f A111DE 7 fl M fl E

NAT'L INST OF STANDARDS & TECH R.I.C.

_ t All 102784082

QC100

Sparks, U56

LarryNO.

L/Thermal conductivity of Hn 88-3086 1988 V19 dl NBS-P ° U

NBS

PUBLICATIONS

THERMAL CONDUCTIVITY OF SELECTED

FOAMS AND SYSTEMS FROM 100 TO 300 K

L.L. Sparks

W.P. Dube

A.J. Slifka

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303-3328

January 1988

QC

100

.1156

# 88 - 1988

C.2

Stimulating America's Progress

1913-1988

Research Information Center

National Bureau of Standards

Gaithersburg, .Maryland 20119* NBSIR 88-3086

THERMAL CONDUCTIVITY OF SELECTED

FOAMS AND SYSTEMS FROM 100 TO 300 K

Chemical Engineering Science Division

Center for Chemical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303-3328

January 1988

Prepared for NASA Langley Research Center

Hampton, Virginia 23665

L.L. Sparks

W.P. Dube

A.J. Slifka

U.S. DEPARTMENT OF COMMERCE, C. William Verity, Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director
'
CONTENTS

Page

List of Tables v

List of Figures vii

List of Units and Symbols ix

ABSTRACT 1

INTRODUCTION 1

APPARATUS 1

SPECIMENS 5

RESULTS 5

DISCUSSION 32

SUMMARY 45

REFERENCES 46

iii

List of Tables

Table Page

1 Test specimens

2 Test summary 5

3 Location index for all data 6

4 Experimental data for PMA51 7

5 Polynomial coefficients for a four-term fit of thermal

conductivity as a function of temperature for PMA51 . ... 7

6 Thermal conductivity (mW/(m«K)) as a function of temperature

(K) from the polynomial coefficients given in table 5 for

PMA51 8

7 Experimental data for PMA71 - 2 11

8 Polynomial coefficients for a four-term fit of thermal

conductivity as a function of temperature for PMA71~2. . . 11

9 Thermal conductivity (mW/(m»K)) as a function of temperature

(K) from the polynomial coefficients given in table 8 for

PMA71-2 11

10 Experimental data for PMA71-1 14

11 Polynomial coefficients for a five-term fit of thermal

conductivity as a function of temperature for PMA71-1. . • 1*4

12 Thermal conductivity (mW/(m*K)) as a function of temperature

(K) from the polynomial coefficients given in table 11 for PMA71-1 15

13 Experimental data for COMPOSITE 18

14 Polynomial coefficients for a four-term fit of thermal

conductivity as a function of temperature for COMPOSITE. .

15 Thermal conductivity (mW/(m*K)) as a function of temperature

(K) from the polynomial coefficients given in table 14 for

COMPOSITE

16 Experimental data for an aluminum/foam composite specimen,

SOFI

v
Table Page

17 Polynomial coefficients for a seven-term fit of thermal

conductivity as a function of temperature for an aluminum/foam composite, SOFI 21

18 Thermal conductivity (mW/(m*K)) as a function of temperature

(K) from the polynomial coefficients given in table 17 for

an aluminum/foam composite, SOFI 22

19 Computed thermal conductivity of the foam component of an aluminum/foam composite, SOFI 25

20 Polynomial coefficients for a seven-term fit of thermal

conductivity as a function of temperature for the foam

component of an aluminum/foam composite, SOFI 25

21 Thermal conductivity (mW/(m*K)) as a function of temperature

(K) from the coefficients given in table 20 for the foam

component of an aluminum/foam composite, SOFI 26

22 Experimental data for PMA71-1-vac 29

23 Polynomial coefficients for a three-term fit of thermal

conductivity as a function of temperature for PMA71 ~1 -vac . 29

24 Thermal conductivity (mW/(m»K)) as a function of temperature

(K) from the polynomial coefficients given in table 23 for

PMA7 1“1 -vac 29

25 Computed thermal conductivity (mW/(m*K)) as a function of

temperature (K) for a polymethacrylimide foam of density

97.5 kg/m3 (6.1 lb/ft3) 42

26 Thermal resistance due to evacuated boundaries, Rg for

PMS71-1 45

vi
List of Figures

Figure Page

1 Photo of Apparatus

2 Schematic of guarded-hot-plate specimen

configuration and environmental chamber

3 Polynomial fit of thermal conductivity (mW/(m*K)) as a function of temperature (K) for PMA51 . Experimental

data are represented by discrete points 9

i] Deviations (%) between experimental and fitted data as a function of temperature (K) for PMA51 10

5 Polynomial fit of thermal conductivity (mW/(m*K)) as a function of temperature (K) for PMA71“2. Experimental

data are represented as discrete points 12

6 Deviations (%) between experimental and fitted data as a function of temperature (K) for PMA71-2

7 Polynomial fit of thermal conductivity (mW/(m*K)) as a function of temperature (K) for PMA71-1. Experimental

data are represented by discrete points 16

8 Deviations (%) between experimental and fitted data as a function of temperature (K) for PMA71-1

9 Polynomial fit of thermal conductivity (mW/(m*K)) as a function of temperature (K) for COMPOSITE. Experimental

are data represented by discrete points 19

10 Deviations (%) between experimental and fitted data as a function of temperature (K) for COMPOSITE

11 Polynomial fit of thermal conductivity (mW/(m*K)) as

a function of temperature (K) for an aluminum/foam

composite, SOFI. Experimental data are represented

as discrete points

12 Deviations (%) between experimental and fitted data as a function of temperature (K) for an aluminum/foam composite,

SOFI

13 Polynomial fit of thermal conductivity (mW/(m*K)) as a function of temperature (K) for the foam component of an aluminum/foam composite, SOFI. Experimental data are represented by discrete points

vii
Figure Page

14 Deviations (%) between experimental and fitted data as a function of temperature (K) for the foam component of an aluminum/foam composite, SOFI 28

15 Polynomial fit of thermal conductivity (mW/(m*K)) as a function of temperature (K) for PMA71 -1 -vac . Experimental data are represented by discrete points 30

16 Deviations (%) of between experimental and fitted data as

a function of temperature (K) for PMA71 - 1-vac 31

17 (a) Possible variations of resin distribution in two foams

of equal density. (b) Possible heat-flow path lengths as

a function of cell geometry for two foams of equal density

and for different directions in a single foam 34

18 Fitted thermal conductivity (mW/(m*K)) as a function of

temperature (K) for PMA51 , PMA71-1, PMA71-2, COMPOSITE

SOFI (PU), and PMA71-1-vac 35

19 Thermal conductivity (mW/(m*K)) as a function of density

(kg/m3) with temperature (K) as a parameter for PMA foams. 38

20 Cross section schematic for the composite specimen .... 39

21 Thickness effect on the measured thermal conductivity of

foams (Jones, 1968) 41

22 Schematic indicating operative modes of heat transfer when

the cut foam surfaces are exposed to an insulating vacuum. 44

viil
List of Units and Symbols

Definition of Symbols

k = thermal conductivity, W/(m*K)

AX = mean specimen thickness, m

A = area of metered section of GHP, m^

AT = steady-state temperature difference, K

Q = power, W

Unit Conversions

Temperature T^ = Tq+273.15

Tc = (T F -32)/1 .8

Tr - 1.8 T K

where T^ is temperature in kelvins,

Tq is temperature in degrees Celsius,

Tp is temperature in degrees Fahrenheit,

and Tr is temperature in degrees Rankine.

