 25.83 122 022 1.14641 610.73 611.53 0.37348 25.86 1 19 023 1.13887 611.10 609.78 0.37264 25.87 118 024 1.13869 610.90 611.80 0.37375 25.76 118 025 1.14179 611.35 610.16 0.37302 25.94 118 026 1.16275 610.88 611.88 0.37379 25.95 120

' 027 1.19277 611.04 610.27 0.37290 25.80 124 028 1.17184 610.57 611.61 0.37343 25.74 122 029 1.19291 611.20 610.20 0.37295 25.92 123 030 1.16272 611.00 611.61 0.37369 25.72 121 031 1.13741 610.35 610.62 0.37269 26.07 1 17 032 1.11931 61 1.76 610.89 0.37372 25.95 115 033 1.16243 610.25 610.56 0.37259 25.82 121 034 1.16647 611.62 610.64 0.37348 25.85 121 035 1.14204 610.27 610.75 0.37272 25.81 119 036 1.17069 611.90 610.54 0.37359 25.67 122 037 1.12064 610.29 610.72 0.37272 25.62 1 1 7 038 1.13265 61 1.47 610.50 0.37330 25.65 118 039 1.13734 610.23 610.94 0.37281 25.25 121 040 1.17376 611.81 610.66 0.37361 25.49 123 041 1.17620 610.24 610.82 0.37275 25.58 123 042 1.16396 611.89 611.03 0.37388 25.49 122 043 1.10074 610.42 609.81 0.37224 26.17 113 044 1.09948 610.98 611.68 0.37372 26.08 113 045 1.16567 610.71 609.85 0.37244 25.83 121 046 1.17663 611.13 612.17 0.37412 25.98 121 047 1.15239 610.77 609.93 0.37253 25.92 119 048 1.16201 610.63 611.97 0.37369 25.69 121 049 1.13219 611.11 610.23 0.37292 26.40 115 050 1.14569 610.89 611.79 0.37374 26.29 117

051 1.15778 610.90 610.13 0.37273 26.03 119 052 1.13913 610.66 611.66 0.37352 26.12 117 053 1.15072 611.19 610.25 0.37298 26.13 118 054 1.14068 611.12 611.50 0.37370 25.98 117

23
Panel ID Mass

(kg) Length (mm)

Width (mm)

Area (m2 ) Thickness (mm)Bulk density (kg-nv) 055 1.07006 610.43 611.16 0.37307 26.12 110 056 1.12219 611.83 610.67 0.37363 26.07 115 057 1.15492 610.37 610.81 0.37282 25.90 120 058 1.15498 612.15 610.88 0.37395 25.93 119 059 1.16159 610.27 610.84 0.37278 25.87 120 060 1.21462 61 1.75 610.88 0.37371 25.81 126

061 1.10081 610.29 610.85 0.37280 26.13 113 062 1.12217 611.76 611.16 0.37388 26.08 115 063 1.15255 610.15 610.67 0.37260 25.75 120 064 1.18817 611.60 610.59 0.37344 25.95 123 065 1.11860 610.13 611.39 0.37303 25.95 116 066 1.16964 611.81 610.88 0.37374 25.85 121 067 1.14153 610.76 610.06 0.37260 26.14 117 068 1.14135 610.90 611.83 0.37377 26.10 117 069 1.14468 610.80 610.02 0.37260 25.76 119 070 1.11146 610.86 611.74 0.37369 25.82 115 071 1.16491 610.76 609.98 0.37255 25.91 121 072 1.12173 611.11 612.14 0.37408 25.92 116 073 1.12098 611.25 610.31 0.37305 26.17 115 074 1.15342 611.18 612.55 0.37438 26.08 118 075 1.16052 611.05 610.31 0.37293 25.84 120 076 1.16589 610.99 611.68 0.37373 25.86 121 077 1.15908 611.08 610.21 0.37289 25.84 120 078 1.16507 610.96 611.90 0.37385 25.79 121 079 1.13272 610.27 610.66 0.37267 26.03 117 080 1.14299 612.05 610.80 0.37384 25.98 118

081 1.14938 610.37 610.48 0.37262 25.73 120 082 1.15524 611.86 610.65 0.37363 25.81 120 083 1.12402 610.14 610.94 0.37276 25.78 117 084 1.14579 611.91 611.02 0.37389 25.81 119 085 1.11773 610.25 610.73 0.37270 26.28 114 086 1.12733 611.72 610.85 0.37367 26.10 116 087 1.14251 610.07 610.72 0.37258 25.88 118 088 1.16444 611.63 611.43 0.37397 25.94 120 089 1.14362 610.34 610.90 0.37286 25.90 118 090 1.14858 612.35 61 1.02 0.37416 25.90 119

091 1.15353 610.99 609.96 0.37268 26.13 118 092 1.18182 610.54 612.06 0.37369 26.03 122 093 1.19095 610.68 610.08 0.37256 25.75 124 094 1.13556 610.81 611.67 0.37361 25.83 118 095 1.15624 610.80 609.94 0.37255 25.81 120 096 1.13250 610.98 611.86 0.37383 25.79 117 097 1.13910 611.21 610.54 0.37317 26.12 117 098 1.14081 610.66 611.82 0.37361 26.04 117 099 1.13039 611.17 610.29 0.37299 25.87 117

100 1.18780 611.00 611.83 0.37383 25.95 122

101 1.14089 611.27 610.26 0.37303 25.91 118 102 1.15616 610.78 611.69 0.37361 25.82 120

103 1.10762 610.11 610.88 0.37270 26.18 114 104 1.13218 611.47 611.15 0.37370 26.04 116

105 1.16749 610.22 610.50 0.37254 25.84 121 106 1.14976 61 1.81 610.56 0.37355 25.96 1 19 107 1.15366 610.15 611.23 0.37294 26.02 119

108 1.15410 611.51 610.89 0.37357 25.83 120

109 1.15485 610.21 610.46 0.37251 26.21 118 110 1.12173 611.41 610.48 0.37326 25.98 116

111 1.13179 610.26 610.57 0.37261 25.82 118

24
ranei iu Mass Length Width Area Thickness Bulk density (kg) (mm) (mm) (m2

) (mm) (kg-rn"

3) 112 1.17517 611.55 610.69 0.37347 25.90 122

113 1.15025 610.26 610.46 0.37254 25.97 119

114 1.13912 611.44 611.14 0.37368 25.80 118

115 1.07447 610.85 610.08 0.37267 26.06 111 116 1.12192 610.63 611.94 0.37367 26.03 115 117 1.18546 610.90 610.04 0.37267 25.83 123 118 1.18503 610.57 611.38 0.37329 25.92 122 119 1.13788 609.96 611.30 0.37287 25.95 1 IS 120 1.17795 610.74 611.84 0.37368 25.85 122

121 1.14709 611.32 610.40 0.37315 26.10 118

122 1.16647 610.99 611.65 0.37371 26.04 120

123 1.15868 610.98 610.16 0.37280 25.82 120

124 1.18168 610.91 611.67 0.37368 25.98 122

125 1.11063 610.97 610.25 0.37284 25.85 115 126 1.15448 610.97 611.87 0.37383 25.76 120

127 1.14412 610.25 610.32 0.37245 26.09 118

128 1.12675 611.78 611.02 0.37381 25.93 116

129 1.18062 610.33 610.54 0.37263 25.79 123 130 1.16665 611.63 611.08 0.37375 25.81 121

131 1.16387 610.31 610.78 0.37277 25.87 121 132 1.13133 611.54 611.15 0.37374 25.74 118

133 1.15076 610.09 610.64 0.37255 26.22 118

134 1.10108 611.70 611.02 0.37376 26.07 113

135 1.13652 610.29 610.62 0.37266 26.05 117

136 1.16872 611.61 610.52 0.37340 26.10 120

137 1.14970 610.41 611.10 0.37302 26.08 118

138 1.10254 611.65 611.06 0.37375 25.94 114

139 1.13972 610.68 609.88 0.37244 26.10 117

140 1.14971 610.51 611.62 0.37340 25.99 118

141 1.16087 610.61 609.84 0.37237 25.74 121 142 1.19183 610.71 611.51 0.37346 25.89 123

143 1.18258 610.86 610.08 0.37267 25.87 123 144 1.16138 610.36 611.56 0.37327 25.76 121 145 1.15147 611.20 610.38 0.37306 26.08 IIS 146 1.06968 610.94 610.89 0.37322 25.94 110 147 1.14651 611.07 610.42 0.37301 25.77 119

148 1.14698 611.21 61 1.76 0.37391 25.84 119

149 1.12615 611.43 610.29 0.37315 25.88 117

150 1.11505 610.98 611.79 0.37379 25.79 116

151 1.10047 610.65 610.68 0.37291 26.04 113 152 1.11863 611.41 610.91 0.37352 26.02 115

153 1.14852 610.47 610.78 0.37286 25.83 119

154 1.12696 611.56 610.83 0.37356 25.76 117

155 1.15228 610.45 610.82 0.37288 25.98 119

156 1.14876 611.74 610.88 0.37370 25.83 119

157 1.12336 611.63 611.17 0.37381 26.58 113

158 1.15833 611.64 610.35 0.37331 26.99 115

159 1.13203 611.82 611.07 0.37386 26.70 113 160 1.15569 610.28 610.94 0.37284 26.66 116

161 1.13572 610.22 611.05 0.37287 26.43 115 162 1.10457 611.90 610.80 0.37375 26.04 113

163 1.11441 610.51 610.34 0.37262 26.09 115 164 1.12297 610.79 611.72 0.37363 25.95 116

165 1.21054 610.57 610.06 0.37248 25.86 126

166 1.13067 610.89 611.72 0.37369 25.82 117

167 1.23314 610.75 610.03 0.37258 25.90 128

168 1.14794 610.72 611.67 0.37356 25.82 119

25
Panel ID Mass

(kg) Length (mm)

Width (mm)

Area (m2

) Thickness (mm)

Bulk density (kg-m'

3 ) 169 1.11604 611.08 610.04 0.37278 26.13 115

170 1.12881 611.21 61 1.53 0.37377 26.04 116

171 1.14443 611.10 610.38 0.37300 25.94 I IX 172 1.13193 610.70 611.75 0.37360 25.83 117

173 1.11926 611.20 610.32 0.37303 25.89 116

174 1.12596 610.88 611.79 0.37373 25.75 117

175 1.11408 610.34 610.89 0.37285 26.18 114

176 1.10366 612.22 610.76 0.37392 26.04 113 177 1.16187 610.09 611.11 0.37283 25.92 120

178 1.14571 611.76 611.10 0.37385 25.95 118

179 1.15042 610.30 611.11 0.37296 26.06 118

180 1.17077 61 1.57 611.04 0.37369 25.91 121

181 1.14671 610.15 610.52 0.37251 26.22 117

182 1.08920 611.97 610.98 0.37390 25.96 112

183 1.15781 610.12 610.74 0.37262 25.82 120

184 1.14512 611.60 610.69 0.37350 25.88 118

185 1.20018 610.11 610.83 0.37267 25.90 124

186 1.10256 61 1.5X 611.02 0.37369 25. SO 114

187 1.14518 610.44 609.89 0.37230 26.16 118

188 1.10250 611.26 611.94 0.37405 26.00 113 189 1.15670 610.89 610.17 0.37275 25.82 120

190 1.15145 610.82 611.67 0.37362 25.96 119

191 1.15948 610.54 609.92 0.37238 25.88 120

192 1.20685 610.75 61 1.47 0.37346 25.86 125

193 1.13247 611.05 610.24 0.37289 25.97 117

194 1.07868 610.81 612.00 0.37382 25.97

195 1.14213 610.96 610.28 0.37286 25.77 119

196 1.10984 610.79 611.52 0.37351 25.84 115

l<>7 1.11919 611.23 610.12 0.37292 25.89 116

198 1.15352 611.00 611.70 0.37375 25.76 120

199 1.12973 610.25 611.11 0.37293 26.35 115 200 1.10731 61 1.76 610.82 0.37368 26.23 113 201 1.12089 610.26 610.67 0.37267 26.00 116 202 1.13515 611.49 610.84 0.37352 25.95 117 203 1.18179 610.09 610.64 0.37255 25.98 122 204 1.13426 611.50 610.94 0.37359 25.74 118 205 1.11970 610.18 610.81 0.37270 26.16 115 206 1.08548 612.21 610.73 0.37390 26.04 207 1.11356 610.36 610.53 0.37264 25.86 116 208 1.14218 611.67 610.87 0.37365 25.92 1 IS 209 1.14201 610.35 611.11 0.37299 25.90 118 210 1.16556 611.76 610.54 0.37350 25.82 121 211 1.13124 610.92 610.07 0.37270 26.05 117 212 1.12840 610.71 611.80 0.37363 26.01 116 213 1.16842 610.56 610.08 0.37249 25.88 121 214 1.14418 610.80 611.64 0.37359 25.84 119 215 1.16701 611.03 610.21 0.37286 25.96 121 216 1.10545 610.63 611.42 0.37335 25.80 115 217 1.12624 61 1.08 610.10 0.37282 26.10 116 218 1.12680 610.92 611.79 0.37375 25.92 116 219 1.15334 610.89 610.38 0.37288 25.82 120 220 1.15179 610.85 611.71 0.37366 25.92 119

221 1.17024 611.06 610.15 0.37284 25.87 121 222 1.09915 610.99 611.83 0.37382 25.73 114 223 1.15226 610.46 610.64 0.37277 26.06 119 224 1.12542 612.11 610.97 0.37398 25.88 116 225 1.15646 610.39 610.89 0.37288 25.76 120

26
Panel ID Mass

(kg) Length (mm)

Width (mm)Area (m2

) Thickness (mm)

Bulk density (kg-nv) 226 1.16833 611.62 610.74 0.37354 25.77 121 227 1.12953 610.22 610.91 0.37279 25.79 117 228 1.13737 61 1.66 611.07 0.37377 25.68 118 229 1.14301 610.16 610.69 0.37262 26.03 118 230 1.12638 611.96 610.75 0.37375 25.88 116

231 1.16284 610.27 610.84 0.37278 25.71 121 232 1.20029 611.90 610.51 0.37357 25.77 125 233 1.16669 610.13 610.83 0.37269 25.75 122 234 1.13291 612.06 610.89 0.37390 25.70 118 235 1.16433 610.82 610.25 0.37275 26.02 120 236 1.15741 610.88 611.63 0.37363 25.89 120 237 1.18919 610.55 609.98 0.37242 25.67 124 238 1.15449 611.01 611.71 0.37376 25.70 120 239 1.13509 610.38 610.41 0.37258 25.76 118 240 1.18396 610.77 611.42 0.37344 25.65 124

241 1.11091 610.78 610.14 0.37266 26.01 115 242 1.10286 610.87 612.05 0.37388 25.80 114 243 1.16182 611.28 610.48 0.37317 25.73 121 244 1.17091 611.09 611.69 0.37380 25.67 122 245 1.18471 610.80 610.16 0.37269 25.91 123 246 1.18464 611.04 611.68 0.37376 25.69 123 247 1.13150 610.43 610.70 0.37279 26.02 117 248 1.13631 612.00 610.77 0.37379 25.81 118 249 1.11462 610.13 611.00 0.37279 25.72 116 250 1.13862 611.82 610.85 0.37373 25.76 118 251 1.11650 610.21 610.70 0.37266 25.81 116 252 1.15906 611.57 610.73 0.37350 25.62 121 253 1.13919 610.26 610.93 0.37283 25.96 118 254 1.10615 612.10 610.92 0.37394 25.76 115

' 255 1.16429 610.26 610.76 0.37272 25.70 122 256 1.14729 611.63 611.09 0.37376 25.81 119 257 1.13116 610.21 610.78 0.37270 25.74 118 258 1.15010 61 1.82 610.78 0.37369 25.65 120 259 1.12227 610.22 611.04 0.37287 26.04 116 260 1.07708 612.02 610.89 0.37388 25.88 111 261 1.15488 610.16 610.90 0.37275 25.77 120 262 1.15963 611.73 610.82 0.37366 25.78 120

263 1.12172 610.26 611.31 0.37306 25.86 116 264 1.12846 611.91 610.70 0.37369 25.83 117 265 1.13800 611.21 610.46 0.37312 25.99 117 266 1.12327 610.84 612.10 0.37390 25.82 116 267 1.14465 611.12 610.47 0.37307 25.65 120 268 1.14092 610.95 611.77 0.37376 25.59 119 269 1.15724 611.18 610.23 0.37296 25.79 120 270 1.14636 610.79 611.67 0.37360 25.59 120

271 1.14040 610.27 610.60 0.37263 25.97 118 272 1.15038 611.86 611.02 0.37386 25.78 119 273 1.16056 610.22 610.90 0.37278 25.63 121 274 1.13994 611.84 610.71 0.37366 25.67 119 275 1.13412 610.26 611.11 0.37294 25.81 118 276 1.14093 61 1.76 611.14 0.37387 25.53 120 277 1.15168 610.14 610.85 0.37270 26.27 118 278 1.16131 611.68 611.01 0.37374 25.96 120 279 1.17856 610.36 610.75 0.37278 25.89 122 280 1.15230 01 1.73 610.72 0.37360 25.75 120

281 1.16368 610.33 611.33 0.37311 26.02 120 282 1.11690 61 1.63 611.33 0.37391 25.64 116

27
Panel ID Mass

(kg) Length (mm)

Width (mm)Area (m2

) Thickness (mm)

