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[List continued on cover page nr]
DEC 3 1957 UNITED STATES DEPARTMENT OF COMMERCE • Sinclair Weeks, Secretary NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Thermal Resistance of Airspaces and Fibrous

Insulations Bounded by Reflective Surfaces

H. E. Robinson, L. A. Cosgrove, and F. J. Powell

Building Materials and Structures Report 151

Issued November 14, 1957

For sale by the Superintendent of Documents, U. S. Government Printing Office, Washington 25, D. C.

Price 20 cents
^

co

to

Contents

Page

1. Introduction 1

. Apparatus and test procedure 1

. Test panels and insulation 3

. Method of presenting results 7

4.1. Definition of symbols 7

4.2. Computation of results ^ 7

5. Results and discussion 8

5.1. Panels insulated only with aluminum-foil membranes 8

a. Effect of moisture condensation 8

b. Effect of air circulation between tandem airspaces through holes in the dividing aluminum-foil membrane 10

c. Effect of nonuniformity of thickness on the thermal resistance of air- spaces 10

d. Effect of minute perforations in a foil membrane forming tandem air- spaces, and some results indicating an effect due to radiation from

the wood framing 11

5.2. Panels insulated with fibrous insulations in combination with reflective surfaces 13

a. Semirigid mineral-wool board insulation without and with reflective surfaces 13

b. Flexible lightweight l)4-in. mineral-wool blanket with aluminum-foil

membrane on warm side—four methods of installation 15

c. Commercial 2-in. mineral-wool blanket, foil-enclosed and kraft-en- closed 16

6. Summary of results 18

7. Appendix _ 20

7.1. Method of calculating airspace conductances 20

a. Radiation coefficient 20

b. Coefficient for combined convection and conduction 21

7.2. Range of experimental conditions at which convection-conduction coeffi- cients were determined 22

ii
Thermal Resistance of Airspaces and Fibrous Insulations Bounded by

Reflective Surfaces

H. E. Robinson, L. A. Cosgrove,1 and F. J. Poweli

Observed insulating values are presented for 28 test panels, of which 23 were insulated with reflective membranes used alone or in combination with fibrous insulations. The

panels were tested at five different orientations corresponding to use as walls, ceilings, or

floors. The observed insulating values of panels are compared with calculated values based on a method and data developed in previous work at the National Bureau of Standards, and

summarized in an appendix to this report. Observed values for panels agreed within 10

percent, in most cases, with calculated values. Departures of observed from calculated values are attributed to such factors as nonuniformity of airspace thickness, moisture con- densation on reflective surfaces, air circulation between tandem airspaces, and effects due

to local high conductance at edges of insulations or radiation from framing members.

1. Introduction

With the publication in 1954 of Housing Research Paper 32, The Thermal Insulating Value of Airspaces,2 based on measurements made at the

National Bureau of Standards, a method and

essential data became available for calculating

the thermal conductance of airspaces of uniform

thickness for various conditions. It was shown

that the total heat-transfer coefficient of an air- space could be separated into two additive coefficients, one a coefficient for heat transfer by

radiation which could be calculated with adequate

accuracy by a relatively simple method, and the

other a coefficient for heat transfer by convection

and conduction combined. Experimental values

for the convection-conduction coefficient for air- spaces of uniform thickness were given as a function of orientation, direction of heat flow, thickness,

temperature difference, and mean temperature.

The method of calculation, and the necessary

data, are summarized in the appendix. These

data were obtained by measurements made on

panels containing one airspace or two tandem

airspaces of uniform thickness and no other

insulating materials. The derived coefficients of

heat transfer by convection and conduction combined represent experimental values for airspaces

of an exemplary or model type, characterized by

smooth, flat, parallel surfaces relatively uniform

in temperature.

The insulating values of airspaces with one or more highly reflective surfaces were found in the

previous work to be of such magnitude that it appeared the insulating effect of installations of

fibrous insulations of blanket, batt, or board form

with adjoining airspaces could be very considerably augmented by making their surfaces highly

reflective, especially for cases of downward heat

1 Aluminum Company of America.

2 U. S. Government Printing Office, Washington 25, D. C. (1954).

flow. However, it was not known how much the

insulating value of an airspace formed in this way

in combination with fibrous insulations might

depart from that of the exemplary type of airspace, as a result of possible changes in the convective

coefficient of the airspace due to nonuniformity of airspace thickness, local variations in the thickness

or conductance of the fibrous insulation, especially near framing members, or other factors. In order to investigate these and similar matters, a research program was undertaken at the National Bureau of Standards with the financial

assistance of Aluminum Company of America,

which also made available for the program the

services of one of the authors.

The major objectives of the program were

(a) to determine the applicability of the data

given in the appendix for calculating the insulating

effect of combinations of reflective and fibrous

insulation, (b) to ascertain experimentally the

insulating values of particular reflective and

fibrous insulation combinations installed in particular ways, and (c) to investigate in some

measure the effects on the insulating value of

airspaces of condensation of moisture on reflective

surfaces, circulation of air between spaces through

holes in the dividing membrane or material, and

of nonuniformity of airspace thickness. The

complete results of the program and discussions

of them are given.

2. Apparatus and Test Procedure

The heat-transfer measurements were made

on test panels in the rotatable guarded hot box

apparatus at the National Bureau of Standards.

The apparatus, designed for panels 5

XA by 8 ft in area, up to 1 ft thick, was mounted on horizontal

trunnions, which allowed the position of the

plane of the panel to be rotated to any angle up

to 90° from the vertical in either direction.

1
SECTION A-A

1, Test panel; 2, rubber gaskets; 3, cold box; 4, guard box; 5, metering

box; 6, refrigerating coil; 7, electric heaters; 8, air-compound thermocouples;

9, surface-compound thermocouples; 10, air-temperature thermocouples;

11, air-circulating fans; 12, baffles; 13, edge insulation; 14, compressionspring handwheels; 15, heater ducts; 16, meter heat diffuser.

The hot box apparatus conformed substantially

to the requirements of ASTM C 236-54T, Method

of Test for Thermal Conductance and Transmittance of Built-Up Sections by Means of the

Guarded Hot Box (Tentative), except for the

additional feature of rotatability on trunnions.

As shown schematically in figure 1 , the apparatus consisted of a cold box (3) and a warm, or guard, box (4), between which the test panel (1) was interposed. The two boxes were held together

by means of long bolts engaging lugs around the

periphery of the joint. The guard box contained

a metering box (5), the open face of which was

pressed against the face of the panel by four

compressing springs (14). The contact between

the metering box and the panel was made substantially airtight by the rubber gasket (2), which bounded the centrally located “metering

area” of the panel, a rectangle 60 in. long and 32

in. wide, through which heat flow was measured

during a test. One-half of the width of the contact

surface of the gasket was within the metering area. The remainder of the panel area constituted a “guard,” through which heat flow was not

measured, but which protected the metering- area against lateral heat flow. Insulation (13) was placed at the edges of the panel to further

reduce lateral heat flow. During measurements, the metering box was

held at the selected temperature by means of

electric heaters (7) controlled by a sensitive

thermistor in the box. The guard-box temperature was automatically made to approximate that

of the metering box by the use of a compound

thermocouple (8) consisting of 10 differential

thermocouples in series, the junctions of each

pair being located opposite each other, 1 in. from the inside and outside surfaces of the meteringbox. The emf from the compound thermocouple

(8) actuated a relay that controlled the heat

input to the guard box as required. The cold

box was held at the desired lower temperature

by means of a refrigerating evaporator coil (6) and a small electric heater (7) controlled by a thermistor in the box. The air in each box was

circulated continuously by fans (11). In the

metering and cold boxes, the circulated air was

constrained by baffles (12) to pass downward

and upward, respectively, along the surface of the panel. The direction of airflow on each side was the same as would result from natural convection at the panel faces. The average air velocity in the metering-box baffle space was

about 40 ft/min, and in the cold-box baffle space was about 90 ft/min. Air temperatures in the

baffle spaces and at other locations in the boxes were measured by means of thermocouples (10), as indicated. These thermocouples, and all others used in these tests, were made with No. 30

AWG copper and constantan wires.

2
All electrical input to the heaters, fan, and other

devices in the metering box was measured by

means of a calibrated watthour meter readable to

1 whr. Under steady temperature conditions,

with the guard-box temperature maintained so that there was no average temperature difference

and thus no heat transfer through the meteringbox walls, all of the heat supplied to the meteringbox was transmitted to the cold box, through the

known metering area (13.33 ft2

) of the panel.

The average rate of beat flow per square foot of

metering area could thus be determined.

To be able to correct for any actual small heat

transfer between the metering box and the sur- rounding guard box, a compound thermocouple (9) was used, consisting of 10 series-connected differ- ential thermocouples with the junctions of each

pair cemented opposite each other in grooves in the surfaces of the metering box. The positions

of the pairs were similar to those of the compound

thermocouple (8) used to control the heat input

to the guard box. It was determined by pre- liminary calibration measurements and by observations during the tests that the heat flow between

the metering and guard boxes was less than 2.8

Btu/lir, or 0.21 (Btu/hr) per square foot of panel

metering area for most tests. Although this was

only a small percentage of the total heat input,

the observed heat input for each test was corrected

for such transfer. The test observations used in computing re- sults were made only after steady temperature

conditions had been attained. The duration of the steady-state test period was in most cases more than 20 hr, and in only two cases less than

14 hr. All thermocouples were read by means of a manually operated potentiometer with which temperature changes of less than 0.05 deg F were

detectable. The steadiness of temperatures for more than 95 percent of the tests was such that

average panel surface temperatures, as indicated

by 10 thermocouples on each face, did not vary more than 0.3 deg F during the test period.

The average conductance of the panel was calculated from the average net heat flow into the panel

per square foot of metering area and the average

temperature difference between the panel faces. Since the metering area included some of the wood

framing around the test airspaces of the panels,

a small adjustment was made to allow for the effect

of the heat conduction through the wood framing.

The adjusted conductance thus obtained repre- sented the average experimental thermal conductance, C, of the panel space including all installed

insulation. In most tests, thermocouples were

placed on the dividing membrane, or on the warm

and cold surfaces of fibrous insulating blankets,

for measurement of surface temperatures with

which the conductance of tandem components

could be determined.

3. Test Panels and Insulation

The thermal conductances (and resistances) of

28 different test panels were determined by usingthree test-panel frames, A, B, and C in figure 2. The panel frames were symmetrical about both

center lines. Frames A and C were constructed

from nominal 2- by 4-in. and 2- by 8-in. clear fir, respectively. Frame B was formed from A yb

the addition of the center stud.

The metering area was the 32- by 60-in. rec- tangle centered on the panel. This included half

of the wood bounding the test space and the center

stud, which totaled about 5, 9, and 12 percent

of the test area for panels A, B, and C, respectively.

The remainder of the panel constituted a guard

area, which was insulated in a manner similar to the test area in all possible respects.

The faces of the panels were made of 19 or 21

gage galvanized sheet steel, painted on both

surfaces with flat white paint having an estimated

average emittance of 0.90. On both faces of the

panels, the sheet covering the metering area was

separated by a /(-in. gap from the sheets over the

guard airspaces to reduce lateral heat conduction

into or out of the metering area. To seal the

airspaces, the face sheets were screwed to the

frames over %6-in. felt strips glued to the wood.

The temperatures of the sheet-metal faces were measured with thermocouples soldered to the

outer surface of the sheet covering the metering- area at 10 positions on eanh face, located as shown

in F of figure 2. The thermocouple leads were cemented to the face of the sheet until they

reached a takeoff point at midlength of the sheet. Both surfaces of each sheet were painted white

after the thermocouples were attached.