Thermal Conductivity X(W/(m*K)) = 0.578 Btu/ (hr *f t *°F

)

= 6.94 (Btu • in) (hr *f t^ *°F

)

Density: p(kg/m3) = 0.06243 lb/ft3

Prefixes: FACTOR PREFIX SYMBOL

o i nano n

10 -6 micro u

10“3 milli m

iC\J o centi c

103 kilo k

10 6 mega M

IX

Thermal Conductivity of Selected Foams and Systems

from 100 to 300 K

L. L. Sparks, W. P. Dube', and A. J. Slifka

Chemical Engineering Science Division

National Bureau of Standards

Boulder, Colorado 80303

The apparent thermal conductivity of five insulating materials was determined in the nominal temperature range from 100 to 300 K

(-280 to 80 °F ) . A guarded-hot-plate apparatus was used and the

testing environment was dry nitrogen gas at near ambient pressure. Cne

specimen was retested in a vacuum environment.

Three of the specimens were neat polymethacrylimide (PMA) foams

with nominal densities of 51 and 71 kg/m3 (3.2 and M . 4 lb/ft3).

specimens tested were a polyurethane foam sprayed on an aluminum

substrate and a sandwich construction specimen utilizing PMA foam of

nominal density 110 kg/m3 (6.9 lb/ft3). The results in nitrogen gas

show the expected conductivity increase with increasing density. The

observed conductivity at 0.67 Pa (5 pm of Hg) is significantly lower

than that in ambient-pressure nitrogen gas. The large relative

difference may be due to increased thermal resistance at the

plate-specimen boundaries.

Key words: foam; insulation; low- temper ature ; polymethacrylimide;

polyurethane; thermal conductivity.

INTRODUCTION

The apparent thermal conductivity of five insulating materials r.a.: • determined in the nominal temperature range from 100 to 300 K. Ir. ea:h i tests were conducted in a dry nitrogen atmosphere at a pressure sli.-nt

ambient. One specimen was retested at a pressure of 0.67 °a '5 „m f

- ; g .

APPARATUS

The system used to make the measurements is g e n e r i

a 1 1 y guarded-hot-plate (GHP). The NBS apparatus is pictured in figure 1 and she

schematically in figure 2. This type of system, is one f

‘ Methods (ASTM, C177) for determining the apparent thermal conductivity of pc

thermal conductors. A detailed discussion of the apparatus used for the

measurements, as it existed in 1981, is given by Smith, 'lust,

(1982); the system was modified to include automated control and da

acquisition capabilities prior to making the current e >: ; t A brief discussion of the apparatus operation is giver. «
The operation of this type of apparatus involves supplying a measured power, Q,

from the main heater plate to the two specimens (fig. 2) and measuring the

resulting steady-state temperature differences across the specimens. The thermal

conductivity is then given by

k , AX . _Q

2A AT

(1)

where AX is the mean specimen thickness, A is the area of the metered section of

the main heater plate, and AT is the steady-state mean temperature difference

across the two specimens. The absolute temperatures and temperature differences

are measured with type E thermocouples.

The accuracy of k depends on the accuracy of measurement of the parameters shown

in eq (1) and on establishment of unidirectional (vertical in this case) heat

flow in the metered area of the specimens. The inner-guard heater plate is

controlled at the temperature of the main heater in order to minimize radial heat

flow in the metered area. Somers and Cyphers (1951) and ASTM C 1 77 indicate that,

when the metered diameter-to-thickness ratio of a specimen is greater than 4, the

errors in k due to edge losses should be less than 1$. The metered section

diameter of the plates is 10 cm (3.94 in) and the specimen thicknesses are given

in the SPECIMENS section.

The most difficult parameters to determine are temperature differences across the

specimens, AT. The correctness of AT measurements depends on plate-to-specimen

thermal contact, on unidirectional heat flow, and on thermocouple calibration and

referencing sources of error. The diverse materials which can be tested in this

type of system cause a wide range of plate-to-specimen contact situations. Tye

and Spinney (1976) found that embedding the thermocouple wires in the specimen,

as opposed to the measuring plates, resulted in higher observed conductivities.

This effect is due to better spec imen- to-thermocouple contact which results in

smaller measured AT and larger k (eq (1)). They also found that the effect of

thermocouple placement was dependent on the conductivity of the specimens. As

the conductivity of the specimen increases, the relative effect of an air gap in

the specimen-to-plate interface becomes larger. As discussed later in relation

to the vacuum tests, specimen-to-sensor contact can strongly affect the observed

conductivity

Thermocouple placement used in obtaining the data reported below consisted of

cementing the wires into machined grooves in the measuring plates (plates

adjacent to the specimens shown in figure 2) so that the thermocouples were flush

with the plate surfaces.

The accuracy of measurements made with this system on fiberglass and fiberboard

reference materials is discussed by Smith et al. (1982). In a qualitative sense

the plate-to-specimen contact should be similar for low-density foams and

fibrous materials. Based on the percentage error estimate given by Smith for

each parameter in eq (1) and the magnitude of these parameters for the current

experiments, uncertainties in the observed values for foam are estimated to be

0.2 mW/(m*K) random and 0.4 mW/(m*K) systematic near room temperature; near 80 K the random and systematic components are 0.1 mW/(m*K).

2
3

Figure

1.

Photo

of

Apparatus.
Figure 2. Schematic of guarded-hot-plate specimen configuration and

environmental chamber.
SPECIMENS

The five specimens studied were supplied by either NASA or a NASA contractor.

They consisted of three commercially available polymethacryl imi de (PMA) foams,

one polyurethane (PU) foam sprayed on an aluminum substrate, and one sandwich

composite made up of PMA foam, aluminized polyimide film, glass cloth, and

adhesive. The specimens are identified in table 1.

Table 1 . Test specimens

SPECIMEN

IDENTIFICATION

COMMENTS*

PMA51

PMA71-2

PMA71-1

COMPOSITE

SOFI

Polymethacrylimide , measured density = 53*3 kg/m3 (3.3 lb/ft-'

" " = 66.3 " (4.1)

" " = 64.0 " (4.0)

Sandwich construction consisting of:

aluminized polyimide film, glass cloth/adhesive,

PMA110, adhesive, PMA110, and glass cloth/adhesive

Sprayed, fluorocarbon-blown polyurethane foam,

measured foam density = 37.6 kg/m3 (2.3)

The diameter of each specimen was approximately 20.3 cm (8 in).

RESULTS

The test summary for the entire series is given in table 2. In each case the

nominal temperature difference established across the specimen was 20 <

indicated in this table, two specimens were tested in the single-sided TEST

This was necessitated by thickness in the case of COMPOSITE and by having

one SOFI specimen. Single-sided operation involves replacing one f specimens shown in figure 2 with another, well known material, and conduct;-..- th*

experiments with no temperature gradient across the substitute material.

Table 2. Test summary

SPECIMEN THICKNESS NUMBER MINIMUM MAXIMUM TEST

IDENTIFICATION cm (in) of TEMPERATURE TEMPERATURE MODE

TEMPERATURES K K PMA51 2.48 (0.976) 10 95.9 288.4 doubl

PMA71-2 2.56 (1 .008) 6 105.8 253-6 doubl

PMA71-1 2.56 (1.008) 19 105.7 317.4 doubl

COMPOSITE 4.90 (1 .929) 6 100.8 258.7 singl

SOFI 2. 30 [ A 1 +PU] (0.945) 12 105.9 303.4 singl

2.10 [PU] (0.827) 12 105.9 303.4 calcu

PMA71 “1 -vac 2.56 (1 .008) 5 155.0 263.5 doubl

5
The apparent thermal conductivity, k, is computed using eq (1). The

experimentally determined parameters used in this equation are actually averages

of the values obtained while the specimen is in thermal equilibrium at a given

temperature. For example, once the specimen and the apparatus have reached

equilibrium, i.e., constant temperature gradients have been established across

the specimen at a constant power input, a series of N measurements of the power,

Q, will be made over a period of time, t. The average Q and its random

uncertainty is computed from these N measurements and is used in eq (1). The

average of the other parameters and their uncertainties are arrived at in a similar manner. These data allow a random uncertainty to be associated with each

value of k. The values of k, computed with eq (1), are referred to as experimental data.

