NATIONAL BUREAU OF STANDARDS REPORT

3030

TEE THERMAL INSULATING VALUE OF AIR SPACES

V

H. E. Robinson

F. J. Powlitch

Report to

Division of Housing Research

Housing and Home Finance Agency

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
U. S. DEPARTMENT OF COMMERCE

Sinclair Weeks, Secretary

NATIONAL BUREAU- OF STANDARDS

A. V. Astia, Director THE NATIONAL BUREAU OF STANDARDS

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NATIONAL BUREAU ©F STANDARDS REPORT

NBS PROJECT mS REPORT

IOO 3

- 3O-IO 15 January 11, 1954 3030

THE THERMAL INSULATING VALUE OF AIR SPACES

fcy

Ho E„ Robinson

F„ Jo Powlitch

Heating and Air Conditioning Section

Building Technology Division

to

Division of Housing Research

Housing and Home Finance Agency

<NBS>

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

The publication, reprlntlt

unless permission isobtal 25.D.C, Such permlsslc

cal ly prepared If that af

Approved for public release by the

'' '* pr° hlb ' fe<i

Director of the National Institute of "““T,"

Standards and Technology (NIST) r0, it, own uw. on October 9, 2015.

THE THERMAL IHSULATIHG VALUE OF AIR SPACES

H. E. Robinson and F„ J. Powlitch

ABSTRACT

This report presents the results of measurements of the heat

transfer coefficients for air spaces of various emissivities and

thicknesses. The data were obtained for five different orientations

and directions of heat flow, ranging from heat flow vertically upward to heat flow vertically downward, and encompass a range of

values of temperature difference across the air space.

The total coefficient for heat transfer across an air space is

shown to be the sum of a coefficient for heat transfer by radiation

and a coefficient for heat transfer by combined convection and conduction. These two coefficients depend upon different variables

characterizing the air space. Curves are given for computation of

the radiation coefficient for spaces of various emissivities and

mean temperatures . Other curves give values of the coefficient for

convection and conduction combined for air spaces of different orientations and directions of heat flow and for various air-space thicknesses and temperature differences. Equations are given for adjusting this coefficient for different mean temperatures.

The method of utilising the data to calculate the insulating

value of a particular air space, or of air spaces in a building

construction, is illustrated by several examples of general interest.

A description is given of the guarded hot box heat transfer apparatus

and of the test air spaces used to obtain the data presented in this

report

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Io INTRODUCTION

In 1945, at the request of the Federal Public Housing Authority,

the National Bureau of Standards reviewed published data on the

thermal conductance of reflective and nonreflective air spaces and

submitted a summary of representative values. These served as a basis for FPHA Bulletin No. 19 "Reflective Insulation", issued in

1945, and were used for reflective insulations in Federal Housing

Administration Technical Circular No. 7 "Calculation of Building

Section Heat Transmission Coefficients", revised in January 1947.

It was recognized in 1945 that the increased availability of

aluminum after the war would lead to greater utilization of aluminum foil and reflective surfaces to form thermally insulating air

spaces in buildings. However, the review referred to indicated

that the then available published data were limited and incomplete

in regard to total heat transfer coefficients for air spaces of

various emissivities and with various orientations and directions

of heat flow, and for the ranges of air space thickness, temperature difference, and mean temperature encountered in building

insulation service.

The total heat flow across a plane air space is the result of

heat flow by radiation, and heat flow by convection and conduction

combined, between its facing surfaces. There are theoretical

reasons for regarding these heat flows as taking place independently. Consequently, the coefficient for the total heat transfer

across a plane air space can be considered as the sum of two coefficients s

(a) A radiation coefficient which depends only upon the

emissivities and temperatures of the surfaces, and

(b) A coefficient for convection and conduction combined

which does not depend upon the emissivities of the surfaces but

does vary with the thickness of the space, its orientation, and

the direction of heat flow and with the temperatures of the surfaces, assuming the latter are reasonably smooth.

Thus, a flexible means of calculating the total heat transfer coefficients for a wide variety of air spaces would be provided if data as to the two component coefficients were made

available.

The radiation coefficient can be calculated readily, by means

of the Stefan-Boltzman law, for given surface emissivities and

temperatures. However, complete and consistent data as to the

convection-conduction coefficient, over a wide range of pertinent

conditions, were not available at the time of the review mentioned,

or later.

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Accordingly, at the request of the Housing and Horn© Finance

Agency, and with its financial support, an apparatus of the guarded

hot "box type was constructed during 1948, suitable for the purpose

of determining the heat transfer coefficients of air spaces of the

kind used in buildings. After use for other measurements desired

by the supporting agency, the apparatus became available in 195^ for

conducting the extensive series of tests required for the above purpose, the results of which are summarised in this report.

2, PRELIMINARY CONSIDERATIONS AND METHOD OF INVESTIGATION

Heat flows across an air space, from the warmer to the cooler

surface, by radiation and by convection and conduction combined. The

component due to radiation depends only upon the absolute temperatures

of the facing surfaces of the space, and upon its effective ©raissivity.

The component due to convection and conduction combined, however, depends upon a number of other factors, such as orientation, temperature

difference, and dimensions of the space. There are good theoretical

reasons for believing that for given air space surface temperatures,

the two components are independent of each other, and that, therefore,

the thermal conductance or coefficient for the total heat transfer

across an air space by all modes combined, C, can be regarded as the

sum of two independent coefficients, as indicated in the following

equation?