Table 1 and figures 2 and 3 give particulars as to the dimensions, configurations, etc., of the panels

and insulations tested. The positioning of membrane or blanket forms of insulation and the

resultant airspaces are indicated by the sections

A-A shovel in figure 3. The details of attaching

the various insulations to the wood framing are shown schematically in the circles of figure 3, referred to in table 1. The temperatures of the

membrane or blanket surfaces were measured with

thermocouples attached, in most cases with

aluminum-foil tape, in accordance with one of the

five major schemes shown as D, E, F, G, and H

of figure 2. In some cases, additional temperatures on the horizontal center line of the metering- area were measured with thermocouples placed on

the foil membrane or blanket surfaces, as shown in sections I and K, and in circles W, X, and Y of figure 3. The total emittances of the surfaces bounding

the airspaces were determined, when feasible, by

separate measurements made on samples of the

materials, most of which were taken from the

panels after completion of the test.

3
PANEL A

3

3/8

- I N . THICK

TEST PANEL FRAMES

PANEL B

3

3/8

- IN. THICK PANEL C

7 '/2

- I N . THICK INSULATION THERMOCOUPLE ARRANGEMENTS

t

LEGEND

+ COUPLES LOCATED ON WARM

SURFACE OF INSULATION O COUPLES LOCATED ON COLD

SURFACE OF INSULATION © COUPLES LOCATED ON WARM

AND COLD SURFACES OF INSULATION

Figure 2. Test-panel frames and insulation thermocouple arrangements.
Table 1. Particulars of test panels

Panel

Test-panel

frame,

Insulation

cross sec- tion A-A,Installation

details,

Insulation thermocouple arrangement NotesRadiation interchange

factor ( E) of airspaces Number of panel orien- tations Number

of tests figure 2 figure 3 figure 3 Figure 2 Figure 3 Warm Cold

tested

A. Aluminum foil (0.001 in.) installed as a midspaee membrane

1 A I S D I 0. 03 0. 03 4 2 A I S D I a .03 .03 3 3_._- A I s I) I b .03 .03 4 10 B K T K .03 .03 5 12 B K u IC c .03 .03 5

15 __ B IC U IC d .03 .03 5

16 C I s e, f .06 .06 5

21 C I s f .03 .03 5 29 C I s F V .03 .03 3

B. Mineral-wool blanket (thickness, IK in.; density, 0.6 lb/ft 3

) faced on warm surface with aluminum foil

4 B M V E g

g, h

0.03 0. 82 4

5 B .1 E .82 3

6 B J E g, h, i g

g, j

.82 1 7 B L E .03 5 8 _ B N F S .03 .82 5

C. Mineral-wool blanket (nominal thickness, 2 in.; density, 1.6 lb/ft 3

) aluminum-foil enclosed 1 (see note k)

9 C o G 0.03 5 6

ii C p w H Z 1 0. 09 .03 5

13 c p w H Z 1 , m .82 .03 3 3

14 c p w H z 1 , n .82 .82 3 3 22 c p w F w .09 .03 1 1

23 c p w F w 0 .09 .03 5 6

24 c Q

p X F X .09 .03 5 5 25 c Y F Y p, q .09 .03 5 5 26 c p Y F Y q .09 .03 3 3 27 c p Y F Y q, r .09 .20 3 3

D. Mineral-wool blanket (nominal thickness, 2 in.; density, 1.5 lb/ft 3

) kraft-paper enclosed (see note k)

28 c p W F 1 0. 82 0.86 5 5

E. Mineral-wool insulation board (thickness, IK in.; density, 9 lb/ft 3

) experimentally faced with aluminum foil in tests 19 and 20

17 c R F 0. 82 0. 82 5 6

18 c R F s .82 .82 5 5 19 c R S F j, t .03 .82 5 6

20 c R s F j, U .03 .03 5 7

Notes

a. Panel 2 was panel 1, sun-dried to remove accumulated moisture.

b. Six holes, 0.58 in. sq, cut at points indicated by squares in D of figure 2. c. Dimension A of circle U in figure 3 equal to K in.

d. Dimension A of circle U in figure 3 equal to 1 in.

e. 0.001-in. aluminum foil perforated with 64 holes per square inch.

f. No thermocouples on foil or in panel spaces in these tests.

g. Center stud in top and bottom guard sections (see B of fig. 2) removed in these tests. h. Like detail of circle V in figure 3, except foil stretched tautly against warm surface plate.

i. Foil surface painted with gray paint of 0.9 emittance.

j. Foil on surface of fibrous Insulation attached to stud in manner shown in circle S in figure 3. k. Breather membrane not sealed to wood framing at top and bottom, except in panels 24 and 26, in which the ends were sealed to framing with aluminumfoil tape.

l. Thermocouples shown in circle W in figure 3 not used in these panels. m. Foil on warm surface painted with gray paint of 0.9 emittance.

n. Foil on both surfaces painted with gray paint of 0.9 emittance.

o. Same as panel 22, but thermocouples shown in circle W in figure 3 reattached.

p. Foil breather membrane with foil removed from areas between arrows in circle Y in figure 3. q. Thermocouples attached to inside of breather membrane with cellophane tape.

r. Foil breather replaced with paper breather of 0.20 emittance on cold side.

s. Both surfaces of insulating board painted with flat white paint of 0.9 emittance.

t. Aluminum foil cemented to the warm surface of the painted board of panel 18. u. Aluminum foil cemented to the cold surface of the painted board of panel 19. v. Kraft-foil laminate perforated with 64 holes per square inch.

1 Vapor barrier membrane of foil laminated to kraft with asphalt; breather membrane of kraft-foil laminate perforated with 64 holes per square inch. Foil

surfaces were outermost.

5
SECTIONS A-A

INSTALLATION DETAILS

LEGEND

NON - REFLECTIVE SURFACE

' "linn REFLECTIVE SURFACE (ONE SIDE)

M II I I II I REFLECTIVE SURFACE (BOTH SIDES)

a THERMOCOUPLE ON MEMBRANE SURFACE

(FOIL COVERED FOR REFLECTIVE SURFACES)

Figure 3. Details of specimens and installations.

6 -i
4. Method of Presenting Results

The results of this investigation are presented

in terms of thermal resistance (the reciprocal of thermal 'conductance), the unit of which is deg F

per (Btu/hr ft2). Resistances, rather than conductances, are used because they are additive for tandem components, and thus comparisons of re- sistances indicate directly the relative insulating

effects of various components. Further, resist- ances are the quantities actually used in most

computations of the insulating effect of constructions. The experimentally determined thermal resist- ances ( R) of the test panels and component air- spaces and other insulations are listed in tables 2

to 8. Included in the tables are calculated re- sistances (R') for the temperature conditions that

existed experimentally, based on the method and

data given in the appendix. The experimental

and calculated values of resistance are conveniently

compared by taking their ratio R/R'

.

The differ- ences between the observed and calculated resist- ances can be obtained from the tabulated values.

For panels containing thick fibrous blankets in addition to airspaces, the temperature differences across the airspaces were often small (10 deg F or

less). Small errors in the measured surface

temperatures could lead to a quite large percentage

error in the temperature difference and therefore

in the experimental airspace resistance.

The observed temperatures and temperature

drops of the tandem components of a test panel can be deduced from the observed resistances and

the tabulated values of panel mean temperature

and temperature difference for each test.

4.1. Definition of Symbols

a =fraction of area of a perforated membrane

represented by apertures.

0= experimentally determined thermal con- ductance; the time rate of heat, flow

through a unit area of a panel or panel

component (adjusted to exclude the ef- fects of wood framing) from one of its surfaces to the other per unit temperature difference between the two surfaces.

Conductances are expressed herein in Btu/hr ft 2 (deg F).

G' =calculated thermal conductance; calculated on the basis of the method and data given

in the appendix.

Ct =over-all panel thermal conductance; the

value determined from the test data,

including the effects of wood framing.

e =surface hemispherical total emittance; the

ratio of the total radiant flux density

emitted by a surface as a consequence of

its temperature to that emitted by a

bla k body at the same temperature.

i?== radiation interchange factor of an airspace;

the combined effect of the surface emittances, e, of the boundary surfaces of an

airspace, calculated in accordance with

eq (3) of the appendix.

hc =convection-conduction coefficient; one component of the calculated thermal conductance, O'. Ar =linear radiation coefficient; a factor in one component of the calculated thermal con- ductance, C'.

1 =the thickness of an airspace, inches.

/£ =observed thermal resistance; the reciprocal

of the experimental thermal conductance,

C. Resistances are expressed herein in deg F per (Btu/hr ft 2 ). R' =calculated thermal resistance ; t he reciprocal

of the calculated thermal conductance,

O'. R/R' =the ratio of the experimental and calculated

resistances of the test panel or any of its components.

0= the temperature difference between the

surfaces of a panel or any of its component elements, deg F.

4.2. Computation of Results

An illustration of the method of computation of

the experimental resistance ( R) and of the cal- lated value ( R') is given below.

For computational reasons, this illustration is worked out in terms of thermal conductances, the

final results being converted to resistances as shown. The following pertinent experimental

data were obtained in test- 117 (table 7):

a. Average temperature of the warm surface

plate = 79.5° F.

b. Average temperature of the warm insulation

surface— 63.8° F.

c. Average temperature of the cold insulation

surface = 13.1° F.

d. Average temperature of the cold surface

plate=— 3.5° F.

e. Average power input to metering box =

30.30 w.

f. Heat transfer from metering box to guard

box, based on average emf of compound differ- ential thermocouple = 0.79 w. The adjusted power input (29.51 w), converted

to the desired units by the factor 0.2513, was

divided by the temperature difference between the

panel faces to yield the over-all thermal conduct- ance ( Gt ) of the panel:

Ct =-7Q 5 _(_3 ^=0.0893 Btu/hr ft- (deg F).

This value includes the effect of heat flow in the

wood framing within the metering area according

to the equation

444414°—57 2 7
Ct =Cwood X

area of wood

total area FtfX

area of space

total area

’

where C is the panel conductance adjusted to remove the effects of the wood framing. In this panel, Croud X (area of wood/total area) equaled

0.0156 and (area of spac.e/total area) equaled 0.883,

thus:

,, 0.0893-0.0156

0.883 =0.0835 Btu/hr ft2 (deg F)’

R—l 1.98 deg F per (Btu/hr ft2 ). The resistances (JR) of components of the

panel were computed by means of the relation

^component. /h panel =Component/Canel > V here 6 IS the

observed temperature drop across the component

or panel. For this test, the resistances of the warm

and cold airspaces and the fibrous blanket were

2.27, 2.39, and 7.32, respectively.

The calculated values (R') for the panel and

components were computed using the method and

data given in the appendix and the pertinent

observed data from test 117, as follows:

a. Direction of heat flow—horizontal.

b. Thicknesses of the airspaces—warm, 2 in.; cold, 3/( in.

c. Values of E for the airspaces—warm, 0.09;

cold, 0.03.

d. Temperature differences across the air- spaces—warm, 15.7 deg F; cold, 16.6 deg F.

e. Mean temperatures of the airspaces—warm,

71.7° F; cold, 4.8° F.

f. Experimental resistance of fibrous blanket=

7.32. The value of 61 3 was 126 for the warm space and

712 for the cold space, for which figure 6 yielded

(after division of (hcl) b0 by /) values of 0.288 and

0.289 for (hc) 5o for the warm and cold airspaces,

respectively. These values, adjusted for departure

from 50° F mean temperature (using eq (4a),

appendix), became 0.282 and 0.302, respectively.