The experimental data for each specimen have been fitted with a power series

polynomial of the form

n

k = J2 A i Ti (2)

i = o

The experimental data, polynomial coefficients, tabular values calculated from

the fits, plots of k = f(T), and plots of deviations between the fitted and

experimental data are presented as indicated in table 3*

Table 3. Location index for all data •

TABLE NUMBERS FIGURE NUMBERS

SPECIMEN EXPERIMENTAL POLYNOMIAL ANALYTICALLY k = f (T) DEVIATIONS

ID DATA COEFFICIENTS GENERATED EXP. -FITTED

DATA

PMA51 4 5 6 3 4 PMA71-2 7 8 9 5 6 PMA71-1 10 1

12 7 8

COMPOSITE 13 14 15 9 10

SOFI ( Al+PU ) 16 17 18 1

12

(PU) 19 20 21 13 14

PMA7 1 ~1 -vac 22 23 24 15 16

PMA1 10 25

6
Table 4. Experimental data for PMA51

TEMPERATURE THERMAL CONDUCTIVITY

(K) (mW/ (m*K)

)

228.966 27.24

248.657 29.93

268.476 32.72

288.356 35.93

134.959 17.11

154.704 19.14

174.521 21 .18

233.904 28.09

253-682 30.86

95.871 12.72

Table 5. Polynomial coefficients for a four-term fit of thermal

conductivity as a function of temperature for PMA51

AO = - . 1 3022901 E+01

A1 = .1871021 9E+00

A2 = - .53^7781 9E-03

A3 = .1 1579740E-05

7
Table 6. Thermal conductivity (mW/(m*K)) as a function of temperature (K)

from the polynomial coefficients given in table 5 for PMA51

T k T k T k

96.0 12.76 162.0 19.90 226.0 27.04

98.0 12.99 164.0 20.11 228.0 27.28

100.0 13.22 166.0 20.32 230.0 27.53

102.0 13-45 168.0 20.53 232.0 27.78

104.0 13-67 170.0 20.74 234.0 28.03

106.0 13.90 172.0 20.95 236.0 28.29

108.0 14.13 174.0 21.16 238.0 28.55

110.0 14.35 176.0 21 .38 240.0 28.81

1 12.0 14.57 178.0 21 .59 242.0 29.07

114.0 14.79 180.0 21 .80 244.0 29.33

116.0 15.01 182.0 22.02 246.0 29.60

118.0 15.23 184.0 22.23 248.0 29.87

120.0 15.45 186.0 22.45 250.0 30.14

122.0 15.67 188.0 22.67 252.0 30.42

1 24.0 15.88 190.0 22.88 254.0 30.70

126.0 16.10 192.0 23.10 256.0 30.98

128.0 16.31 194.0 23.32 258.0 31 .26

1 30.0 16.53 196.0 23.54 260.0 31 .55

1 32.0 16.74 198.0 23.77 262.0 31 .84

134.0 16.95 200.0 23.99 264.0 32.13

1 36.0 17.17 202.0 24.22 266.0 32.42

1 38.0 17.38 204.0 24.44 268.0 32.72

1 40.0 17.59 206.0 24.67 270.0 33.02

1 42.0 17.80 208.0 24.90 272.0 33.33

1 44.0 18.01 210.0 25.13 274.0 33.64

1 46.0 18.22 21 2.0 25.36 276.0 33.95

1 48.0 18.43 21 4.0 25.60 278.0 34.26

150.0 18.64 216.0 25.83 280.0 34.58

152.0 18.85 218.0 26.07 282.0 34.90

154.0 19.06 220.0 26.31 284.0 35.23

156.0 19.27 222.0 26.55 286.0 35.56

158.0 19.48 224.0 26.79 288.0 35.89

160.0 19.69

8
THERMAL

CONDUCTIVITY,

mW/m-K

TEMPERATURE, K

Figure 3* Polynomial fit of thermal conductivity (mW/ m*K) a: i :

of temperature (K) for PMA51 . Experimental data are r* ;

1 by discrete points.

9
Y

(OBS)-Y

(CRLC)

)

100/Y(0BS)

0.75

0.50 -

0.25 -

0.00

-0.25 -

-0.50 -

-0.75 uLt i 75 100 125 150 175 200 225 250 275 300

TEMPERATURE, K

Figure i|

. Deviations ($) between experimental and fitted data as a function

of temperature (K) for PMA51

10
Table 7. Experimental data for PMA71-2.

Table 8.

Table 9.

T

106 . 108 . 110 . 112 . in.

116 . 118 . 120 . 122 . 124.

126.

128.

130.

132 . 134.

136.

138.

1 40.

1 42.

144.

146.

148.

150.

152.

154.

TEMPERATURE

(K)

229.061

253.61

105.769

130.167

164.703

194.235

THERMAL CONDUCTIVITY

(mW/ (m »K)

)

28.71

32.18

15.02

17.93

21 .57

24.80

Polynomial coefficients for a four-term fit of thermal

conductivity as a function of temperature f or PMA71-2.

A0 = -.521 12427E+01

A1 = .27824329E+00

A2 = -.10417 420E -02

A3 = .20725273E:-05

Thermal conductivity (mW/(m •K)) as a function of temperatures (K)

from thei polynomial coefficients given in table 8 for PMA71-•2.

k T k T k

0 15.05 156.0 20.71 206.0 26.02

0 15.30 158.0 20.92 208.0 26.24

0 15.55 160.0 21 .13 210.0 26.47

0 15.80 162.0 21 .34 212.0 26.70

0 16.04 164.0 21 .54 21 4.0 26.94

0 16.28 166.0 21 .75 216.0 27.17

0 16.52 168.0 21 .96 218.0 27.41

0 16.76 170.0 22.17 220.0 27.65

0 16.99 172.0 22.37 222.0 27.89

0 17.22 174.0 22.58 224.0 28.14

0 17.45 176.0 22.79 226.0 28.39

0 17.68 178.0 23.00 228.0 28.64

0 17.91 180.0 23.21 230.0 28.89

0 18.13 182.0 23.42 232.0 29.15

0 18.35 184.0 23.63 234.0 29.41

0 18.58 186.0 23.84 236.0 29.68

0 18.79 188.0 24.05 238.0 29.94

0 19.01 190.0 24.26 240.0 30.21

0 19.23 192.0 24.48 242.0 30.49

0 19.44 194.0 24.69 244.0 30.77

0 19.66 196.0 24.91 246.0 31 .05

0 19.87 198.0 25.13 248.0 31 .33

0 20.08 200.0 25.35 250.0 31 .62

0 20.29 202.0 25.57 252.0 31 .92

0 20.50 204.0 25.79
THERMAL

CONDUCTIVITY,

mW/m-K

TEMPERATURE, K

Figure 5. Polynomial fit of thermal conductivity (mW/(m*K)) as a function of temperature (K) for PMA71~2. Experimental

data are represented by discrete points.

12
Y

(

OBS )

- Y

(

CflLC

)

1

00/ Y

(

OBS

)

0.4

0.3 -

0.2 -

0.1 -

0.0

o

-0.2 -

-0.3 ' 1 " i I * * * 100 120 140 160 180 200

TEMPERRTURE, K

220 240 260

Figure 6. Deviations (?) between experimental and fitted data as a function of temperature (K) for PMA71-2.

13
Table 10. Experimental data for PMA71-1.

TEMPERATURE THERMAL CONDUCTIVITY

(K) (mW/ (m*K)

)

285.390 37.28

251 .216 31 .93

261 .064 33.53

270.901 35.25

317.404 43.02

1 38.819 18.62

1 49.494 19.73

159.252 20.45

105.689 14.65

115.326 15.82

125.338 16.94

154.718 20.02

179.663 22.51

204.344 25.20

194.286 24.20

209.119 25.82

224.1 21 27.83

238.864 29.75

297.795 39.97

Table 11. Polynomial coefficients for a five-term fit of thermal

conductivity as a function of temperature for PMA71-1.

