Estimating temperature gradients and dew point temperatures for building envelopes

Publisher’s version / Version de l'éditeur: Building Practice Note, 1982-03-01

READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE.

https://nrc-publications.canada.ca/eng/copyright

Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la

première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n’arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca.

Questions? Contact the NRC Publications Archive team at

PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the first page of the publication for their contact information.

NRC Publications Archive

Archives des publications du CNRC

For the publisher’s version, please access the DOI link below./ Pour consulter la version de l’éditeur, utilisez le lien DOI ci-dessous.

https://doi.org/10.4224/20337944

Access and use of this website and the material on it are subject to the Terms and Conditions set forth at

Estimating temperature gradients and dew point temperatures for

building envelopes

Scheuneman, E. C.

https://publications-cnrc.canada.ca/fra/droits

L’accès à ce site Web et l’utilisation de son contenu sont assujettis aux conditions présentées dans le site LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D’UTILISER CE SITE WEB.

NRC Publications Record / Notice d'Archives des publications de CNRC: https://nrc-publications.canada.ca/eng/view/object/?id=2aa64730-07e9-40de-8bf1-a9c6f995bf61 https://publications-cnrc.canada.ca/fra/voir/objet/?id=2aa64730-07e9-40de-8bf1-a9c6f995bf61

ESTIMATING TFNPEBATURE

GRADIENTS

DEW

TEMPERATURES

FOR BUILDING M E L O P E S

Division

of Building

Research, National

R ~ S ~ T C ~

Council of

Canada

ESTIMATING TEMPERATURE GMDIEMTS AND DEW PQINT TEMPERATURES FOB

BUILDING

E.C. Scheuneman

It is useful and often essantfal t o h o w the temperature a d moisture conditions that exist throughout buildlng assemblies and

components. Such temperature and mofsture information may be utilized when d e s i g d u g a

.new

in

building, and planning t o retrofit a building. The temperature gradient and smkr/winter temperature extremes are of

ten

d e t e d n e the materials t o be used in a building envelope (exterior

s h e l l ) . A knawledge of air-mo$~ture/temperature conditions and

relationships I s essential in locating the vapour barrier d t h respect

to other components in the building assembly.

The following sections give simplified versions of temperature and dew point calmlations that are generally useful for a variety of

purposes. Results

from

TEMPERATURE Gl?ADmm

During c o l d weather the temperature at the interior surface of the building envelope, except for w i n d m s , will be close to t h e room

temperature. Moving outward through t h wall

or

becomes increasingly colder u n t i l 1 t reaches the outdoor tersgerature j u s t beyond the exterior fFnish. It: is poesXble to calculate and chart these tenperature changes through the various building caponents; this is

known

weather the outdoor temperature may be greater than the indoor temperature, h t the same general rules and procedures apply.

( 5 ) Temperature Change for Components

Before performing such calculations,

we

t h e basic relationshfp between thermal resistance of the building components and temperature drop {change) through each component.

The information in t h i s Note is based on reports given by DBR personnel

If we assttme that heat flows through each component under steady-

s t a t e parallel heat f l o w conditions,

then

where

AT =

%

ATT = total temperature change from interior to exterior

This assumption of steady-state condition means that the calculation w f l f be subject to errors, especially for rapidly changing outside a i r

temperatures. Nonetheless, i t provides useful information.

The forms, Ffgures 1

and

calculation

and

as

(These £ o m may be reproduced t o carry out your awn s t u d i e s , ) The general procedure

i a

a

(Bus) are found from Appendix A and used with the known interior and exterior teqexatures t o calculate the values (R, R/%, AT,T) t o

complete the cable. The temperatures are then plotted an the graph to give a p i c t o r i p l repreeedtation of the calculations. Note that. the Winter AT and T columns

are

Interior T; the S m r

AT

T

T.

TEM P E R A T U

RE

G

R A

I)

I

E N T

T A B L E

COMPONENT

DATE

ASSEMBLY

H O R I Z O N T A L A S S E M B L Y

OC

We w i l l now use the simple e q l e shown in Figure 3 to follow thtough the step-by-step procedure, The results are

shown

Determine the temperature gradient for the i l l u s t r a t e d wall assembly

(Fig. 3) with an interior temperature of 2 0 . 0 ° ~ and an exterior temperature of -15.U°C.