The radiation coefficients, Ehr , were 0.093 and

0.021 (using fig. 5) for the warm and cold airspaces,

respectively. Thus the thermal conductances were

calculated to be, for the warm airspace,

calculation was the experimentally determined

value, in this case 7.32. The calculated resistance

of the panel in test 117 was thus

/?' =2.67 +7.32 +3.1 0 = 13.09.

The experimental values (R) are compared with

the calculated values (R') by means of the ratio

R/R'which for this test had values of 0.92, 0.85,

and 0.77 for the panel and the warm and cold air- spaces respectively.

5. Results and Discussion

Because of the diversity of materials investigated and of factors affecting the heat transfer,

the experimental results are discussed in several

sections in two main divisions: (5.1) panels in- sulated only with aluminum-foil membranes and

(5.2) panels insulated with fibrous insulations in combination with reflective surfaces.

In each of these sections, airspaces are considered that differed in some respects from airspaces

of the exemplary, or model, type, on which the

data given in the appendix were based. Except

for these variables, the construction of the panel

and the conditions existing during the measure- ments were substantially the same as those used

in establishing the data on which the calculated

resistances are based. Consequently, the differ- ences between the measured and calculated values

are in reality the differences between the measured

results in two separate experiments, and these

differences are the experimentally determined

effects of the variable factors, within the precision

of the measurements. In each section, when the

observed and calculated results differed significantly, a discussion of the differences is presented.

5.1. Panels Insulated Only With AluminumFoil Membranes

The data in table 2 are for 3%-in. panels with

two tandem airspaces separated by an aluminumfoil membrane at midspace.

C" =0.282 +0.093 =0.375, a. Effect of Moisture Condensation

R' =2.67,

and for the cold airspace,

C' =0.302 +0.021 =0.323,

7?' =3.10. The thermal resistance of a panel space containing a fibrous blanket with tandem adjacent warm

and cold airspaces (as in test 117) is the sum of the

thermal resistances of the component parts. The

thermal resistance of the blanket used in each

The results given in part A of table 2 were obtained with panels 1 and 2, each of which had a continuous membrane (without holes or perforations) at midspace. Although the observed panel

resistance values ranged from about 3.5 to about

12, depending on the orientation and direction of heat flow, the values of R/R' for the panels ranged

only from 0.86 to 0.98. For the cold airspace, the

R/R' values were substantially constant and equal

to about 1.03. However, for the warm airspace,

the value of R/R' varied with the orientation of the panel, ranging from about 0.87 when the panel was vertical and the heat flow was horizontal,

8
Table 2. Thermal resistance of two tandem airspaces formed by an aluminum-foil membrane at midspace of a 3

3/s-in. panel

Resistances are expressed in deg F per (Btu/hr ft 2

)

Panel Warm airspace® Cold airspace Test Direction of heat

flow Mean

temperature

Temperature dif- ference R R' R/R' R R' R/R' R R' R/R'

A. Panels 1 and 2, without holes in membrane.

5 Down... .

o p

34.7

deg F

77.5 11.8 13.4 0. 88 4. 63 6.69 0.69 7. 17 6. 74 1.06

10-- . _ do _ 34.4 77. 1 11. 5 13. 3 .86 4. 55 6.58 . 69 6. 95 6. 75 1. 03

4 45° down.. 33.6 60. 1 6. 30 7.09 .89 2. 87 3.68 .78 3.43 3.41 1.01

6 . _do 34. 5 69. 6 6. 04 6. 74 .90 2. 69 3. 52 3. 35 3. 22 1. 04

i Horizontal . _ _ 34.6 56.5 5. 00 5. 25 .95 2. 35 2.69 .87 2.65 2. 56 1.04

7 34. 6 66.9 4. 73 4. 96 .95 2. 23 2. 54 .88 2. 50 2. 42 1.03

8 do 34.7 67.4 4. 68 4. 99 .94 2. 20 2. 57 .86 2. 48 2. 42 1.02

2 45° up... . .. 34. 6 55.7 4.35 4.46 .98 2. 10 2. 27 .92 2. 25 2. 19 1.03

9 _ Up 34.4 64.4 3.43 3. 73 .92 1.59 1.92 .83 1.84 1.81 1.02

B. Panel 3, with holes in membrane to allow air circulation between spaces b

14 Down 34.4 79.0 13.6 13.4 1.01 6. 40 6. 60 0. 97 7. 19 6. 83 1.05

11 Horizontal .... .. 34.5 65.5 3.99 4. 95 .81 1.97 2.53 .78 2. 02 2. 42 .84

13 45° up--_ 34.8 65. 1 3. 68 4. 26 . 86 1. 82 2. 15 .85 1. 86 2. 11 .88

12 Up 34.5 65.0 3.59 3.73 .96 1.87 1.87 1.00 1.72 1.86 .92

“ For part A, condensed moisture was observed on the membrane on the cold side of this airspace,

t The holes approximated 0.4-in. 2/ft width of panel, and were spaced 56.5 in. apart longitudinally.

to 0.69 and 0.83 when the panel was horizontal

and the heat flow was down and up, respectively.

The differences between the measured and cal- culated values of resistance of the panel were entirely due to the differences between the values

for the warm airspace. No significant part of

these differences can be attributed to uncertainty

in the calculated coefficient for combined convection and conduction. There is good evidence that

they were due to impairment of the thermal re- flectance of the foil surface on the cold side of the

warm airspace, as a result of moisture condensation. At the end of the tests of panels 1 and 2, examination showed that water vapor had con- densed and caused visible staining of this foil sur- face near the bottom of the metering section, over about 10 percent of the test area, and moisture was observed on this area when the panels were

opened. The other surface of the foil was everywhere unstained.

There is evidence that a film of water a few

thousandths of an inch thick has an emittance, at ordinary temperatures, of 0.9 or greater. On the

basis that condensation of moisture on the membrane increased locally the absorption of heat radiated across the warm airspace, it is calculated

that the wetting of 4 to 14 percent of the foil area would account for the decrease of the experimental

warm-airspace resistance from the calculated values. The observed stained area of the foil was

about 10 percent, in fair agreement with the above

estimates.

There is reason to believe that the distribution

of condensation on the foil changed with orientation. In the vertical position, the foil was cooler near the bottom, for the same average temperature, than it was in the horizontal positions with

upward or downward heat flow, chiefly because of

the behavior of the convection air currents, and

thus condensation would be more likely, and more

concentrated, in this orientation. For a horizontal

airspace with downward heat flow, moisture on a

cool reflective surface would tend to be widely dis- tributed because of local heating of wetted areas due to their increased absorptance for radiant

energy.

Since the warm faces of the panels were nearly

perfect vapor barriers, the moisture on the foil in these tests must have come chiefly from the wood

framing. The wood was in approximate moisture

equilibrium with the laboratory atmosphere (average relative humidity about 50 percent) when the

panels were closed, and within a few hours the

panel was subjected to air temperatures of about

75° F on the warm side and —3° F on the cold side. Normally, there would be a period of many weeks

during which the framing in an actual building

could dry slowly before the membrane reached a low temperature at which condensation might

occur. Of equal or greater importance in this connection is the fact that in an actual building, unless

the construction on the warm side of the airspace were practically impervious to the passage of vapor,

the vapor pressure inside the building would cause permeation of vapor into the space and continuing

condensation on the foil when its temperature was

below the dewpoint in the building. The possibility of loss of some of the insulating value of an

airspace with a reflective surface on its cold side

warrants careful analysis (e. g., by the method

given by Woolley 3

) of the temperatures of the

3 H. W. Woolley, Moisture condensation in building walls, NBS Building

Materials and Structures Report BMS63 (1940).

9
reflective surface under the conditions of use, unless condensation is prevented by the use in such

a position of a reflective membrane of low vapor

resistance as compared to that of the construction on the warm side of the membrane.

The stains made by condensation on the foil in a period of about 2 weeks were easily visible, but

the emittances of the stained areas after drying were found by measurement to be the same as those of unstained areas of the foil (0.03).

b. Effect of Air Circulation Between Tandem Airspaces

Through Holes in the Dividing Aluminum- Foil Membrane

Part B of table 2 gives data for a panel (No. 3)

in which the effect of air circulation through holes

in a midspace aluminum-foil membrane was investigated. The membrane was perforated at each

end by a set of three holes, each 0.58 in. square as shown in D of figure 2. The distance between

centers of the two sets of holes was 56.5 in. Each

set of holes had a total area of 1 in. 2

, thus approximating an average aperture of 0.4-in. 2 /ft width of

panel.

When the panel was horizontal and heat flow was upward or downward, the R/R' ratios showed

good agreement between experimental and calculated resistances for the panel, and for each of the

airspaces. However, when there was a difference

of elevation of the two sets of holes, as was the

case when heat flow was either horizontal or 45°

upward, the panel and airspace R/R' ratios were

decreased by roughly 15 percent as a result of air circulation through the holes.

It appears from these results that the effect of

air circulation through small holes at the ends of a membrane dividing horizontal airspaces was

negligible for downward heatflow, and probably

small for upward heatflow. However, when the

holes had a considerable difference in elevation,

there was a reduction of thermal resistance of the

airspaces, ranging from 12 to 1 8 percent for the test conditions (approximately 32 deg F temperature

difference across each air space) . These results apply, of course, only for air circulation induced solely

by the thermal conditions in the interconnected air- spaces, and not for air movements induced by

external-pressure differences.

c. Effect of Nonuniformity of Thickness on the Thermal

Resistance of Airspaces

Table 3 gives results obtained in investigating

the effect of nonuniformity of thickness of an air- space on its thermal resistance. The data were

obtained with a 3%-in. panel having an aluminumfoil membrane installed between framing members

in a plane oblique to the plane of the panel,

dividing the panel airspace into two tandem

wedge-shaped spaces. The details of the three

installations tested are shown in figure 3 (see

section K, and circles T and U). The three

shapes of the wedge-shaped spaces are indicated

Table 3. Thermal resistance of tandem wedge-shaped air- spaces formed in a 8%-in. panel by an obliquely installed aluminum-foil membrane a

Resistances are expressed in deg F per (Bt.u/hr ft 2

)

Panel

Test Direction of beat flow Mean

temperature

Temperature dif- ference R *>R’ R/R'

A. Panel 10 (details K and T of fig. 3), A= ]A 6 in.

4fi Down .

° F

34.1 deg F74.7. 11 13.6 0. 52

45 45° down.. _ _ . . 33.8 68.5 4. 64 6. 76 .69

42 Horizontal 34.8 65. 4 3. 76 5.02 .75

43 45° up. . .. ... 35.0 64.7 3. 29 4. 28 .77 44 Up 34.8 62.2 2. 92 3. 76 .78

B. Panel 12 (details K and U of fig. 3), A=Yi in.

59 Dow-n .. .. 34.6 76.1 8. 72 13. 5 0. 65

58 45° down __ ... 34. 5 69.3 5. 19 6. 72 .77

55 Horizontal 35.2 67. 4 4. 22 4.97 .85 56... 35.2 66. 1 3. 65 4. 24 . 86

57 Up 34.9 63.3 3. 18 3. 74 .85

C. Panel 15 (details Iv and U of fig. 3), A—l in.

71 Down.. 34. 5 76. 6 10. 2 13. 5 0 76 70 45° down _ _ _ __ 34. 0 69.0 5. 50 6.72 .82 69 Horizontal . . . - 34.3 67. 5 4.31 4. 97 .87

67 45° up _ ... 51. 4 67.0 3. 74 4. 27 .88 68 Up 54.7 59.8 3. 34 3. 84 .87

a For each panel, the thickness of each wedge-shaped space is given at its narrow edge by A, and at its thick edge by (.ifi—A).

b The resistance R' is given for two tandem airspaces, each of uniform

l'Mo-in. thickness, and with E«,=i?r =0.03.

bv the thickness of each space at its narrowest

edge (A) , and that at its thickest edge (3% —A)

near the opposite longitudinal framing member.