AO = - . 241 9^91 0E+02

A1 = . 72667067E+00

A2 = -.49017294E-02

A3 = .16082458E-04

A 4 = -.1811 3899E-07

14
Table 12. Thermal conductivity (mW/(m*K)) as a function of temperature (K)

from the polynomial coefficients given in table 11 for PMA71-1.

T k T k T k

106.0 14.62 178.0 22.36 248.0 31 .33

108.0 14.91 180.0 22.57 250.0 31 .65

110.0 15.18 182.0 22.77 252.0 31 .97

112.0 15.45 184.0 22.98 254.0 32.29

114.0 15.71 186.0 23.19 256.0 32.61

116.0 15.96 188.0 23.41 258.0 32.94

118.0 16.21 190.0 23.62 260.0 33.27

120.0 16.46 192.0 23.84 262.0 33.60

122.0 16.69 194.0 24.06 264.0 33-94

124.0 16.92 196.0 24.29 266.0 34.28

126.0 17.15 198.0 24.52 268.0 34.62

128.0 17.37 200.0 24.75 270.0 34.96

130.0 17.59 202.0 24.98 272.0 35.30

132.0 17.81 204.0 25.22 274.0 35.64

134.0 18.02 206.0 25.46 276.0 35.99

136.0 18.23 208.0 25.70 278.0 36.33

1 38.0 18.43 210.0 25.95 280.0 36.68

140.0 18.64 212.0 26.20 282.0 37.03

142.0 18.84 214.0 26.46 284.0 37.38

144.0 19.04 216.0 26.71 286.0 37.73

146.0 19.23 218.0 26.98 288.0 38.07

148.0 19.43 220.0 27.24 290.0 38.42

150.0 19.62 222.0 27.51 292.0 38.77

152.0 19.82 224.0 27.78 294.0 39.12

154.0 20.01 226.0 28.06 296.0 39.47

156.0 20.21 228.0 28.34 298.0 39.81

158.0 20.40 230.0 28.62 300.0 40.15

160.0 20.59 232.0 28.91 302.0 40.50

162.0 20.78 234.0 29.20 304.0 40.84

164.0 20.98 236.0 29.49 306.0 41.18

166.0 21 .17 238.0 29.79 308.0 41 .51

168.0 21 .37 240.0 30.09 310.0 41 .84

170.0 21 .56 242.0 30.40 312.0 42.17

172.0 21 .76 244.0 30.70 314.0 42.50

174.0 21 .96 246.0 31 .02 316.0 42.82

176.0 22.16

15
TEMPERATURE, K

Figure 7. Polynomial fit of thermal conductivity (mW/(m*K)) as a function of

temperature (K) for PMA71~1. Experimental data are represented by

discrete points.

16
(

sao

)

a/oo i

(

oiyo

)

a-

(

sao

)

x

1

0.75

0.50

0.25

0

-0.25

-0.50

-0.75

-1

. ^T"1

' * 1 11

1

' »

o ; o

o

: o o O

O

- O -

• o

0 .

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• o

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o

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1 o -

1 1 1 -t-J-Ldb Imim.+nLmk, . , O ‘ - 100 125 150 175 200 225 250 275 300 325

TEMPERATURE, K

Figure 8. Deviations (%) between experimental and fitted dat-i as a function of temperature (K) for PMA71-1.

17
Table 13. Experimental data for COMPOSITE.

TEMPERATURE

(K)

233.994

258.677

130.102

159.518

100.793

189.179

THERMAL CONDUCTIVITY

(mW/ (nvK)

)

33.37

37.69

22.24

25.72

16.88

29.27

Table 14. Polynomial coefficients for a four-term fit of thermal

conductivity as a function of temperature for COMPOSITE.

AO = -.27171 067E+02

A1 = .70904743E+00

A2 = -. 329491 91 E~02

A3 = .58809892E-05

Table 15. Thermal conductivity (mW/(m*K)) as a function of temperature (K)

from the polynomial coefficients given in table 14 for COMPOSITE.

T k T k T k

100.0 16.67 154.0 25.36 208.0 30.68

102.0 17.11 156.0 25.58 210.0 30.89

104.0 17.55 158.0 25.80 21 2.0 31 .09

106.0 17.97 160.0 26.02 21 4.0 31.31

108.0 18.38 162.0 26.23 216.0 31 .52

110.0 18.78 164.0 26.43 218.0 31 .74

112.0 19.17 166.0 26.64 220.0 31 .97

114.0 19.55 168.0 26.84 222.0 32.19

116.0 19.92 170.0 27.04 224.0 32.43

118.0 20.28 172.0 27.23 226.0 32.67

120.0 20.63 174.0 27.43 228.0 32.91

122.0 20.97 176.0 27.62 230.0 33.16

124.0 21 .30 178.0 27.81 232.0 33.42

126.0 21 .62 180.0 28.00 234.0 33.68

1 28.0 21 .94 182.0 28.19 236.0 33.95

1 30.0 22.24 184.0 28.38 238.0 34.23

132.0 22.54 186.0 28.56 240.0 34.51

1 34.0 22.83 188.0 28.75 242.0 34.80

136.0 23.11 190.0 28.94 244.0 35.10

1 38.0 23.38 192.0 29.13 246.0 35.41

1 40.0 23.65 194.0 29.32 248.0 35.72

1 42.0 23.91 196.0 29.51 250.0 36.05

1 44.0 24.17 198.0 29.70 252.0 36.38

146.0 24.42 200.0 29.89 254.0 36.72

1 48.0 24.66 202.0 30.08 256.0 37.08

150.0 24.90 204.0 30.28 258.0 37.44

152.0 25.13 206.0 30.48

18
THERMAL

CONDUCTIVITY,

mW/m-K

TEMPERATURE, K

Figure 9. Polynomial fit of thermal conductivity (mW/(r*K) as a function of temperature (K) for COMPOSITE. Experiner* . data are represented by discrete points.

19
(

sao )

a/oo i

(

(cnuG)

A-isao )

a

1.5

0.5

D

- 0.5

o

-1

100 125 150 175 200

TEMPERATURE , K

225 250 275

Figure 10. Deviations (%) between experimental and fitted data as

a function of temperature (K) for COMPOSITE.

20
Table 16. Experimental data for an aluminum/foam composite specimen, SOFI

TEMPERATURE THERMAL COND

(K) (mW/ (m*

105.788 15.00

125.255 17.60

144.932 20.52

164.538 23.01

184.286 25.43

204.193 27.26

233-973 26.68

224.085 27.22

243.750 25.71

263.635 24.53

283.488 26.30

303.443 28.12

Table 17. Polynomial coefficients for a seven-term fit of thermal

conductivity as a function of temperature for an aluminum/

foam composite, SOFI.

AO = - .744951 71 E+03

A1 = .25852200E+02

A2 = -.3581 3007E+00

A3 = .25738209E-02

A 4 = -. 1 0054371 E-04

A5 = . 2022881 5E-07

A6 = -.16405909E-10

21
Table 18. Thermal conductivity (mW/(m»K)) as a function of temperature (K)

from the polynomial coefficients given in table 17 for an aluminum/foam composite, SOFI.