13 mrn G Y P S mrn M E T A L S I D I N G mm P L Y W O O D

Figure 3,

A

Stew 1

List the components in appropriate sequence in t h e table (Figure 4).

Step 2

Using a ruler or other straight-edge, draw the assembly on the

graph a f t e r choosing a s u i t a b l e scale. Designate the coupanents by

number. Step 3

Using t h e appropriate data from Appendix A, f i l l in the lt column in the t-kble.

S t e p 4

Add up a l l the R's t o give

%

bottom of t h e R column. Step 5

Calculate t h e ratio K/RT for each component. Total up the ratios

in this column and enter them in the TOTAL row at bottom of the R/% column. Note that t h i s total should always be very c l o s e or equal to

1.00; if not, recheck your c a l c u l a t i o n s for t h i s column.

S t e p 6

Write the i n t e r i o r ( 2 0 , 0 ° ~ ) and exterior ( - 1 5 . 0 " ~ ) temperatures in she appropriate p l a c e s under the Winter

T

S t e p 7

Calculate

ATT

Enter t h i s figure 135.0) in the TOTAL row at bottom of he AT column. (If the Exterior T is greater than the Interior T, subtract the Interior

T from t h e Exterior T . ) Step 8

Calculate AT for each component by m u l t i p l y i n g each R / K ~ times

ATT

should equal, or be very close ta, ATT. Lf not, recheck the calculations.

S t e p 9

F i l l in the Winter T column by adding the first component No. 1,

AT (0.4) to t h e T in the row above (Exterior T of -15.0) and p l a c i n g t h i s new T ( - 1 4 . 6 ) i n t h e row below component No. 1. Continue t h i s sequence of adding each AT to t h e T above and entering the new T i n t h e r w below. (When Exterior T is greater than Interior

T,

As

coqonent A T added to the preceding T (1.8

+

By glancing down t h e T column in the completed table, one sees the

temperatures on each s i d e (interface) of each component.

On the graph, mark the temperatures ( T ' s ) at each coqonenr edge

( i n t e r f a c e ) , and then draw s t r a i g h t lf nes joining e a c h p o i n t to t h e next. This completes both the arithmetic and graphic representations of t h e temperature or thermal gradient.

( i f ) Temperature at a S p e c i f i c P o i n t and Location of a Certain Temperature

We

the

temperature w i l l occur. Et is possible t o deternine these temperatures or points

by

Suppose we wish to know

(1)

(a) Graphical Method

'Phis is the easiest and quickest method. Use a straight-dge

r u n d a g vertically t o l i n e up with 35 mm from the cold side of the batt (73 mm from interior) and note the point of interaeckion with the

teqerature gradient line. This gives a value of about -lo. See vertical dashed line on Figure 4.

Use a straight-edge ruaaing horfzwtally t o line up with 5' and note the point of intersection with the temperature gradient l i n e . This gives a value of about 41 nua into the batr

from

4.)

(b) Arithmetic Method

This method may be preferred by many as it gives more exact values

than the graphical me tho& h e f ollawf ng

f

a

where

T

Tw

L

_T

A = temperature change across component

The following f o r m l a w i l l yield the location of a certain

temperature:

where

L

specific temperature

T

AT

$

For this e-ple dealfng with component No.

4,

which yields

The above two results are t h e same as those obtafned graphically (Figure 4 ) .

Note: The temperature gradient calculations for the Table qnd the

k i t h t i c Method are s h m w i t h a precis1 on of 1 or 2 decimal places; thig is done to maintain the relatfonship between the

d i f f e r e n t Rts, R / R ~ ~ s , AT'S and T's, It is m a t h a t i c a l l y convenient with electrouic calculators t o use t h i s degree of precision. The final results of calculaeions are rounded to the nearest whole unft of degrees C e l s i u s (OC) or m f l l t ~ t r e s (mm).

As previously mentioned, the temperature gradient

calculations assume steady-state conditioa~ which means that the rasulte are usually leas accurate than the nearest whole u n i t . However, the calculated values are generally close enough to be

useful, e s p e c i a l l y when looking at extreme or worst-case

situations.