The distance between the framing members was

14% in. The values of R' in table 3 were based on two tandem airspaces of uniform l^r-in.

thickness, assuming EW =EC =0.03. The results in talde 3 show by the RIR' ratios

that the resistance of the panel decreased as the

dimension A decreased (i. e., as the nonuniformity

of airspace thickness increased) for all directions

of heatflow. This is also shown in figure 4, in which the average observed thermal resistance

per space is plotted versus the space thicknesses at the narrow and thick edges. The points plotted

at an edge thickness equal to 1 % in. give the

value of R' for a space of uniform thickness equal

to half that of the panel space. Figure 4 shows further that the effect of nonuniformity of thickness increased, in both absolute

and relative reductions of resistance, as the thermal resistance, R', for a uniform airspace in- creased in accordance with orientation and direction of heatflow. The wedge shape of these

spaces caused a lateral temperature gradient in the

foil membrane, which promoted greater convection in each airspace than would have existed in a uniform airspace with little lateral temperature

gradient in the foil. Since the thermal resistance

of an airspace with highly reflective surfaces

chiefly depends on the convective activity in the '

10
THICKNESS OF AIRSPACE AT THICK EDGE ,in. 3 3/8 3 2 1/2 2 I 1/2

Future 4. Average thermal resistance of a wedge-shaped

airspace 14% in. wide, versus thicknesses at edges, for five directions of heat flow.

•, observed; O, calculated for a space of uniform UJ/lo-in. thickness with E,„=E'= 0,03.

space, those spaces in which convection is normally

small (i. e., those of high resistance, such as horizontal spaces with heatflow downward) are most

affected by the augmentation of convection due to nonuniform temperatures at a boundary of the

airspace.

It is evident that uniformity of airspace thick- ness and surface temperatures is of major importance in realizing maximal thermal resistance

for horizontal airspaces with heatflow downward,

but is of much less importance for the same application with heatflow upward, or for other orientations.

d. Effect of Minute Perforations in a Foil Membrane

Forming Tandem Airspaces, and Some Results Indicating An Effect Due to Radiation From the Wood

Framing

The results in table 4 are for two tandem 3.8-in. airspaces formed in a 7%-in. panel by means of a membrane at midspace of the panel.

For part A, the membrane was a specially

prepared 0.001-in. aluminum foil perforated with

64 minute holes per square inch. The objective was to determine the effect of the perforations.

With a perforated highly reflective membrane

at midspace, there is, in addition to the heat

transfer across each airspace with an imperforated

membrane, a further heat transfer due to radiation

from the warm face of the panel through the apertures to the cold face. In effect, this is a transfer

of heat between the highly emissive panel faces in

parallel with the normal transfer calculated by the

procedure given in the appendix, because the radiant energy entering an aperture in the membrane

is almost wholly absorbed by the cold-side face of

the panel beyond, due to its high absorptance and

the high reflectance of the foil membrane on the

warm side of the cold airspace. The fraction of

the incident radiant energy that passes through

the apertures and is absorbed by the cold face of

the panel is therefore approximately equal to a, the fraction of the membrane area represented by

the apertures, if a is small. The correspondingheat transfer, per square foot of panel area, is equal to 6 ( ahr ), where 9 is the temperature differ- ence from face to face of the panel, and h T is the

linear coefficient for radiation (see eq (2), appendix) at the mean of the temperatures of the

panel faces. The total calculated heat transfer per square

foot of panel (q') is closely the sum of the above

quantity and that calculated by using the method

given in the appendix, or —9 (ahr) -(-

where R' is the average of the individual calculated thermal resistances of the two airspaces.

The experimental panel resistance, R, is computed as 9/q, where q

is the observed heatflow rate per square foot of panel. Conforming to this, the

calculated panel resistance, R'v , is given, with the

aid of the equation above, by

T>! Tl „ —

0 2ir 2

q' 1T2R'ahr l/R'-\-2ahr The denominator of the last fraction is equivalent to C

r -\-2ahT), or approximately, using eq (1) of the appendix, to hc J

r (E-\-2a)hr , where hc and hT are average values for the two airspaces. Thus,

in effect, the perforations increase the ordinary

radiation interchange factor, E, for each airspace

(see eq (3), appendix) by an amount approximately equal to 2a, for the case of tandem air- spaces made reflective by an intermediate per- forated highly reflective membrane.

The perforations in the foil membrane of part

A were made in effect with a punch against a resilient backing. Microscopic examination showed

that indentations were formed, about 0.025 in. sq at the top, tapering to ruptures or tears at the

bottom, yielding apertures of irregular shape.

Measurements on perforations indicated that the area of the apertures, viewed perpendicular to the

membrane, ranged from about 24 to 56 percent

of the indented area. Assuming an average value

of 40 percent, it was estimated that the area of

apertures in the membrane was approximately

1.6 percent of the membrane area. For the membrane of part A, E was taken as equal to the value ascertained for bright foil (0.03),

If
Table 4. Thermal resistance of a 7%-in. -panel with a perforated or non perforated membrane in midspace

Resistances arc expressed in deg F per (Btu/hr ft 2

)

Pane] Warm airspace Cold airspace Test Direction of heat flow Mean

temperature

Temperature dif- ference

Ii RR/R’ R R’ R/R' R R’ R/R'

A. Panel 16, perforated foil membrane (EW =EC =0.062 virtual)

74 Down.. _ _ _ _

° F

35.0

deg F

82. 2 15. 0 15. 5 0. 97

73 45° down... ... . ... 35. 1 70. 7 6. 10 6. 26 .97 72 Horizontal.. 34.4 67.3 4. 65 4. 89 .95

75 45° up . ... . .. 34.6 66.8 4.01 4. 18 .96 76 Up 34.2 65. 2 3. 61 3.90 .93

7. 34

3. 12

2. 45

2. 10 1.96

8. 11

3. 14

2. 44

2. 08 1.94

B. Panel 21, nonperforated foil membrane {Ew =Ec =0M)

103 Down.. . . ... .. . 104 45° down .. 105 Horizontal... ... _ _ __ 106 45° up _ . _ 107 Up34.8

35. 2

35. 5 36.0

35.7

82.4

71.2

68.7 67.3

66. 2

14.9

5.91

4. 62

3. 94 3.59

19.4

6. 84

5. 21 4.42

4. 10

0. 77 .86

.89

.89

.88

9. 43

3. 44

2. 63

2. 23

2. 07

10.0

3. 40

2. 58

2. 19

2. 03

C. Panel 21, nonperforated foil membrane (EW =EC =0.03)

109 Down... _ _ __ _ 110 . 45° down. . 111 Horizontal

112 45° up

113 Up

66.4 133. 2

66. 2 117. 7 64.3 109. 2 63.6 106. 2 63.4 103. 2

9. 64 17.7

4. 48 5.98

3. 80 4. 67 3.40 3. 96

3. 08 3.71

0. 54

. 75

.81 .86

.83

8. 82

3. 03

2. 37

2. 01 1.89

8.83

2. 95

2. 30

1.95 1.82

D. Panel 29, perforated foil-luaft paper laminate a (E w =Ec — 0.03)

151 Down.. ... 49. 2 102.3 14.4 18.3 0. 79 6. 21 9. 21 0. 67 8. 20 9. 12 0. 90

152 Horiz.ontaI _ _ .. 50.4 84.9 4. 50 5. 04 .89 2. 24 2.57 .87 2. 26 2.47 .91 153 Up — 46.3 75. 8 3. 70 3. 96 .93 1. 74 2. 03 .86 1.96 1.93 1.02 154b __ Horizontal. _ ... 49.6 86. 4 4. 55 4. 97 .92 2. 51 2. 46

“ Kraft-paper side faced warm airspace, and foil side faced cold airspace. Warm side of warm airspace was surfaced with aluminum foil.

<> Duplicate of test 152; no thermocouples on membrane.

and a was approximately 0.016; thus, the virtual

radiation interchange factor for each of the air- spaces was about 0.062. The values of R' in

part A, for each space and for the panel, were

calculated by using this value of the factor. Measurements of the emittance of the perforated

foil membrane were also made with a radiometer.

For similar imperforated foil, an emittance of 0.028 was obtained; for the perforated foil, the emittance was 0.034 when it was applied to a convex tar- nished brass surface, and 0.040 when the brass was painted to have a measured emittance of 0.94. For the last observation, the measured emittance

(0.040) should be equal to 0.028 (1— a)+0.94a,

whence a is calculated as equal to 0.013. This is consistent with the estimate obtained from the

microscopic examination.

The values of R/R' for the panel in part A approximate 0.96. Since the membrane temperature was not measured in these tests, values of R

for each space could not be determined. The re- duction in panel resistance due to the increase of Ew and Ec for panel 16 from a value of 0.03 to a value of 0.062 as a result of radiation through the

membrane perforations is indicated by comparison

of corresponding values of R' for panels 16 and 21. Air circulation through the perforations of the

membrane appears to have had little effect on re- sistance, even though the perforated area totaled

about 27 in. 2 in the 1,678 in. 2 of membrane in the

test areas of the panel. If it occurred, its effect would be greatest when the panel was vertical

(test 72) and least when the panel was horizontal

and heat flow was downward (test 74), as shown

by the results in part B of table 2. The corre- sponding R/R' ratios for the panel were 0.95 and

0.97, respectively, indicating that there was substantially no air circulation effect, within the

precision of the results. The tests in part B of table 4 were made with an

unperforated foil membrane in the same panel

frame for comparison with the perforated membrane. The values of R for the panel in part B

agreed with the corresponding values in part A

within about 1 percent. Because there were no

perforations in the membrane of part B, and be- cause the test temperatures were so closely

matched as to obviate differences in convection

from that cause, the close agreement of the results

of parts A and B suggested that some additional

heat transfer occurred in the tests of part B.

Upon analysis, it was found that the values of R' for the panel in part B would agree substantially with the observed values of R for all the

directions of heat flow, if Ew had values between

0.13 and 0.17, instead of 0.03, as assumed in cal- culating the values of R' in part B. When new

values of R' for part B were calculated on the '

12
assumption that Ew =0.15 and Ec =0.03, the values

of the ratio R/R' in part B became, in order, 1 .04, 1.00, 1.00, 0.99, 0.97. The fact that this one assumption holds reasonably well for all five di- rections of heatflow makes it appear that the

reflectance of the foil on the cold side of the warm

airspace was reduced by condensation (as in the

tests of part A of table 2). The tests in part C of table 4 were made with

the same panel and membrane as those of part B,

but with considerably increased warm-side temperatures and panel temperature differences. The

values of observed panel resistance were decreased more than would be expected for the greater

temperature differences and mean temperatures,

especially for the case of downward heat flow when

the panel was horizontal. Analysis of the results

of part C along the lines used for part B indicates

inferred values of Ew between 0.2 and 0.3 for all of the tests except that for downward heat flow. In the latter case, the inferred value of Ew is about

0.8, corresponding to a reduction of the reflectance

of the foil facing the warm airspace to a value of about 0.1. It is probable that due to the higher

warm-side temperatures used in these tests, con- densation on the foil surface was greater in the

tests of part C than in those of part B. Unfortunately, membrane temperatures were not measured

in tests 103 to 113, and consequently comparisons

of warm and cold airspace performance could not

be made to examine the hypothesis of condensation on the reflective surface of the warm airspace.