Bulk density (kg-m

1 ) 283 1.12053 611.02 609.99 0.37272 25.91 116 284 1.12628 610.83 611.87 0.37375 25.82 117 285 1.12822 610.77 609.85 0.37248 25.63 118 286 1.14708 610.83 611.84 0.37373 25.67 120 287 1.13461 611.09 610.06 0.37280 25.82 118 288 1.14216 611.01 611.75 0.37379 25.68 119 289 1.16081 610.55 610.17 0.37254 25.91 120 290 1.15201 610.70 611.73 0.37358 25.83 119

291 1.18236 61 1.02 610.23 0.37286 25.66 124 292 1.20610 610.93 611.97 0.37387 25.58 126 293 1.18124 611.13 610.29 0.37297 25.73 123 294 1.19497 610.86 611.82 0.37374 25.58 125 295 1.11555 610.76 610.91 0.37312 25.90 115 296 1.12221 611.64 610.97 0.37369 25.83 116 297 1.16962 610.24 611.00 0.37286 25.68 122 298 1.12113 611.60 610.38 0.37331 25.68 117 299 1.18001 610.25 610.66 0.37266 25.89 122 300 1.15708 611.65 610.74 0.37356 25.85 120

301 1.13965 610.51 611.21 0.37315 25.93 118 302 1.16369 612.01 611.01 0.37394 25.83 120 303 1.15664 610.32 610.25 0.37245 25.69 121 304 1.17066 611.83 610.78 0.37369 25.58 122 305 1.15275 610.24 611.14 0.37294 25.77 120 306 1.15196 611.65 610.86 0.37363 25.59 121 307 1.11287 610.30 610.71 0.37272 26.01 115 308 1.11155 61 1.96 610.65 0.37369 25.78 115 309 1.18160 610.41 610.92 0.37291 25.71 123 310 1.13664 612.17 61 1.08 0.37408 25.64 119

311 1.17607 610.21 611.13 0.37292 25.78 122 312 1.14976 611.76 610.96 0.37376 25.59 120 313 1.11391 611.57 610.32 0.37325 26.17 114 314 1.12859 611.34 611.88 0.37407 25.82 117 315 1.13903 611.49 610.20 0.37313 25.83 118 316 1.15524 611.34 611.82 0.37403 25.59 121 317 1.14585 610.89 610.32 0.37284 25.83 119 318 1.14134 611.06 612.28 0.37414 25.58 119 319 1.12044 610.47 610.83 0.37289 25.97 116 320 1.14848 611.78 610.65 0.37358 25.74 119

321 1.13955 610.21 610.55 0.37256 25.59 120 322 1.18656 611.65 610.53 0.37343 25.58 124 323 1.14363 610.26 611.17 0.37297 25.71 119 324 1.12941 612.01 610.76 0.37379 25.58 118 325 1.12908 610.29 610.75 0.37273 26.04 116 326 1.11530 611.60 611.10 0.37375 25.77 116 327 1.14984 611.54 611.00 0.37365 25.54 121 328 1.17150 610.14 610.73 0.37263 25.74 122 329 1.15462 610.38 610.87 0.37286 25.83 120 330 1.19245 611.63 610.96 0.37368 25.61 125

331 1.11002 610.89 610.02 0.37266 26.06 114 332 1.11409 611.02 612.06 0.37398 25.92 115 333 1.15996 610.80 610.08 0.37264 25.85 120 334 1.14948 611.01 61 1.76 0.37379 25.70 120 335 1.14968 610.86 610.03 0.37264 25.81 120 336 1.14833 610.84 611.47 0.37351 25.62 120 337 1.11168 610.72 611.36 0.37337 25.96 115 338 1.15613 610.39 611.28 0.37312 25.80 120 339 1.13794 610.92 611.66 0.37368 25.58 119

28
Panel ID Mass Length Width Area Thickness Bulk density

(kg) (mm) (mm) (m2

) (mm) (kgm 3

) 340 1.16806 610.69 609.96 0.37250 25.74 122 341 1.13174 610.79 611.57 0.37354 25.54 119 342 1.20857 610.65 610.36 0.37272 25.81 126 343 1.19092 610.40 610.41 0.37259 25.93 123 344 1.16103 611.26 610.19 0.37298 25.78 121 345 1.15199 610.32 610.80 0.37278 25.61 121 346 1.15974 611.72 610.63 0.37353 25.55 122 347 1.16944 610.50 611.16 0.37311 25.75 122 348 1.16051 611.18 611.28 0.37360 25.56 122 349 1.14241 611.63 610.82 0.37360 25.83 118 350 1.15930 610.26 609.55 0.37198 25.87 120

351 1.18083 610.25 610.24 0.37240 25.63 124 352 1.19973 611.55 609.96 0.37302 25.66 125 353 1.18032 610.39 610.64 0.37273 25.73 123 354 1.18271 611.57 610.49 0.37336 25.59 124 355 1.15426 610.79 610.41 0.37283 25.91 1 19 356 1.14209 610.83 612.08 0.37388 25.82 118 357 1.15940 611.05 611.66 0.37375 25.68 121 358 1.14864 610.96 610.10 0.37275 25.73 120 359 1.12883 611.01 610.12 0.37279 25.87 117 360 1.14216 611.88 610.73 0.37369 25.68 119

361 1.11953 609.67 610.82 0.37240 26.09 115 362 1.11271 611.24 610.51 0.37317 25.90 115 363 1.14569 609.75 611.44 0.37283 25.79 1 19 364 1.17146 611.11 610.95 0.37336 25.84 121 365 1.12071 609.71 610.97 0.37251 25.95 116 366 1.13998 611.40 610.46 0.37324 25.84 118 367 1.15645 609.99 610.12 0.37217 25.95 120 368 1.11160 611.07 610.36 0.37297 25.84 115

' 369 1.13781 609.95 610.70 0.37250 25.71 119 370 1.16704 611.77 610.96 0.37377 25.90 121 371 1.15589 610.19 610.62 0.37259 26.16 119 372 1.16458 611.56 610.41 0.37330 25.82 121 373 1.13037 611.43 610.70 0.37340 26.03 116 374 1.13509 610.36 610.36 0.37254 26.05 117 375 1.13933 611.77 610.37 0.37341 25.89 118 376 1.14735 610.42 610.73 0.37280 25.78 119 377 1.15165 610.18 610.75 0.37267 25.99 119 378 1.12077 611.74 611.05 0.373SO 25.84 116 379 1.14561 609.56 610.59 0.37219 26.06 118 380 1.13070 611.18 610.51 0.37313 25.97 117

381 1.13951 611.27 610.89 0.37342 25.86 118 382 1.17555 609.72 611.21 0.37267 25.77 122 383 1.18423 609.92 611.06 0.37270 25.90 123 384 1.15178 611.18 611.12 0.37350 25.74 120 385 1.15335 609.62 610.46 0.37215 26.05 11') 386 1.14326 611.54 610.47 0.37333 25.98 118 3X7 1 . 1 5922 609.72 611.07 0.37258 25.85 120 388 1 . 1 76 16 611.36 610.84 0.37344 25.80 122 389 1.14528 609.85 610.92 0.37257 25.91 119 390 1.12592 611.51 611.04 0.37366 25.75 117

391 1.10491 611.78 610.31 0.37338 25.97 1 14 392 1.14697 610.11 610.11 0.37223 26.10 118 393 1.17312 610.86 611.68 0.37365 25.85 121 394 1.16409 610.31 610.41 0.37254 25.87 121 395 1.13563 611.41 610.52 0.37328 25.81 118 396 1.12737 610.42 610.32 0.37255 25.80 117

29
Mass Length Width Area Thickness Bulk density

I and iU

(kg) (mm) (mm) (m2

) (mm) (kg-nY3 ) 397 1.12446 609.92 610.47 0.37234 26.02 116 398 1.13107 611.25 610.72 0.37330 25.98 117 399 1.18159 609.98 611.04 0.37272 25.82 123 400 1.14921 611.26 610.73 0.37331 25.72 120

401 1.15779 609.91 610.90 0.37259 25.90 120 402 1.18384 611.37 610.30 0.37312 25.77 123 403 1.13230 609.68 610.67 0.37231 26.06 117 404 1.12078 611.12 610.14 0.37287 25.98 116 405 1.16446 609.53 610.78 0.37229 25.78 121 406 1.16640 611.17 610.55 0.37315 25.81 121 407 1.17233 609.89 611.16 0.37274 25.87 122 408 1.15803 611.35 610.81 0.37342 25.80 120 409 1.12828 609.88 610.48 0.37232 26.09 116 410 1.12721 611.00 610.50 0.37302 26.04 116

411 1.13190 609.64 610.81 0.37237 25.79 118 412 1.13524 611.35 610.35 0.37314 25.78 118 413 1.16936 609.92 610.63 0.37244 25.95 121 414 1.17367 611.25 610.78 0.37334 25.81 122 415 1.14648 609.95 610.18 0.37218 26.05 118 416 1.16491 611.39 610.27 0.37311 26.07 120 417 1.18124 610.18 610.01 0.37222 25.77 123 418 1.16297 611.39 610.07 0.37299 25.91 120 419 1.15894 610.17 610.43 0.37247 25.86 120 420 1.16947 611.39 610.38 0.37318 25.88 121 421 1.10972 609.74 610.01 0.37195 25.91 115 422 1.16210 612.29 610.59 0.37386 26.19 119 423 1.14198 611.52 610.68 0.37344 25.76 119 424 1.12701 610.96 610.47 0.37297 25.84 117 425 1.16333 609.99 610.74 0.37255 25.81 121 426 1.15951 611.39 610.53 0.37327 25.73 121 427 1.15653 610.60 610.97 0.37306 25.94 120 428 1.14459 611.42 610.84 0.37348 25.83 119 429 1.15007 609.50 61 1.43 0.37267 25.76 120 430 1.18758 611.45 611.27 0.37376 25.74 123 431 1.15141 610.07 610.87 0.37267 25.76 120 432 1.18976 611.34 610.84 (1.37343 25.67 124 433 1.13035 610.16 611.05 0.37284 26.14 116 434 1.10330 610.82 610.53 0.37292 25.94 114 435 1.1291

1

610.05 611.47 0.37303 25.88 117 436 1.16151 611.85 611.55 0.37418 26.02 119 437 1.11141 6 10. IS 612.08 0.37348 26.06 114 438 1.10603 611.15 611.51 0.37372 25.99 1 14 439 1.14723 61 1.34 610.40 0.37316 25.98 118 440 1.12041 611.47 610.21 0.37313 25.80 116

441 1.17187 611.31 610.37 0.37313 25.73 122 442 1.17465 611.22 610.61 0.37322 25.70 122 443 1.17317 610.83 610.77 0.37308 25.87 122 444 1.11966 611.25 610.75 0.37332 25.63 117 445 1.14264 610.98 610.50 0.37300 26.34 1 16 446 1.17901 610.72 611.63 0.37353 26.39 120 447 1.18299 611.29 610.45 0.37316 25.83 123 448 1.14721 611.01 611.02 0.37334 25.89 119 449 1.12229 611.24 610.86 0.37338 25.87 116 450 1.13701 611.13 610.88 0.37333 25.77 118

30
6.3.2 Graphical Analyses Each quantity in Table 3 (mass, length, width, area, thickness, and bulk density) was subjected to a four-step graphical analysis to investigate the homogeneity of the material lot

(i.e., between-panel results). For each set of data, the graphical analysis verified the underlying assumptions of an ideal measurement process: a) stability (that is, fixed location and

variation), b) randomness, and c) normality. It should be noted that initial diagnostic checks, using similar graphical data analyses (not presented), were applied to each group

(50 panels) of data immediately after measurement completion to verify that measure- ment process was in control. Figures 4-9 illustrate the four step graphical analysis for panel mass (mo), length (/2 ), width

(Is), area (As ), thickness (Lm), and bulk density (p), respectively, for the 450 panels. Each

figure consists of 4 plots: a) run-sequence plot; b) lag plot; c) histogram; and d) normality

plot. The four-step method was applied for verification of the four characteristics indicating

statistical control of a process.

1) Run sequence plot plots values in the order obtained versus a sequence surrogate index (x, versus i) and checks for systematic and random changes.

2) Lag plot plots adjacent values (x, versus x,_i) and also checks for randomness

(specifically, lack of autocorrelation).

3) A histogram of values (x,) checks the frequency distribution. 4) Normal probability plot of values (of x,) checks the normality assumption.

Diagnostic plots of the forms shown in Fig. 4-9, the so-called 4-plots, and in Annex 1 and Annex 2, were done throughout the data logging stages of the experiment to check the

integrity of the data as the data were being taken, to check for outlying points or entire outlying samples, and to check that values - of mo, I2, h, As, Lm, and resultant p - were

within their anticipated ranges.

6.3.2.1 Panel Mass (w0 ) In Fig. 4 (mo), the run sequence shows no obvious drift or modulation. The lag plot shows no autocorrelation and both the histogram and normal (Gaussian) probability plot are compatible with a normality assumption for the data, with the possible exception of

just a few of the tail (extreme end) points, which are routinely observed with empirical

data.

6.3.2.2 Panel Length and Width (l2 and /5 ) In Fig. 5 and Fig. 6 (h and I5, respectively), there are suggestions of multimodality, that is, two or more underlying populations of lengths and widths, respectively. This is evident in the histograms (directly visible), the normal probability plots (multiple line segments with comparable slopes but different intercepts conjoined in a single plot), and even the run se- quence plots (high/low excursions from the mean values). The presence of multi-modes is almost certainly due simply to the fact that the boards are not quite square, so that pairs of

sides do not match exactly in length. The lag sequence plots are not suggestive of any

autocorrelation, or systematic departure from randomness.

31
o

Q.

LU

to

OLOOIOOLOO cocnjc\Jt-v-oo ooooooo iDLn-jrcocNjT6>( 'x Aouanbajj

Figure 4. Graphical analysis of panel mass (n = 450): (a) run sequence plot, (b) lag plot, (c) histogram,

(d) normal probability plot (normality index). Summary statistics: mean = 1.1466 kg, standard deviation =

0.0250 kg, range = 0. 1 635 kg.

32
Figure 5. Graphical analysis of panel length (n = 450): (a) run sequence plot, (b) lag plot, (c) histogram,

(d) normal probability plot (normality index). Summary statistics: mean = 610.92 mm, standard deviation = 0.62 mm, range = 2.85 mm.

33
o_J

QO CM *- O C5 CO cm •<- O O)

T- r- T- T~ O T~ T- T- T- O (£) CO CO CO CO CO CO CO CO CO LULU 'X UJUJ 'X

Figure 6. Graphical analysis of panel width (n = 450): (a) run sequence plot, (b) lag plot, (c) histogram,

(d) normal probability plot (normality index). Summary statistics: mean = 610.85 mm, standard deviation = 0.56 mm, range = 3.00 mm.

34
jJW 'X

Figure 7. Graphical analysis of panel area (n = 450): (a) run sequence plot, (b) lag plot, (c) histogram,

(d) normal probability plot (normality index). Summary statistics: mean = 0.37318 m

2

, standard deviation = 0.00051 m

2

, range = 0.00243 m

2

.

35
O

^ (£j m O

(£j

IT) uS o

iri oooooooo (O lO 00 CM •<- CM C\J CN CM C\l ujlu 'x Aouanbaj-j

Figure 8. Graphical analysis of panel thickness (n = 450): (a) run sequence plot, (b) lag plot, (c) histogram,

(d) normal probability plot (normality index). Summary statistics: mean = 25.88 mm, standard deviation =

0. 1 8 mm, range = 1 .74 mm.

36
Figure 9. Graphical analysis of panel bulk density {n = 450): (a) run sequence plot, (b) lag plot, (c) histo- gram, (d) normal probability plot (normality index). Summary statistics: mean = 118.7 kg-m3

, standard

deviation = 2.9 kg-m3

, range = 18.0 kg-m3

.

37
6.3.2.3 Panel Area (40

In Fig. 7 (As), both the histogram and normal probability plots are strongly suggestive of

underlying bimodality, viz. two underlying populations. However, the difference in the histogram peaks of approximately 0.3 % is not considered significant. While not suggestive of autocorrelation, the patterned heavy overstrike in the lag plot is apparent.

6.3.2.4 Panel Thickness (Lm) In Fig. 8 (Lm), the histogram and normal probability plots are good, with the exception of some obvious outlying tail observations (common with empirical data, as mentioned in Sec. 6.3.2.1 for Fig. 4). The flywheel appearance of the lag plot, clearly attributable to only a small subset of the overall set of measurements, is interesting. The obvious, ap- proximately contiguous, high lying and low lying points in the run sequence plot may be

the cause of these linear excursions from the random mass at the center of the lag plot.

6.3.2.5 Panel Bulk Density (p) In Fig. 9 (p), the plots look good (randomness - good, normality - good), meaning that the measurement process for p was in statistical control. It is interesting to note that much of the bi-modality present in the area plot (Fig. 7) does not appear in the density

plots due, in part, to stronger contributions from mass and thickness.

6.3.3 Summary Statistics Table 4 provides summary statistics for mass, length, width, area, thickness, and bulk

density of the 450 panels. Overall, the values for length and width are within acceptable

limits. The large range and small standard deviation for thickness indicate that some of

the panels are probably unacceptably thin or thick (as discussed in Sec. 6.3.6). The bulk

density mean and standard deviation values are acceptable, but the mean is near the low

limit specification of the manufacturer.