C = Ehr 4* hj, (l)

The two terms on the right-hand side of equation 1 represent, re- spectively, the radiation coefficient and the coefficient for con- vection and conduction combined.

The coefficient for heat transfer by radiation across an air

space, per unit of temperature difference of its surfaces, is given

by Ehr , where E is the effective emissivity of the space and, in

Btu/hr ft2 (deg F),

hr

o.4 4

0.1?2 x 10“s

(Ti - T2 ) (Tx

- tT)

= 0.00686 approx. ( 2 )

TX and T2 are the absolute temperatures (®F +> 460°) of the warmer

and cooler surfaces, respectively, of the air space, and t m equals

l/2(TX + T2 ). Values of hr for various air space mean temperatures

(expressed in Fahrenheit degrees) are given by the curve of Figure 1.
• - , III -
The effective emissivity, E, of an air space of uniform thickness,

and of extent large compared to its thickness, is calculated by means

of the equation

i 4 i ” 1 ( 3)

E e]_ &2

where and e£ are the total emissivities of the facing surfaces.

Values of E for various values of and &2 are given by the curves of

Figure 2.

The component of heat transfer across a plane air space due to

convection and conduction depends upon the orientation ©f the air space

and the direction of heat flow, on its thickness and the temperature

difference across it and, to a lesser extent, upon the mean temperature

of the space.

The heat transfer by convection and conduction combined cannot be

less than would take place by conduction alone through still air, but

when convection occurs in the space, the heat transfer may increase

materially above that value. The coefficient for heat transfer by con- vection and conduction combined, per unit of temperature difference of

the surfaces, can be represented by h*., the value of which depends upon

the circumstances enumerated above.

Since values of hp cannot be calculated analytically at present,

it was necessary to determine them experimentally. To do this, measurements were made on a number of air spaces under various conditions of

temperature and orientation to determine for each condition the total

heat transfer coefficient, or thermal conductance, C, of the space,

per unit of temperature difference between its facing surfaces. The

value of the radiation coefficient, Ehr , was computed for each measurement, using equations 2 and 3 and values of and ©2 determined by

separate measurements made on samples of the materials which formed

the surfaces of the air spaces used. The value ©f he for a particular

test condition was obtained by subtracting Ehr from the total coefficient, C, in accordance with equation 1. The dependence of the value

of he upon the various geometric and temperature conditions was then

determined by dimensional analysis of the collected data. This

analysis led to a method of making adjustments of the results to cor- respond to one mean temperature ( 50 ® F was selected), and to equations

for adjusting values at 50 ° F to other mean temperatures, as set forth

later.

In most of the measurements for determining he, the air spaces

used had low effective emissivities , E, so that the quantity Ehr was

a small fraction of the magnitude of the measured quantity C or the

derived quantity he. However, tests were also made with spaces having

large and intermediate values of E to test the experimental validity

of equation 1.

3. test apparatus and test method

h

_ at transfer measurements were made on air spaces in test

^

joniorded hot "box apparatus, shown schematically

panels by means of a guarded^ot box W

of Plate 2. The

in the drawing of Plate l ana in « sj & - @ize to one apparatus was designed or pane ® h g mounted on horizontal

foot thick, and as shown by ^

be rotated to posiofirpan.1 at any angle up to 90- froTM the vortical

in either direction.

hot box apparatus conformed substantially to the require-

- &C5TM 2 ^6- Met hod of Test for Thermal Conductance and

ments jf ASTM

Sect ions by Means of the Guarded Hot Box ,

except^fofthe°additional future of' rotatability on trunnions.

As shown in Plate 1 S S* p^fafwai

3 ’

iterZZl °

riS

a

Wo ?ois iere hold together by means of long bolts

interposed. periphery of the joint, as shown in the

The ^ard box contained a five-sided metering box 5),

photograph. The guard

el the face of the panel by

the open

.urines ( 19) . The contact between the metering box

four compression p s * tiallv airtight by the rubber gasket (2),

th%ri n^fth Cr th^ centrally located "metering area"

‘of t^ef“I rectangle 60 inches hig^and

which heat ““

t

”®a®U

»^uar4r

n?hrough which heat flow was not

-^r^-f-ec^th metering area

flow. Peripheral insulation (13) was placed at the edges or

panel to minimize lateral heat flow.

Daring measurements, the guard and metersl"g boxes were b,eld at

rolir^Ui^L^^^S. cold box was held

at the desired c »“‘“^nJect^ic reheating coil (7) controlled by

« -f‘a The air in each ~ ~

Son ofS; flow on lach side was the same as would result from

tion of air now on

The average air velocity in

thfmfering^ofbaffle space was about 39 “^^.^JSe'wfl.

:» rs r.:»” ;; i>; : r; r

-.- » —•< copper-constantan thermocouples (10) as indicated.

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... . « - ' - : . • , . ' • • ’ r v •' .' . . -

:.

'. . i:. •

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All electrical input to the heaters, fan, and other devices in

the metering "box was measured by means of a calibrated watt-hour meter

readable to one watt-hour. Under steady temperature conditions, and

with the guard box temperature adjusted to correspond to the metering

box temperature, so that there was no average temperature difference

or heat interchange through the metering box walls, all of the heat furnished to the metering box was transmitted to the cold box through the

known metering area (13.33 *0. ft) the panel. The average rate of

heat flow per square foot of metering area could thus* be determined.