Further explanation and examples can be found

in

(iii) Extreme Temperatures at Outer Surfaces

Qulte often the temperature of the outer surface of a b u t l d i n g assembly can be significantly higher or lower than the outside air

temp eratare. Higher temperatures result from absorption of solar (short-wave) radiation by the surface. Lower temperatures result from the surface g i v i n g o f f infrared (long-wave) radiation t o a clear n i g h t

sky or to o t h e r b o d i e s .

The following formulae have been developed to account for these

two effects on roof assemblies ( 4 , 5 ) . The references use degrees Fahrenheit (OF); this paper uses the formulae in degrees Celsius

(*C)-

terrrperature.

(a) High Heat Capacity Substrate

(such as concrete under the surface material)

HIGH DAY-TIME TEMPERATURE

TS =

TA

+

TS = TA

+

from other surf aces) LOW NIGHT-TIME TEMPEUTURE

TS =

TA

(such as insulation under the surf ace mater-lal)

HIGH DAY-TIME TEMPEMTURE

TS =

TA

+

TS = TA

+

from other s u r f a c e s )

LOW MZGHT-TIME TFXPERATURE

(clear night sky)

The deftnitions far the symbols are as follows: TS= temperature of surface ( O C )

TA = temperature of air (OC)

a = solar absorption coefficient (no units)

Appendix B gives a t a b l e of solar absorption coefficients for d i f f e r e n t

materzals. The value can be hfghly variable if the s u r f a c e

deteriorates, accumulates d i r t , or i s covered with water.

These extreme temperatures and temperature g r a d i e n t s s h o u l d b e u t i l i z e d when choosing materials requfred to withstand extreme

Example 2

A f l a t roof assembly built of a 100 m concrete deck (high density) with 25 mm extruded polystyrene on t o p covered w i t h built-up raaflng covered with grey gravel. Determine the extreme temperature gradients for this roof that receives no reflected sunshine for a summer high air temperature of 35% and a d n t e r low air temperature of -30°C. The following temperatures are u t i l i z e d :

-

-

Reace, mintmum surface temperature T = TA

-

TS = -30°

-

lo0

Hence, maximum surface temperature

TS

where a = 0.75 {from Appendix

B)

Since the max5mm and mfnimum temperatures occur on the surface material rather than i n the

air,

R,

AT

according

For comparison, the procedure has been carried out in Figure 6 with no surface temperature effects ( s o l i d line)

and

Figure 5 added (dashed lines). There is

a much

m i n i m temperature gradients. This illustrates that the heating effect

of solar radiation is nuch larger than the cooling efEecr produced by long-wave radiation, as shorn also by the temperature equations. For

further explanation

and

8 . DEW POINT TEIfFEBATURES

Relative humidity Ls the percentage ratio of the actual mount of water vapour h e l d in the air compared t o the maxtmrm I t could hold a t a given temperature. Far example, a relative humidity

CR.H.)

that the air is carrying o n e h a l f the total amount of water vapmr it is capable of holding at that temperature. Air with 100% R.H. has reached i t s saturation point; the water vapour I t holds will begin t o condense if the temperature drops or moxe moisture is added. The water vapour

wfll

T

is

Understanding the dew p o i n t and the moiature capacity of air is c r u c i a l to understanding condensation/moie ture problem f n bu i l d i n g a . When the temperature af air decreases, the m a d m u m amount of water vapour that the a i r can carry is reduced. For example, if air at 2 1 * C and 50% R.H. is cooled t o 1l0C, the RtR, w i l l reach 100% (the dew p o i n t ) . If the tenperature is lowered further, water w i l l condense out

of the a i r to maintan the R.H, at 100%. hferences 2b, 6 and 7 give further explanation and d e t a i l .

A

me

lines

fram

scale

(f) Finding the Dew Point Temperature

Par a Laom value of air temperature and relative humidity (R.H.]

one can use the psychromtric chart to f i n d the dew p o i n t temperature. The procedure is as folluws:

Step 1

Determine the air temperature inside the house by using a

thermonreter (or an assumed value),

Step 2

D e t e d n e the relative humtdfty i n s i d e the house using a sling psychrometer or a hygrometer (ar an assumed value). The R.R. values

recorded by hygrometers may be in error by as rsuch as

20%

S t e p 3

On

Starting at the intersection p o i n t , run a straight-edge parallel to the bottom OC scale and left to cross the curved lOOX R.H. line. The crossing point gives the dew point temperature.