Table 4. Summary statistics for the SRM 1450d production run (450 panels)

Statistic Mass

(kg) Length

(mm)

Width (mm)Area (m2) Thickness (mm)Bulk density

(kg-rn

3

) Mean 1.1466 610.92 610.85 0.37318 25.88 118.7

Std. dev. 0.0250 0.62 0.56 0.00051 0.18 2.9 Range 0.1635 2.85 3.00 0.00243 1.74 18.0 Minimum 1.0697 609.50 609.55 0.37195 25.25 109.8 Maximum 1.2331 612.35 612.55 0.37438 26.99 127.8

6.3.4 Between- and Within-Panel Thickness Variations

Figures 10a and 10b plot the individual panel thickness mean and standard deviation, re- spectively, for the 450 panels. Each plot is rank ordered from lowest to highest value.

38
27.0

26.5

o) 26.0 ><

25.5

25.0

-3s, 25.33 mm

- a)

0 50 100 150 200 250 300 350 400 450

Index

50 100 150 200 250 300 350 400 450

Index

Figure 10. a) Graphical analysis of between-panel thickness variation represented by the means of the indi- vidual panel thickness measurements. Panels outside the control limits of three times the standard deviation (±35, where s equals 0.18 mm from Table 4) are as follows: low-limit, 039; high-limit 158, 159, 160, and 157. b) Graphical analysis of within-panel thickness variation represented by the standard deviations of the individual panel thickness measurements.

39
6.3.4.1 Between-Panel Variation Figure 10a shows graphically that the mean panel thickness ranges from 25.25 mm to nearly 27.0 mm. There are five panels outside the lower and upper limits equal to the grand mean plus-or-minus three times the standard deviation (±3s). These five panels were identified and removed from the material lot (low: 039, high: 157, 158, 159, and

160). The consecutive ID numbers imply that four of these panels were cut from the same mold.

6.3.4.2 Within- Panel Variation Figure 10b plots the standard deviation of the thickness measurements for each panel in- dicating the range of panel thickness variation. The individual panel variation ranges from less than 0.05 mm to about 0.35 mm. For most of the data, the variation is less than

0.3 mm (or about 0. 1 % of the grand mean panel thickness given in Table 4).

6.3.5 Between-Panel Bulk Density Variations

Figure 1 1 plots the individual panel bulk density for the 450 panels, rank ordered from

lowest to highest value. There are two panels outside the lower and upper limits equal to the grand mean ±35. The panels were identified and removed from the material lot (low: 055, high: 167).

Figure 11. Graphical analysis of between-panel bulk density variation. Panels outside the control limits of

three times the standard deviation (±3s, where s equals 2.9 kg-m"3 from Table 4) are as follows: low-limit, 055; high-limit 167.

40
6.3.6 Anomalous Panels (Outliers) The following seven panels were removed due to thickness measurements and bulk density determinations outside of their respective acceptable limits. The excluded panels repre- sented only 1.6 % (7 of 450) of the material lot (443 panels were accepted, or 98.4 %). - 039 (less than acceptable thickness limit) - 157,158, 159,160 (greater than acceptable thickness limit) - 055 (less than acceptable bulk density limit) - 167 (greater than acceptable bulk density limit)

6.4 Establishing and Demonstrating Traceability

6.4.1 Mass

The digital weighing balance is checked for self-consistency with a set of class 1, stainless steel weights having nominal mass values of 100 g, 200 g, 300 g, 500 g, and

1 kg and expanded uncertainties (k = 2) of: 0.065 mg, 0.12 mg, 0.25 mg, 0.30 mg, and

0.50 mg, respectively. The manufacturer calibration of these weights is based on apparent mass versus a material having a density of 8.0 g-cnf

3

. The vendor measurement re- sults are traceable to mass standards maintained at NIST. Additionally, the digital weighing balance is serviced annually by a technical representative from the balance manufacturer.

6.4.2 Length Dimensions The laboratory length standards are square cross-section steel gage blocks, which have nominal lengths defined in the English system (1 inch = 25.4 mm). The blocks are cali- brated at' 20 °C by comparison with U.S. standards maintained by the NIST Engineering

Metrology Group, most recently in 2009. The expanded uncertainties (k = 2) for the length of the gage blocks are less than 70 nm, which are negligible in comparison to uncertainty sources introduced in the thickness calibration hierarchy. The gage blocks are used as check

standards for the digital height gages described in Sec. 6.2.

6.5 Bulk Density Uncertainty

Replacing the area term (As) in Eq. (1) with the expression in Eq. (12) yields the following equation for the bulk density determination.

P, (16)

For the simple multiplicative expression in Eq. (16), the relative uncertainties associated with each component are combined in quadrature.

Uc ,rel{Ps)

«.(p.)

p,

1 (17)

41
Standard uncertainties for Eq. (17) are derived in Annex 3. Substituting the standard uncertainty values (Annex 3) and the minimum quantity estimates from Table 4 yields the following relative uncertainty estimate for bulk density.

If 0.000 187^1

2 J

0324

) W0.156Y

'[ 1.0697 J { 609.50 J 1,609.55 J U5.25J

«,.,v/(p.v)-^ L069? J +

[ 60950 J +

[ 609.55 J A 2525 J ^

uc rel (pj = ^/(0.000175)

2 +(0.00053 1)

2 + (0.00053l)2 +(0.00619)2 = 0.0062 (19) Urel (ps ) = 2u,(ps ) = 0.012 (20)

Expressed as a percent (x 100), £/re/ is equal to 1.2 %. The dominant contributory uncertainty in Eq. (19) was the uncertainty determination of the panel thickness u (Lm). The main uncertainty contribution for the panel thickness was due

to the Type A evaluation of the pooled panel thickness standard deviations of 0.156 mm

(Annex 3). This uncertainty estimate is representative of the within-panel thickness variation shown in Fig. 10b.

42
7 Thermal Conductivity Measurements

Section 7 describes the initial model for steady-state thermal conductivity measurements,

the experimental design, the selection of test specimens and guard insulation, and the guarded-hot-plate test method.

7.1 Experimental Design and Initial Model

The experimental design for the determination of thermal transmission properties is based on a model for bulk density and temperature. Building on the results of the previous version, SRM 1450c [10], the initial model for thermal conductivity (k) as a function of bulk

density (p) and temperature (7) was assumed to be X = (p,T) = aQ +al p + a2 T (21)

7.1.1 Model Input Quantities - Bulk Density (p) and Temperature (7) Table 5 summarizes a full factorial design having three levels for p and three levels for T. This design checks the adequacy of Eq. (2 1

) and also allows checking for the necessity of

quadratic terms for p and for T. Each cell in Table 5 represents one measurement of a

different pair of specimens (nine tests in total). The benefit of testing a unique pair of specimens at each combined level of temperature and density is that independent infor- mation is obtained at each such level.

Table 5. Full factorial (3 X 3) experimental design Density level Temperature level (K) 280 310 340 Low 1 obs.* © 1 obs. ® 1 obs. ©

Mid 1 obs. ® 1 obs. ® 1 obs. ®

High 1 obs. © 1 obs. © 1 obs. ©

*obs. = observation

The experimental design given in Table 5 is balanced in the sense that an equivalent amount of information is obtained at each setting of the independent variables. If either extra information had been obtained at some of the settings, or worse, critical information omitted at one setting, the design would be unbalanced and the resulting statistical analysis would suffer. The test sequence in Table 5, shown as circled numbers (©), was ran- domized to mitigate systematic effects.

7.1.2 Other Quantities Other quantities that were considered "nuisance" or influence parameters were either fixed at specified levels during testing in the guarded-hot-plate apparatus or, in some

cases, only recorded. Fixed parameters include the following: The direction of heat flow across the thickness of the specimens was fixed in the

vertical (up/down) direction for the double sided mode of operation.

43
The temperature difference (A T) across the specimen was fixed at 25 K and fol- lowed standard practice for selecting test temperatures [17].

• The clamping pressure (J ) applied to the specimens was maintained at a nominal

value of 490 kPa for all tests. The chamber air temperature (Ta) of the apparatus chamber was controlled to within 0.1 K, or less, of the mean specimen temperature ( T„,). Recorded parameters include the following:

. The chamber air pressure (pa) was uncontrolled and varied with changes in the barometric pressure. The chamber relative humidity was, in general, maintained below 10 % RH by us- ing a dry-air purge during the tests. The relative humidity, however, varied with

the chamber dry-bulb air temperature (7^).

7.2 Guarded-Hot-Plate Guard Insulation Table 6 summarizes the mass, dimensional, and bulk density measurements, rank ordered by bulk density for the 25 sheets of guard insulation prepared from the auxiliary material described earlier. The purpose of the auxiliary material was to function as radial guard

Table 6. Physical properties of guarded-hot-plate guard insulation Index ID Mass

(kg) Area (m2

) Thickness (m) Bulk density (kg-m"

3 )

1 22 1.29664 0.4365 0.02544 116.8 2 01 1.31080 0.4367 0.02538 118.3

3 07 1.32077 0.4378 0.02546 118.5 4 06 1.34583 0.4383 0.02590 118.6

5 02 1.34312 0.4380 0.02585 118.7

6 23 1.34539 0.4367 0.02596 118.7

7 08 1.34656 0.4378 0.02568 119.8

8 17 1.34565 0.4383 0.02557 120.1 9 12 1.35763 0.4402 0.02564 120.3 10 10 1.35535 0.4382 0.02563 120.7

11 20 1.34345 0.4363 0.02550 120.7

12 14 1.35243 0.4359 0.02565 120.9

13 09 1.34849 0.4390 0.02536 121.1 14 04 1.37192 0.4375 0.02585 121.3

15 16 1.37639 0.4373 0.02591 121.5

16 11 1.34186 0.4365 0.02530 121.5

17 18 1.38021 0.4367 0.02599 121.6

18 21 1.38539 0.4397 0.02584 121.9

19 19 1.37329 0.4388 0.02564 122.1 20 13 1.35383 0.4374 0.02535 122.1 21 05 1.35820 0.4380 0.02532 122.5 22 03 1.38218 0.4388 0.02565 122.8 23 15 1.36588 0.4373 0.02531 123.4 24 25 1.39927 0.4370 0.02589 123.7 25 24 1.39067 0.4352 0.02559 124.9

44
insulation for the panels during thermal testing in the guarded-hot-plate apparatus. The

guards were prepared by cutting a 1 0 1 6 mm diameter circular section from the center of

each sheet and removing a center square (void) 610 mm by 610 mm. Supplementary mass and dimensional measurements were carried out to determine the bulk density for the guard insulation (Table 6).

7.3 Specimen Selection The 450 panels (Table 3) were rank ordered by bulk density and divided into 25 subsets of 18 panels. The average bulk density was computed for each of the 25 subsets of 18 panels and cross-matched, as closely as possible, with the corresponding guard insulation bulk density in Table 6. The cross-matching process retained the same number of density

levels given in Table 5 (low, mid, and high) resulting in a final selection of 18 (nine pairs

of) panels and their corresponding guard insulation. The specimens for guarded-hot-plate

testing were assembled by placing an insulation panel in the equivalent sized void in the center of the corresponding guard insulation. Table 7 summarizes the bulk densities for the nine specimen pairs and guard insulation.

Table 7. Test specimens for (3x3) experimental design Density Specimen ID Bulk density (kg-m 3

) level pair Panel Guard Panel Guard Low 1 182 22 112.2 116.8 437 01 114.2 118.3 Low 2 049 07 115.0 118.5 086 06 115.6 118.6 Low 3 397 02 116.1 118.7 266 23 116.4 118.7 Mid 4 257 12 117.9 120.3 137 10 118.2 120.7 Mid 5 184 20 118.5 120.8 369 14 118.8 120.9 Mid 6 339 09 119.1 121.1 355 04 119.5 121.3 High 7 345 18 120.7 121.6 030 21 121.0 121.9 High

028 13 121.9 122.1

8 118 05 122.5 122.5 High

009 25 123.3 123.7

9 192 24 125.0 124.9

7.4 Thermal Conductivity Apparatus

7.4.1 Guarded-Hot-Plate Method

The thermal conductivity measurements were determined using the NIST 1016 mm

guarded-hot-plate apparatus operated in the double sided mode. Figure 12 shows the essential features of the guarded-hot-plate apparatus designed for operation near ambient temperature con45
ditions. The apparatus is cylindrically symmetric about the axis indicated in Fig. 12. The

plates are horizontal and heat flow (Q) is vertical (up/down) through the pair of specimens. The specimens, which have nearly the same density, size, and thickness, are placed on each

surface of the guarded hot plate and clamped securely by the cold plates. The guarded hot plate and the cold plates provide constant-temperature boundary conditions to the specimen surfaces. With proper guarding, lateral heat flows (Qg and Qe) are reduced to negligible proportions and, under steady-state conditions, the apparatus provides one-dimensional heat flow (Q) normal to the meter area of the specimen pair. A secondary guard is provided by an enclosed chamber

that conditions the ambient air surrounding the plates to a temperature near to the mean speci- men temperature (i.e., average surface temperatures of the hot and cold plates in contact with

the specimens).

Cold plate 1 Guarded hot plate (Meter plate)

Guard plate

Ambient gas

1 . Principle: Tc < Th ; Tc1 = Tc2 = Tc 2. Practice: Tc < Th ; Tc1 ~ Tc2 « Tc

Figure 12. Guarded-hot-plate schematic, double-sided mode of operation - vertical heat flow.

Equation (22) is the operational definition [18] for the experimental thermal conductivity of the specimen pair (^exp )

^exp A[(AT/L\+(AT/L)2 ] (22)

The thermal transmission properties of heat insulators determined from standard test methods typically include several mechanisms of heat transfer, including conduction, radiation, and possibly convection. For

that reason, some experimentalists will include the adjective "apparent" when describing thermal conductivity of thermal insulation. However, for brevity, the term thermal conductivity is used in this report.

46
where Q and A are defined in Terminology and (AT/L)\ is equal to the ratio of the surface- to-surface temperature difference {Th - Tc) to the thickness (L) for Specimen 1. A similar expression is used for Specimen 2. When the temperature differences and the specimen thicknesses are nearly the same, re- spectively, Eq. (22) reduces to K' = ^t (23)

In the double-sided mode of operation, the thermal transmission properties correspond to a mean temperature Tm given by Tm = {Th+ Tc)/2.

7.4.2 1016 mm Guarded-Hot-Plate Apparatus

The NIST 1016 mm guarded-hot-plate apparatus and uncertainty assessment, under operat- ing conditions near room conditions, have been described previously [16]. The apparatus

plates, 1016 mm in diameter, were fabricated from 6061-T6 aluminum alloy and the surfaces

in contact with the specimens were anodized black to have an emittance (s) of 0.89. The meter plate is nominally 406 mm in diameter and is physically separated from the surrounding

guard plate by an air gap (Fig. 12).

7.5 Establishing and Demonstrating Traceability

Section 7.5 describes the metrological traceability for measurement results for the NIST

1016 mm guarded-hot-plate apparatus. Table 8 summarizes the calibration information for the input quantities for Eq. (2) and the influence quantities described in Sec. 7. 1 .2. The quantities are ultimately traceable to reference standards retained by other organizations at NIST

which maintain practical realizations of the base SI units. The expanded uncertainties in Table 8 are used as part of the uncertainty analysis described in Sec. 7.6 and Sec. 8.4.

Table 8. Calibration information for the NIST 1016 mm guarded-hot-plate apparatus

Quantity Calibration laboratory Expandeduncertainty (k = 2) Interval NIST Quantum Electrical Metrology Division 0.000 000 5 Q 1 year vm, vs Manufacturer of digital multimeter 0.029 %* 2 year Th, Te NIST Thermometry Group < 0.005 °C 10 year L NIST Engineering Metrology Group < 70 nm 1 0 year

fo, ri Internal check - pin gages 0.01 mm

a Handbook data (Standard Reference Data) 20% N.A. F NIST Mass and Force Group 0.001 % 2 year

8 Internal check - infrared reflectometer 4%

Ta Internal check - thermistor probe 0.4 °C 5 year Pa NIST Pressure and Vacuum Group 52 Pa 5 year RH Manufacturer of relative humidity instrument 1 % 5 year *30 mV range

47
The first six rows of Table 8 represent the input quantities for the determination of A, from

Eq. (2). The last five rows are influence quantities that can affect the determination of A, dur- ing a test and are either fixed at a particular level or are generally neglected due to the small

effect and limited ("floating") range. Sections 7.5.1 through 7.5.5 describe, in detail, the

calibration information given in Table 8.

7.5.1 Specimen Heat Flow - Q

The specimen heat flow Q is essentially determined by measuring the direct current and

voltage provided to the meter-plate heater (Qm). The measurement approach for Qm is shown schematically in Fig. 13. A direct-current (DC) power supply provides current (I) to the circuit which is determined by the measurement Vs across the four-terminal 0. 1 Q. stan- dard resistor placed in an oil bath at 25.00 °C.

Oil Bath 25.00 °C Vs < >

A/WV

Vm < >

A/WV

DC Power

Supply

0.1 Q

Standard

Resistor, R=

56 Q

Meter-plate

Heater, Rm

Figure 13. Electrical schematic for meter-plate power measurement.

The equation for the determination of Qm is

Qm = IVm = —Kn ( 24) R

where / is the current (Vs /Rs) measured at the standard resistor and Vm is the voltage drop in the meter-plate heater measured across voltage taps located at the midpoint of the gap be- tween the meter plate and guard plate.