To assure that there was little or no heat interchange between

the metering box and the surrounding guard box, a compound thermocouple

(9) was used, consisting of 10 series-connected differential thermocouples with the Junctions of each pair cemented opposite each other

in grooves in the surfaces of the metering box. The metering box,

except for the hardwood nosepiece which carried the gasket (2), was

made entirely of selected balsa wood, glued and doweled, forming walls

2.5 in. thick with a nearly uniform conductance of 0.16 3tu/hr ft z (deg F).

It was determined by calibration measurements that for a reading of

100 microvolts on the compound thermocouple (9), the heat flow between

metering and guard boxes was approximately 3.5 Btu/hr, or 0.26 Btu/hr

per square foot of panel metering area. For most tests of this investigation, the average reading of this thermocouple during a test was less than 30 microvolts, indicating that heat interchange between

guard and metering boxes was a very small percentage of the total heat

input; nevertheless, for each test the observed heat Input was corrected

for such interchange.

The guard-box temperature was made to correspond automatically to

that of the metering box by means of the compound thermocouple (8) con- sisting of 10 differential thermocouples in series arranged similarly

to those of compound thermocouple (9) but with their Junctions in the

air about one inch from the surfaces of the metering box. The emf

from the compound thermocouple (8) controlled a relay which supplied

heat to the guard box as required. This system of control was very

sensitive, and automatically kept the reading of compound thermocouple

(9) steadily near zero throughout the tests.

The temperatures of the surfaces of the test panels bounding the

air spaces were determined by means of 10 thermocouples on each sur- face of the panel, as indicated in the description of the test panels

(Plate 3).

All test measurements were made under steady temperature conditions following a prior period during which these conditions were

attained. The duration of the steady state test period, during which

the periodic observations wers taken from which the results were calculated, was in no case less than 16 hours, and in most tests was
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more than 20 hours. All thermocouples were read manually "by means of a

potentiometer with which temperature changes of less than 0.05 deg F

were readable. The steadiness of temperatures during almost all of the

tests was such that average air or panel surface temperatures did not

vary as much as 0.2 deg F during the test period.

The average test conductance of the panel space 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 sur- faces. Since about 5 percent of the metering area included the wood

members bounding the metering area air space, a small correction was

made to allow for the effect of heat conduction through the wood. The

adjusted conductance thus obtained represented the average thermal

conductance, C, of the panel air space, or one half the average con- ductance of each air space if the panel space was divided into two

approximately equal spaces in tandem.

4. TEST PANELS AND AIE SPACES

The air spaces used were of various thicknesses and had various

effective emissivities due to the use of different materials for their

bounding surfaces. In order to vary the air-space thicknesses, several

test panel frames of clear fir, substantially alike except for thickness, were used, as illustrated in Plate 3»

The test area was the 60-ineh rectangle at the center of the

panel, and included half of the wood bounding the test air space, which

constituted 5 percent of the tesu area. The other air spaces of the

panel constituted a guard area and were made similar to the test space

in all possible respects.

The faces of the panels were made of 19-gage galvanized sheet

steel, painted on the outer surface as indicated in Plate 3° The sheet

covering the metering area on both sides wag separated by a l/8-ineh

gap from the covers of the guard air space® to minimize lateral heat

flow into or out of the metering area. To seal the air spaces, th©

several sheets were screwed to the frames over l/l6-inch felt strips

glued to the wood.

Thermocouples for measuring the temperature of the sheet metal

faces were permanently soldered to the outer surface of the sheet at

ten positions on each face, as shown in Plate 3° The thermocouple

leads were cemented to the face of the sheet until they reached a take-off point at the center of the sheet. The surface was painted

after the thermocouples were attached.

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For those tests in which the inside surface of the warm side of

the air space was highly reflective, very bright and clean aluminum

foil was cemented to that surface,. For some later tests, where it was desired that this surface he one of high emissivity, the aluminum foil

was removed and the surface was painted with black or white paint. In

all of the tests, the inner surface of the cold side of the panel was painted with either black or white paint of high emissivity,.

Single or double air spaces in the panel were obtained as indicated by the "sections A-A" of Plate 3° Table 1 gives particulars as

to the dimensions and nature of the spaces on which measurements were

made; the decimal part of the "Panel Modification Number" differentiates panels in regard to thickness.

Table 1. Description of Panels and Air Spaces Tested

Test

panel

1

1

1

1

Spaces

Space No . 1 Space No . 2

8

1

8

Orientations

0

!

1

8

Tests

Thickness

1 1 E* Thickness" E*

1 1

1 No. ' in. 1

' in. 1 8 No. 1 No.