Examination of the foil membrane after test 113

showed no evidence of staining, although staples at the bottom of the test area had rusted considerably, showing that moisture had been present.

The absence of staining is not conclusive, because

foil known to have experienced condensation has

later been found to be unmarked by it. The panel of part D of table 4 was prepared in order to conduct some tests with a midspace

membrane and with thick reflective airspaces

without effects due to condensation on the reflec- tive surfaces. The membrane was a laminate of

kraft paper with 0.00035-in. aluminum foil on the

side facing the cold airspace. The warm airspace was made reflective by means of perforated

aluminum foil cemented to the inner surface of t he

warm face of the panel. The laminated membrane

was perforated with 64 holes per square inch;

microscopic examination indicated the actual

apertures in the foil totaled 0.1 to 0.2 percent

of the area, and that in the majority of cases the

kraft-paper backing was not actually perforated.

Condensation could not materially affect the value

of the radiation interchange factor, E, for each

space, because this was controlled by the low

emittance of the reflective warm side of each space. The values of R/R' in part D, for panel 29, and

for each airspace, especially the warmer space,

are enough lower than unity to warrant further

consideration. Test 154, which was a repeat of

test 152 with a new membrane installed, con- firmed the approximate reproducibility of the

results with this panel. Further, the values of

R/R' in part D are in general lower than those

for panel 16 in part A, which had the same

geometry and which also could not have been

subject to condensation on the reflective surfaces.

A possible explanation is that the impaired

performance of panel 29 was due to radiation

from the sides of the framing members. In both

panels, the area of wood framing members

exposed to each test airspace was about 3.8 ft2

, and the membrane area was about 5.8 ft2

; the

emittance of the wood framing was on the order

of 0.9. In the case of panel 29, radiation from

the wood framing would be largely absorbed by

the highly absorptive kraft surface of the membrane on the cold side of the warm airspace; in panel 16, the membrane surface was highly

reflective, and little of the incident radiant

energy would be absorbed. Thus, other things

being the same, the resistance of the warm airspace

of panel 29 would be less than that of panel 16

because of absorption of the radiation from the

framing. The cold airspaces of both panels were

alike in this regard, but consideration of probable

temperature gradients in the wood framing

indicates that the effect would be materially

reduced in the colder of two tandem airspaces, as the results in part D also indicate. Assuming

that it was responsible for the difference between

the calculated and observed resistances of the

warm airspace in test 151, the effect was evaluated

from those results and applied as a correction to the calculated resistances for tests 152 and 153,

which then agreed within a small percentage

with the observed values for these tests. The results of the tests in part D thus possibly

indicate that radiation from framing may appreciably reduce the thermal resistance of a thick

reflective airspace when the colder side of the

airspace is not the reflective surface. It was not

feasible to investigate this effect further experimentally in this program, although it may have a bearing upon the most effective use of reflective

surfaces in airspaces of considerable thickness.

It is probable that the effect would be at least proportionately less for airspaces of lesser thickness.

5.2. Panels Insulated With Fibrous Insulations

in Combination With Reflective Surfaces

a. Semirigid Mineral-Wool Board Insulation Without

and With Reflective Surfaces

The data of table 5 are for a test panel containing a semirigid mineral-wool-board insulation, 1/ in. thick, installed to form a 2-in. warm airspace and

a 4-in. cold airspace. The board had a density of about 9 lb/ft3

, and had a thermal conductivity

of 0.241 Btu/hr ft2 (deg F/in.) at 55.8° F and of

0.249 at 72.8° F as measured by the guarded hotplate method (ASTM C177-45). The hotplate

13
Table 5. Thermal resistance of a 7Ys-in. panel with a lfi-in. semirigid mineral-wool-hoard insulation in approximate midspace without and with reflective aluminum-foil surfaces

Resistances are expressed in deg F per (Btu/hr ft 2)

Direction of

Panel Warm airspace,

2 in. Cold airspace,

4 in. Board,

1.5 in. Test heat flow Mean

temperature

Temperature

difference R R’ RIR' R R' RjR' R R' RIR' R

A. Panel 17, board installed as received (EW =EC =0.82 estimated)

78...

o F

43.3

deg F

88. 7 9. 03 8. 81 1. 02 1. 07 1 00 1 07 1 72 1.57

1. 28

1. 10 .99

6. 24 79 45°dowm._ 43.4 86. 7 7. 83 7.85 1. 00 .94 . 94 1. 00 1 . 26 5. 63 80 Horizontal 43. 7 86.

7. 05 7. 10 .98 .82 .88 .93 1. 12 1. 17 .90 5. 11 81 45° up- 43.7 87. 6 7.36 7. 42 . 99 .82 .84 .98 1.08 1. 12 .90 5. 46

82 Up 43.8 89. 6 7. 98 8.07 .99 .77 .81 .95 1.04 1.09 .95 6. 17

B. Panel 18, both surfaces of board painted white ( EW = EC =0.82 estimated)

84 Down _ 43. 2 88. 4 9. 00 8. 71 1.03 1.09 1.01 1.08 1.77 1 . 56 1.13 0. 14 85 45° down 43.4 88. 0 8. 33 8.23 1.01 . 97 . 94 1.03 1.35 1. 28 1.05 0. 01 86 Horizontal, . . . 43. 0 88. 1 8.02 7.98 1.01 .88 .88 i.oo 1. 22 1. 18 1.03 5. 92

87 13.

88. 5 7. 85 7. 81 1. 01 . 80 . 84 1. 02 1. 14 1. 12 1 . 02 5. 85

88 Up 43.6 89.7. 79 7. 87 .99 . 79 .81 .98 1.03 1.09 .95 5. 97

C. Panel 19, aluminum foil cemented on board, warm surface only (_E«,=0.03; Ec = 0.82 estimated)

90 Down... 44.8 94. 5 13.8 14.9 0. 93 6. 09 7. 34 0.83 1.76 1.62 1.09 5. 92

91

45° down _ . 44.6 91. 6 10. 7 10.8 .99 3.42 3. 52 .97 1.35 1.31 1.03 5.97 92 Horizontal . .. 44.8 91. 2 9. 84 9.85 1.00 2. 75 2. 77 .99 1. 21 1. 20 1.01 5. 88

93 45° up. 44. 6 91.3 9.31 9.35 1.00 2. 41 2.43 .99 1. 13 1. 15 .98 5.77

94 Up 44. 5 91. 1 8. 90 8. 89 1.00 2. 25 2. 14 1.05 1.01 1. 11 .91 5. 04 D Panel 20, aluminum foil cemented on board, both surfaces (E» =EC =0.03)

90 Down.. _ __ 44.4 97. 4 21.0 22. 7 0. 93 6. 10 7. 50 0.81 9. 66 9. 95 0. 97 5. 24

101 45° down 43. 1 92. 7 12.8 13. 2 .97 3. 52 3. 71 .95 3. 56 3. 71 .96 5. 76 98 Horizontal.. . . 43. 5 91.4 11.4 11.5 .99 2. 80 2. 88 .97 2. 86 2. 89 .99 5. 71 99 42. 8 91. 3 10. 7 10. 7 1.00 2. 51 2. 50 1 . 00 2. 44 2. 52 .97 5. 71 100 Up 42.7 91.4 9. 88 9.93 .99 2.31 2. 21 1.04 2. 17 2. 32 .94 5. 40

data indicate that at a mean temperature of 45° F,

which was approximately the mean temperature

of the board in the panel tests, the conductivity was 0.236, equivalent to a thermal resistance for the board of 6.36 deg F per (Btu/hr ft2 ). Measurements were made on the panel with (a)

the surfaces of the board in the as-received condition, (b) both surfaces painted with a flat white

paint of 0.9 emittance to inhibit air permeation

through the board, (c) aluminum foil of 0.03

emittance cemented to the warm surface of the

painted board, and (d) aluminum foil of 0.03

emittance cemented to both surfaces. Table 5 presents the values of R, R', and R/R'

for the panel and each of the airspaces, and R for the board.

The values of R for the board in part A of the

table show a variation with direction of heat flow,

the smallest value being obtained with horizontal

heat flow when the difference of elevation of the

ends of the test airspace was greatest. The obvious

explanation is that the effective resistance of the

board was decreased by air circulating between the

two airspaces through the board as a result of the

unequal weights of unit columns of air in the two

spaces. The greater uniformity of R for the board

in part B, for the several directions of heat flow,

indicates that air penetration was substantially

arrested by the two paint films. The average value of R for the unpainted board

obtained in the hotbox panel tests under conditions

in which air circulation through the board was

minimal (6.21 for the two horizontal orientations)

agreed within about 2 percent with the value

(6.36) obtained from the hotplate tests. The

average value of R for the painted board in part

B (5.98) was slightly less than the average value

for the horizontal orientations in part A (6.21) cor- responding to conditions of little or no air circulation. The decrease is attributed to paint filling

the voids between fibers of the board to a depth

of %2 to }{ 6 in. The values of resistance of the

board were substantially independent of the direction of heat flow in parts B and C, and in part D

for directions of heat flow other than vertically

upward or downward. In the latter case, the

resistance was unaccountably about 8 percent

lower.

Because of the nature of the board, it was not

feasible to measure the emittance of its surfaces

either before or after painting. For both cases the

surface emittances were taken to be 0.9, yielding an estimated value of 0.82 for the radiation interchange factor, E, of the airspaces for calculating '

14
R'

.

For the spaces made reflective by aluminum

foil cemented to the board, the value of Ewas 0.03, as determined from measurements made on the

foil used to surface the board.

Considering the results in parts B, C, and D for the individual airspaces, the average of the R/R'

ratios for the 30 cases was 0.99, the extremes being

0.83 and 1.13. For the 15 cases where the airspace was not highly reflective, the average of the R/R'

ratios was 1.02; for the 15 highly reflective spaces

it was 0.96. The major departures of the R/R'

ratio from unity occurred in the cases of downward and upward heat flow, chiefly the former.

Comparing the test results directly, the observed

resistances for the nonreflective cold airspace in part C agree well with the corresponding values in part B ; similarly, those for the reflective warm air- space in part D agree well with the values in part C. For the panel, the R/R' ratios averaged 0.99,

with extremes of 0.93 and 1.03. Because the observed resistance of the board in each test had to be used in calculating R' for the panel, the R/R'

ratio should be expected to be nearly unity when

the airspaces were not highly reflective and therefore contributed only a small fraction of the total resistance of the panel installation. In parts C

and D, the one or two reflective spaces added much

to the panel resistance, and even in these cases the

agreement of the observed and calculated panel

resistances was good.

Comparison of corresponding observed resist- ances R for the panel in parts B, C, and D of table 5 shows the very substantial increases in insulating effect that resulted when the airspaces

adjoining the fibrous insulation were made highly

reflective, especially for heat-flow directions other

than vertically upward.

The results of the work with this panel are considered to show that the over-all and component

resistances for tandem installations of fibrous in- sulation and reflective or nonreflective airspaces can be calculated with adequate average reliabil- ity (i. e., to within less than 10 percent, and considerably better in most cases), if the fibrous insulation and the airspaces are of uniform thickness,

and the airspaces are sealed.

b. Flexible Lightweight lVi-in. Mineral-Wool Blanket

With Aluminum- Foil Membrane on Warm SideFour Methods of Installation

Table 6 presents data for four installations in a

3%-in. panel of a commercial flexible-blanket insulation consisting of IK in. of 0.6 lb/ft 3 density

mineral wool faced on one side with 0.001-in. alu- minum foil. As measured in the guarded hotplate

(ASTM C177-45) with the blanket compressed to a thickness of 1 in., the thermal conductivity of the fibrous material was 0.277 Btu/hr ft 2 (deg F/in.) at 74° F mean temperature. On the basis of a

thickness of 1% in., this yields an estimated thermal

resistance of 4.8 deg F per (Btu/hr ft 2

) for the

blanket at its approximate mean temperature

(30° F) in the panel tests.