7.5. 1 . 1 Standard Resistor Calibration The standard resistor (Fig. 13) is a commercial, double-walled manganin resistor [19] manufactured in 1913. For 33 years, the resistor has been calibrated by the NIST Quantum Electrical Metrology Division in a mineral oil bath at 25 °C. Since 1990, the NIST calibrations have been based on the quantum Hall effect used as the U.S. representation of the ohm [20-

21]. The 2010 calibration (at a test current of 0.316 A) assigned a value of 0.10006939 Q. ±

0.000 000 5 Q (expanded uncertainty, k = 2) to the resistor.

48
7.5.1 .2 Digital Multimeter Calibration A digital multimeter (DMM), which is part of an automated computer data acquisition sys- tem, is used for the DC voltage measurement of Vs and Vm. At 2 year intervals (Table 8), the DMM and data acquisition unit are removed from laboratory service and calibrated by

the manufacturer to their specifications, typically at an offsite location. The measurement

results supporting the calibration are traceable to NIST. After return, the DMM and data

acquisition unit are placed in service and performance checks of the hardware are con- ducted manually and with computer software.

7.5.2 Temperature Difference - AT

The temperature difference across the specimen is determined by small capsule industrial plati- num resistance thermometers (PRTs) located in the hot and cold plates (7), and Tc, respectively). Each thermometer is constructed of a strain- free platinum element supported in a goldplated copper cylinder 3.18 mm in diameter by 9.7 mm long backfilled with helium gas and

hermetically sealed. The operational range is from -260 °C to 260 °C and the nominal electri- cal resistance is 100 fl at 0 °C. The electrical resistance of each 4-wire PRT is measured with

the DMM and automated data acquisition system described in Sec. 7.5.1.2. For 29 years, the PRTs have been calibrated by the NIST Thermometry Group by compari- son with a standard platinum resistance thermometer (SPRT) in a stirred liquid calibration bath [22]. The PRTs were initially calibrated in 1981 at the triple point of water (which is 0.01 °C by definition), 10 °C, 20 °C, 30 °C, 40 °C, and 50 °C. In 1993, the PRTs were re- moved from the apparatus and calibrated over an extended temperature range, thereby ex- tending the range of the guarded-hot-plate apparatus. All temperatures for the 1993 and 2008 calibrations were based on the International Temperature Scale of 1990 (ITS-90) [23-

24]. For the 2008 calibration, the expanded uncertainty (k = 2) in the bath temperature measurements from -70 °C to 0 °C did not exceed 0.0023 °C, from 0 °C to 95 °C did not exceed

0.0024 °C, and from 95 °C to 300 °C did not exceed 0.0048 °C.

7.5.3 Specimen Thickness - L

For semi-rigid specimens such as SRM 1450d, the specimen thickness {L) is measured in- situ using eight (four for the top specimen and 4 for the bottom specimen) linear position transducers located at the periphery of the plate. The calibration hierarchy for these trans- ducer measurements is described in Sec. 7.5.3.1 and Sec. 7.5.3.2.

7.5.3.1 Fused-Quartz Spacers One set of nominal 25.4 mm spacers was cut and ground, collectively, by the NIST Glass

Fabrication Shop from quartz tubing (25 mm outer diameter). Fused-quartz tubing was se- lected because of its low thermal expansion coefficient (5.5xl0~

7 K~') and high elastic modulus (72 GPa). The set of spacers was measured using either a digital caliper or a digital height gage referenced to a datum surface.

7.5.3.2 Linear Position Transducers For 1450d, the in-situ thickness of the specimen is determined by averaging four linear position transducers attached to the periphery of each cold plate at approximate 90° arc inter- vals. Each positioning system consists of a digital readout and a slider translating on a tape

49
scale bonded to a precision ground plate of a low thermal expansion iron-nickel (FeNi36)

alloy. The electrical windings on the scale are inductively coupled with the slider and the

resulting output signal from the scale is resolved by the digital readout. The digital read- outs are reset by placing one set of fused-quartz spacers of known thickness between the cold plate and hot plate.

7.5.4 Meter Area - A

The meter area is the mathematical area through which the heat input to the meter plate Qm

flows normal to the heat-flow direction under ideal guarding conditions (i.e., lateral heat flows = 0) into the specimen. The circular meter area was calculated from Eq. (25).

^ = fx(C+>r) x

(

1 + aA7;,)

2 (25)

where r0 is the outer radius of the meter plate (m); r, is the inner radius of the guard plate (m); a is the coefficient of thermal expansion of 6061-T6 aluminum (K"

1 ); and, ATmp is the temperature of the meter plate (7}7 ) minus 20 °C (in kelvin).

7.5.4.1 Plate Dimensions The design dimensions for the meter plate and the guard plate diameters are 405.64 mm and

407.42 mm, respectively. A coordinate measuring machine (CMM) measured the roundness of the meter plate at six locations at the periphery and the diameter was determined to be

405.67 mm (within 0.03 mm of the design dimension). A uniform gap width of 0.89 mm

was established using three precision pin gages spaced between the meter plate and guard

plate at equiangular intervals. The uncertainty of the pin gages was +0.005 mm/-0.000 mm.

Based on these check measurements, the input values for ra and r, for Eq. (25) were deter- mined to be 0.20282 m and 0.20371 m, respectively, and the standard uncertainty (k = 1) for both input values was taken to be 0.0254 mm.

7.5.4.2 Thermal Expansion Effects For a, an input value of 23. 6x1

0"6 K"

1 at 20 °C was obtained from aggregated handbook

data [25] for 6061-T6 aluminum. The standard uncertainty (k= 1) for the value of a was

estimated conservatively to be 10 % (2.36xl0~6 K"

1 ). The standard uncertainty (k = 1) for ATmp was based the uncertainty for the plate temperature (Sec. A4.3.3).

7.5.5 Influence (Secondary) Quantities

Several other quantities can affect the thermal conductivity measurement of insulating materials including the clamping load, plate emittance, chamber air temperature, pressure, and

relative humidity, among others. These quantities are either controlled at a fixed value dur- ing a test or recorded. The quantities were not included in the uncertainty analysis.

7.5.5.1 Plate Parameters The clamping load (F) for each cold plate is measured by a 4.4 kN load cell connected to a dual-channel digital readout. The load cells and readout were removed from the apparatus and calibrated, as a system, by the NIST Mass and Force Group by application of dead

50
weights. The calibration standard uncertainty (k = 1) for the applied calibration force is 0.0005 % [26]. The plate emittance (e) is periodically checked with a portable infrared re- flectometer [27]. The emittance measurements of the anodized black aluminum plate sur- faces in contact with the insulation specimens are 0.89. The standard uncertainty (k = 1) of

the measurement was estimated to be 2 % of the reading.

7.5.5.2 Environmental Parameters The NIST 1016 mm guarded-hot-plate apparatus is enclosed by a temperature-controlled chamber. The ambient air temperature surrounding the apparatus is determined by averaging

five Type-T thermocouples located at different positions in the chamber. A thermistor temperature probe and digital display are used to check the ambient temperature measurement. The standard uncertainty (k = 1 ) of the probe and thermometer was estimated to be 0.2 K. The chamber pressure is monitored by an absolute pressure gauge calibrated by the NIST

Pressure and Vacuum Group against a gas lubricated piston gauge [28]. The expanded uncertainty (k = 2) of the pressure gauge was determined to be 52 Pa. The chamber air relative humidity was measured by a relative humidity (RH) probe calibrated by the manufacturer

with an expanded uncertainty (k = 2) of 1 % RH.

7.6 Identification of Uncertainty Sources

Table 9 presents a comprehensive, but not exhaustive, list of relevant uncertainty sources

for the input quantities for Eq. (2). The assembled list of uncertainty sources include the following metrology areas - electrical for the voltage and resistance measurements (Q); temperature for AT, and, dimensional for the meter area (A) and thickness (L).

Table 9. Uncertainty sources for the NIST 1016 mm guarded-hot-plate apparatus

1) Specimen heat flow (Q)

a) Repeated measurements (Qmj) b) Direct current (DC) power measurement (Q,„)

i) Standard resistor calibration

ii) Standard resistor drift

iii) PRT power input (to meter area)

iv) Voltage measurement meter-plate heater ( Vm) v) Voltage measurement standard resistor (Vs) c) Parasitic heat flows - i.e., lateral heat flows

i) Guard-gap (Qg)

ii) Edge effects (QE ) 2) Temperature difference (AT)

a) Repeated measurements (AT,

)

b) Measurement (7), , Tc)

i) PRT calibration

ii) PRT curve fit for calibration data

iii) Electrical resistance measurement

c) Miscellaneous sources

i) Temperature rise due to PRT self-heating

ii) Plate temperature variations in the radial dimension

iii) Plate temperature variations in the axial dimension

51
3) Thickness (L)

a) Multiple measurement locations

b) Instalment (in-situ) measurement (i.e., linear position system)

i) Gage block calibration

ii) Fused-quartz spacer length dimensions

( 1 ) Multiple locations

(2) Micrometer uncertainty

iii) System uncertainty

iv) Short-term repeatability

c) Plate characteristics

i) Flatness

(1) Multiple locations

(2) Coordinate measuring machine (CMM) uncertainty

ii) Deflection under axial loading of cold plates 4) Meter area (A)

a) Plate dimensions

b) Thermal expansion effects

c) Temperature measurement

52
8 Data and Uncertainty Evaluation

Section 8 presents the thermal conductivity measurements, analysis of data, final model

determination, and assessment of measurement uncertainties.

8.1 Experimental Design Modification The thermal conductivity measurements were initially completed using the experimental

design shown in Table 5. Least squares fits of multiple models of the thermal conductivity data revealed that, for the densities studied, A,exp was insensitive to bulk density (p). In other words, A.exP was found to be a function only of temperature (T). To confirm this finding, the experimental design was modified by adding two intermediate temperature

levels at 295 K and 325 K. The resulting full factorial design with three levels for density and five levels of temperature is shown in Table 10. The corresponding test sequence in Table 10, from 10 to 15 (shown as circled numbers), was randomized to mitigate the in- fluence of any systematic effects.

Table 10. Full factorial (3 X 5) experimental design Density level Temperature level (K) 280 295 310 325 340 Low 1 obs.*© 1 obs.© 1 obs.© 1 obs. © 1 obs.©

Mid 1 obs. 0 1 obs.0 1 obs.© 1 obs. © 1 obs.©

High 1 obs. 0 1 obs. 0 1 obs.© 1 obs. © 1 obs.©

*obs. = observation An additional 12 test specimens (six pairs) were selected from the material lot to augment

the original 18 specimens selected in Table 7. Table 1 1 summarizes the selection for the

six additional specimen pairs and corresponding guard insulation. Some insulation guards were re-used for these subsequent tests.

Table 1 1 - Additional test specimens for (3><5) experimental design Density

level Specimenpair ID

Panel Guard

Bulk density (kgm 3 ) Panel Guard Low 10 103 01 113.5 118.3 332 07 114.9 118.5 Low 11 308 06 115.4 118.6 164 02 115.8 118.7 Mid 12 074 10 118.1 120.7 087 20 118.5 120.7 Mid 13 107 14 118.9 120.9 155 09 118.9 121.1 High 14

105 34705

03

121.3 121.7122.5 122.8 High 15 129 351

15 25

122.9 123.7123.7

124.9

53
8.2 Guarded-Hot-Plate Data

8.2.1 Data Acquisition Thermal test data (7}„ Tc, and Q) were collected every 2 min during a 4 h steady-state period (n = 120 observations per parameter) using a computer-controlled data acquisition system. The variability (s) for each measured parameter was checked against the accept- able tolerance limits summarized in Table 12. Estimates for each measured parameter were (subsequently) taken as the arithmetic means of the observations.

Table 12. Required tolerance limits for acceptable steady-state test data Quantity Description Limits Units Th Hot surface ±0.0025 K

Tc Cold surface ±0.005 K

AT Temperature difference ±0.005 K

Q Meter-area heat flow ±0.01 W

v* Thermopile voltage ±0.7 uV

Ta Chamber air temperature ±0.05 K

RH Chamber relative humidity maintained < 10 % RH

Pa Chamber air pressure uncontrolled kPa

8.2.2 Data Summary (Tabular Format)

Table 13 summarizes the experimental results specimen information, input estimates, influencing factor estimates, and the output estimate for measured thermal conductivity

(^exP

) - for the 15 specimen pairs specified in the experimental design (Table 10). The

rows of data in Table 13 are grouped by Tm from 280 K to 340 K and, within each level of Tm, the average specimen densities (pv ) are arranged from lowest to highest value. The

columns of data are grouped into four major sections: 1) specimen identification (ID) and

material properties; 2) input quantities for Eq. (23); 3) secondary quantities; and

4) resultant thermal conductivity (X). The notations "1" and "2" in Table 13 designate the top and bottom specimen, respectively, as illustrated in Fig. 12. The bulk density parameter ps (Table 13, column 6) is the average of pi and p2 . The range for ps defines the "certified" bulk density range for SRM

1450d from 1 13.5 kgm 3 to 123.8 kg-nf3 (rounded7 from 1 14 kg-rn

3 to 124 kg-m"3

). The

input temperature estimates, Th, Tc\, and Tco, were within 0.01 K, or less, of their respective set-point temperatures. The estimates of QI2 ranged from 3.9 W to 4.8 W for Tm at 280 K and 340 K, respectively. For a fixed value of Tm, the variation of QI2 due to changes in p, was much smaller. The estimates for A have been corrected for thermal ex- pansion effects of the meter-plate radius using Eq. (25). The estimates for the in-situ test thickness L were determined by averaging the digital outputs of the eight linear position transducers (four for each cold plate) discussed in Sec. 7.5.3. The resultant estimates for

A,eXp include an extra digit to reduce rounding errors.

7 The panel bulk densities (p, and p2 ) given in Table 13 were determined using the in-situ test thicknesses (L). Consequently, the values for p, and p2 are slightly different (by 0.5 %, or less) than the values given in Table 3, which were determined using the mean thickness (Lm) of the surface plate measurements (Figure 3a).

54
* £

0.03112 1

0.03096 10.03090 1

0.03245 10.03249 1

0.03261

0.03409 10.03428 10.03422 10.03572 10.03597 10.03599 1

0.03752 10.03760 10.03782 |

Secondary

quantities

(Pa) rr- r-m-3- oo o xO

-r cs

rTi- -roo

<fr xCom

00

DC

xj- inT

ON

-r cm

xT

-1- :c

r--

tj- <N

cox*

RH g

oo oo ON en (N

"v

(kPa)

99.3 99.6

100.6 100.5 9

001

100.2) 100.1 |

98.6 199.7 |

100.51 101.3 1

97.5 199.7 |

101.3 1

99.1 |

g

280.0 280.0 280.0 295.0 295.0 295.0 310.0 310.0 310.0 325.0 325.0 325.0 340.0

340.0 |

340.0 |

Input

quantities

for

Eq.

(22)

(mm) 25.93 25.80 25.56 26.02 25.82 25.80 26.13 25.76 25.76 25.85 26.00 25.73 |

25.98 25.78 25.85

0.12980 0.12980 oDCO^r 1 O0.12989 0.12989 0.12989 0.12998 0.12998 0.12998

0.13007 10.13007 10.13007 1

0.13016 ]0.13016 |

0.13016 |

1

Q/2 3.895 3.894 3.924 4.050 4.086 4.105 4.240 4.324 4.317 4.494 4.499 4.549 4.701 4.747 4.760

g

267.50 267.51 267.49 282.50

282.50 |

282.50 297.50 297.50 297.50 312.501

312.50 312.50 327.50 327.50 327.49

267.50 267.50 267.50

282.50 |282.50 1

282.50 ]

297.50 1

297.50 1

297.51

312.50 |

312.50 312.50 327.49

327.50 |327.50 1

g

292.50 292.50

292.50 |

307.50 307.50 307.50

322.50 |

322.50 322.50 337.50 337.50 337.50 352.50 352.50 352.50

Specimen

properties

Q.

'g in

co

in

dc 121.2 |

tn

-t q

ON 121.5 |

oo

in od 122.4 t>

in ON

OO 123.2 DCin ON 123.8

114.3 118.7 121.4 115.2 119.1 121.8 115.6 118.9 122.8 116.1 118.9 123.9 116.4 119.7 124.3

<£

112.8 |

118.3 |

121.0 |

113.5 |

118.9 |121.1 |

116.0 |118.5 1

122.0 115.2 oq

od 122.5 115.3 118.6 123.3

9

r-m-T m

omo

<Nm

rDCz> r-m

NO

DCo

ONNOm

oo

nC in

in m

co

nC

xCr i >ninco

CN

ON Q

r i DCr-- in

(N

>n

-t- rn m- C-o m ON-To

tDC

DCr | OOOom

o ri ronco co

co

ONoo g

oycr i odc<N ODCri

inr ] inri m3nr | o 3m

o

m mr | m

mriCO mriro o

-tcn oT

co o

t

co

55
During a test, the (secondary) influence quantities (Ta, pa, RH, and/) were either controlled or only recorded. The chamber air temperature (7^) was controlled to be the same

temperature as Tm (within 0.1 K, or less). The chamber air pressure (pa) varied with the

site barometric conditions from 97.5 kPa to 101.3 kPa. The chamber RH was maintained

at less than 10 % RH by a dry-air purge. However, the value varied with the chamber

dry-bulb air temperature (Ta ). The clamping pressure if) was determined by averaging

the loading force (F) applied by each cold plate divided by the surface area of the cold

plate, which was corrected for thermal expansion effects. Table 14 provides summary statistics for test quantities given in Table 13 that were fixed

at one value across all tests. As noted in Sec. 7. 1.2, the temperature difference (AT) of

25.001 K was based on standard practice for selecting test temperatures [17].

Table 14. Summary statistics for fixed- and recorded-value quantities AT L Pa /

(K) (mm) (kPa) (Pa) Mean 25.001 25.85 99.9 476

Std. Dev. 0.003 0.14 1.0 19

Prior to testing, each specimen pair was assembled with its respective guard insulation and was placed in an oven at 100 °C for a minimum of 3 h. The panels and guard insulation assemblies were weighed prior to, and after, the guarded-hot-plate tests. The average mass regain for the specimen assemblies was approximately 8 g (or 0.3 %).