1.1 1 1 ' 5/8 • 0 .028 a

8 — 1 — i 5

1 15

1.2 1 1

8 7 /Q 8 .028 a

8 =•-= 1 — 8 58 17

1.3 1 1

“ 11/2 8 .028 a 8 — ' — 8 5

1 22

1.4 1 1

* 33/8 .028 a » 8 8 5

8 20

2.1 s 2

8 1 11/16 8 .014 b

8 1 11/16 8 0.028 a

8 58 22

Number of tests of highly-reflective spaces, total 96

3.1 1 2

8 1 11/16 8 0 .219 c

8 1 11/16 8 0.219 c8 58 17

4.1 8 2

8 1 11/16 8 .195 <18 1 11/16 8 .193 d8 30 3

5.1 1 2

8 1 11/16 8 .764 ©

8 1 ll/l6 8 .764 e8 3

8 3

6.1 8 1 • 5/8 1 .712 f

1 8 8 5I 11

6.2 8 1

8 1 1/2 8 .712 f

8 8 „„„ 8 5

i 16

Number of tests of spaces of moderate and high emissivity, total $0

*E is the effective emissivity of the air space, bounded by surfaces

indicated by letters as listed belows

Nature and emissivities of surfaces of air spaces

a - Aluminum foil, e = 0.028; black paint , e s 0.852

b - Aluminum foil, e = 0.028; aluminum foil, e = 0.028

c - Reflective coated paper, e = 0.229; black paint, e =s 0 832

d - Reflective coated paper, e - 0.198; white paint, e 3 0„92?

e - Brown kraft paper, e = 0.813; white paint, e - 0.92?

f - Black paint, e = 0.832; black paint, e ~ 0.832

The total emissivities of the surfaces of the materials used to

bound the air spaces were determined by separate measurements made on samples of the materials, most of which were taken from the panels after

the tests . The emissivities were determined by measuring the thermal

radiation from the surface and the radiation from a black re-entrant

cone at the same temperature, using a sensitive total radiation pyrometer at a different temperature . The emissivity was calculated as the

ratio of the two readings times the estimated virtual emissivity of the

re-entrant cones used (0,98 and 0,99)

5 . RESULTS

Values of hc

, the coefficient for heat transfer across air spaces

by conduction and convection combined, as determined by these measurements, are shown in a form convenient for general use by the curves of

Figures 3* 4, 5, 6, and ?.

Each figure represents one orientation of the air space and direction of heat flow, as indicated, e.g., a horizontal air space with

heat flow upward (Figure 3) - The several solid curves on each figure

give values of (hc )^o. the convection-conduction coefficient at an air

space mean temperature of 50° F, versus the thickness of the space,

in inches, for several selected values of the temperature difference

across the space, 0, in degrees F. The dashed line gives the calculated heat transfer coefficient for the space with heat transfer by

conduction only, with no convection* In a sense, this curve represents

the limiting value of (hc )^o as the temperature difference, 0, approaches zero*

Examination of these figures and curves shows that except for a

horizontal space with heat flow downward, the convection-conduction

coefficient is considerably greater than that for conduction only, and

that the effect of convection becomes greater as the temperature difference across a given space increases. However, when the thickness

of the space is reduced to a small enough value, the coefficient approaches that for conduction only, regardless of the temperature difference, although the critical thickness is smaller for the larger

temperature differences.

The effect of mean temperature on the value of the coefficient

hc depends upon whether convection is a factor in the heat transfer.

For cases in which convection is a factor (that is, where (hc )^o departs from the near neighborhood of the ’’conduction only” curve), the

value of he for an air space mean temperature, t (®F), is given approximately by

(hc ) t - (he

50 [l " 0.001 (t - 50)] (4)

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lor cases in which convection is practically negligible (that is, where

(hc )^Q lie 6 very close to the "conduction only” curve) the value of

(hc )t is given approximately by

(hc ) t = (hc ) 50 \l + 0 . 001? (t - 50S (5)

For intermediate cases, where (hc )^o is on the order of $0 percent

greater than the corresponding value indicated by the "conduction only"

curve, the temperature coefficient approaches zero and mean temperature

has little effect.

These adjustments for mean temperature are on the order of 1.0 to

1.7 percent of (110)50 f° r a change of 10 degrees F in the air space

mean temperature. For many purposes in estimating the total conductances of building air spaces, especially of those which are not highly reflective, the change of hc with mean temperature may be of little

practical importance.

For the vertical air space, and the spaces at 45 ° with heat flow

upward or downward, the curves (Figures 5 » 4 , and 6, respectively)

show that (1^)50 has a minimum value at a space thickness of an inch, more or less, depending upon the orientation and temperature difference, then increases slightly and finally decreases slowly, as the

space thickness increases. Thus, for a given vertical or oblique

orientation and temperature difference, there is an optimum thickness

at which the insulating value of the space is greater than for thick- nesses somewhat larger or smaller than the optimum value. However, at

considerably larger thicknesses, the insulating value of the space may

be even greater than at the optimum thickness occurring at a value

near one inch.

The results presented as curves in Figures to 7 were based upon

the curves given in Figure 8, which show in a more compact way the

relationship between (hc )5Q and the variables 0 and^ , for each orientation. The curves of Figure 8, which were derived by dimensional

analysis of the test data, are plotted on bilogarithmic coordinate

paper, and show the variation of (hc ^)cQ for each orientation versus

the coordinate dl 3 . The curves were drawn smoothly through the

plotted points, which represent all of the values of hc obtained in

the 96 tests made on highly reflective air spaces (test panels 1.1

through 2 . 1 ). Only 88 of the test points are plotted, since eight

practically coincided with eight others.