Measurements were made with the insulation

installed in the panel in four different ways considered to be of practical interest, as indicated in table 6. The panel resistances, R, in table 6 show that

the greatest insulating value, for all directions of

heat flow, was obtained with the midspace installation A; installation B with the blanket bowed

into the space from the warm side was next in effectiveness. Installations C and D gave approximately similar results, except when heat

flow was downward. D is considered a less desirable method of installation from the standpoint of possible moisture condensation on the

aluminum-foil vapor barrier, because the foil temperature under the framing must approach

that of the sheathing applied to the framing.

The blanket resistances were maximal for installation A, in which the fibrous material was uncompressed, and were minimal for installation D,

in which the fibrous material, in addition to being

compressed near the framing members as in B

and C, was further restrained from its full expansion even near the center of the space by the

tautness of the foil facing. The resistance of the

blanket in installation A for downward heat flow

(4.62) agrees within 4 percent with the value (4.8)

inferred from the hotplate test. For a blanket of approximate convex-lens shape

(i. e., thicker at the middle than at the edges),

the average thermal resistance, over all its area,

is less than the apparent resistance obtained when

the temperature drop through the blanket, as determined with thermocouples attached to its faces at points midway between the longitudinal

framing members (see fig. 2, arrangement E), is divided by the average observed rate of heat flow

per square foot of blanket. Thus, the tabulated

values of apparent blanket resistance, which were

obtained in this way, tend to be a little greater

than the actual average or effective resistance of

the blanket in the case of installations B, C, and D

(especially B and D), in which a convex-lens shape

for the fibrous material was most marked. Accordingly, since the R' values for the panels were

based on the tabulated values of the blanket

resistance, which are greater than the effective

values, the R/R' ratios for the panels are necessarily less than unity in these cases. For installations C and D, this effect was somewhat offset by

the small observed thermal resistances at the

contact between the blanket and the warm and

cold faces, respectively, of the panel, which were

not allowed for in calculating R'

.

Considering the R/R' ratios, installation A

developed from 88 to 97 percent of the calculated

panel insulating value. The departures are chiefly

due to the departures from unity of the R/R' ratio

for the reflective warm airspace, which nevertheless contributed very substantially to the insulating value of the panel. Installation B, with the

blanket bowed into the panel space, developed

about 80 percent of the thermal resistance calcu444414° —57 3 15
Table 6. Thermal resistance of a 3

3/g-in. panel insulated by four methods of installation with a 0.6 Ibjft 3 density, l}i-in. mineral-wool blanket faced on warm surface with aluminum foil

Resistances are expressed in deg F per (Btu/hr ft 2

)

Panel Warm airspace Cold airspace Blanket

Test Direction of heat flow Mean

temperature

Temperature

difference R R' R/R' R R' R/R' R R’ R/R' R

A. Panel 8, fibrous blanket installed at midspaee with no compression CEu,=0.03, Ec =0.82 estimated)

Down.

o F

34. 7 deg F75.9. 43 10. 7 0. 88 3. 43 4. 66 0. 74 1.38 1. 39 0.99 4. 62

45° down 34.8 74. 6 8. 83 9. 75 .91 3. 01 3. 88 . 78 1. 28 1.32 .97 4. 55 Horizontal.. 34.9 74. 6 8. 38 8. 85 .95 2. 66 3.05 .87 1. 20 1. 28 .94 4. 52

45° up 34.7 74. 5 7. 70 7. 94 .97 2. 09 2. 30 .91 1.09 1. 11 .98 4. 53 Up 34.6 74. 2 7. 34 7.59 .97 1.82 2. 06 .88 1.02 1.03 .99 4. 50

B. Panel 4, installed over warm side of studs and pushed halfway into stud space (i?«,=0.03; Ec = 0.82 estimated)

19 Down.. _ ... 34.8 75.6 8.64 10.4 0. 83 3. 75 4. 65 0.81 0. 53 1.42 0. 37 4. 37

16 Horizonal ... . 34.7 73. 6 6. 83 8. 70 .79 2.00 3. 16 .63 . 61 1.32 .46 4. 22

18 45° up_._ 34.8 73.8 6. 50 7. 84 .83 1. 62 2. 37 .68 .61 1. 20 . 51 4. 27

17 Up 34.6 74.2 6. 21 7. 51 .83 1.35 2. 13 .63 .57 1. 09 .52 4.29

C. Panel 5, installed tautly over warm side of studs with foil against warm surface plate (Ec =0.82 estimated)

22. __ Down 34. 4 69.9 5. 53 5. 40 1. 03 0. 50 1. 12 1.49 0. 75 20. __ 35. 4 70. 0 4. 93 4. 83 1.02 0. 50 .80 1. 20 .67

21 _ Up 35. 2 70. 6 4. 67 4. 68 1. 00 0. 47 .60 1. 08 .56

23 “ Horizontal. 35.4 69. 4.93 4.91 1.00 0. 39 .83 1. 19 .70

D. Panel 7, installed over cold side of studs and compressed with blanket against cold surface plate (Ew =0.03)

27 Down.. .. . .. 26. _ 45° down_.

24 Horizontal

28 _ 25 Up..!

34.0 74.1 33.5 70.

33. 5 70.3

33. 5 69. 1 33.9 68.8

7. 42

5. 42

4. 85

4. 54

4. 32

10.0

6. 16

5. 26 4.84

4. 60

0. 74 .88 .92

.94

.94

4. 36 7. 26

2. 40 3. 44

1.96 2.66

1. 73 2. 32

1. 51 2. 08

0.60

.70

. 74 .75

.73

0. 31 .30

. 29 .29

.28

2. 75

2. 72

2. 60

2. 52

2. 52

a Repeat of test 20 with foil surface painted (panel 6).

lated on the basis of equal uniform airspaces on the

two sides of the blanket, or about 87 percent of the

insulating value of A. Some of the decrease was

due to compression of the blanket at the edges;

further, the resistance of the cold airspace was

seriously reduced, possibly because the airspace was quite nonuniform in thickness, and probably

less than K in. thick at the center. In installation

C, there was no intentional airspace between the

tautly stretched aluminum-foil membrane of the

blanket and the panel face, and accordingly, the

panel with this installation had less resistance than

with installations A or B. However, there was

an observed temperature drop of about 7 deg F

from the panel face to the foil in the tests of installation C, which was equivalent to a thermal

resistance of about 0.5. A resistance approximately of this magnitude presumably could be

expected in field applications similar to C, although

if feasible an installation like B would be preferable. Test 23 was made to duplicate test 20, but with

the foil surface painted. The resistance between

the panel surface plate and the foil was reduced to 0.39 by this change. The large space formed in installation D made this installation better than

or approximately equal to C in insulating effect,

in spite of the reduction of blanket thickness and

resistance due to constraint by the taut foil. However, in view of the probability of moisture

condensation on the foil under the framing, application D is considered less desirable than the

others.

c. Commercial 2-in. Mineral-Wool Blanket, Foil- Enclosed and Kraft- Enclosed

Tables 7 and 8 present the data obtained with

various applications of a typical nominal 2-in. enclosed blanket insulation in a 7%-in. panel. In

table 7, the effects of high and low thermal emittances of the blanket faces are shown; in table 8, tests of the blanket with various modifications of

the breather membrane are presented.

Table 7 shows a considerable variation in the

observed blanket resistance, R, among the four

blanket specimens, ranging from an average of

5.94 for A to 8.79 for D. The thermal conductivity of the fibrous material, as determined by a guarded hotplate measurement, was 0.259 Btu/hr

ft2 (deg F/in.) at 73.5° F mean temperature, cor- responding to a thermal resistance of about 4.0 deg F per (Btu/hr ft2

) per inch of thickness, or

8.1 for a 2-in. thickness, at the mean temperatures

of the panel tests. There was considerable variation of the thick- ness of fibrous material from place to place in the

16
Table 7. Thermal resistance of 7

h/s-in. panels insulated with commercial 2-in. mineral-wool blankets, foil enclosed and kraft paper enclosed

Resistances are expressed in deg F per (Btu/hr ft 2)

Panel Warm airspace Cold airspace Blanket

Test Direction of heat flow Mean

temperature

Temperature

difference R R' R/R' R R’ R/R’ R R' R/R' R

A. Panel 9, foil-enclosed blanket against warm surface (Ec = 0.03)

40 Down...

o F

41.

1

42.6

43.3

42.9

42.7

deg F

92.3

88.0

88.7

87.4

87.9

13.

1

9. 03

8. 40

8. 11

7. 91

16.0

9. 83

9. 00

8. 51 8.30

0. 82

.92

.93

.95

.95

0.28

.28

.27

.25

. 21

6. 82

2.80

2. 18 1.93 1.83

9. 97 3.89

3.05

2. 58

2. 44

0. 69

.72

.71 .75

.75

6. 01

5. 94

5. 95

5. 93

5. 86

39

41_ _ 37 45° up... _ _ __ 38_ _ Up !.

B. Panel 11, blanket from same roll as A; installed with 2-in. warm and 3J.*>-in. cold airspaces (E« = 0.09; Ec = 0.03)

52 Down.. 45.8 98.3 17.3 21.7 0.80 3. 92 5. 01 0. 78 6.81 10. 1 0.67 6. 56

51 45° down... 45.4 95.8 12.0 13.8 .87 2. 53 3. 16 .80 2. 70 3. 87 .70 6. 76

48 Horizontal.. . . 45.5 95. 1 10.8 12.

1

.89 2. 07 2. 55 .81 2.16 3. 02 .72 6. 54

49 45° up 45. 5 95.3 10.3 11.5 .89 1.80 2. 28 . 79 1. 90 2.65 .72 6. 55

50 Up 45. 7 95.7 10.

1

11.3 .89 1. 50 2. 10 . 71 1.80 2.42 .74 6. 79

C. Panel 23, foil-enclosed blanket from second roll; installed like B ( JE„=0.09; Ee =0.03)

15 Down.. ... 38.0 87.1 18.0 22.

1

0. 81 4.06 4. 75 0. 85 6. 70 10. 2 0. 66 7. 19

16 45° down... _ 38.

1

83.9 13.0 14.6 .89 2. 66 3. 43 .78 3. 06 3. 89 .79 7. 25

17 Horizontal. _ _ _ _ 38.0 83.0 12.0 13.

1

.92 2. 27 2. 67 .85 2. 39 3. 10 .77 7.32

18 45° up 37.8 82.7 11. 4 12. 5 .91 1.90 2. 34 .81 2. 10 2. 74 . 77 7.37

19 Up 37.9 83.5 11.5 12.6 .91 1.63 2. 16 . 75 1.96 2. 50 .78 7. 94

D. Panel 28, commercial blanket similar to A, B, and C but kraft enclosed; installed like B (Ew = 0.82; EC =0.S6 estimated)

137 Down.. . .. .. .. 40. 1 88.0 11.4 11.4 1.00 1.02 1.01 1.01 1. 57 1.55 1.01 8. 81 38 45° down . 40. 2 87.7 10.8 10.8 1.00 .95 .96 .99 1. 27 1. 29 .98 8.58

39 Horizontal . .. . 40. 6 87.6 10.8 10.8 1.00 .93 .91 1.02 1.18 1. 20 .98 8. 66

40 45° up 40.