8.2.3 Data Screening (Graphical Analysis)

Figures 14a and 14b plot values of ^exp from Table 13 as a function of the design model

(Eq. (21)) input variables p, and Tm, respectively. For Fig. 14a, the individual data points

are plotted as filled circle symbols corresponding to Tm levels of 280 K, 295 K, 310 K, 325 K, and 340 K. The error bars represent expanded uncertainties of 0.86 % (Sec. 8.4.1). For Fig. 14b, the individual data points are plotted as filled circle, square, and triangle symbols (without error bars for clarity) corresponding to the three main levels selected for bulk

density.

8.2.4 Data Evaluation - Characterization The data in Fig. 14 strongly suggest that, in the range of ps and Tm covered for the 450

specimens comprising the current SRM:

1 ) ^exP

is insensitive to ps (in contrast with previous 1450 version materials); and,

2) the dependence of ^exp on Tm is strongly linear. The first assertion is born out by linear least squares fits to the 3-point horizontal profiles

visible in Fig. 14a. Table 15 summarizes the slopes of the lines shown in Fig. 14a and

their corresponding /-values. For the three inner horizontal profiles, the slope of the fitted profile is statistically indistinguishable from zero (\t\ < 2) at 95% confidence for the

3 10 K and 325 K lines and only marginally significant (|/| = 2) for the 295 K line. For the two outer horizontal profiles (280 K and 340 K), the slopes are statistically significant, but quite small.

56
0.030 110 115

Bulk density, kgm

120

3 125

039 "

038 "

037 -

036 "

035 "

034 ~

033 -

032 "

031 "

030 "

Low Bulk Density Mid Bulk Density High Bulk Density

270 280 290 300 310 320

Temperature, K

330 340 350

Figure 14. 1450d: a) Graphical analysis of thermal conductivity versus bulk density. Error bars represent ex- panded uncertainties of 0.86 %. b) Graphical analysis of thermal conductivity (without error bars for clarity) versus temperature.

57
Table 15. Summary of linear profiles for A.cxp versus p.v (Fig. 14a) Tm (K)

Slope (W-m2 -K'-kg"')

/-value (dimensionless) 280 -2.939xl0"5 -12.1 295 2.114X10"5 2.0 310 1.850xl0"5 0.8 325 3.314xl0 5 1.6 340 3.741xl0"5 6.4 A fit of the no-intercept line model ^exp = aiTm yields excellent fit statistics (^-square =

0.997) and is visually an excellent fit as well (Fig. 14b). The residual standard deviation

for the fit is 0.00012 Wm'-K 1 . Table 16 summarizes the regression statistics for the nointercept linear fit to temperature.

Table 16. Summary of regression statistics for A,£xP versus Tm (Fig. 14b) Regression

coefficient Slope (Wm'-K 2

)

s of Slope (Wm'K'2

) /-value (dimensionless) 1.10489xl0"4 l.OlOxlO"7 1094

For comparison and further model validation, other models were fit including: - bilinear in p and T, with and without constant term; and, - quadratic and cubic in T, with and without constant term. For all the models assayed, one or more fitted coefficients were non-significant, with the exception of the pure third power model (T }

) with no constant, linear, or quadratic term. But visually and statistically, all other models were found to be inferior to the simplest

first power (linear) model in Twith no constant term.

8.3 Final Model

Equation (26) gives the final model for SRM 1450d.

i = (l.l0489xl0~4 )xr (26)

Figure 15 plots the deviations (7iexp - %)/% (in percent) versus Tm by bulk density (filled

circle, square, and triangle symbols corresponding to low-, mid-, and high- levels of bulk

density, respectively). The deviations for mid- and high-bulk densities are randomly and

interchangeably scattered (i.e., no discernible pattern) around zero. The low-bulk densities, however, are biased low (about -0.5 %), with the exception of one low-temperature

point. The same pattern is visible on close inspection in Fig. 14b.

8.4 Uncertainty in Experimental Thermal Conductivity (X,exp) The uncertainty in Xexp was evaluated by two methods: 1) an extensive uncertainty budget

prepared in Annex 4; and, 2) 95 % Working-Hotelling [29] simultaneous confidence bands around the experimental data.

58
1.0

0.5

CO I 0.0

CO

-0.5

-1.0

Low Bulk Density Mid Bulk Density High Bulk Density

270 280 290 300 310 320 330 340 350

Temperature, K

Figure 15. 1450d: Graphical analysis of deviations (in %) for the fit given in Eq. (26).

8.4.1 Uncertainty Budget

For the multiplicative expression of Eq. (23), the relative combined standard uncertainty

in Xexp can be expressed as the relative uncertainties associated with each factor combined

in quadrature.

AT

(27)

The standard uncertainties and input quantities used in Eq. (27) are derived in Annex 4. The maximum combined standard uncertainty for ^eXp was determined at T,„ of 340 K.

( 0.0074'f + r°-o77

i

2 f 0.065N

j

2 f 0.000043 V

I 4.736 ,

) 1,25.001 J +

l25.85 y

1 +

{ 0.13016 J (28) Km (KP ) =

V(0.00156)

2 +(0.00308)2 +(0.00251)

2 +(0.00033)2 = 0.0043 (29) uJKv ) = 2uc JKx \ = 0.0086 (30)

59
Expressed as a percent (x 100), Urei is equal to 0.86 %. The relative contribution for the first term in Eq. (29) is 13.3 %; for the second, 51.9 %;

for the third, 34.2 %; and, for the fourth, 0.6 %. The major contributory uncertainties for SRM 1450d are due to the empirical determinations for specimen temperature difference (AT) and thickness (Lavg). These findings are consistent with results from previous uncertainty analyses [16].

8.4.2 Confidence Limits (Working-Hotelling Bands)

Figure 16 shows simultaneous 95 % confidence bands (dashed lines) about the nointercept linear regression of A,exp on T. The bands are actually hyperbolic segments, more constricted towards the middle of the temperature range, flaring out towards the ex- tremes of the range, where the least squares predictions are less certain. The "simultane- ous" refers to the fact that for any fixed value of T, a bona fide 95 % interval for thermal

conductivity can be derived from the picture by drawing a vertical line segment at that value of T intersecting the lower band, fitted line, and upper band. The lower and upper band ordinate values thus determined form a 95 % confidence interval for the true value of X at that T. The uncertainty from this approach is derived from the vertical segments at the ends of the temperature range (280 K or 340 K). Rounded up slightly, it is ±0.5 %.

0.039 "

0.038 - f 0.037 " ^ 0.036 "

= 0.034 h

8 0.033

03£ 0.032 -

CD 0.031 "

0.030 "

• Low Bulk Density Mid Bulk Density

a High Bulk Density

b L 270 280 290 300 310 320

Temperature, K

330 340 350

Figure 16. 1450d: 95 % Confidence Limits (Working-Hotelling Bands [29]) about the no-intercept linear regression line Xnp on T.

60
8.4.3 Comments on Uncertainty Approach

The extensive uncertainty budget presented in Annex 4 has been developed over thirty years [30, 10, 16] and has been updated consistent with current international guidelines

[15]. The budget uncertainty for this work was determined to be 0.86 % (k =2) which is a more conservative estimate than the maximum value based on the Working-Hotelling

95 % confidence bands of 0.5 % for the experimental data. For convenience to the SRM

user, the uncertainty for 1450d has been rounded up to the nearest whole integer of 1 %.

8.4.4 Supplemental Thermal Conductivity Data As part of the imbalance experiment, specimen pair 184-369 was re-measured from 280 K to 340 K. The test results and analysis are presented in Annex 5.

61
9 Certification

Section 9 presents important summary information on the properties of interest, values and uncertainty, statement of metrology traceability, and instructions for use for Standard Reference Material 1450d. This information is intended to provide supplementary documentation for the 1450d Certificate.

9.1 Properties of Interest Standard Reference Material 1450d is a high-density molded fibrous glass board certified for bulk density, p, and thermal conductivity, X. Each SRM unit consists of a square

panel of fine-glass fibers and phenolic binder molded into a semi-rigid board. The nominal dimensions of a unit are 611 mm by 61 1 mm by 26 mm (Table 4) and the bulk density ranges from 1 14 kg-m"3 to 124 kg-m"3 (Table 13).

9.2 Values and Uncertainties Each unit of SRM 1450d is individually certified for bulk density, p (Table 3), and batch

certified for thermal conductivity with Eq. (31):

^ = (l.l0489xl(T4 )x7;; (31)

where X is the predicted thermal conductivity (W-rn^-K" 1 ) and Tm is the mean specimen

temperature (K). The test temperature difference across the specimen (A7) was 25 K

(Table 14). Equation (31) is only certified to be valid over the temperature range of 280 K to 340 K. The expanded uncertainty for X values from Eq. (31) is 1 % with a coverage factor of approximately k = 2.

9.3 Statement of Metrological Traceability The input quantities for the determination of bulk density and thermal conductivity are metrologically traceable to working references maintained at NIST as described in Sec. 6.4 and Sec. 7.5, respectively.

9.4 Instructions for Use

Standard Reference Material 1450d is intended for use as a proven check for the guardedhot-plate apparatus (or other absolute thermal conductivity apparatus) and for calibration of a heat-flow-meter apparatus over the temperature range of 280 K to 340 K. NIST can- not exclude the use of SRM 1450d for other purposes, but the user is cautioned that other purposes are not sanctioned by the 1450d Certificate.

9.4.1 Storage

For protection and identification, it is recommended that the reference material be stored

in the original packaging in a clean, dry environment at temperatures between 1 5 °C and

30 °C.

62
9.4.2 Preparation and Conditioning Before Measurement

Prior to the thermal conductivity measurement, the reference material should be conditioned in laboratory conditions of 20 ° C to 25 °C and from 40 % RH to 65 % RH until the mass of the unit is stable (i.e., two successive measurements within 24 h are less than

I %).

9.4.3 Thermal Conductivity Measurement

Thermal conductivity measurements should be conducted in accordance with the appropriate ASTM Test Method C 177 [1], C 518 [2], or other similar international standard.

9.4.4 Guidelines and Precautions The following guidelines and precautions are provided for the user. Stacking: Certified values of thermal conductivity are valid for a single unit, and

are invalid for stacked units. Slicing: Certified values of thermal conductivity are invalid for a unit where the thickness of the material has been modified by slicing. Cutting: It is possible to cut the reference material unit into smaller pieces. It is imperative to verify that bulk density of each piece is within the certified range of

bulk density (Sec. 9.1). Upper Temperature Limit: The upper temperature limit for this reference material

is limited to the decomposition point of the binder, approximately 473 K (200 °C)

[10]. As a precaution, this reference material should not be heated above 380 K

(107 °C). It should be noted that oven drying, as opposed to desiccant drying, can remove other volatiles and potentially affect chemical or physical properties of

the material. Lower Temperature Limit: A lower temperature limit for SRM 1450d has not been established but, in principle, there is no known lower limit. Atmospheric Pressure: The effect due to changes in ambient atmospheric pressure

is negligible for this material. 10 Acknowledgements

The authors appreciate the comments and discussions with D. R. Flynn, retired from the National Institute of Standards and Technology, Dr. D. L. McElroy, retired from the Oak

Ridge National Laboratory. The authors express appreciation for the computer program- ming provided by A. N. Heckert and for the initial statistical assessment of materials by

D. D. Leber of the NIST Statistical Engineering Division. II References

1. ASTM Standard CI 77- 10, "Test Method for Steady-State Heat Flux Measurements and Thermal

Transmission Properties by Means of the Guarded-Hot-Plate Apparatus," Annual Book ofASTM Standards, ASTM International, West Conshohocken, PA (2010).

2. ASTM Standard C5 18-10, "Test Method for Steady-State Thermal Transmission Properties by Means

of the Heat Flow Meter Apparatus," Annual Book ofASTMStandards, ASTM International, West Conshohocken, PA (2010).

63
3. ASTM Standard C1363-05, Test Method for Thermal Performance of Building Materials and Envelope Assemblies by Means of a Hot Box Apparatus," Annual Book ofASTMStandards, ASTM International, West Conshohocken, PA (2010).

4. Federal Register, "Federal Trade Commission 16 CFR Part 460: Trade Regulations: Labeling and Advertising of Home Insulation," (August 27, 1979, revised January 2010) pp. 50218-50245; see also Code of Federal Regulations, [Web page], http://www.gpoaccess.gov/cfr/index.html [last updated

January 2010].

5. NIST Standard Reference Materials, Natl. Inst. Stand. Technol., [Web page], https://wwws.nist.gov/srmors/viewTable.cfm?tableid=l 17 [last updated August 201 1]. 6. ASTM Subcommittee CI 6.30, "Reference Materials for Insulation Measurement Comparisons," Ther- mal Transmission Measurements ofInsulation, ASTMSTP 660, R. P. Tye, Ed. (1978) pp. 7-29.

7. NBS, "Research Highlights of the National Bureau of Standards: Annual Report, Fiscal Year 1959," Miscellaneous Publication 229, December 1959, p. 88.

8. M.C.I. Siu, "Fibrous Glass Board as a Standard Reference Material for Thermal Resistance Measure- ment Systems," Thermal Insulation Performance, ASTM STP 718, D. L. McElroy and R. P. Tye, Eds. (1980) pp. 343-360.

9. J.G. Hust, "Standard Reference Materials: Glass Fiberboard SRM for Thermal Resistance," NBS Special Publication 260-98, Natl. Inst. Stand. Technol., August 1985.

10. R. R. Zarr, "Standard Reference Materials: Glass Fiberboard, SRM 1450c, for Thermal Resistance from 280 K to 340 K," NIST Special Publication 260-130, Natl. Inst. Stand. Technol., April 1997. U. R. R. Zarr and D. D. Leber, "Evaluation of Thermal Insulation Materials for NIST SRM 1450d, Fi- brous-Glass Board," Thermal Conductivity 30/Thermal Expansion 18, D. S. Gaal and P. S. Gaal Eds. (2010) 386-392.

12. W. May, R. Parris, C. Beck, J. Fassett, R. Greenberg, F. Guenther, G. Kramer, S. Wise, T. Gills, J. Colbert, R. Gettings and B. MacDonald, "Standard Reference Materials'* : Definitions of Terms and Modes Used at NIST for Value-Assignment of Reference Materials for Chemical Measurements," NIST Special Publication 260-136, Natl. Inst. Stand. Technol., January 2000.

13. ISO Guide 30:1992(E)/Amd. 1, "Terms and definitions used in connection with reference materials, Amendment 1 : Revision of definitions for reference material and certified reference material," International Organization for Standardization, Switzerland, 2008.

14. ASTM Standard C 168-10, "Standard Terminology Relating to Thermal Insulation," Annual Book of ASTMStandards, ASTM International, West Conshohocken, PA (2010).

15. JCGM 100:2008, "Evaluation of measurement data - Guide to the expression of uncertainty in measurement

(ISO GUM 1995 with minor corrections)," Joint Committee for Guides in Metrology, BIPM, Paris, France, 2008, available at http://www.bipm.org/utils/common/documents/icgin/JCGM_100_2008_E.pdf; see also B. N. Taylor and C. E. Kuyatt, "Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results", NIST Technical Note 1297, U.S. Government Printing Office, Washington, D.C., 1994, available at http://physics.nist.gov/Pubs/guidelines/TN1297/tnl297s.pdf. 16. R. R. Zarr, "Assessment of Uncertainties for the NIST 1016 mm Guarded-Hot-Plate Apparatus: Extended Analysis for Low-Density Fibrous-Glass Thermal Insulation," J. Res. Natl. Inst. Stand. Technol., 115, 23-59 (2010).

17. ASTM Standard C 1058/C1058M-10, "Standard Practice for Selecting Temperatures for Evaluating and Reporting Properties of Thermal Insulation," Annual Book of ASTM Standards, ASTM International, West Conshohocken, PA, 2010.

18. ASTM Standard C 1045-07, "Standard Practice for Calculating Thermal Transmission Properties Under Steady-State Conditions," Annual Book of ASTM Standards, ASTM International, West Conshohocken, PA, 2010.

19. J. L. Thomas, "Stability of Double-walled Manganin Resistors," J. Res. National Bureau of Standards, 36,107-110,(1946).

20. N. B. Belecki, R. F. Dziuba, B. F. Field and B. N. Taylor, "Guidelines for Implementing the New Representations of the Volt and Ohm Effective January 1, 1990," NIST Technical Note 1263, Natl. Inst. Stand. Technol., June 1989.

21. R .E. Elmquest, D. G. Jarrett, G. R. Jones Jr., M. E. Kraft, S. H. Shields and R. F. Dziuba, "NIST Measure- ment Services for DC Standard Resistors," NIST Technical Note 1458 , Natl. Inst. Stand. Technol., De- cember 2003.