In general, the plotted points representing the test data con- form to within a few percent to the values indicated by the smooth

curves, except for the ca^e of a horizontal space with heat flow

downward for values of greater than 300 . The accuracy of the

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results is "best indicated "by the congruence of the curves for a vertical

space, and for spaces with heat flow downward to the horizontal dashed

line for conduction only, at low values of 0^3. The fact that these

three curves "become asymptotic to a horizontal line, at a value of

(hc

£)«r0 ©f about 0 . 175 , is equivalent to a determination of the thermal

conductivity of air at 5°® 2? as equal to 0.175 Btu/hr ft 2 (deg F/in.),

as compared to 0.173 as given for dry air at 50® S' in the NBS-NACA

Tables of the Thermal Properties of Gases (Table 2.42, 1950)

The data for the spaces with heat flow upward did not extend to

values of ©^3 small enough for them to approach the conduction only

line? these curves have been extended by dashed lines to indicate

their probable trend. The curves of Figures to 7 are also represented by dashed lines where they are based upon this extrapolation.

The 50 tests conducted on air spaces of moderate and high emissivity (panels 3»1 through 6.2) provided information as to the practical validity of equation 1. Values of (hg^O^Q were obtained from

the test results in the same manner as those calculated from the re- sults obtained with highly reflective spaces. These values were divided by values of (hc 2)^Q taken from the curves of Figure 8 at cor- responding values of 9^3. The average value of the 5© quotients so obtained was 1.009. The limits of the average quotient, determined

for a 95 percent confidence interval for a group of 5© values, were

found to be 1.028 and 0.989. Since these limits bracket closely the

ideal value 1.000, it is concluded that the practical validity of

equation 1 is substantiated, and conversely, that the method and data

given in this report for calculating the total conductance apply

equally well for air spaces of low and of high emissivity.

6. LIMITATIONS ON APPLICABILITY OF THE DATA

The values of hc in this report apply for air spaces of uniform

thickness, with reasonably flat surfaces of moderate smoothness, and

with no leakage of air into or out of the space, or between spaces

where two were used. In addition, the ratio of the height (or length)

of the air space to its thickness ranged from about 18 to 96 and the

average temperature gradient of its surface in the direction of the

height (or length) was not greater than about 0.2 degree F per foot

for each Btu/hr ft^ of heat transfer across the air space. A large

proportion of the air spaces encountered in buildings conform

reasonably well to the characteristics described above, and the re- sults herein should be applicable and appropriate for such spaces.

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However, it must be recognized that some air spaces encountered or used in building constructions may depart significantly from the characteristics for which these data are pertinent. For example, two air

spaces of nonuniform thickness may be formed by a membrane of foil or paper laid over the faces of studs and bellied into the stud space.

Again, the membrane dividing two air spaces may not be completely

sealed at the edges or ends, or may be perforated or torn, allowing

air to circulate between them. Farther, a reflective dividing mem- brane may be inappropriately installed in such a situation that vapor

may condense upon it under certain conditions, in which case its re- flectivity might be impaired by an indeterminate amount. For cases such as these, there would be uncertainty in applying the results

given in this report? in the first two cases because appropriate

values of hc would not be known, and in the last case because the

appropriate value of E would not be known. It is believed that, in

general, the heat transfer across such off-characteristic air spaces

would be significantly greater than for the spaces considered in this

investigation. Evaluation, even approximately, of the effect of such

variables on the space conductance would be desirable but would en- tail further experimental study.

7. UTILIZATION OF THE DATA

The total thermal conductance of a particular air space can be

readily computed if the air space thickness, orientation, effective

emissivity, temperature difference, and mean temperature are known.

For example, consider a vertical air space 1 l/2 inches thick, with

surfaces such that its effective emissivity is 0.05, and having a temperature difference across it of 20 deg F and a mean temperature

of 50® F. From Figure 5 for vertical spaces (or Figure 8), (h^^g

is 0.308° From Figure 1, (hr )^g is O.9I0 The conductance of the

space, in accordance with equation 1, is therefor© 0.308 +0.05

(0.9l) - 0.35^ Btu/hr ft^ (deg F) , and its thermal resistance, which

equals the reciprocal of the conductance, is x/0„35^ or 2.8 deg F

per Btu/hr ft^. The computation for an air space mean temperature

of 30® S’, instead of 50® F as above, is also straightforward. Using

equation 4, (hc )^Q - (hc )^n x [l - 0.001 (30= 50 J

- 0.308 x 1.02 =

0.31^° From Figure 1, (hjjjg = 0.8l. Hence, the conductance of the

space at 30° F mean temperature, C^q, is 0„3l4 + 0.05 (°8l) - 0.35^

Btu/hr ft*- (deg F). It happens that in this instance C-^q equals

O5O9 but this would not necessarily be true in other cases although

the difference may be practically negligible.

Values of the thermal resistance of 1 1/2- inch air spaces at a

mean temperature of 50° F and for a temperature difference of

20 deg F are given in 'Table 2 for various orientations and effective

emissivities E. The tabulated resistance values indicate in an

= 12“
,

N
approximate way the relative insulating values of air spaces in different orientations and with different emissivities , and will he useful in making calculations for particular building constructions involving air spaces, as indicated later

Table 2 . Thermal Resistances* of 1 l/ 2-inch Air Spaces

Temp, diff • - 20 deg F Mean temp . s 50® F

Orientation

1

1 Direction of

1

0 Effective emissivity (E) of space

of space 8 heat flow

8

0

0 0.05

1

8 0.20

0

1 0.50

1

1 0.82

Horizontal

8

8 Down

8

!