Example 3

Three examples are s h m in Fl.gure 8:

3(a) The house interror a i r temperature is 2S°C and the R.B. is

60%. The dew point teqerature at: which water v a p w r w i l l

condense as l i q u i d for this situation is 16.5OC.

Water vapour w i l l condense out as l i q u i d at 10.5V

3(c) T = 17%

R.H. = 25%

Water vapour will condense o u t as ice a t the dew point

temperature of -3*C.

Cii) Finding the New B.H. After a Temperature Change

As previously noted, the capacity of a i r t o hold water vapour 3 s

different fur different temperatures. The hfgher the

air

The procedure to f i n d the new R.H. after a temperature change is

as follows:

S t e p 1

Locate the point on the psychrametric chart that corresponds to the o r i g i n a l teuperature and relative humidity.

Step 2

U s i n g a straight-edge, p r o j e c t a horfeontal l i n e to the new

temperature. The point of intersection with the curved

R,H.

Example 4

Three examples are shown in Figure 9 :

4(a)

a i r

R.H.

R.E1. when the a i r Is cooled to 10°C? (R.H. becomes 75%,) 4(b)

T

R.H. = 80%

What is the R.B. when t h i s

warm,

4(e)

T

What is the R.H. when t h h c o a l outside air is brought into

the house and warmed to 20"C? {R.B* becomes 8X which is very d q .

1

LOCATION OF DEW

POINT

A double-glazed window has temperature gradients as shown in

F i g u r e 10. When t h e house T = 22°C and

R.H.

Ue calculate the values to complete the t a b l e and draw the

temperature profile. Referring to the psgchroretric chart ( F i g . 7 ) , we

f i n d that air at 22%

and

As the glass l a colder than the dew point, water vapour will condense as

l i q u i d on the wf n d w .

Since the i n s i d e glass of a window is usually the coldest surface in a room, it determines the m a d u u m R.H. that can be maintained without condensation. U s i n g t r i p l e glazing raises the inside glass temperature and, thus, the maintained R,H.

T E M P E R A T U R E G R A D I E N T

T A B L E

NAME

DATE

ASSEMBLY

FIGURE 10.

E X A M P L E 5

Example 6

We have a partly-insulated wall as s h m fn Figure: 11. Where

will

barrier? The conditions are as follows: Interior T = 18OC

Exterior T = -35OC inside R.H. = 30%

The table and profile are calculated and drawn, The psychrometric

thart reveals that the dew point temperature is 0°C- (1) Graphical Method

We can see at a glance that: O°C lies within the rack wool insulation. By drawing a horizontal line from the O 0 point on the teqerature scale, we find that 0' occure at about 22

mm

Interior s i d e of t h e batt (35 mm f r o m interior surface), Arithmetic Hethcd

using $pu.ation (33,

Results from both ti) and (ii) agree.

Note: This discussion applies when the temperature og the

-

iasulation has reached

or is

Uuder steady-stalte conditions the water vapour would

continue to d i f f u s e through those tnsulatLons that have little resistance t o moisture flow; the water vapour would condense on the next colder interface such as the exterior sheathing which has a

much

insulation or other materiah in the assembly have a high resistance to moisture flow Cdlffusion), a vapour pressure

gradient s h w l d be drawn (see R e f erenee 71.

When

water

warm a i r f l o w rather than vapour diffusion, condensatton can occur within the insulation unless the velocity of the aZr flow ia high enough t o warm up the insulation and carry the vapaur

T E M P E R A T U R E G R A D

1

E N T

T A B L E

I

COMPONENT

I

I

I

SUMMER

I

WINTER

I

G R A P H

NAME

DATE

ADDRESS

ASSEMBLY

A c e i l h g is going to be reinsulated with

new

f i k r g l a s s batts over the origxual

63

we

mm

before adding the new i~aulation?

Lf

The c o d i tioas are as follaws: inside T = 20%

attic

T

inside

R.H.

The table and temperature profile are completed as in Pigtrre 12.

Using the psychrometric chart w e find that condensation should occur at about 2°C. h o k i n g at the table and p r o f i l e we see that the vapour barrier temperature is 4°C. Since this 2s alightly higher than the dew p o i n t temperature, no condensation should occur under these condirions as the vapwr barrier w i l l prevent water vapour from reaching the dew p o i n t temperature which is located within the new insulation.