T k T k T k

106.0 14.99 172.0 24.14 238.0 26.16

108.0 15.44 174.0 24.43 240.0 26.02

110.0 15.83 176.0 24.71 242.0 25.89

112.0 16.19 178.0 24.98 244.0 25.75

114.0 16.50 180.0 25.25 246.0 25.62

116.0 16.79 182.0 25.50 248.0 25.50

118.0 17.05 184.0 25.74 250.0 25.39

120.0 17.30 186.0 25.97 252.0 25.29

122.0 17.53 188.0 26.18 254.0 25.19

1 24.0 17.75 190.0 26.38 256.0 25.12

126.0 17.96 192.0 26.56 258.0 25.06

128.0 18.17 194.0 26.72 260.0 25.02

130.0 18.39 196.0 26.87 262.0 24.98

132.0 18.60 198.0 26.99 264.0 24.98

134.0 18.82 200.0 27.10 266.0 24.99

1 36.0 19.04 202.0 27.19 268.0 25.03

138.0 19.27 204.0 27.26 270.0 25.08

1 40.0 19.51 206.0 27.32 272.0 25.16

1 42.0 19.76 208.0 27.35 274.0 25.26

1 44.0 20.01 210.0 27.37 276.0 25.38

1 46.0 20.27 212.0 27.37 278.0 25.51

1 48.0 20.55 21 4.0 27.35 280.0 25.68

150.0 20.82 216.0 27.32 282.0 25.85

152.0 21.11 218.0 27.27 284.0 26.05

154.0 21 .40 220.0 27.20 286.0 26.26

156.0 21 .70 222.0 27.12 288.0 26.48

158.0 22.00 224.0 27.03 290.0 26.72

160.0 22.31 226.0 26.93 292.0 26 . 96

162.0 22.62 228.0 26.82 294.0 27.19

164.0 22.92 230.0 26.70 296.0 27.43

166.0 23.23 232.0 26.57 298.0 27.65

168.0 23.54 234.0 26.44 300.0 27.87

170.0 23.84 236.0 26.30 302.0 28.07

22
TEMPERATURE, K

Figure 11. Polynomial fit of thermal conductivity (mW/(m*K)) a.- function of temperature (K) for an aluminum/f oar. : 0 m; .* , SOFI . Experimental data are represented by discr* ^ . .

23
2

CO

CD

2 i h

oo . o

o o a:

o

co

CD

o

-2

100 125 150 175 200 225 250

TEMPERATURE, K

275 300 325

Deviations {%) between experimental and fitted data as a function of temperature (K) for an aluminum/foam composite,

SOFI

2*J

Figure 12.
Table 19. Computed thermal conductivity of the foam component of an aluminum/foam composite, SOFI.

TEMPERATURE THERMAL COND

(K) (mW/ (m»

105.789 13.11

125.256 15.37

1 44.932 17.90

164.538 20.09

184.286 22.18

204.193 23-75

233.974 23.34

224.085 23.80

243.751 22.52

263.636 21 .52

283.488 22.97

303.443 24.55

Table 20. Polynomial coefficients for a seven-term fit of thermal

conductivity as a function of temperature for the foam

component of an aluminum/foam composite, SOFI.

AO = -.61 108028E+03

A 1 = .21 218929E + 02

A2 = -.29384951 E+00

A3 = .2111 3743E-02

A 4 = -.82434748E-05

A5 = .16570060E-07

A6 = -.13421 171E-10

25
Table 21. Thermal conductivity (mW/(m*K)) as a function of temperature (K)

from the coefficients given in table 20 for the foam component

of an aluminum/foam composite, SOFI.

T k T k T k

106.0 13.10 172.0 21 .05 238.0 22.91

108.0 13.48 174.0 21 .30 240.0 22.79

110.0 13-82 176.0 21 .55 242.0 22.68

112.0 14.12 178.0 21 .78 244.0 22.57

114.0 14.40 180.0 22.01 246.0 22.46

116.0 14.65 182.0 22.23 248.0 22.36

118.0 14.87 184.0 22.44 250.0 22.26

120.0 15.09 186.0 22.63 252.0 22.17

122.0 15.29 188.0 22.82 254.0 22.09

124.0 15.48 190.0 22.99 256.0 22.03

1 26.0 15.67 192.0 23.15 258.0 21 .97

128.0 15.86 194.0 23.29 260.0 21 .94

130.0 16.05 196.0 23.42 262.0 21 .91

1 32.0 16.24 198.0 23-53 264.0 21 .90

1 34.0 16.43 200.0 23.63 266.0 21 .90

1 36.0 16.63 202.0 23.71 268.0 21 .93

1 38.0 16.83 204.0 23.77 270.0 21 .97

1 40.0 17.04 206.0 23.82 272.0 22.03

1 42.0 17.26 208.0 23.86 274.0 22.11

1 44.0 17.48 210.0 23.88 276.0 22.21

146.0 17.71 21 2.0 23.88 278.0 22.32

148.0 17.95 21 4.0 23.87 280.0 22.45

150.0 18.19 216.0 23.85 282.0 22.60

152.0 18.44 218.0 23.81 284.0 22.76

154.0 18.69 220.0 23.76 286.0 22.94

156.0 18.95 222.0 23.70 288.0 23.13

158.0 19.21 224.0 23.62 290.0 23.32

160.0 19.47 226.0 23.54 292.0 23.53

162.0 19.74 228.0 23.45 294.0 23.73

164.0 20.01 230.0 23.35 296.0 23.94

166.0 20.27 232.0 23.24 298.0 24.13

168.0 20.53 234.0 23.1 4 300.0 24.33

170.0 20.79 236.0 23.02 302.0 24.50

26
TEMPERATURE, K

Figure 13. Polynomial fit of thermal conductivity (mW/(m*K a: function of temperature (K) for the foam componer* f an aluminum/foam composite, SOFI. Experiments', da* •. are represented by discrete points.

27
Y

(

OBS )

- Y

(

CRLC

m

00/Y (

OBS

)

2

1.5

1

0.5

0

-0.5

-1

- 1.5

-2

100 125 150 175 200 225 250 275 300 325

TEMPERATURE, K

Figure 1^. Deviations (?) between experimental and fitted data as a function of temperature (K) for the foam component of an aluminum/foam composite, SOFI.

‘ ' 1

28
Table 22. Experimental data for PMA7 1 ~1 -vac

TEMPERATURE

(K)

263.525

263.^55

243.695

223.960

184.457

154.989

THERMAL CONDUCTIVITY

(mW/ (m*K)

)

33.32

25.04

20.48

17.09

11.97

9.56

Table 23. Polynomial coefficients for a three-term fit of therna

conductivity as a function of temperature for PMA71~1 -vac

AO = .21870026E+02

A1 = - . 208461 64E+00

A2 = .835273672-03

Table 24. Thermal conductivity (mW/(m*K)) as a function of temperature (K) fror

the polynomial coefficients given in table 23 for PMA71 -1 -vac.

T k T k T k

156.0 9.68 192.0 12.64 228.0 17.76

158.0 9.78 194.0 12.86 230.0 18.11

160.0 9.90 196.0 13-10 232.0 18.46

162.0 10.02 198.0 13.34 234.0 18.83

164.0 10.15 200.0 13.59 236.0 19.19

166.0 10.28 202.0 13.84 238.0 19.57

168.0 10.42 204.0 14.10 240.0 19.95

170.0 10.57 206.0 14.37 242.0 20.34

172.0 10.73 208.0 14.65 244.0 20.73

174.0 10.89 210.0 14.93 246.0 21 .14

176.0 11 .05 212.0 15.22 248.0 21 .54

178.0 11.23 214.0 15.51 250.0 21 .96

180.0 1 1 .41 216.0 15.81 252.0 22.38

182.0 11.60 218.0 16.12 254.0 22.81

184.0 11 .79 220.0 16.44 256.0 23.24

186.0 11 .99 222.0 16.76 258.0 23.69

188.0 12.20 224.0 17.09 260.0 24.13

190.0 12.42 226.0 17.42 262.0 2U . 59

29
THERMAL

CONDUCTIVITY,

mW/m-K

TEMPERATURE, K

Figure 15. Polynomial fit of thermal conductivity (mW/(m*K))

as a function of temperature (K) for PMA71~1~vac.

Experimental data are represented by discrete points.

30
Y

(

OBS )

-Y

(

CRLC

))

100/Y(0BS)

1.5

1

0.5

0

- 0.5

-1

17 i i

1

|

'i rrrf tt-tt |i i i

1 1

|

i r r i |

i i i i

|

i r r i pr i i i

|

i t-tt-] i-t t r ; -r-i

O

o

o

o

150 160 170 180 190 200 210 220 230 240

TEMPERATURE , K

250 260 270

Figure 16. Deviations (J) between experimental and fitted data a: a function of temperature (K) for PMA71“l~vac.