1 5.7

1

1

1 3.2

S

0 1.7

I

8

0 1.1

45 ° angle 1 Down

8

8

8 3.9 ! 2.6 8

8 1 = 5

!

1 1.0

Vertical 8 Horizontal

8

0

0 2.8 11 2.0 80 1.3 8

a 0.9

45 0 angle ' Up

8

»

0 2.3 0

0 1.8 01 1.2 00 .9

Horizontal ' Up

0

0

0 2.0 88 1.6 00 1.1 80 .8

*Degrees F per Btu/hr ft^

Calculation of the conductance (or thermal resistance) of an air

space in a building construction such as a wall is a little more com- plicated because the temperature difference across such a space depends upon the temperature difference across the construction, and

upon the ratio of the thermal resistance of the space to the total

thermal resistance of the construction including that of the air space

(or spaces) o In other words, it is necessary to know or assume the

conductance or resistance of the space (or spaces) before a close

computation can be made. The "trial and error®1 procedure required

leads quickly to a correct result, as shown below.

Consider the building construction (wall) shown in Figure 9 , with two air spaces formed by a central membrane dividing the 2 by 4

stud space. Using the quantities indicated in Figure 9 9 the temperature drop,t2~ t^, between the gyplath and sheathing, is given by

t 2

- t 3 = (tj - t 4)x

r2.

3 + ( Rl_2 + H3.4) {6)

- 13-
.

.
The term (E2-2 + RWj.) is seen to he the thermal resistance of the con- struction and the surface air films, exclusive of the resistance of the

air space or spaces, and is readily calculated for a given construction

using data given in references such as FHA Technical Circular No. 7 or the ASHVE "Guide”

Similarly, the average mean temperature of the air space or spaces

is given by , , Ryi4

- + j

(*2- 3

) tm = t4 +

Tr’i-2 + R3-4I

These equations can he solved to obtain approximate values of

t 2

~ tjj and t

ffl if appropriate values of R2_7 are assumed. In general,

it will he found that the thermal resistances tabulated in Table 2

will serve to provide good first approximations to R2-

3

. To obtain

a value of R2„x, an approximate value of the resistance per space is

taken from TablLe 2, using an appropriate value of E, which can be taken

as the average of the effective emissivities of the spaces, if there

are more than one, as determined by the values of the surface emissivities 62» ©2 9 » e '3» etCo an(i

^ means of Figure 2. For values of E

not given in the table, interpolation is permissible.

For example, assume t^ - 70 ® F, t^, = 0® F, e 2 and e-^ = 0.9

(ordinary building surfaces), and 62 8 and e

8 -? = 0.05 (reflective foil

surfaces). Then each of the air spaces will have an effective emissivity E of 0.05 (Figure 2) and the average value is Q.05o Referring

to Table 2, the resistance of one space for this case is given as 2.8,

and R2-3 f° r ^wo spaces is, therefore, 5*6. For the construction indicated in Figure 9, Ri-2 “ 1 = 03 and R3-4 s 2.11. Accordingly

tz ' ‘3 - <?o) * 5 .6

5

;

6

3 .i4

' 70 * 8^ ' 45 4e « 7

2.11 + 2- ( 5 . 6 ) t m = 0 + 70 x g

Tf5

= 70 * lift - 39

s I

The temperature difference per space, since there are two spaces, is

”<t2

“ t^) or 22.5 deg F. Considered rigorously, the two spaces have

different mean temperatures, given approximately by 39® F ± 22.5/2,

or 50° F and 28° F, but for the purposes of this calculation, the

average value of 39° F is satisfactory. Actually, as indicated in

the earlier example, the effect of mean temperature for this case is

negligible, and this example is therefore worked out using values for

a 50 ® F mean temperature.

- 14-
.
Using Figure 5* (hc )^o f°r a vertical space 1 0 8 inches wide with

a temperature difference of 22.5 deg F is 0.32, and adding the radiation coefficient (Ehr )^o» which equals 0.046, it is found that C^q is

O .366 and the air-space resistance is 2.73 • This is so close to 2.8,

the trial resistance, that recomputation is not necessary, and using

the value 2.73, the U-value of the construction is given by

(&1-2 + r3~4) + 2(2.73)» whence U = —I- = 0.116 Btu/hr ft^(deg F)

U

v 8.6

If a recomputation had been made, using 2.73 as a trial resistance for

each air space, the results would have been t 2 - t-x - 44.5, tm = 39-4,

and an average air space resistance equal to 2 . 73 * as before, indicating that the first results were satisfactorily correct.

Before leaving this example, it is pertinent to notice that the

membrane temperature in this case is approximately the same as the

mean temperature of the 2 by 4 stud space, or 79® F Tf the membrane

consisted of a metallic foil impermeable to water vapor, the vapor

pressure on its warm side would be substantially equal to that in the

building, and condensation might occur on the foil when the dewpoint

temperature indoors exceeded 39° F.