64
22. G. F. Strouse, B. W. Mangum, C. D. Vaughn and E. Y. Xu, "A New NIST Automated Calibration System

for Industrial Grade Platinum Resistance Thermometers," NISTIR 6225, Natl. Inst. Stand. Technol., Sep- tember 1998.

23. H. Preston-Thomas, "The International Temperature Scale of 1 990 (ITS-90)," Metrologia, 27, 3- 1 0 ( 1 990).

24. B. W. Mangum, G. T. Furukawa, K. G. Kreider, C. W. Meyer, D. C. Ripple, G. F. Strouse, W. L. Tew, M.

R. Moldover, B. Carol Johnson, H. W. Yoon, C. E. Gibson and R. D. Saunders, "The Kelvin and Temperature Measurements," J. Res. Natl. Inst. Stand. Technol., 106, 105-149, (2001).

25. Y. S. Touloukian, R. K. Kirby, R. E. Taylor and P. D. Desai, Thermophysical Properties ofMatter, Tlie TPRC

Data Series, Volume 12: Tlxermal Expansion: Metallic Elements andAlloys. IFI/Plenum, New York (1977) pp. 1028-1033.

26. T. W. Bartel, S. L. Yaniv, and R. L. Seifarth, "Force Measurement Services at NTST: Equipment, Procedures and Uncertainties," ( 1 997) NCSL Workshop & Symposium, Atlanta. 27. ASTM E408-7 1(2008), "Standard Test Methods for Total Normal Emittance of Surfaces Using Inspection- Meter Techniques," Annual Book of ASTM Standards, ASTM International, West Conshohocken, PA

(2010).

28. J. W. Schmidt, K. Jain, A. P. Miiller, W. J. Bowers and D. A. Olson, "Primary pressure standards based on

dimensionally characterized piston/cylinder assemblies," Mehvlogia, 43, 53-59 (2006). 29. H. Working and H. Hotelling, "Application of the theory of error to the interpretation of trends," Journal ofthe American Statistical Association, Supplement (Proceedings) (1929) 24, 73-85.

30. B. G. Rennex, "Error Analysis for the National Bureau of Standards 1016 mm Guarded Hot Plate," NBSIR

83-2674, Natl. Inst. Stand. Technol., February 1983 (reprinted in Journal of Thermal Insulation, 7, 18-51

(July 1983)). 31. V. Miller, "Recommended Guide for Determining and Reporting Uncertainties for Balances and

Scales," NISTIR 6919, Natl. Inst. Stand. Technol., January 2002.

32. T. Doiron and J. Stoup, "Uncertainty and Dimensional Calibrations," J. Res. Natl. Inst. Stand. Technol., 102, 647-676(1997).

33. M. H. Hahn, H. E. Robinson and D. R. Flynn, "Robinson Line-Heat-Source Guarded Hot Plate Apparatus," Heat Transmission Measurements in Thermal Insulations, ASTMSTP 544 (1974) pp. 167-192.

34. R.J. Roark, Formulas for Stress and Strain, 4th Ed. McGraw-Hill Inc., New York ( 1 965) p. 2 1 9, Case 1 1

35. G. J. Lieberman and R. G. Miller, "Simultaneous tolerance intervals in regression," Biometrika, 50, (1 and 2), 155 (1963).

65
Annex 1

Annex 1 - Mass Plots

Hill 11111 11111

Figure Ala. Panel ID=l-25: Multiple mass observations (in kilograms) as a function of elapsed time (in seconds) for insulation panels 001 through 025. Linear fit for data (shown as solid line) was backextrapolated to elapsed time zero (t0 ) to determine m0 for each insulation panel.

66
Annex 1

I I 1 I 1

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Figure Alb. Panel ID=26-50: Multiple mass observations (in kilograms) as a function of elapsed time (in seconds) for insulation panels 026 through 050. Linear fit for data (shown as solid line) was backextrapolated to elapsed time zero (/0) to determine m0 for each insulation panel.

67
Annex 1

| | | | |

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Figure Ale. Panel ID=5 1-75: Multiple mass observations (in kilograms) as a function of elapsed time (in seconds) for insulation panels 051 through 075. Linear fit for data (shown as solid line) was backextrapolated to elapsed time zero (t0) to determine mQ for each insulation panel.

68
Annex 1

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Figure Aid. Panel ID=76-100: Multiple mass observations (in kilograms) as a function of elapsed time (in seconds) for insulation panels 076 through 100. Linear fit for data (shown as solid line) was backextrapolated to elapsed time zero (/0) to determine m0 for each insulation panel.

69
Annex 1

91 HSU ! U U U H I

Figure Ale. Panel ID= 1 0 1 - 1 25 : Multiple mass observations (in kilograms) as a function of elapsed time (in seconds) for insulation panels 101 through 125. Linear fit for data (shown as solid line) was backextrapolated to elapsed time zero (/0) to determine m0 for each insulation panel.

70
Annex 1

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Figure Alf. Panel ID=126-150: Multiple mass observations (in kilograms) as a function of elapsed time (in seconds) for insulation panels 126 through 150. Linear fit for data (shown as solid line) was backextrapolated to elapsed time zero (t0) to determine m0 for each insulation panel.

71
Annex 1

nin nil! miss

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Figure Alg. Panel ID=151-175: Multiple mass observations (in kilograms) as a function of elapsed time (in seconds) for insulation panels 151 through 175. Linear fit for data (shown as solid line) was backextrapolated to elapsed time zero (/0) to determine m0 for each insulation panel.

72
Annex 1

I I I I 1

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Figure Alh. Panel ID= 176-200: Multiple mass observations (in kilograms) as a function of elapsed time (in seconds) for insulation panels 176 through 200. Linear fit for data (shown as solid line) was backextrapolated to elapsed time zero (/0 ) to determine m0 for each insulation panel.

73
Annex 1

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Figure Ali. Panel ID=201-225: Multiple mass observations (in kilograms) as a function of elapsed time (in seconds) for insulation panels 201 through 225. Linear fit for data (shown as solid line) was backextrapolated to elapsed time zero (/0 ) to determine m0 for each insulation panel.

74
Annex 1

I I I I I

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Figure Alj. Panel ID=226-250: Multiple mass observations (in kilograms) as a function of elapsed time (in seconds) for insulation panels 226 through 250. Linear fit for data (shown as solid line) was backextrapolated to elapsed time zero (/0) to determine m0 for each insulation panel.

75
Annex 1

1

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Figure A lk. Panel ID=25 1-275: Multiple mass observations (in kilograms) as a function of elapsed time (in seconds) for insulation panels 251 through 275. Linear fit for data (shown as solid line) was backextrapolated to elapsed time zero (/0) to determine m0 for each insulation panel.

76
Annex 1

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Figure All. Panel ID=276-300: Multiple mass observations (in kilograms) as a function of elapsed time (in seconds) for insulation panels 276 through 300. Linear fit for data (shown as solid line) was backextrapolated to elapsed time zero (/0) to determine w0 for each insulation panel.

77
Annex 1

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Figure Aim. Panel ID=301-325: Multiple mass observations (in kilograms) as a function of elapsed time

(in seconds) for insulation panels 301 through 325. Linear fit for data (shown as solid line) was backextrapolated to elapsed time zero (t0) to determine m0 for each insulation panel.

78
Annex 1

| 1 1 | | | | 1 | | M M 1

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Figure A In. Panel ID=326-350: Multiple mass observations (in kilograms) as a function of elapsed time (in seconds) for insulation panels 326 through 350. Linear fit for data (shown as solid line) was backextrapolated to elapsed time zero (t0) to determine m0 for each insulation panel.

79
Annex 1

1 | | M 1 1 1 1

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Figure Alo. Panel ID=35 1-375: Multiple mass observations (in kilograms) as a function of elapsed time (in seconds) for insulation panels 351 through 375. Linear fit for data (shown as solid line) was backextrapolated to elapsed time zero (t0 ) to determine w0 for each insulation panel.

SO
Annex 1

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Figure Alp. Panel ID=376-400: Multiple mass observations (in kilograms) as a function of elapsed time (in seconds) for insulation panels 376 through 400. Linear fit for data (shown as solid line) was backextrapolated to elapsed time zero (t0) to determine m0 for each insulation panel.

8
Annex 1

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Figure Alq. Panel ID=40 1-425: Multiple mass observations (in kilograms) as a function of elapsed time (in seconds) for insulation panels 401 through 425. Linear fit for data (shown as solid line) was backextrapolated to elapsed time zero (t0) to determine m0 for each insulation panel.

82
Annex 1

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Figure Air. Panel ID=426-450: Multiple mass observations (in kilograms) as a function of elapsed time (in seconds) for insulation panels 426 through 450. Linear fit for data (shown as solid line) was backextrapolated to elapsed time zero (/0) to determine m0 for each insulation panel.

83
Annex 2

Annex 2 - Thickness Plots

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Figure A2a. Panel ID=001-025: Thickness measurements (in millimeters) at locations 1 through 8 (Fig. 3b)

for insulation panels 001 through 025. Mean is shown as solid line (with numerical values for mean and

standard deviation (SD) in the title of each frame).

84
Annex 2

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for insulation panels 026 through 050. Mean is shown as solid line (with numerical values for mean and

standard deviation (SD) in the title of each frame).

85
Annex 2

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Figure A2c. Panel ID=05 1-075: Thickness measurements (in millimeters) at locations 1 through 8 (Fig. 3b)

for insulation panels 051 through 075. Mean is shown as solid line (with numerical values for mean and

standard deviation (SD) in the title of each frame).

86
Annex 2

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for insulation panels 076 through 100. Mean is shown as solid line (with numerical values for mean and

standard deviation (SD) in the title of each frame).

87
Annex 2

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Figure A2e. Panel ID=101-125: Thickness measurements (in millimeters) at locations 1 through 8 (Fig. 3b)

for insulation panels 101 through 125. Mean is shown as solid line (with numerical values for mean and

standard deviation (SD) in the title of each frame).

88
Annex 2

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Figure A2f. Panel ID=126-150: Thickness measurements (in millimeters) at locations 1 through 8 (Fig. 3b)

for insulation panels 126 through 150. Mean is shown as solid line (with numerical values for mean and

standard deviation (SD) in the title of each frame).

89
Annex 2

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Figure A2g. Panel ID=15 1-175: Thickness measurements (in millimeters) at locations 1 through 8 (Fig. 3b)

for insulation panels 151 through 175. Mean is shown as solid line (with numerical values for mean and

standard deviation (SD) in the title of each frame).

90
Annex 2

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o co d J. 1

+ S -

i

- s

+

i : I : I

* i - i

+ : 1 E

N a - a

o 111 111 mm 11111 s a a a a a a lililllll

2|d - i

CO S 1

I 8 I' s I 1 r

: I

: i : i : 1

TM

?

Q

+ "

? TM

! linn mini 11111

p a a a a a a 1111111

"

I

"

1 K

9

N a i + i i

i : 1 : 1 : I

TM

?

+ N

!

gj i i § gl Si iiiiin s s ^ i 1 ^ man

p limn

"

!

I !i

K i

i . : a I 1 1. : I

: I : I : i

!

~ i

N !

N

!

p 1111111 iiuii 11111 11111 i i 1 1 s 1

Figure A2h. Panel ID=176-200: Thickness measurements (in millimeters) at locations 1 through 8 (Fig. 3b)

for insulation panels 176 through 200. Mean is shown as solid line (with numerical values for mean and

standard deviation (SD) in the title of each frame).

91
Annex 2

il

- = 11111 iliiii 111111

11111 111111 111111 "111111 "1111111

^ S ^ S s s

- 8

I 1

1111 s s s I i s sssslis

s s I s I iiiiii mini iiiiiiii a 3 3 a s a a

I 1

: i

1 1 1 1

1

1111 8 S S 8 §s s s s a 1 1 1 1 1 nun

Figure A2i. Panel ID=20 1-225: Thickness measurements (in millimeters) at locations 1 through 8 (Fig. 3b)

for insulation panels 201 through 225. Mean is shown as solid line (with numerical values for mean and

standard deviation (SD) in the title of each frame).

92
Annex 2

1

! .

1

. g

: I

. §

* g

» s

: I

"

!

00 0

* g

« s

: I ! ?

: I

1 1 Hill 131 sua 11111 I I 1 1 1 1111111

- §

" g I s

: I

"

5

Q

- !

n g

1

: 1

+ . 6

- 1 I 1

;

j

+

•* g

: s

: I

-

1

+

111111111 1111111 111111 1111111 111111

i *.

5

1

: 1

TM

!

+ N

g

:

*

: I

n ?

+

*

CO 3 " g

1

: 1

: i

* 8

: i "

?

+

+

+ 1.1111 "111111 11111 iiiJii 11111

3=

227

MEAN

=

25.79

SD

=

0.1 " £ 1

: 1

TM

?

+

s

N g

: I

* £

: a !i

: I

TM

s 1111! 1 1 1 1

11111 11111 mmm

3£L

- 1

s g

«> si : 1

0

K

g

•° S

: I

N

?

9

- g

<° 5

: 1

N

5

p *. II III 111111 °lllllltll "lllllllll 11I11II

Figure A2j. Panel ID=226-250: Thickness measurements (in millimeters) at locations 1 through 8 (Fig. 3b)

for insulation panels 226 through 250. Mean is shown as solid line (with numerical values for mean and

standard deviation (SD) in the title of each frame).

93
Annex 2

!

• mm mil " isiisiiisi 11111 iiinii

mini siiiiiii 11111 niiii imiii

mm iiimi umi iiiii iimi

mini 11111 inii mm iiinii

11111 11111 mm iiii

Figure A2k. Panel ID=25 1-275: Thickness measurements (in millimeters) at locations 1 through 8 (Fig. 3b)

for insulation panels 251 through 275. Mean is shown as solid line (with numerical values for mean and

standard deviation (SD) in the title of each frame).

94
Annex 2

si

*

1

? 3333533

9

1 11 1 1 1

= IHTI

11 1 1 s i s

s1

i

*

?

*

. .

25.70 25.65 25.60 25.55 25.50

1

s "I

I 1

I

I 1

!

+ gl

N

!

11111 11111

1111111 111111 11111

111111

5393333 111111 111111

333333 ssssssss

11111 11111

I

(2s

i

*

5

*

00 o

N

a

: s

: I

+

3333533 1111111

S?

: I

! ? "11111 si $ s s I

: I

25.90 25.80 25.70 25.60 25.50 25.40 26.10 26.00 25.90 25.80 25.70 25.60

Figure A21. Panel ID=276-300: Thickness measurements (in millimeters) at locations 1 through 8 (Fig. 3b)

for insulation panels 276 through 300. Mean is shown as solid line (with numerical values for mean and

standard deviation (SD) in the title of each frame).

95
Annex 2

D

=

305

MEAN

=25

77

SD

=0.17 s s

: i

: I

^ 8

I I

: I

a

I I

: 1

+

niiii niiii "1111111 1 1 s 1

1

imiiiiii

I

- ?

: |

„

5

+ iI

1

N s

» s

^ I

+

co O

- s

» s

: I

+

sd s s s s iiiiiii mini isaaimii

i1

.

i

3

=

313

MEAN

=26

17

SD

=

0.3

co I

: I -

i

- 1

I s

«

I

+

"1111111 mini 9

§ g 1 1

1

lllllll

s1

*

i

a

- s : I

3

=

312

MEAN

=

25.59

SD

=

0.0

- s

: I

+

+ I I

"

? 1111111

9 iiiii mm I s 1 s s s

s1

*

1

- |

10 s

- s

: I

- 9

*

i

i

s

+

• !

I 1

I 1

"

!

9

: 1

a s i a i g

a iiiiie

1 1 i g a

" issssssss iiim

Figure A2m. Panel ID=30 1-325: Thickness measurements (in millimeters) at locations 1 through 8

(Fig. 3b) for insulation panels 301 through 325. Mean is shown as solid line (with numerical values for mean and standard deviation (SD) in the title of each frame).

96
Annex 2

1 1 1 1

ii

+

1 s s s s

1rmmi

£

g

i

+

5

I?

D

=

334

MEAN

=257

SD

:0

1'

11111

1111111

i

. "iiiiin

i.

i

•

!

Q

111111 "1111111 "1111111

00 ?

" s

- s

n i

oo 1

N s

- id : I

! ?

9 1

2

3

4

5

=

344

MEAN

=25 +

12

3

45

D

-

349

MEAN

- 25 linn iiiini iiiii

imiii iimiiii

i

mill linn

imiii mini mini iiiii

D

=

348

MEAN

=25

56

SD

=

0-1

}

=

347

MEAN

=25

75

SD

=

0.2

1111111

I

'

! s 3 a a a s 3

Figure A2n. Panel ID=326-350: Thickness measurements (in millimeters) at locations 1 through 8 (Fig. 3b)

for insulation panels 326 through 350. Mean is shown as solid line (with numerical values for mean and

standard deviation (SD) in the title of each frame).

97
Annex 2

- g

- 1

- 1

+

. . .

- 1

N ?

9

"

i I a - 1 -

f

p

+

00 o

g

"I 1 1 1 I mim 1 1 1 1

1

9 iiiii

i

I

• I

+

" 1

-

1

I s « 1

-

1

+

N

1

» i TM

?

q

+ ; i

- 1

"1

1 1 1

1

E

S 1 1

26

00

25.95 25.90 25.85 25.80 25.75 25.70 S § f 1

1

i ^ s s i s

- g

CO «

* 5 - 1

+

+

N s

: i

: I

- §

CO ci N 8

I s

: 1

- i

+ " s

I 1

« I

-

1

+

~S I ess s s s imii 1 i s s s s mini 1

1

g

a 1

1

i1

*

i

*

?