31
DISCUSSION

Heat is conducted through a foamed material by four mechanisms: solid conduction,

gas conduction, gas convection, and radiation. The presence of the two

nonconduc t i ve modes, convection and radiation, results in the possibility that

the measured thermal conductivity is thickness dependent. Thermal conductivity

is an intrinsic property of the material and does not depend on specimen geometry.

The data presented here are the apparent thermal conductivities because of the

nonconduct ive modes of heat transfer. With this understanding, the word apparent

is generally not included in the remainder of this report.

Skochdopole (1961) has shown that convective heat transfer will not occur in

cells whose dimensions are less than about 3 mm. The manufacturer indicates that

the cell diameters of the materials tested here are less than 0.5 mm. Nonstatistical characterization using an optical microscope suggests that this is

true. The convective mode will therefore be ignored in the remaining discussion.

It is important to keep in mind, however, that if cracks develop in the

insulation, either due to thermal or mechanical stresses or debonding, convection

can become a dominant mode of heat transfer.

Radiant heat flow through foam insulation is due to both direct plate-to-plate

transmission and to absorption and reradiation. Resins used for making

polyurethane foams (specimen SOFI) are partially transparent in the 2 to 20 pm

range of wavelengths (Skochdopole, 1961). Sections associated with thermal

insulations are normally optically thick (thickness » photon mean free path),

however, so that direct transmission will be small. Specific optical properties

of the polymethacryl imide foams are unavailable. If each cell is opaque, the

conductivity due to radiant heat transfer, k r , can be estimated by

e k r

= 4o L ) £T3 ( 3 ) where o is the S t e f an-Bol tzman constant (5.67 X 10~8 w*m“ 2 *K~^), e is the

emissivity of foam, i is the average cell dimension parallel to heat flow, and T is the average temperature of the specimen.

Heat flow through the solid component of polymeric foams is through the cell

struts and the cell membranes. The component of thermal conductivity which is

transmitted through the foam is a function of the thermal conductivity of the

resin, the density of the foam, and the distribution of the resin within the

struts, membranes, and joints. Qualitatively, the conductivity of the resin,

an amorphous solid, is a monotonic function of temperature. At temperatures

between approximately 100 and 300 K, the dependence is nearly linear:

k res = A + BT ( 4

)

where k res is the thermal conductivity of the resin. The conductivity of the

solid portion of a foam can be expressed as

^s = k res C D (5)

32
where C is the factor used to account for distribution of the resin within the

cellular structure and D is the foam density expressed in terras of the ratio of

resin volume to foam volume. As an example of how the resin distribution

contributes to k s> consider the two different cell structures sketched in Figure

17(a). The macroscopic density of the foams made up of these cell structures

could be assumed to be equal, but the conductivities would be expected to vary

considerably. The necked-down strut structure would represent a high resistance

to heat flow since k s is proportional to the cross section perpendicular to the

heat flow (eq 1). The effective path length parallel to the direction of the

heat flow is a function of the cell geometry and cell orientation and also

contributes to the observed thermal conductivity. Figure 17 (b) illustrates the

path length variability both as applied to two foams of the same density and as applied to heat flow parallel to different axes of a single foam. The observed

conductivity is inversely proportional to the effective path length (eq 1).

The remaining mode of heat transfer is conduction through the gas occupying the

foam cells. When a mixture of gases is present, the conductivity, k g , can be

estimated by

n kg = k mixture = Xpkp

i=1

where thermal conductivities of the individual species are given by k X : represents the corresponding mole fraction, and n is the number of species

present. The kp are temperature dependent and are nearly linear functions r temperature. Total gas conduction is given by

k

g

X

CC1

3 F

k

CC1

3

F

+ (1 XCC1

3 F

; *air (7

for cell gas consisting of air and CCI3F. Harding (1964) indicates that thvalues predicted by this simple molar mixing approach tend to be slightly - than those computed using kinetic theory (Tsederberg, 1965).

Although it is not rigorously correct to add the modes of heat transfer 'trey

not independent of one another), the total apparent conductivity, k j

,

using this approximation is acceptable for insulating foams (Gorr. v

Churchill, 1961):

kT

= k

f + k s

+ k r

This k-p approximates the apparent thermal conductivities determine

research reported here. Quantitative application of the principles : above to the experimental results is not possible because of tr*

characterization data for the specimens. They can be used, r wr- .

• • , qualitative explanations for the observed differences in the fiv>

composite thermal conductivity as a function of temperature : • shown in figure 18.

33
Figure 17. (a) Possible variations of resin distribution in two foams of equal

density. (b) Possible heat-flow path lengths as a function of cell

geometry for two foams of equal density and for different directions

in a single foam.

314
THERMAL

CONDUCTIVITY,

mW/m-K

- ]5C I t 2~Z 22~ 2ZZ

TEMPERATURE, K

Figure ‘5. Fitted thermal conductivity rW • F as e f

temperature (X) for PMA51 , PYA***-* , PYA" 1 -:, '

: . SOFI (PU), and ?YA 71 -'-vac.

35
Attempts to increase our knowledge of the PMA materials by inquiries to the

manufacturer were only partially successful due to proprietary restr ictions

Literature made available by the distributor indicates that rapid diffusion of

air and fill gas occurs. Pending further information from the manufacturer or an in-house characterization, it is only possible to establish circumstantial

reasons for the observed thermal conductivity relationships.

Pol ymethacry 1 imide series: Specimens with nominal densities of 51 kg/m3 (PMA51

)

and 71 kg/m3 (PMA71 - 1 and PMA71-2) were tested in dry nitrogen gas and PMA71-1

was also tested at a pressure of approximately 0.67 Pa (5 pm of Hg).

The observed conductivities of

a function of the densities provided

the PMA specimens would be expected

the following assumptions are true:

to be

( 1 )

( 2 ) (3)

(4)

the resin is identical in each foam,

the cell shape, not necessarily size, is the same in each foam,

the distribution of resin is identical in each foam, and

the cell gas, both type and pressure, is the same in each foam.

Based on the experimental results, the most likely scenario is as follows:

(a) The gas in the cells is the same for all three specimens; (b) the gas is

air; and (c) the assumptions (1), (2), and (3) are essentially true.

The following argument is the basis for the conclusion that the gas in the cells

of each foam is air. k

g can be expected to account for roughly 50-60$ of the

conduction if the cell gas is made up of heavy molecules, such as one of the

f luorocarbons or isopropanol, and 60-80$ if the cell gas is air. The difference

in thermal conductivity of air and a heavy gas is on the order of a factor of 2.

As discussed later, k

g

(S0FI), below about 200 K, is due to air. Below this

temperature, k-p for SOFI and PMA51 are essentially the same. The slopes of the

thermal conductivity data below 200 K suggest that k gfor all PMA and SOFI is due

to the same gas. The solid conduction component of PMA51 must also be

essentially equal to that of SOFI below 200 K. Since k s is expected to be a linear function of temperature, k s of SOFI and PMA51 should also be nearly equal

at 300 K.

From previous

foams (Sparks

1 3 mW/ (m*K)

relative to the

work relating density and thermal

and Arvidson, 1985), k s for

Applying the factor of 2 for

fluorocarbon results in k

g

(PMA51

)

k T (PMA51 ) = k

g

+ k s

= 26+11

conductivity for polyurethane

is 11 mW/(m*K) and k

g

is

of air

SOFI

the increased conductivity

= 26 mW / ( m • K

)

= 37 mW/(m-K)

This is in agreement with the experimental value.

36
If the assumptions that the cells of the PMA specimens contain air are correct,

the differences in observed conductivities among PMA51 , PMA71 -

1, and PMA71-2 are

due primarily to k s. As indicated in eq 5, k s is related to the combined effects

of density, resin distribution, and molecular structure of the resin.

k r also contributes to the heat transfered through the foams, but experience with

polyurethane foams indicates that this contribution differs by only about 556 over

the range of densities tested here. Other factors being equal, k r would tend to

increase the conductivity of PMA51 relative to the more dense specimens.