The temperature of the inner surface of single glass windows,

with 70° F indoors and still air at 0° F outdoors, would not ordinarily exceed 35 ° F, and an indoor dewpoint of 39 ® F could not be

maintained without considerable condensation on the windows. Accordingly, condensation on a foil membrane would, in this case, be

unlikely if single glass windows in the house were free of excessive

condensation. However, if storm sash or double glass were used in

all the windows, the indoor dewpoint might rise to about 5°° F before

window condensation occurred, and there would be considerable risk of

condensation on the foil membrane. This risk could be eliminated by

applying a vapor barrier such as another sheet of foil, or a membrane

of equal vapor resistance, at some position on the warm side of the

stud space, such as position 2 in Figure 9°

The U-values of several typical wall, ceiling, and floor con- structions used in houses, with various insulation applications, are given in the following pages. The U-values are expressed in Btu/hr

ft^ per degree F of air temperature difference on the two sides of

the construction.

These values were calculated using the methods and data presented

in this report, insofar as air spaces are concerned, and using for

other components of the construction coefficients taken from FHA Technical Circular No. 7, revised January 1947. In accordance with the

U-value calculations given in T.C. No. 7, no allowance was made for

the effect of wood studs or joists on the average U-value of the construction. In most cases, where the calculated U-value for the between-members area is of the magnitude of 0.08 to 0.14, the effect of

- 15-
.

-

.

•
the wood members is small,. If it is desired to take into account

the effects of heat flow through studs or joists, the procedure

for parallel heat flow given in the section ’’Computed Heat Transmission Coefficients" on pages 182-4 of the 1953 A.SHYE "Guide" may

be used.

WALLS

1. 4-in. brick, 4-in. cinder block, 25/32-in.

furring space, l/2-in. plaster on 3/8-in.

gyplath.

Assumed air temperatures ; 70° and 0° F

(a) Ordinary furring space, E of space

(b) Reflective coated paper on gyplath

(c) Aluminum foil backing on gyplath, 1 (d) Space filled with fibrous insulati

2. fellow pine lap siding, 25/32-in. wood

sheathing, 2x4 stud space, l/2-in.

plaster on 3/8-in. gyplath.

Assumed air temperatures s 70° and 0° F

(a) Stud space uninsulated, one space, E = 0.82 .24

(b) Aluminum foil backing on gyplath, one space, E = 0.05 .18

(c) Stud space divided equally by ordinary kraft

paper or cardboard, 2 spaces, E = 0.82 for each .19

(d) Stud space divided equally by vapor-permeable

reflective paper sheet, 2 spaces, E = 0.20 for each .138

(e) Stud space divided equally by aluminum foil

sheet, 2 spaces, E = 0.05 for each .116*

(f) Stud space divided equally by 1-in. fibrous

blanket insulation with aluminum foil on warm side, 2 spaces, E = 0.05 and 0.82 .091

(g) Two-inch fibrous blanket insulation against

gyplath, with vapor-permeable reflective

paper on cold side, one space, E = 0.20 .078

(h) Same as (f), with ordinary paper on cold side

of blanket, one space, E = 0.82 .085

(i) Stud space divided into 3 equal spaces by

two sheets of aluminum foil, E (avg.) = 0.04 .077

*There may be danger of condensation of moisture on the foil surface,

depending upon temperature conditions and the relative humidity inside the building.

= 0.82 0.25

, E of space =0.20 .20

E of space =0.05 -18 on (if dry) .17

- 16 -
.
CEILINGS

3. l/2-irio plaster on 3/8-in. gyplath, 2x8 joist space,

25/32“in. yellow pine flooring.

Uw

is the U-value for winter conditions, with heat flow upward

and assumed air temperatures of 80® (room) and 10° F (attic)

Ug is the U“value for summer conditions, with heat flow down

ward and assumed air temperatures of 120® (attic)

(room)

(a)

0>)

No insulation in joist suace one space

E = 0„82

Aluminum foil hacking on gyplath, one space,

E = 0„05

(c) Reflective paper hacking on gyplath, one

space, E = 0 o 20

(d) Aluminum foil sheet dividing joist space

equally, 2 spaces, E = 0 o 05 for each

(e) Vapor-oe~meahle reflective paper sheet dividing

joist space equally, 2 spaces, E = 0„20 for ea

(f) 1 wo"inch blanket of fibrous insulation resting

on gyplath, with vapor“permeable reflective

paper on top side of blanket, one space,

E = 0„20

(g) One- inch blanket of fibrous insulation dividing

joist space equally, with aluminum foil mem- brane on underside of blanket, 2 spaces,

E = 0.05 and 0 o 82

(h) Four inches of fibrous

gyplath, one space, E

(i) Construction as shown,

reflective paper laid over joists in place

the wood flooring, one space, E = 0 o 20

top-surface film coefficient for reflective

paper taken as 1,30 Btu/hr ft^ (deg F) for

Uw and lo?0 for Ug

insulation resting on

=: 0o82

but with vapor-permeable

of

. 90® F

JSl. Us

0,30 0.25

.22 .038

.24 .156

.146* .052

l .170 .105

.084 o073

0IO5 .065

.055 »053

30 ,20

There may be danger of condensation of moisture on the foil surface

depending upon temperature conditions and the relative humidity

inside the building,.

“ 17“
I > ' \
FLOORS

4, 13/l6 “in 0 hardwood, flooring,

building paper, 25 / 32“in 0 yellow pine subf loo ring,

2 x 10 joists.