1

87.8 10.8 10. 7 1 . 01 .87 .86 1.01 1. 18 1. 14 1.04 8. 72

.41 Up 40. 5 88.6 11. 1 11. 1 1.00 .83 .83 1.00 1. 10 i. ii .99 9.19

E. Panel 13, same as B, with warm foil surface painted (Ew =0.82 estimated; _E e =0.03)

62 Down.. ... 44.3 95.3 14.0 17.5 0.80 0. 92 0. 97 0.95 6. 23 9. 74 0.64 6. 82

60 Horizontal . _ 44. 5 91.8 9. 23 10. 2 .90 .74 .88 .84 2. 08 2. 95 .71 6.41

61 Up 44. 5 92.7 8. 96 9. 77 .92 .63 .82 .77 1.76 2. 38 .74 6. 57

F. Panel 14, same as B, with both foil surfaces painted (EW =EC = 0.82 estimated)

63 Down.. . __ 43.8 89.5 9. 58 9. 09 0. 99 0.91 1.00 0. 91 1.56 1.58 0. 99

64 Horizontal .. . 44.4 88.9 8. 59 8. 83 .97 .79 .89 .89 1.06 1. 20 .88 65 Up 45.4 90.2 8.41 8. 77 .96 .64 .82 .78 .93 1. 11 .82

several blanket specimens used, as observed upon

examination after the tests. Although measure- ments were made of the thickness of the adjoining

airspaces in the various panel installations, the

actual thickness of the fibrous material between

the blanket membranes could not be ascertained

under the test conditions as the panel orientation was changed. The observed blanket resistances

for each specimen indicate slightly different effec- tive thicknesses at different panel orientations.

The greater differences in resistance, among the

blankets of parts A, B, C, and D, seem attributable to initial compression in the shipped form

with variable self-expansion as installed, depending on the constraints imposed by the breather

membrane.

The effect of highly reflective blanket surfaces

in increasing the insulating value of the application is indicated only partially by comparison of

the observed panel resistances, R, for specimens

A to F in table 7. The apparent effect shown by

this comparison is, in general, less than the real

effect, because of the differences in actual blanket

resistance—the real effect is shown by adding to a fixed nominal blanket resistance the observed

resistances of the airspaces, as taken from the

table. The nearest approach to this more appropriate comparison is afforded by the panel resist- ances of specimens B, E, and F. The R/R' ratios for the panels were, in general,

between 0.89 and 0.95 when one or more panel

airspaces had a highly reflective surface, for all directions of heat flow except downward. For

this case, panel R/R' ratios were approximately

0.8. When the panel airspaces did not have a

highly reflective surface, panel R/R' ratios were

nearly unity.

IT
The panel T\’/R' ratios simply reflect the R/R'

ratios for the two individual airspaces. The

warm airspace, when it had a highly reflective

surface, had R/R' ratios clustering about 0.8, and

when it did not have a highly reflective surface,

had R/R' values between 0.77 and 1.02. The

warm-side foil of this blanket was imprinted over about 15 percent of its area with lettering, the

lettered and unlettered areas having measured

emittances of 0.30 and 0.06, respectively. This was taken into account in calculating the average

value of E for the warm airspace as 0.09; however,

because the printed areas had about 5 times the

absorptance of the plain foil for the radiant

energy emitted by the other side of the airspace,

they probably tended to be at a higher temperature, and thus to affect the normal development

of convection currents in the space, depending on

the airspace orientation and direction of heat flow. The R/R' ratios in table 7 for the cold airspace

with an aluminum-foil surface on its warm side were between 0.7 and 0.8 for all heat flow directions

except downward, for which the values of R/R'

approximated 0.67.

In table 8, specimen Ci was the same blanket

as specimen C, with the breather membrane

detached from the nailing flange and installed

tautly between the framing members, as shown

in detail X of figure 3. For this application, and

especially for the downward heat-flow direction,

the R/R' ratios for the cold airspace were substantially greater than the corresponding values

for specimen C. A similar improvement is noted

in the R/R' ratios for the warm airspace for heatflow directions other than downward. These

results suggest that irregularities of shape and

lower thermal resistance at the flanks of the

conventionally installed blanket caused augmentation of convection currents in the adjoining

airspaces, thus decreasing their thermal resistance.

Conduction of heat by the foil of the breather

membrane where it passes from the nailing strip on the warm side to the cold side of the blanket

might be responsible for some part of the effect mentioned above. To investigate this possibility,

specimen C2 in table 8 was prepared with the same

blanket as used in C and Ci, with the perforated

foil laminate breather reattached to the nailing

Table 8 . Thermal resistance of 7

5/s-in. panels insulated with commercial 2-in. foil-enclosed mineral-wool blankets with modifications of the breather membrane

Resistances are expressed in deg F per (Btu/hr ft -)

Direction of

Panel Warm airspace,

2 in. Cold airspace, 354 in. Blanket

Test heat flow Mean

temperature

Temperature

difference R R’ R/R' R R’ R/R’ R R’ R/R' R

C. Panel 23 (data from part C of table 7 repeated)

115 Down

0 F

38.0

deg F

87.

18.0 22.0.81 4.06 4. 75 0. 85 6. 70 10.2 0. 66 7. 19 116 45° down.... . . 38. 1 83.9 13. 0 14.0 .89 2.66 3. 43 .78 3. 06 3.89 .79 7. 25 117 Horizontal. 38.0 83.0 12.0 13. 1 .92 2. 27 2.67 .85 2. 39 3. 10 .77 7. 32

118 45° up. ..... 37.8 82.7 11. 4 12. 5 .91 1.90 2. 34 .81 2. 10 2. 74 .77 7. 37

119 Up 37.9 83. 5 11. 5 12.6 .91 1.63 2. 16 .75 1.96 2.50 .78 7. 94

Ci. Panel 24, breather removed from blanket edges of panel 23 and stapled tautly to framing (Ew =0M\ Ec = 0.03)

121 Down... . 42.2 95.3 19.8 21.9 0. 90 3.89 4. 62 0. 84 8. 47 9. 78 0. 87 7. 47 122 45° down... 42. 1 91. 7 13. 9 14. 9 .93 2. 75 3. 34 .82 3.36 3. 77 .89 7. 76 123 Horizontal 41.8 90.8 12.7 13. 4 .95 2. 35 2. 62 .90 2. 62 2. 99 .88 7. 75

124 45° up 41.8 91.2 12. 5 12.9 .97 2. 06 2.30 . 90 2. 40 2. 62 .92 7. 99 125 Up 41.9 91.6 12. 5 13.0 . 96 1.87 2. 09 .90 2. 16 2. 44 .89 8. 47

C2 . Panel 25, foil removed at edges of breather (see note p of table 1) (E w =0.09: Er = 0.03)

126 Down 41.9 94.18. 7 22. 5 0. 83 4. 09 4. 63 0. 88 6. 73 10. 1 0. 67 7. 84

127 45° down _ . _ ___ 41.8 91.3 12.9 14. 7 .88 2.56 3.35 .76 2.88 3. 87 . 74 7. 50 128 Horizontal . 41.9 91. 1 12. 2 13.3 .92 2.28 2.61 .87 2. 36 3. 08 . 77 7.59

129 45° up 42. 0 91. 5 12. 1 12.9 .94 2. 00 2. 30 .87 2. 15 2. 68 .80 7. 90

130 Up 42. 1 92.3 12.3 13.0 .95 1. 74 2. 11 .83 2. 13 2.43 .88 8. 48

C3 . Panel 2(5, same as C2 but with breather ends sealed to framing (.E„=0.09: Ec = 0.03)

132 Down 41.8 94.8 18.8 22.

0. 84 3. 99 4. 63 0. 86 7. 00 10.0 0. 70

131 Plorizontal. 41. 9 91. 7 12. 6 13. 4 . 94 2. 30 2. 63 . 87 2. 59 2.99 .87

133 Up 41. 9 92.3 12.13.0 .95 1. 77 2. 11 .84 2. 20 2. 41 .91

Ci. Pafrel 27, perforated foil breather replaced by reflective paper breather (E»=0.09; Ee =0.20)

Down 39.9 91.0 16.8 18.0 0. 93 4.39 4. 95 0. 89 4. 11 4. 75 0. 87 Horizontal. 40. 1 88. 2 12. 1 12. 6 .96 2. 34 2. 62 . 89 2.01 2. 16 .93 Up 40.2 89. 5 12.2 12.9 .95 1. 76 2. 09 .84 1. 68 2.00 .84

18
strip after the foil had been removed from the

flank area (between the arrows shown in detail Y

of fig. 3). The R/R' ratios for both airspaces were greater for specimen C2 than for specimen C

for the upward heat-flow directions, indicating a

slight improvement when the foil was removed at the flank. The average resistance of the blanket

for C2 (7.86) was about 5 percent greater than for C (7.41), but not significantly different from that

for Ci (7.89), which also did not have aluminum

foil passing around the edge of the blanket. However, the R/R' ratios for the airspaces, particularly

the cold airspace, were in general less for specimen

C2 than for specimen Ci, suggesting that the greater irregularity of shape of the cold space with

specimen C2 than with Ci had some effect in lowering its thermal resistance.

For all of the previous tests of this blanket,

except Ci, the breather membrane was not sealed

to the framing at the top and bottom, in accord- ance with ordinary installation practice. For the

tests of C3 , the breather ends of specimen C2 were

sealed to the framing with aluminum tape, thus

preventing circulation of air between the fibrous

material and the cold airspace except through the

minute breather perforations. The R/R' ratio for the cold airspace for horizontal heat flow (for

which circulation would be a maximum) was, for

C3 , substantially the same as for Cx , and greater

than the value of 0.77 for other specimens with

the reflective breather unsealed at top and

bottom. The blanket resistance for specimen

C3 for horizontal heat flow also agreed with that

for Ci and, in general, was greater than the values

ob tamed in the tests with the breather unsealed.

Specimen C4 had a laboratory-applied breather

membrane of kraft paper reflectively coated on

the cold side. The measured emittance of the

reflective side was 0.20, yielding a cold airspace

radiation interchange factor of 0.20. Comparison

of the resistance of the cold airspace for specimen

C4 with the values for corresponding heat-flow

directions for specimens B, D, E, and F of table 7, and C and C2 of table 8, shows that the airspace

with a reflectively coated paper breather had in general less resistance than a similar space with

an aluminum-foil breather, but considerably more resistance than a space without a reflective

surface, especially for downward heat flow.

6. Summary of Results

1

.

Observed insulating values for panels were

in agreement with calculated values within 10

percent or better in almost all cases where the

airspace conditions conformed to those of the

exemplary spaces with which the original data were obtained. (Calculated values for panels

I containing fibrous insulations were based on

observed rather than estimated values of the

thermal resistance of the fibrous component.)

Significantly wider departures of observed from

calculated values for panels were observed as a

result of such factors as condensation of moisture on reflective surfaces, lack of uniformity of air- space thickness, air circulation between tandem

airspaces, and effects attributed to local high

conductance at edges of insulating blankets or

radiation from framing members.

2. Condensation of moisture on reflective surfaces decreased the insulating effect of an air- space. The decrease observed ranged from 30

percent for a horizontal airspace with downward

heat flow to 10 percent for other orientations.

Condensation on a reflective membrane used in a critical position can be avoided by making the

membrane adequately vapor permeable.