: I

: a

+

: i

"

i - i

N ?

+

25,80 25

75

25

70

25,65 25

60

25.55 25.50 mini s 1 $ s s id

Q a a a g g

9 mini

12

3

4

5

6

78

D

=

361

MEAN

=26

09

SD

=0

2 - 1

i

<° 3

- 8 : 1

N

!

+

+

. 5

* 5

CO «

- a M mini § s s

s a' a III id a a a Id a Id mill

Figure A2o. Panel ID=35 1-375: Thickness measurements (in millimeters) at locations 1 through 8 (Fig. 3b)

for insulation panels 351 through 375. Mean is shown as solid line (with numerical values for mean and

standard deviation (SD) in the title of each frame).

98
Annex 2

3

=

380

MEAN

=25

97

SD

=0

1

- 8

: I

: I

n

?

°

cc o

N s I 1 : 1

TM !

+

- !

: i ~

?

+

" 8

: i

: I

: f

+

SSISSSS 111111111 "1111111

9 III ill 111111

I

I

'

!

*

: i : I

+ - £

: i

i I : I "

!

* g

i i

: i

*

?

9 "III 1 1 1 "1111111 1111111 i W W t W s i 1 £ Si £ £

I l

+

CO S 1:0 d

N

s

: 3

: I

H

!

+ : i

: I

* ?

o

CO 1

" 8

<° $

« s

: I

- I

+

a a a a a s a linn 1111111 1111111

g mini

D

=

377

MEAN

=25

99

SD

=

0.1 * i

i i

=

i

I 1

: 1

~

?

m o

N 8

I £

: I

°

+ . 3

K

8 I 1

: I "

! "11111 iimi 111111 11111111

° + 8

i

!

Q

00 d

N 8

: i

: 1

+

+ : I

= 5

N 8

» s : 1

+

• 2

8

: a

i I

+

....... 1111111 nun

9 mill 1111111 iniiii

Figure A2p. Panel ID=376-400: Thickness measurements (in millimeters) at locations 1 through 8 (Fig. 3b)

for insulation panels 376 through 400. Mean is shown as solid line (with numerical values for mean and

standard deviation (SD) in the title of each frame).

99
Annex 2

linn

!

i!

o . . . mini

I I

f 1111111 "1111111 1111111 "11111

1111

11111111 1 1 1

1 s

+ 1

i : 1

3

§ S S 3 ^ S i s ^

<° 5

10 !

: !

: a

: i

s1 1111111 1 I £ £ si Id £ s a a a s a

- !

« a +

: I

"

! 1 111111

9 illllii iinii

- 2

" s :: i

^ g

: §

ES K I

CO ?

» s 4 :: i

' TM

!

+ : I

"

5

: I "

! 1111111 11111 1

CO d + CO o -

i

g

~ a- g* g" 1

a I 1 I

1

: i : i

I

+ : 1 : I

+ : I

+ ~

f

" 5 Hiii 1 1 1 1

1

linn 9 1

1

1 1

1

Figure A2q. Panel ID=40 1-425: Thickness measurements (in millimeters) at locations 1 through 8 (Fig. 3b)

for insulation panels 401 through 425. Mean is shown as solid line (with numerical values for mean and

standard deviation (SD) in the title of each frame).

100
Annex 2

iimi iiiii

-

i

- a

i . I 1

i

- : 1

?

TM

f linn iiiiiii 1111111

1111111 1 1

1

1111111

111 S 5

1111111 llllfll

IIHlllH 1111111

5

s K 8

1 I I

I

+ : I

!

iiiiii

- iiiii

I

=

43C

MEAN

=26

02

SD

=0

;

I ? 11111 1111111

111111 iiiii

•° s

: I : I

~

!

9

: ?

a a a s s s a 11111 111111 111111 a a a a a ~

Figure A2r. Panel ID=426-450: Thickness measurements (in millimeters) at locations 1 through 8 (Fig. 3b)

for insulation panels 426 through 450. Mean is shown as solid line (with numerical values for mean and

standard deviation (SD) in the title of each frame).

101
Annex 3

Annex 3 - Bulk Density Uncertainty, Extensive Details

A3.1 Mass Uncertainty (/m0) A3. 1.1 Digital Balance Uncertainty

The measurement uncertainty of the digital weighing balance was evaluated following

NIST recommended guidelines for determining and reporting uncertainties for balances

[31]. The basic measurement equation for the balance is: Indication = Applied load ±

Uncertainty. Equation (A3-1) calculates the expanded combined uncertainty (k = 2) for the balance.

where uc,bai is the combined standard uncertainty for the balance; us is the standard uncertainty for the standard mass artifact; and, sp

is the process standard deviation. For the 1 kg mass standard artifact, the standard uncertainty (us) was 0.000 000 25 kg. Assuming a uni- form distribution, the process standard deviation (sp) was determined from Eq. (A3-2).

where d is equal to one display unit (i.e., the resolution) of the balance. For d equal to 0.000 1 kg, sp

is equal to 0.000 058 kg. From Eq. (A3-1), the expanded combined uncertainty (k = 2) for the balance was determined to be 0.000 12 kg. A3. 1.2 Regression Analysis Uncertainty (/w0) The Type A standard uncertainty // (/«o)a was determined by computing the individual standard deviations for the 450 fitted slopes m0 (Annex 1). The maximum standard deviation over all the slopes, 0.000 178 kg, was taken as a conservative estimate for u (wo)a- A3. 1.3 Combined Expanded Standard Uncertainty for /wo The combined standard and expanded (k =2) uncertainties for mo were determined from

Eq. (A3-3) to be 0.000 187 kg and 0.000 374 kg, respectively.

(A3-1)

(A3-3)

102
Annex 3

A3.2 Length Uncertainties A3.2.1 Height Gage Uncertainty The measurement uncertainties of the two height gages were determined following sug- gested guidelines for dimensional calibrations [32]. Eq. (A3-4) calculates the expanded

combined uncertainty (k = 2) for the gages.

Ugage = 2 uc, gage = 2y\K+s2p +it;+u;+ul ( A3-4)

where:us = standard uncertainty for the standard length artifact (i.e., gage block);

sp = standard uncertainty of the process (i.e., instrument uncertainty);

u\ = standard uncertainty of reference datum (i.e., granite surface plate); ih = standard uncertainty due to thermal expansion effects

«3 = standard uncertainty due to elastic deformation of the insulation material Table A3-1 summarizes the uncertainty budget for the height gage measurements. The

standard uncertainties, in millimeters, for the length/width (lateral panel dimensions) and

thickness measurements are given in the last two columns. The uncertainties in the gage

block calibrations (us) are negligible in comparison to the other standard uncertainties. For the thickness measurement, the standard uncertainty due to the datum surface («i) was assumed to be zero because the insulation panel was re-positioned to the same location for each measurement and the height gage remained stationary at its tare position. The analysis included the effect of thermal expansion at laboratory ambient of 23 °C on

the gage blocks (ih).

Table A3-1 . Uncertainty budget for height gage measurements

Identifier Description Standard uncertainty (mm)

Length, width (I) Thickness (L) us

1 inch* gage block 0.000014

Us Two 12 inch* gage blocks 0.000212

Sp Height gage 1 (300 mm) 0.0127

Sp Height gage 2 (610 mm) 0.019050

"l Datum surface (granite plate) 0.015240 0

111 Thermal expansion (23 °C) 0.017 0.00081

"3 Elastic deformation of insulation Negligible 0.05 Combined standard unc. (k= 1) 0.0297 0.052 ueaee Expanded uncertainty (k = 2) 0.0594 0.103 *Nominal lengths defined in the English system ( 1 inch = 25.4 mm)

As described in Sec. 6.2.2, the thickness measurements were conducted with a modest

load of approximately 43 N applied to the top surface of the panel. Under this load, any

deformations due to the 36 g circular workpiece (Fig. 3a) and the height gage touch probe

(Fig. 3a) were neglected. The elastic deformation (113) of the insulation panel thickness was estimated to be 0.05 mm based on compression tests of loaded and unloaded insula103
Annex 3

tion panels. The elastic deformations of the length and width dimensions due to the material weight itself were neglected. A3.2.2 Type A Uncertainty (/ and L)

The Type A standard uncertainties u (/)a and u {L)\ were computed from the pooled (av- eraged) standard deviations of the multiple measurements for the nine panels on which more extensive measurements were conducted. The standard uncertainties for u and

u (L)a were 0.322 mm and 0.147 mm, respectively. A3.2.3 Combined Standard Uncertainty for / (length, width) and L (thickness) The combined standard and expanded {k =2) uncertainties for / and L were determined from Eq. (A3-5) and Eq. (A3-6), respectively.

U(l) = 2uc (!) = 2^u2 (l)A+ ulgage{ (A3-5)

U(L) = 2uc (L) = 2^ir(L)A+ ir gage2 (A3-6)

The combined standard uncertainty and expanded (k =2) uncertainty for / were deter- mined to be 0.324 mm and 0.648 mm, respectively. The combined standard uncertainty and expanded (k =2) uncertainty for L were determined to be 0.156 mm and 0.312 mm,

respectively.

104
Annex 4

Annex 4 - Thermal Conductivity Uncertainty, Extensive Details

A4.1 Quantification of Uncertainty Components

The detailed analysis of the uncertainty components identified in Table 9 - heat flow (Q), temperature difference (AT), thickness (L), and meter area (A) - is presented in this Annex. The uncertainty evaluation presented here is based on the uncertainty budget developed for SRM 1450c [10] and has been updated most recently for one-sided guarded-hot-plate measurements [16]. Each uncertainty component is treated separately and quantified as

either a Type A or Type B (or both) evaluation [15]. A4.2 Specimen Heat Flow (Q)

Equation (24) for Qm essentially defines the specimen heat flow, Q, under ideal guarding.

The parasitic heat flows Qg and Qe (i.e., lateral heat losses or gains), that are typically very small (less than 0.001 W) under steady-state conditions, can have significant uncertainty associated with each term. Sections A4.2.1-A4.2.3 discuss the uncertainty evaluation for Qm, Qg

, and Qe . A4.2.1 u (Qm,i)\ - Type A Evaluation The standard uncertainties u (Qmj)\ associated with the time-averaged observations taken over the 4 h steady-state measurement period were determined using Eq. (9) where n was

equal to 120. The standard uncertainties u (Q,„)a were subsequently computed from the pooled experimental standard deviations for each level of Tm (and summarized in Table A4-1). A4.2.2 Direct Current Meter-Plate Heater Power Measurement (Qm) The contributory uncertainty sources for (Qm) include: 1) calibration of the standard resistor (Type B evaluation); 2) PRT self-heating (Type B evaluation); and, 3) voltage measurements

for Vs and Vm (Type B evaluations). The Type A uncertainties for Vs and Vm were included

in the repeated input power (Qmj ) observations described in Sec. A4.2. 1

A4.2.2. 1 Calibration of Standard Resistor As described in Sec. 7.5.1.1, the 2010 calibration assigned a value of 0.10006939 Q. ±

0.0000005 Q (expanded uncertainty, k = 2) to the resistor. Based on historical data, the

drift in the resistor calibration was determined to be 0.000 000 025 Q/year and neglected. A4.2.2.2PRT Power Input Under normal operating conditions, the meter-plate PRT (nominally 1 00 Q) dissipates about 0.000 1 W due to the 1 mA excitation current. This value, which was small in comparison to the meter-plate heater power input (Q) of approximately 8 W to 10 W (Table 13), was neglected in further analysis.

105
Annex 4

A4.2.2.3 u (0„i)b - Type B Evaluation Based on Voltage Measurements for Vs and Vm The Type B standard uncertainty for u (Qmh was determined by application of Eq. (4) to Eq. (24) which yields

«e (Qm) = y[4~^Vj+4s ir(R ?+clm u

2 (Vj (A4-1)

with _ dQm _ Vm

Cv

° ~ dv ~ R dQm 8RS V

OR R'

The input values for Eq. (A4- 1 ) are described as follows. Based on the 20 1 0 calibration, the assigned values for the standard resistor are Rs equal to 0.100 069 39 Q and u (Rs ) equal to 0.000 000 25 Q. (k = 1). The Type B standard uncertainties for Vs and Vm (Fig. 13) were

based on the 1 -year manufacturer specification for the integrating voltmeter. A uniform rec- tangular distribution was assumed for the accuracy specification with a symmetrical half- width d computed from one of the following equations (where reading is in volts).

300 mV Range for Vs: d = 0.00008

x

reading + 8 uV + 0.000 \x reading (A4-2)

30 V Range for Vm

: d = 0.00008

x

reading + 300 uV + 0.000 \x reading (A4-3)

For Tm equal to 280 K, the measured observation of Vs and Vm were 37 mV and 20.8 V, respectively. From Eq. (A4-2) and Eq. (A4-3), t^oomv and J30V are 14.7 uV and 4 mV, respectively. Substitution in Eq. (A3-2) yields 8.5 uV and 2.3 mV for u(Vs) and u(Vm), respectively. Table A4-1 summarizes the standard uncertainty components for u(Qm) for each level of Tm. The Type B evaluations in Table A4-1 are about 3 times greater than the Type A evaluations.

Table A4-1 . Summary of standard uncertainty components for // (Qm) Tm u(Qm)A u(Qm)B (K) (W) (W)

280 0.00061 0.0020 295 0.00062 0.0021 310 0.00068 0.0021 325 0.00068 0.0022 340 0.00072 0.0023

106
Annex 4

A4.2.3 Lateral Heat Flows (Qg, Qe) Three sets of imbalance tests were conducted at Tm of 280 K, 3 10 K, and 340 K for specimen

pair 184-369 to investigate the effects of moderate temperature differences on Qg and Qe. Table A4-2 summarizes the imbalance settings for two treatments for the five test conditions. The last row in Table A4-2 is actually a balanced condition. (The supplementary thermal

conductivity data at the balance point are presented in Annex 5). The test sequence (not shown in Table A4-2) was randomized to minimize the introduction of bias in the results.

Table A4-2. Nominal settings for imbalance study (Yates order) ve Tm - Ta Index GiV) (K)

1 -50 -4

2 +50 -4

3 -50 +4

4 +50 +4

5 0 0

Table A4-3 summarizes the test results from the imbalance study at Tm of 280 K, 310 K, and 340 K. The response variable (y) and input variables {x\, xi) were normalized with re- spect to the balance point.

Table A4-3. Test results for imbalance study (Yates order)

Index Tm AT Qm y (Qm-Qmo)

X\ iYg- vs°)

X2 [(Tm -Ta) -(Tm -Ta)o\ (K) (K) (W) (W) (uV) (K)

1 280 25.00 7.7029 -0.1078 -50.06 -3.99 2 280 25.00 7.9360 0.1253 49.98 -4.00

3 280 25.00 7.6985 -0.1122 -50.02 3.92 4 280 25.00 7.9272 0.1165 49.96 4.11

5 280 24.99 7.8107 0 0 0

1 310 25.00 8.5163 -0.1348 -50.02 -4.00 2 310 25.01 8.7703 0.1192 49.96 -4.00

3 310 25.00 8.5031 -0.1480 -50.01 4.00 4 310 25.00 8.7591 0.1080 49.99 4.00

5 310 25.00 8.6511 0 0 0

1 340 24.99 9.3444 -0.1365 -49.96 -3.99 2 340 24.99 9.6104 0.1295 50.05 -3.98

3 340 25.00 9.3401 -0.1408 -49.96 4.00 4 340 24.99 9.6041 0.1232 50.01 4.00

5 340 25.00 9.4809 0 0 0

The data in Table A4-3 were fit to the model given in Eq. (A4-4). The presence of an offset coefficient bo was initially considered but, because the term is predicted to be nearly zero from theory [16], the term was not included.

107
Annex 4

y = V, + b2 x2 = AQ = Qm - Qm0 = b} ( Vg - Vg0 ) + b2 [(Tm -Ta )-( Tm - T )Q ]

( A4-4)

Table A4-4 summarizes the parameter estimates and approximate standard deviations from

multiple variable linear regression for coefficients b\ and bi at Tm of 280 K, 3 10 K, and 340 K.

Table A4-4. Parameter estimates and standard deviations for b\ and b2 in Eq. (A4-4) Tm b\ sib,) b2 s(b2) Residual SD

(K) (WuV 1 ) (W-uV 1 ) (W-K 1 ) (W-K"1 ) (W)

280 2.310xl0"3 7.96x1

0"5 -8.257xl0"4 9.94x1

0"4 0.0080 310 2.550xl0'3 1.96xl0"4 -1.531xl0'3 2.45 xlO"

3 0.0196 340 2.650xl0"3 8.85xl0"5 -6.605xl0"4

1 . 1 1 x 1

0

3 0.0088

Application of Eq. (4) to Eq. (A4-3) yields

uc (AQ) = yJc

2

ht if (b,) + c;u

2 (x^ + clu

2 (b2 ) + c]ic (x2 ) (A4-5)

with g(Ag)

c =«= 6 dxt Table A4-5 summarizes the input values for Eq. (A4-5) and the corresponding estimates for itc(AQ) at Tm levels of 280 K, 310 K, and 340 K. Under steady-state test conditions, the

input estimates for x\ and X2 are nearly zero. The standard uncertainties u(x\) and u(xi) were estimated to be ±0.01 K (converted to microvolts in Table A4-5 for the guard gap

thermopile voltage), and ±0.5 K, respectively. The input values for bi and u (bi) = s (bi) were obtained from Table A4-4.