Assumed conditions? heat flow downward, from air at 65® (room)

to 3

^° 3P (under floor),

U

(a) Uninsulated floor 0,28

(b) Sheet of aluminum foil fastened to bottom of

joists, one space, E = 0„05 0 O7O

(c) Sheet of reflective paper fastened to bottom

of joists, one space, E = 0,20 ,114

(d) Sheet of l/2-inch rigid insulation board fastened

to bottom of joists, one space, E = 0,82 ,160

(e) Same as (d) but with sheet of aluminum foil

dividing joist space equally, 2 spaces,

E = 0,05 for each ,044

(f) Same as (d) but with sheet of reflective paper

dividing joist space equally, 2 spaces,

E = 0,20 for each ,075

(g) Two-inch fibrous blanket insulation installed

at midheight of joist space ,082

8, DISCUSSION AND HEMARES

Study of the U-values for the various constructions indicates,

among others, the following practical conclusions?

(1) The insulating effect of a furring or stud space can be

markedly increased at low cost by use of a reflective surface on

the back of the gyplath or other plaster base (compare Walls lb and

lc with la and Id, and Wall 2b with 2a)

(2) We 11- insulated walls can be made using reflective sheets

to subdivide the stud space. However, circulation of air between

spaces must be prevented by adequate sealing of each dividing membrane, and in the case of vapor-impermeable membranes, consideration

must be given to the possibility of moisture condensation on their

surfaces.

(3) The great value of reflective air spaces in reducing heat

flow downward is indicated by comparisons of the U-values for sum- mer and winter conditions for the ceiling constructions, and by

the very considerable insulating effect of reflective spaces used

under floors.

- 18-
. ' » \

'• I1

...

r \
One ceiling insulation application, not covered directly by the

data of this report, is worth consideration,, In the case of Ceiling

3i, the U-value for summer conditions (Ug = 0,20) does not tell the

whole story for the temperature conditions existing in an attic

heated by the sun—actually , a considerably better insulating effect

is achieved. The computations for the ceilings are based upon an

assumed temperature of 120° F for the attic air near the floor and

approximately that temperature for the attic surfaces „ In actual

fact, during the hours of solar heating, the underside of the roof

may reach temperatures of 140® F or more, Radiation from these hot

surfaces to floor or insulation surfaces of low reflective quality

(e = 0.9) may heat them to temperatures as high as 120° F, and for

such surfaces the temperature conditions assumed for the calculated

U-values are appropriate. However, for a reflective surface such

as a reflectively-coated paper (e = 0,2), the roof radiation is

largely reflected and the reflective surface temperature would not

exceed about 100° F for similar attic conditions. Consequently,

the effect of high reflectivity of the top surface of a ceiling

construction (the part that ’’sees'11 the roof) is to reduce markedly

the temperature difference acting to cause heat to flow through the

construction. For this reason, ceiling constructions such as 31*

and others having reflective exposed top surfaces, are more advantageous for summer conditions than the calculated U-value indicates.

Because the reflective surface in effect reduces the temperature

difference acting on the ceiling construction, its effect is, approximately, proportionately the same regardless of the insulating

value of the rest of the construction.

Since many attics are unfloored, at least in part, the advantages of reflective top surfaces can be provided at low cost, yet

with marked benefit under summer conditions, especially in hot sunny

climates. This may be accomplished by use of a blanket insulation

with a reflective surface on its top (or cold in winter) side,

placed between the joists, or by stretching a reflective sheet

material over the top of the joists, either parallel or perpendicular to them, whichever is more convenient. It should be pointed

out, however, that the reflective surface mu u. be quite permeable

to water vapor to avoid the possibility of moisture condensation on

its underside in winter, unless a better vapor barrier is also used

near the warm side of the const ruct ion.

-19-
. 1I_I '
SECTION A-A

. . ©

V .

\-T7-

Ji—

® TEST PANEL

® RUBBER GASKETS

® COLD BOX

@ GUARD BOX

© METER BOX

© REFRIGERATING COIL © ELECTRIC HEATERS

® AIR COMPOUND THERMOCOUPLES

® SURFACE COMPOUND THERMOCOUPLES © AIR TEMPERATURE THERMOCOUPLES

© AIR CIRCULATING FANS @ BAFFLES @ EDGE INSULATION

@ COMPRESSION SPRING HANDWHEELS © HEATER DUCTS © METER HEAT DIFFUSER

PLATE I

M IS

Plate 2

19 GAGE GALVANIZED SHEET

A

l6oc -'|

A

1 6 oc 32 0 c

O CD

CD G)

I6| 32oc

65J- I6f

3 FRAMES MADE 5/8 7/8,3 3/8, INCLUDING

FELTS GLUED TO FACES

COLD SIDE

_i 1 1 ,—1

WARM SIDE AL FOIL -

C S

BLACK PAINT

%

1

1 1

• f

1

1 1 / i

1

1 1 1 1 W.SREFL COATED PAPER BLACK PAINT

W S

C S

'A '/s '/ $ 8 fW.S

5.

| 8 .

1 1"

DIMENSIONS IN INCHES TEST PANEL s- SECTION A-A

PLATE 3

BTU

/

HR-FT

2

(

DEG.

F)

t~ rH~

MEAN TEMPERATURE 1

70 80

° F

FIGURE I

FIGURE

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AIR

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THICKNESS

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FIGURE

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o



THE NATIONAL BUREAU OF STANDARDS

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