Figure 19 shows the density dependence of k-p with temperature as a parameter.

These data were obtained from the polynomial relationships for PMA51, PMA71, and

COMPOSITE. The rationale for including data for the composite specimen in this

figure is given below.

COMPOSITE: The cross section of the composite specimen is shown in figure 20.

The thermal conductivity of this specimen should be dominated by the PMA110

components. The thermal resistances, R = AX/ k-p, of the other components at 250 K are

R (polyimide film)

R(aluminum)

R(adhesive)

R (COMPOSITE

)

0.0004 (m2 *K)/W

8 x 10"7,

0.0009,

1 .36

The computed resistance balance is

R(COMPOSITE) = R(PMA110) + [R(polyimide film) + R(aluminum)

+ 3 x R(adhesive)]

= R( PMA1 1 0 ) + [0.0031]

so that R( COMPOSITE) = R(PMA110).

The thickness of the upper and lower PMA components of the composite

were determined to be 2.3846 and 2.3702 cm respectively using an c ‘

. microscope. Table 25 was computed using the relationship given in eq 'D

k(PMA1 1 0) = thickness (PMA 1 1 0) x k(C0MP0SITE)/thickness(C0MP0SITE'

37
THERMAL

CONDUCTIVITY,

mW/m

Figure 19. Thermal conductivity (mW/(m*K)) as a function of density

(kg/m3) with temperature (K) as a parameter for PMA foams.

38
O

*-> E

o

CO

o

CNJ o

0

1©

>

CO©

.cT3

<

£*-« O

O

(0

CO

CO

O)

in

N-’

E

o

CNJ r—CO

o

0

1 g

u C

o o ©

>

t:o

® >> N *- CO CM

O CO©

o

CO co -5; CM h» x: o

CD c O CO T3 o

CSJ © d CM <***. o

8 T3

1 1 JC.

+->

i o © © O o E *“ 3 3

> *“

*“ O

CO *C0 T— C

< 03 I E o. 5

©

-C <

CO

CO E

•o « _3

< CL 0 <

E

o

O)

oT"o

0

1 |

il

©D

|’>*

wgm&

4m

&$

k$*

»>-<% V.A< |l

if1 Si

fiEssssa

'<*?.*°bi&t ()o-Q'C

’i •2°VoA&fospi

1SSc)asSj^b*i;

:.*JI

39

Figure

20.

Cross

section

schematic

for

the

composite

specimen.
The computed value of k(PMA110) may include (1) a thickness effect not present in

the values for the other PMA specimens if the aluminum-filled adhesive near the

center of the composite specimen does not provide an effective radiation shield,

or (2) if the adhesive is an effective radiation shield, it would have the net

effect of increasing the observed thermal resistance over that for a similar

construction where there is no radiation shield. Figure 21 indicates in a general way that the conductivity determined using a thick specimen, e.g., no radiation shield, would be higher than that for

the values given in table 25 would be higher

experimentally on specimens similar in thickness

the adhesive does serve as an effective radiation shield, however, the values

computed for k(PMA110) in table 25 would be lower than would be experimentally

determined for specimens similar to the other PMA specimens. Pending further

information regarding the emissivity of the aluminum filled adhesive, no estimate

of the shielding effectiveness can be made. In either case the errors introduced

into the data given in table 25 should not exceed about ± 5 % since this is the

approximate value expected for the radiative component. The density of the

PMA110 component of the composite specimen was determined to be 97.5 kg/m3 (6.1

lb/ft3)

a thin specimen. In this case

than if they had been determined

to the other PMA specimens. If

SOFI: The thermal conductivity was experimentally determined for the

foam/aluminum composite. Data are presented for both the composite and for the

foam component. The foam component data were computed using literature values

for the conductivity of aluminum 2219 - T87. The experimentally determined

density of the sprayed polyurethane foam was 37.6 ± 1.4 kg/m3 (2.3 lb/ft3).

The thermal conductivity data shown in figures 11 and 13 exhibit the expected

temperature dependence for an expanded plastic with a fluorocarbon fill gas.

The characteristic curve results when the gas conduction component of the thermal

conductivity changes as the mole fraction of heavy gas decreases due to heavy-gas

condensation. Equations (6) and (7) can be used to relate the following argument

to the observed temperature dependence: (1) At temperatures above about 264 K,

the gas conduction is dominated by the unsaturated fluorocarbon gas. Its

conductivity is approximately one half that of air, which is the other gas

present. (2) Between 264 and 212 K the fluorocarbon has reached saturation

conditions and a vapor-liquid mixture exists in the cells. kg increases as the

mole percent of the fluorocarbon gas decreases. (3) Below 212 K essentially all

of the fluorocarbon has condensed and kg is entirely due to air.

The polynomial fitting procedure used to represent the experimental data for this

specimen is not the optimum for this complicated function of temperature. This

is evident from the deviation plots given in figures 12 and 14: the deviations are about a factor of two greater than those for the PMA specimens. The

inability to accurately represent the experimental data is also evident in

figures 11 and 13. The analytical minimum at 264 K is too high by 2 % and an artificial wiggle at about 140 K causes the analytical value to be too low by

The rapid decrease in conductivity below 110 K, figure 18 and tables 18 and

is also an artifact created by extrapolation of a polynomial.

2 %.

21 ,

40
iJI

Thickness

effect

on

the

measured

thermal

conductivity

of

foams.

(Jones,

1968)
Table 25. Computed thermal conductivity (mW/(m*K)) as a function of

temperature (K) for a polymethacryl imide foam of density

97.5 kg/m3 (6.1 lb/ft3).

T k T k T k

100.0 16.17 154.0 24.61 208.0 29.77

102.0 16.61 156.0 24.82 210.0 29.97

104.0 17.03 158.0 25.04 212.0 30.17

106.0 17.44 160.0 25.25 21 4.0 30.38

108.0 17.84 162.0 25.45 21 6.0 30.59

110.0 18.23 164.0 25.65 218.0 30.80

1 12.0 18.61 166.0 25.85 220.0 31 .02

1 14.0 18.97 168.0 26.04 222.0 31 .24

116.0 19.33 170.0 26.24 224.0 31 .47

118.0 19.68 172.0 26.43 226.0 31 .70

1 20.0 20.02 174.0 26.62 228.0 31 .94

122.0 20.35 176.0 26.80 230.0 32.18

124.0 20.67 178.0 26.99 232.0 32.43

126.0 20.98 180.0 27.17 234.0 32.69

128.0 21 .29 182.0 27.35 236.0 32.95

130.0 21 .58 184.0 27.54 238.0 33.21

132.0 21 .87 186.0 27.72 240.0 33.49

134.0 22.15 188.0 27.90 242.0 33.77

1 36.0 22.43 190.0 28.08 244.0 34.06

1 38.0 22.69 192.0 28.26 246.0 34.36

1 40.0 22.95 194.0 28.45 248.0 34.67

1 42.0 23.21 196.0 28.63 250.0 34.98

1 44.0 23.45 198.0 28.82 252.0 35.30

1 46.0 23.70 200.0 29.00 254.0 35.64

148.0 23.93 202.0 29.19 256.0 35.98

150.0 24.16 204.0 29.38 258.0 36.33

152.0 24.39 206.0 29.58

42
PMA71 - 1 - vac: The low-pressure data in this experimental set were obtained using

the same specimens as were tested earlier at ambient pressures. After

reinstalling the specimens in the apparatus, an ambient pressure data point was taken to assure that no undue specimen changes had occured and that the

reinstallation itself did not introduce significant differences in the measured

conductivity. The result of the new, ambient-pressure data point was

k-p = 33.32 mW/(m*K) at 263.525 K. This is within 1.656 of the previous data and

is within the combined random uncertainty of the two data sets.