It should be noted that changing conditions can alter the s i t u a t i o n .

(i) If the R.H. of the house rises t o 3 5 % , the dew poFnt teuperature rises to 4OC. Water vapour can condense at the vapoux barrier (if vapour can pass through the c e i l i n g ) and then d r t p or d i f f u s e back d w n to the ceiling.

Iii) If the a t t i c temperature drops to -35°C instead of -30°C, then the vapour barrier temperature becomes 2.4' which is close to t h e dew point temperature,

When the vapour barrier temperature fs below the dew polnt temperature as a result of very cold weather a x high indoor R.H., there may nat be a condensation problem if t h i s situation occurs for only a few days each heating season s i n c e the building assembly can hold

certain

moisture with no

problem- This analysis assumes that the vapour barrier is camplete and that there are no air leakage paths through the polyethylene vapatr barrier.

T E M P E R A T U R E

G R A D I E N T

T A B L E

COMPONENT SUMMER

WINTER

R R/RT *

A T I

T

A T I

r

NAME

DATE

ASSEMBLY

T E M P E R A T U R E ,

FIGURE

1 2 ,

E X A M P L E

7

The following references . e v e more detailed and technical

explanat I o n of the concepts discussed in this paper,

( 1 ) LatEa, J.K. and Garden, G.K., Temperature Gradients Through

Building Envelapea, Matima1 Research Council of Canada, D i v i s i o n of Build- Research, CXD 36, 1962 (corrected 1968).

(2) Latta, J8K-b Walls, Windows and Roofs for the Canadfan Climate,

National Research Council of Canada, Divlsion of Building Research, Special Technical Publication No. 1, 1973.

NRCC 13487.

(3) Baker, M.C., Roofs: Design, Application a d Maintenance,

National Research Council of Canada, (Multiscience Publications Limited,

Montreal),

1980,

( 4 ) Stephenson, D.G., Extreme Temperaturea at the Outer Surfaces of Buildings, Nat ianal Research Council of Canada, M v i s i o n o f Building Research, CBD

47,

(5) Garden,

G.K.,

( 6 ) Hutcheon, N.B., Humidity id Canadian Buildings, National

Research Council of Canada, Divf sion of Buildt ng Research,

CBD

1960 (corrected 2968).

(7) Lettta, J.K. and Beach, R.K., Vapour Diffusion and Condensation,

N a t i o n a l Research Council of Canada, Division of Building

THERMAL

RESISTANCE

-

a/-

Rockwool Loose Fill (Blown-In)

Rodcwol Loose F i l l (Poured) Cellulose Pibre (Blown) Cellulose Fibre (Poured)

Expanded Mica

(Vermiculite, Zonollte, etc.)

Polystyrene Loose Pill

Expanded PoIystyrene { U g t d ) Extruded Polystyrene (figid] Polyurethane (Rigid)

Polyurethane ( F o a i ~ d i n Place)

Fibreglass Sheathing

Urea Formaldehyde (Foamed in Place, After Curiug)

Wood Fibre

Wood Shavings Cork

Glass F i b r e Roof Hoard

Mineral Aggregate Board Coupressed Straw Board Fibrebaard

Structural Haterials

Saf m o d Lumber (except Cedar) Cedar Logs and Lumber

Concrete 2400 kg/m3 (150 l b / f t 3 ) Concrete 176U k g l m 3 (1 10 l b / f t3)

Concrete 480 kg/m3 (30 l b / f t 3 1

* H E E n Scheuneman, S .

Moff a t t and M. Adelaat, Canadian General Standards Board. CGSB 51-GP-42MP, Ottawa, July 1980.

THERMAL RESISTANCE OF SOME COMMON BUILDING MATERIALS (Cont'd) Thermal Res 1 stance

Building Material or Component S.I. R/mm For I m p e r i a l Rlin. Po r Thickness Listed Thickness L i s t e d Structural Materials ( C o n t ' d )

Concrete Block (3 Oval Core) Sand and Gravel Aggregate

100 mm (4") 200 mm ( 8 " ) 300 mm (12") Cinder Aggregate

loo

Conrmon Brick, Clay, 100 nrm ( 4 " )

Common Brick, Concrete, 100 mm ( 4 " )

Stone ( L i m e or Sand)

S t e e l

Aluminum

Glass (No Air F i l n r s ) 3

-

(1/8"

-

Air

-

Enclosed Air Space (Non-Reflective) Heat F l o w Up, 25

-

(1'. - 4 " ) ---

Heat Flow Down, 25

-

(1"

-

--

25 - 100 mm (1" - 4 " )

--

---

Outside Air Film (Pioving A i r ) -- 0.03

---

Horizontal, Heat F l o w Up

-

--

S l o p i n g 4 5 " , Heat Flow Up

-

-

--

-

THERMAL

BUILDING

-

B/mm For

in.