Table A4-5. Estimates for uc (AQ)

Tm X\ u(br ) bi u(xx ) u(b2) b, u(x2) uc(AQ)

(K) (M-V) (W-uV 1 ) (W-iliV"

1 ) (HV) (K) (W-K" 1 ) (W-K"1 ) (K) (W)

2X0 -0.0087 7.96x1 0"5 0.002310 2.42 -0.0070 9.94X10"4 -0.00083 0.5 0.0056 280 -0.0138 7.96x1 0"5 0.002310 2.42 -0.0017 9.94x10^ -0.00083 0.5 0.0056 280 0.0266 7.96x1 0"5 0.002310 2.42 -0.0110 9.94X10"4 -0.00083 0.5 0.0056 310 0.0079 1.96x10-* 0.002550 2.53 -0.0043 2.45 xlO"3 -0.00153 0.5 0.0065 310 0.0569 1.96X10"4 0.002550 2.53 0.0000 2.45 x 10

' -0.00153 0.5 0.0065 310 -0.0247 1.96- 10

1 0.002550 2.53 0.0000 2.45 x 10

3 -0.00153 0.5 0.0065 340 0.0099 8.85 xlO"5 0.002650 2.63 0.0018 1.11x10"' -0.00066 0.5 0.0070 340 0.0130 8.85xl0"5 0.002650 2.63 0.0039 1.11 xlO"3 -0.00066 0.5 0.0070 340 -0.0390 8.85 xlO"5 0.002650 2.63 -0.0048 1.11 M0 3 -0.00066 0.5 0.0070

10S
Annex 4

A4.2.4 Combined Standard Uncertainty u (Q ) The combined standard uncertainty u (Q ) was computed from Eq. (A4-6).

uc (0 = yjir(Qm ) A +ir(QJB +ir(AQ) (A4-6)

Table A4-6 summarizes the input values for Eq. (A4-6) and the corresponding estimates for uc (Q) at Tm levels of 280 K, 310 K, and 340 K. For subsequent calculations using Eq. (28), the uncertainty estimate uc {Q) of 0.0074 W was used.

Table A4-6. Combined standard uncertainty (k = 1) for uc (Q) Tm u(Qm)A uc(AQ) uAQ) 0/2 Uc.rel(Q) (K) (W) (W) (W) (W) (W) (%) 280 0.00061 0.0020 0.0056 0.0060 3.904 0.15 310 0.00068 0.0021 0.0065 0.0069 4.294 0.16 340 0.00072 0.0023 0.0070 0.0074 4.736 0.16

A4.3 Temperature Difference {AT)

A4.3.1 u (AT; ) A - Type A Evaluation The standard uncertainties u (AT) )a associated with the time-averaged observations taken over the 4 h steady-state measurement period were determined using Eq. (9) where n was

equal to 120. The standard uncertainty u(AT)A was subsequently computed from the pooled experimental standard deviations for the 15 tests and found to be 0.00024 K which,

in comparison to other temperature uncertainty estimates, was neglected. A4.3.2 u(T)- Temperature Measurement Uncertainty Sources The contributory uncertainty sources for u{T) include: 1) PRT calibration, ii\ (T)b; 2) curve

fit of calibration data, W2 (T)a; 3) electrical resistance measurement of the PRT, u?,(T)b; 4) temperature rise of sensor due to PRT self-heating, u4 (T)B; 5) plate temperature variation

in the radial dimension, u5 (T)q; and, 6) plate temperature variation in the axial dimension,

"6(T)b. A4.3.2.1 w, ( 77

)

B - PRT Calibration From the meter-plate PRT calibration, the expanded uncertainty (k = 2) for the bath temperature measurements was reported to be 0.01 K. Therefore, the standard uncertainty estimate of 0.005 °C (k = 1) was used for the uncertainty analysis. A4.3.2.2 u2 (T)A - PRT Regression Analysis For each PRT, the individual observations (in ohms) were converted to temperature with

the curve fit for the NIST Thermometry calibration data (Sec. 7.5.2). The standard uncertainty was computed from the pooled residual standard deviations for each curve fit of the

calibration data and was 0.0052 K (k = 1).

109
Annex 4

A4.3.2.3 «3 (T)b- PRT Electrical Resistance Measurement The standard uncertainty for electrical resistance measurement of the PRT was based on the 1-year manufacturer specification for the integrating voltmeter. A uniform rectangular dis- tribution was assumed for the accuracy specification with a symmetrical half-width d computed from Eq. (A4-7) (where reading is in ohms).

300 Q Range : d = 0.000 1 5 x reading + 8 mQ + 0.000 1 x reading ( A4-7

)

For a reading of 131.372 Q,d20on is 0.041 Q. (from Eq. (A4-7)). Substitution of 131.372 Q

± (0.041 Q/2) in the PRT calibration curve fit, yields a corresponding temperature half- width of 0.105 K. Final substitution of the half-width of 0.105 K in Eq. (A3-2) yields a standard uncertainty of 0.0607 K. A4.3.2.4 Ui, {T )b - Temperature Rise due to PRT Self-heating As described in Sec. A4.2.2.2, the nominal 100 Q. PRT dissipates about 0.0001 W for a 1 mA

excitation current. For the cold plate PRTs, the thermal conductance of the metal-to-air-to- metal interface between sensor and plate is estimated to be 0.058 WK" . Thus, the temperature

rise (0.0001 W/0.058 W-K"1 ) is 0.0017 K. For the meter-plate PRT, a thin layer of thermally conductive silicone paste was applied to the sensor exterior surface to improve thermal contact. A4.3.2.5 u5 (T)b - Radial Plate Temperature Variation From previous measurement data [30], an estimate for the radial sampling uncertainty was

taken to be 0.015 K. In these separate experiments, the temperature profiles of the meter

plates were estimated utilizing independent thermopile constructions placed between the

plate surfaces and semi-rigid specimens. A4.3.2.6 «6 (T)b - Axial Plate Temperature Variation A rigorous analytical analysis by Peavy published in Hahn et al. [33] shows that, for typical specimen insulations, the differences between the temperature of the meter-plate PRT at the mid-plane of the guard gap and the average surface temperature of the meter plate is less than 0.01 % and, thus, neglected in further analyses. A4.3.3 Temperature Measurement Combined Standard Uncertainty

Table A4-7 summarizes the standard uncertainty sources Ui {T), their descriptions, and cor- responding uncertainty estimates for the PRT temperature measurement.

Table A4-7. Standard uncertainty components (k= 1 ) for T

Source Description Uncertainty (K) Evaluation u(T)A Repeated observations Negligible A

HT) PRT calibration by NIST Thermometry Group 0.005 B

u2(T) PRT calibration data curve fit 0.0051 A

u3(T) Electrical resistance measurement/conversion 0.0607 B

u4(T) Temperature rise due to PRT self-heating 0.0017 B

Temperature variation - radial dimension 0.015 B

Temperature variation - axial dimension Negligible B

110
Annex 4

Equation (A4-8) computes the combined standard uncertainty (k= 1) for the temperature measurement.

K(T) = ^r(T)J+ ±u;(T) (A4-8)

Substituting the standard uncertainty components from Table A4-7 into Eq. (A4-8) yields a value of 0.063 K. A4.3.4 Combined Standard Uncertainty u (AT)

For a double-sided guarded-hot-plate test, the temperature difference (AT7) across the specimen pair was determined from Eq. (A4-9). AT = Th -(Tc] +T 2 )/2 (A4-9)

Applying Eq. (4) to Eq. (A4-9) and setting uc{Th) = uc{Tc \) = uc(Tc2) = uc(T) yields

uc (AT) = J- x ir.

( T ) = >/l.5 x 0.063

2 = 0.077K (A4-10)

For AT equal to 25.001 K (Table 14), uc>rel (AT) was equal to 0.31 %. A4.4 Thickness (L) A4.4.1 u (L)\ - Type A Evaluation The standard uncertainties u (L)a associated with the mean of the eight linear positioning transducers were determined using Eq. (9) where n was equal to 8. The standard uncertainty u (L )a was subsequently computed from the pooled experimental standard deviations for the 15 tests and found to be 0.0582 mm.

A4.4.2 u, (L) - Thickness Contributory Uncertainties The other contributory uncertainty sources for u(T) include: 1) gage block calibration; 2) fused-quartz spacer length dimensions; 3) in-situ linear position transducers uncertainty and repeatability; and, 4) plate characteristics including the measured flatness and calculated

deflection under axial loading. The uncertainty estimates for these sources are summarized

in Sec. A4.4.3 (Table A4-8).

A4.4.2. 1 u i (I)B - Gage Block Calibration As described in Sec. 6.4.2, the expanded uncertainty {k = 2) for the gage block calibration was 70 nm. Therefore, the standard uncertainty was divided by 2, for an estimate of 35 nm

(0.000035 mm) (k =1).

1 1
Annex 4

A4.4.2.2 i(2 (X)a - Fused-Quartz Spacers The standard uncertainty was computed from the pooled standard deviations of multiple measurement locations of the four fused-quartz spacers and was 0.001 14 mm (k= 1). A4.4.2.3 «3 (L)b - Micrometer Uncertainty The standard uncertainty for the micrometer used to determine the lengths of the fused- quartz spacers was based on a uniform rectangular distribution with a symmetrical half- width d of 0.0025 mm. Substitution of the half-width in Eq. (A3-2) yields a standard uncertainty of 0.00 1 5 mm (A' = 1 ). A4.4.2.4 U4 {L)b - Linear Positioning System The standard uncertainty for the linear position transducers was based on the accuracy specification from the manufacturer as 0.005 1 mm (k = 1 ). A4.4.2.5 lis (X)a - Repeatability of Linear Positioning System

The short-term repeatability of the linear position transducers was found to be 0.0064 mm

and was determined from prior studies described in Ref. [16]. A4.4.2.6 «6 (L)A and w7 (L)B - Plate Flatness The standard uncertainty associated with the mean of 32 thickness measurements of the meter plate was determined to be 0.0023 mm [16]. The standard uncertainty for the coordinate measuring machine (CMM) used to determine the meter-plate thickness was based on the accuracy specification from the manufacturer as 0.0051 mm (k = 1). The standard uncertainty for the plate flatness was estimated from Eq. (A4-1 1) to 0.0079 mm.

uc (Z6>7 ) = ^2x(,r(L6 ) + ,r(L7 )) (A4-1 1)

A4.4.2.7 «8 (L)b - Plate Deflection The mechanical deflection of the (large) cold plates under mechanical loading was evalu- ated as a Type B uncertainty using classical stress and strain formulae for flat plates. Clamping forces (F\ and Fi) were transmitted axially as shown in Fig. 12 and distributed over a circular area at the center of each cold plate. For a uniform load over a concentric

circular area of radius r/, the maximum deflection ymax at the center of the cold plate is given by the following formula [34]. Uniform support loading was assumed because the

test specimen was a semi-rigid material.

us (L) 3F(m-\)

\6nEm2

t

3 (A4-12)

where:

112
Annex 4 F = applied load (N); m = reciprocal of Poisson's ratio (dimensionless); E = modulus of elasticity (N-rrf

2

); tc = thickness of cold plate (m); and,

rp = radius of (cold) plate (m). From Table 14, the average clamping pressure /for the guarded-hot-plate tests was 476 Pa re- sulting in an applied load of approximately 87 N (for a plate diameter of 1.016 m). For alumi- num alloy 6061-T6, the values for m and E were taken to be (0.33V

1 = 3.0 and 6.9xl07 kPa,

respectively. The cold plate thickness was 25.4 mm; radius of uniform loading was 108 mm;

and, the cold plate radius was 508 mm. Substituting these values into Eq. (A4-12) yields a value of 0.026 mm for;w, which was one of the dominant components of the thickness uncertainty. A major limitation for this assessment approach is that the cold plate is not a solid plate, but is actually a composite construction to allow the flow of coolant internally within the plate. A4.4.3 Combined Standard Uncertainty uc (L) Table A4-8 summarizes the contributory uncertainties u, (L ) for the thickness measurement.

Table A4-8. Standard uncertainty components (k= 1) for L

Source Description Uncertainty (mm) Evaluation

u(L)A Multiple measurement locations 0.0582 A

ui(L

)

Gage block calibration Negligible B

m(L ) Fused-quartz spacers - multiple measurements 0.0011 B

m(L

)

Fused-quartz spacers micrometer 0.0015 B

ulL ) Linear positioning system 0.0051 B

u5(L) Repeatability of linear positioning system 0.0064 A

uAU.i

)

Plate flatness 0.0079 B

u*(L) Cold plate deflection 0.026 B

Equation (A4-13) computes the combined standard uncertainty (k = 1) for the temperature measurement.

uc (L) = 1ju2 (L)A+ j^uf{L) (A4-13)

Substituting the component standard uncertainties from Table A4-8 into Eq. (A4-13) yields a value of 0.065 mm. For L equal to 25.85 mm (Table 14), uc, rei (L) was equal to 0.25 %. A4.5 Meter Area (A) The application of Eq. (4) to Eq. (25) yields

UM) =

yj c

l "

2 (n, ) + c\ ir (r. ) + c; u

1 (a) + u2 ( AT,~

) (A4-14)

1 13
Annex 4

with

°r. = f

" -l(l + «AT,)

2

c,. = — = nr. (\ + aAT Y

dr., V p}

Ca = f[

= ^(r>^)x(l + aA^)

= = Hr2 + ^) x

( 1+aA7^)

Table A4-9 summarizes the contributory uncertainties for the meter-area calculation.

Table A4-9. Standard uncertainty components (k - 1 ) for A

Source Description Estimate Uncertainty Evaluation

u\{r0 ) Meter-plate outer radius 202.82 mm 0.0254 mm B

u2(ri

)

Guard-plate inner radius 203.71 mm 0.0254 mm B

u3(a ) Linear thermal expansion coefficient 23.6xlO"

fi K"' 2.36x1

0"6 K"

1 B

u4(ATmD ) Temperature difference (Tm = 280 K) -0.65 K 0.063 K B

u4(ATmp ) Temperature difference (Tm = 310 K) 29.4 K 0.063 K B

u4(ATmD ) Temperature difference (T,„ = 340 K) 59.4 K 0.063 K B

Table A4-10 summarizes the combined standard uncertainties for A at three levels of Tm. Values ofA were computed with Eq. (25).

Table A4-10. Combined standard uncertainty (k= 1) for uc {A) A uc(A) uc. rel (A) (K) (m2 ) (m2

) (%)

280 0.12979 0.000023 0.018 310 0.12998 0.000029 0.022 340 0.13016 0.000043 0.033

The estimates for uc (A) are quite small, especially near ambient temperature, but increase

as 7), departs from ambient conditions.
Annex 5

Annex 5 - Supplemental Thermal Conductivity Measurements

A5.1 Description of Measurements As part of the imbalance heat-flow tests described in Annex 4, a series of supplemental

thermal conductivity measurements were conducted for specimen pair 184-369. These measurements were conducted sequentially at different temperatures without removing the specimens from the apparatus. Table A5-1 summarizes the test results.

Table A5-1. Thermal conductivity data for specimen pair 184-369 Tm Th Tci Tc2 Q/2 A L Ta Pa RH /

(K) (K) (K) (K) (W) (m2

) (mm) (°C) (kPa) (%) (Pa) (W-rn'-K-1 ) 280 292.50 267.51 267.51 3.905 0.12980 25.75 280.0 99.6 8 465 0.03010 295 307.50 282.50 282.50 4.110 0.12989 25.79 295.0 99.8 3 495 0.03265 297 309.54 284.54 284.54 4.138 0.12990 25.79 297.0 98.1 3 511 0.03287 310 322.50 297.50 297.50 4.326 0.12998 25.79 310.0 99.5 2 511 0.03433 310 322.50 297.50 297.50 4.313 0.12998 25.83 310.0 97.9 2 493 0.03428 325 337.50 312.50 312.50 4.533 0.13007 25.82 325.0 99.8 1 513 0.03599 340 352.50 327.50 327.50 4.741 0.13016 25.88 340.0 99.9 1 497 0.03770

* Extra digit included for rounding A5.2 Analysis of Data

Figure A5a plots the thermal conductivity data of Table A5-1 (diamond symbols), fitted line for the certification thermal conductivity data (Table 13), and 95 %-95 % simultaneous

tolerance intervals for the certified line. The simultaneous (Lieberman-Miller) tolerance bounds [35] have an interpretation exactly similar to that of the Working-Hotelling bounds

except that here the intersection points of the upper and lower curves with a vertical line segment at a fixed temperature define 95 %-95 % tolerance bounds for the certified conductivity value at that temperature. The bounds capture 95 % of any data taken from a

fully comparable experiment with 95 % confidence. Here it is observed that all the sup- plemental points in Fig. A5a fall very close to the certification line (Eq. (26)) and well within the tolerance bands.

115
Annex 5

270 280 290 300 310 320 330 340 350

Temperature, K

Figure A5a. Re-measured thermal conductivity versus temperature for specimen pair 184-369. The solid

line represents the fitted model for certification data from Table 13. The dashed lines represent Miller- Lieberman 95 %- 95 % simultaneous tolerance intervals [35].

116