3. The insulating effect of tandem wedgeshaped airspaces formed by an intermediate

oblique highly reflective membrane was materially less than that of airspaces uniformly of the same average thickness. The reduction of thermal resistance varied approximately linearly

with the departure of the wedge-shaped airspace

from uniformity of thickness. For the tandem

wedge-shaped spaces formed by aluminum foil stretched diagonally from the front to back faces

of adjacent 2 by 4 studs on 16-in. centers, the

observed resistances were 53, 75, and 78 percent

of those calculated for tandem uniformly thick

spaces formed by a foil membrane midway

between the panel faces, when heat flow was

downward, horizontal, and upward, respectively.

4. Circulation of air between tandem airspaces

through three holes near each end of the dividing

aluminum-foil membrane caused reductions of

18 and 12 percent in the insulating effect of the

airspaces when they were vertical or at a 45° angle, respectively. The holes were 0.58 in. square,

and at each end totaled 1 in. 2 in area in a membrane 30 in. wide. No significant loss of insulating effect was observed when the airspaces were horizontal.

5. It is shown that minute perforations in a highly reflective aluminum-foil membrane dividing two tandem airspaces, intended to make it vapor permeable, decrease the insulating effect of

the membrane as a result of radiation through

the apertures. The perforations, in the case

described, increase the effective radiation interchange factor of each of the airspaces by an amount approximately equal to twice the frac- tional area of the apertures. The reduction in airspace resistance from this cause depends on

orientation and direction of heat flow, and is estimated to range from about 20 percent for downward heat flow to about 5 percent for upward heat flow for a membrane having 64 perforations per square inch, totaling 1.6 percent of the

area. Air circulation through the perforations

described had no appreciable effect on the insulat19
ing value of the two adjoining airspaces, in any

orientation.

6. Tests of tandem airspaces, each 3.8 in. thick

and 14.4 in. wide, indicated that the thermal

resistance of a thick airspace with one reflective

surface may depend to some extent on the position of that surface because of effects due to radiation from the sides of the framing.

7. Comparison of observed and calculated re- sistances for panels insulated with a board-type

fibrous insulation of uniform thickness, without

and with reflective surfaces on the board, indicated agreement within 7 percent, and considerably better in most cases. Observed resistances

for individual airspaces agreed with the calculated values within 6 percent in 13 of the 15 cases

in which aluminum foil was applied to the board

insulation.

8. For 7%-in. panels insulated with 2-in. mineral-wool aluminum-foil-enclosed blanket insulation in approximate midspace, observed resistances were within about 10 percent of the calculated

values, except for cases of downward heat flow,

in which departures of about 20 percent were

found. Observed resistances for individual air- spaces were in a few extreme cases as much as 30

percent lower than calculated values, the departures being attributed chiefly to the effects of nonuniform thickness and conductance of the

blanket as installed. The reduction of thickness

and conductance of the blanket was especially

great at the flanks near framing members. For

the four samples of nominal 2-in. blanket insulation used, observed blanket resistances differed

by about 40 percent.

9. Tests with four different applications of a

1/4-in. low-density mineral-wool blanket with

aluminum foil on its warmer side showed that

applications with the blanket in midspace of the

panel, or bowed into the space from the warm

side, were materially more effective than those in

which it was stretched tautly over the warm or

cold faces of the framing members.

The authors acknowledge with appreciation the

services of Mervin M. Mosley, who made the

majority of the test-panel installations and con- ducted the panel measurements, and Thomas W.

Watson, who measured the thermal conductivity

of the fibrous blankets by the guarded hotplate

method, and determined the emittance of some of the surfaces of the vai'ious airspaces. They also thank James L. Brandt (Aluminum Company of

America) for additional emittance determinations.

7. Appendix

7.1. Method of Calculating Airspace Conductances

It is convenient to consider that the transfer of heat between the warmer and the cooler surfaces

20

of an airspace takes place by radiation, and by

convection and conduction combined. The heat

transfer by radiation depends only upon the absolute temperatures of the surfaces bounding the

airspace, and upon a radiation interchange factor

that takes account of the geometry of the space

and of the emittances of its surfaces. It does not

depend on the orientation of the airspace or direction of heat flow. The heat transfer by convection and conduction combined, however, depends

on a number of factors, such as the orientation of

the airspace and the direction of heat flow, the

temperature difference across the airspace, its di- mensions, and its mean temperature.

It was postulated that for given airspace surface

temperatures, the two components of the total heat transfer are independent of each other, and

therefore, that the calculated thermal conductance,

or coefficient for the total heat transfer across an

airspace by all modes combined, O', can be ex- pressed as the sum of two independent coefficients, as indicated by the equation

C'=EhT +hc . (1) The two terms on the right-hand side of eq (1) represent, respectively, the radiation coefficient and the coefficient for combined convection and

conduction.

a. Radiation Coefficient The coefficient for heat transfer by radiation

across an airspace, per unit of temperature differ- ence of its surfaces, is given by Ehr , where E is the radiation interchange factor referred to above

and described below, and hT is obtained (in Btu/hr

ft2 (deg F) ) from the Stefan-Boltzmann law as

follows:

, 0.172X10-8 (Tt-T|)

T ~ (Ti—T2)

=0.00686^^

)

3 approx. (2) Tx and T> are the absolute temperatures (° F

460°) of the warmer and cooler surfaces, respectively, of the airspace, and Tm, the mean temperature of the airspace, equals -\-T2 ). Values of hT for various airspace mean temperatures (expressed in deg F) are given in figure 5. The radiation interchange factor, E, is calculated

by means of the equation

where ex and e2 are the total hemispherical emittances of the warm and cold surfaces of the air- space. Equation (3) applies rigorously for the

case of parallel planes of infinite extent. For

parallel facing rectangles of limited area, the direct i radiation interchange factor between them be-
0 10 20 30 40 50 60 70 80 90 100 NO

MEAN TEMPERATURE , °F

Figure 5. Linear radiation coefficient for heat transfer across an airspace, for a radiation interchange factor, E, of unity. comes less than the value given by eq (3) as the

spacing between them increases. However, as the

spacing increases, reradiation between the faces

and side boundaries of an airspace partially offsets the decrease of the factor. Procedure for obtaining the radiation interchange factor between gray

source-sink surfaces forming part of an enclosure,

with reradiation taken into account, has been

given by Hotteld

When the value of E as computed by eq (3) is small (less than 0.2), it differs very little from the

factor obtained by the more elaborate procedure

given by Hottel, for airspaces of the dimensions

under consideration. For an airspace of long rec- tangular shape, such as the space between framing members on 16-in. centers, with facing sur- faces of high emittance (0.9) spaced 4 in. apart,

for which the value of E as computed by eq (3) would be 0.82, the cited procedure yields a value

of about 0.72. For this rather extreme case, the

error in resistance introduced by using eq (3) for computing E would be approximately 10 percent

for a space having a total resistance of 0.8 to 1.2 deg F per (Btu/hr ft2

), depending on temperatures,

orientation, and direction of heat flow. The overall error in computing the insulating effect of a

typical wall or section introduced by the above

error is negligible from a practical point of view.

Thus, for purposes of practical use and simplicity,

values of the radiation interchange factor, E, as computed by eq (3), seem adequate.

b. Coefficient for Combined Convection and Conduction

Values of the coefficient for heat transfer by

convection and conduction combined (hc in eq (1))

had to be determined experimentally.

4 W. H. McAdams, Heat transmission, 3d ed., eq (4-33), p. 76 (McGrawHill Book Co., Inc., New York, N. Y., 1954).

To do this, 96 heat-transfer measurements were made in the rotatable liotbox apparatus described

in this report on a number of 5.4- by 8-ft panels

with sheet-metal faces enclosing 1 or 2 tandem

airspaces of uniform thicknesses from % to 3 % in. All of the airspaces had one or more highly reflec- tive surfaces yielding values of E on the order of

0.03. The measurements were made for five dif- ferent conditions of panel orientation and direction of heat flow: Horizontal, with downward heat

flow; 45° from the vertical, with downward heat

flow; vertical, with horizontal heat flow; 45°, with

upward heat flow; and horizontal, with upward

heat flow. The results, after slight corrections to take

account of heat conduction in the wood framing

that formed the lateral boundaries of the 32- by

60-in. test airspace located centrally in the panel,

yielded experimental values of the total thermal

conductance of the airspace or spaces corresponding to the test conditions. Upon subtracting the

calculated radiation component, Ehr , from the

total coefficient, values of hc for particular test conditions were obtained.

Using dimensional analysis, the results were

reduced to the form presented in figure 6. A

separate curve based on the data is given for each

panel orientation and direction of heat flow, usinglogarithmic coordinate paper. These relate values

of the product hc l to values of Ol3

, for an arbitrarily selected value of 50° F for the mean temperature of the airspace, where l is the thickness

of the airspace in inches, and 9 is the temperature

difference across it, in deg. F. The dashed horizontal line corresponds to the case of conduction

only, with no heat transfer by convection ; the value

of (hc l)r0o for this line (0.175) is the thermal conductivity of still air at 50° F as determined by

21
Figure 6. Convection-conduction coefficient for heat transfer across an airspace, for five orientations of the airspace and directions of heat flow.

the trend of the test data at low values of OP. The effect of the mean temperature of the air- space on the value of li c depends upon whether

convection is a significant factor in the heat

transfer. Consideration of the variations with

temperature of the properties of air involved in conduction and in natural convection (thermal

conductivity, thermal expansion, and kinematic

viscosity), indicated the practicability of adjusting values of (h c )&0 to values for other moderately

different mean temperatures by means of the

approximate equations: For (hcl)soj>0.3,

(hc ) , = (he )60 [ 1 - 0 .00 1

(t -- 50 )] , (4a)

and for (W)so<0.2,

(hc )i= (Ac )5o[l +0.0017 (t —50)]. (4b)

For intermediate values of (hc l)so, the temperature

coefficient in the above equations is variable, and

passes through zero in value, so that mean

temperature has little effect on hc . To investigate the practical application of eq

(1), which was postulated, 50 measurements were made with panels containing one or more airspaces

for which the radiation interchange factor E, as computed by eq (3), had values from about 0.2 to

0.76. Values of (hcl)50 were obtained from the

results in the same manner as those described

above. These values were divided by values of

{licl ) so taken from the curves of figure 6 at the

corresponding values of 6

3

. The average value

of the 50 quotients so obtained was 1.009. The

limits of the average quotient, determined for a

95-percent confidence interval for a group of 50

values, were found to be 1.028 and 0.989. These

limits bracket closely the value 1.000, thereby

establishing the practical utility of eq (1).

7.2. Range of Experimental Conditions at

Which Convection-Conduction Coefficients

Were Determined

The data shown by the plotted points of figure 6 were obtained with airspaces of uniform thickness,

with surfaces of moderate flatness and smoothness,

and with no leakage of air into or out of the spaces or between spaces where two tandem spaces were

used. The average temperature gradient of the

surfaces of the test panel bounding the test airspaces, in the direction of its length, was not

greater than about 0.2 deg F/ft for each Btu/hr

ft2 of heat transfer across the airspace.

The test airspaces were approximately 60 in. in height or length, and 32 in. wide; the spaces

1 ranged in thickness from % to 3% in. In the

various measurements by which the plotted points were obtained, the temperature difference across : a space ranged from 15 to 1 19 deg F, and airspace

mean temperature ranged from 17° to 112° F. The surface emittances of the two facing surfaces

of the airspaces, as determined by separate

measurements, had values of 0.03 and 0.83, or , 0.03 and 0.03.

u Washington, July 19, 1957.

22 U. S. GOVERNMENT PRINTING OFFICE: 1957
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