Thickness Thickness

Listed L i s t e d

Asphalt Roll Roofing

--

Asphalt Shingles -.- 0 -08

Wood Shingles (Cedar Shakes)

--

--

Crushed Stone ( N o t Dried) 0.00055

--

Saftwoad Plywood

Mat-Formed Particle Board

Insulating Fibreboard Sheathing Gypsum Sheathing

Sheathing Paper

Asphalt-Coated W a f t Paper

Polyethylene Vapour

Barrier

-

--

---

---

--

-

--

Hardboard,

High Density Hardboard,

11 mm (7116")

Softwood Siding (Lapped)

Drop, 18 x 184 m (3/4" x 7

t " )

--

-

Bevel, 18 x 235 nm (3/4" x

9

--

Plywood, 9 tam (3/8")

--

Woad Shingles

_-

Brick (Clay or Shale) 100

mm

(4")

-

loo

mm

---

.

THERMAL RBSISTANCE OF SOW

COMMON

Building Material

or Component

S.I. I m p e r i a l

R/w For

in.

Thf ckness Thicknes s

Listed L f s t e d

Cladding MaterLals (Conr'dj Hecal Siding

Horizontal Clapboard Profile

Horizontal Clapboard w i t h

Backing

Vertical V-Groove Profile

Vertical Board and Batten Profile

Interior Finishes

Gypsum Boaxd, Gypsum Lath,

Drywall, 13 mm

(4")

( 3 " )

nrm

0")

Maple or Oak (hardwood), 19 mm ( 3 1 4 " )

Pine or Fir ( s o f t w o o d ) ,

19 mm ( 3 1 4 " )

Plywood, 16 nrm (518") Mat-formed Particle Board,

16 mm (5/8")

Wood F i b r e Tiles, 13 ma

Linoleum, Tile ( r e s i l i e n t ) ,

3 mm ( 1 1 8 " )

Terrazzo, 25 rmrt (I")

Carpet, Typical Thickness

with F i b r o u s Underlay

T H E W

RESISTANCE

S.I.

n.

(including i n s i d e and outside

air

Insulated Glass (.Double Pane)

5 mm (3116") Air Space 6 mm

E*")

6 mm

(i")

13 mm

{i")

19

aun

S t o m Wtndows

Single Pane

+

-

(1"

-

+

T a b l e B-1. Roofing Materials

Copper

-

-

-

-

Galvamized Iron

-

- weathered S t e e l

-

white

-

-

-

Lead Sheeting

-

~ s b e s t o s / ~ e w n t :

-

-

Table B-2. Masonry Bricks

-

-

-

-

-

Sandstune

-

fawn

-

-

-

-

0 -42

0.8U Granite

-

-

Grey Gravel - weathered 0.75 White Gravel

-

Table B-3. Faints

(can vary for different shades)

-

-

-

-

-

-

*

of

References for Appendix 3

Baker, M.C., Roofs: Design, Application and Maintenance, Multiscience

Publications Limited, Montreal, 1980, page 134.

M f i e , J.A., and W.A. B e c h n , Solar Energy Thermal Process, Wiley- Interscfence, John Wiley & Sons, Toronto, 1974, page 97.

Garden, G.K., Therraal Considerations in Roof Design, Canadian Building Digest 70, National Research Council, O t t a w a , October 1965,

page 70-3.

Kreider, 3 . F . , and F. Kreith, Solar Heating and Cooling: Engineering,

Practical

Pub1,isMng Corporation, McGraw-Hill, Toronto, 1977, page 247.

S t r o c k , C., and R.L. Koral, Handbook of A i r Conditioning Heating and Ventilating, Second Edition, Industrial P r e s s , New York, 1965, p. 1

-