As seen in figure 18, the thermal conductivity of the PMA71 - 1 - vac, determined in

a vacuum environment of 0.67 Pa (5 pm of Hg), is significantly lower than that

for the same specimens in an ambient-pressure, dry-nitrogen environment. The

temperature dependence of the conductivity is also different. These observe:

differences are assumed to be due to the change in the thermal contact between

the GHP plates and the specimens. In the nitrogen environment heat is transfere i between the plates and the specimen by solid and gaseous conduction and radiatior.

The vacuum environment reduces the gas conduction component. The temperature

drop across the boundary layer created by cut and damaged cells is shown

schematically in figure 22 and can be computed using eq (10).

AT D ^

. , Boundary = total

AXr

"resin rt resm + MaET3AXB

A vacuum

( 10 )

In order to determine the temperature drop across the boundary layer, •//-., several parameters shown in eq (10) must be known: k res p n , the conductivity of

the resin; the emissivities of the resin and the apparatus plates,

e plate e resin

E = — 3

e plate + e resin e plate e resin

contact areas of the resin, A re3 i n , ancl the vacuum, Avacuum ; and the effec ; thickness of the layer of broken or damaged cells, AXg. A quantitative

evaluation of eq (10) cannot be made without knowledge of the above para'- *. . It is possible, however, to separate the overall boundary resistance from that

the bulk foam since

^observed , vacuum

= ^boundary , cold + r PMA 71 - 1 + ^boundary , hot

Ml)

= r PMA71-1 + 2 r b

Table 26 gives the average boundary resistances computed using this . relationship (approximate since the resistance of the boundary at th*-

would be larger than that at the hot plate).

43
w tO ®O c®E ®o

-O o T3 ® ® ®

CO

a CO 3 CO 3 O

CO JC

Q

CO > 3 >

LU CD LU

X3 "O

a

C

® c

CO CO c iZ c

to to to

0) to

®

tr

O OC <

Figure

22.

Schematic

indicating

operative

modes

of

heat

transfer

when

the

cut

foam

surfaces

are

exposed

to

an

insulating

vacuum.
Table 26. Thermal resistance due to evacuated boundaries, Rg, for PMA71-1.

TEMPERATURE R(gas) R(vacuum) AR Rb 2Rg/R(vacuum)

(K) ( (m2 *K)/W) ( (m2 «K)/W) ( (m2 *K)/W) ( (m2 *K)/W) {%)

150 1 .30 2.73 1 .43 0.72 53

200 1 .03 1 .88 0.85 0.42 45

250 0.81 1.17 0.36 0.18 31

The boundary reisistances are seen to represent a significant portion of the

observed overall resistance and become increasingly dominant as the temperature

decreases

SUMMARY

The thermal conductivity of five thermal insulations was determined in the

approximate temperature range from 100 to 300 K. Three specimens were expanded

polymethacrylimide and another was a sandwich construction utilizing a more dense

polymethacrylimide foam. The fifth specimen was a composite made by spraying

polyurethane foam onto an aluminum substrate. All tests were conducted in a guarded-hot-plate apparatus. The environment for the tests was ambient pressure

nitrogen gas with one exception: one PMA specimen was retested at 0.67 3 a (5 pm of Hg)

The results for the PMA tests indicate density dependences which are nominally

expected for most expanded plastics. The straight-line temperature dependence of

these materials indicates that the unknown cell gas does not condense in th^

temperature range investigated or that its conductivity is near that of air.

contrast, the data for the polyurethane specimen show a temperature dependence

typical for condensation of a heavy gas component in an air/heavy-gas mixture.

The vacuum environment data suggest an unexpectedly strong effect due to the f layer made up of broken cells. Not only is the magnitude of the conduc t i v i t . reduced significantly, but the form of the temperature dependence is 1 1

- affected.

Characterization of the specimens was limited to density. Without kn

parameters such as resin conductivity, species and pressures of gas present : the cells, cell size, shape, and orientation, a quantative determ i na v

:

•

' contribution of the various modes of heat transfer cannot be made.

45
REFERENCES

ASTM. Annual Book of standards. American Society for Testing and Materials,

Philadelphia, PA, Standard C 1 7 7 , Steady-State Thermal Transmission

Properties by Means of the Guarded Hot Plate, Part 18.

Gorring, R. L. and Churchill, S. W. (1961), "Thermal Conductivity of

Heterogeneous Materials," Chem. Eng. Prog., 57, 53~59.

Harding, R. H. (1964), "Heat Transfer Through Low-Density Cellular Materials," I and EC Process Design and Development, 3» 117-125.

Jones, T. T. (1968), "Effect of thickness and temperature on Heat Transfer

through Foamed Polymers", Proceedings of the Seventh Thermal Conductivity

Conference, NBS Spec. Publ. 302, 737“748.

Skochdopole, R.E. (1961), "The Thermal Conductivity of Foamed Plastics," Chem.

Eng. Prog., 57, 55-59.

Smith, D. R., Hust, J. G., and Van Poolen, L. J. (1982), "A Guarded-Hot-Plate

Apparatus for Measuring Effective Thermal Conductivity of Insulations

Between 80 K and 360 K," NBSIR 81-1657, National Bureau of Standards,

Boulder, CO.

Somers, E. V. and Cyphers, J. A. (1951), "Analysis of Errors in Measuring Thermal

Conductivity of Insulating Materials," Rev. Sci. Instrum., 22, 58

—586

Sparks, L. L. and Arvidson, J. M. (1985), "Thermal and Mechanical Properties of

Polyurethane Foams at Cryogenic Temperatures" , J. of Thermal Insulation, 8,

198-232.

Tsederberg, N. V. (1965), Thermal Conductivity of Gases and Liquids , Cambridge,

MA, MIT Press, p. 144.

Tye, R. P. and Spinney, S. C. (1976), "Thermal Conductivity of Concrete:

Measurement Problems and Effect of Moisture," Bull. Int. Froid, Annexe

1976-2, 119-127.

46
NBS-114A irev. 2-80

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See in struction s)

1. PUBLICATION OR

REPORT NO.

NBSIR 88-3086

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

January 1988

4. TITLE AND SUBTITLE

Thermal Conductivity of Selected Foams and Systems from 100 to 300 K

5. AUTHOR(S)

L. L. Sparks, W. P. Dub£, and A. J. Slifka

6. PERFORMING ORGANIZATION (If joint or other than NBS, see in struction s)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No. L85254B

8. Type of Report & Period Covered

Final, May -July 1986

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

NASA Langley Research Center

Hampton, VA 23665

10. SUPPLEMENTARY NOTES

J Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bl iography or literature survey, mention it here)

The apparent thermal conductivity of five insulating materials was determined in the nominal temperature range from 100 to 300 K

(-280 to 80 °F ) . A guarded-hot-plate apparatus was used and the

testing environment was dry nitrogen gas at near ambient pressure. One

specimen was retested in a vacuum environment.

Three of the specimens were neat polymethacrylimide (PMA) foams

with nominal densities of 51 and 71 kg/m3 (3.2 and 4.4 lb/ft3). Other

specimens tested were a polyurethane foam sprayed on an aluminum

substrate and a sandwich construction specimen utilizing PMA foam of

nominal density 110 kg/m3 (6.9 lb/ft3). The results in nitrogen gas

show the expected conductivity increase with increasing density. The

observed conductivity at 0.67 Pa (5 pm of Hg) is significantly lower

than that in amb i ent-pressure nitrogen gas. The large relative

difference may be due to increased thermal resistance at the

plate-specimen boundaries.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key word-, by foam; insulation; low-temperature; polymethacrylimide;

polyurethane; thermal conductivity.

13. AVAILABILITY

[xj Unlimited

| | For Official Distribution. Do Not Release to NTIS

7] Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

|Xj Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGE

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15. Pr

it U.S. GOVERNMENT PRINTING OFFICE: 1988-575-000/85,118 REGION NO. 8