Moisture in transient heat flow

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Heating, Piping, Air Conditioning, pp. 137-142, 1955-11

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Moisture in transient heat flow

Solvason, K. R.

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Moisture in Transient Heat

Flow

By

I<.

R. Solvason*, Ottawa, Canada

CALCULATION of building heat losses and gains is normally based upon coefficients obtained for dry materials. The presence of moisture, when taken into account, is usually con- sidered to influence the heat transmission by increasing the thermal conductivity. Moisture, according to this simple concept, introduces little additional complication into the calculation of heat flow if it remained stationary within the materials involved. Hutcheon and Paxtonl have shown that in a hygroscopic material such as wood sawdust the moisture migrates under changing temperature conditions, thus providing a substantial additional mechanism of heat transmission.

Hutcheon and Paxtonl demon- strated that for wood sawdust, the final redistribution of moisture following imposition of a fixed temperature gradient on the moist sample, could be predicted from the

'Assistant Research Officer, Division of Build- ing Research, National Research Council.

'Moisture M i ration in a Closed Guarded Hot Plate by N fl. Hutcheon and J. A. Paxton (ASHVE TRANSACTIONS, VOI. 58, 1952, p. 301). For presentation at the G2nd Annual Meeting of the AMERICAN SOCIETY O P HEATING A N D AIR- CONDITIONING ENGINEERS, Cincinnati. Ohio, Jan- uary 1956.

SUMMARY

-

Measuremeiits were made of the effects of mois- ture upon the heat flow in simple cases of transient heat flow es- tablisliecl under control in lab- oratory apparatus. Samples of various materials, but mainly of the building insulation type, 7

in. square and up to 2 in. thicli were enclosed in a special cell, between hollow plates through which liquid was circulated for heating or cooling. Variatiol~ of heat flow with time is shown for various amounts of moisture present and compared to both tlie experimental ancl calculated transient conditions for clry ma- terials. Very substantial modi- fications to tlie heat flow uncler trcnsient conditions result from the presence of moisture.

known hygroscopic properties of the sawdust. Following their method the moisture redistribution throughout a sealed sample of sawdust containing

8 percent moisture by weight, has been calculated, and is shown in Fig. 1, for a change from a uniform temperature of 60

F

throughout, to 100

F

one side and 6 0 F on the other.

If the sample thickness is 4 in. and the density of dry material is 6 lb per cu ft, approximately 0.022 Ib of water per sq ft of sample area must be evaporated in the region from

x / L

= 0 to

x / L

= 0.6, migrate as vapor, and be condensed in the region from

x / L

= 0.6 to

x / L

= 1.

Assuming the latent heat of evaporation to be 1000 Btu per Ib, a heat flow of 22 Btu per s q f t across the plane

x / L

= 0.6 results because of the vapor flow.

Once redistributed, the moisture, at least i n sawdust, adds little to the heat transfer rate for the dry material. During the redistribution, however, the heat transmission is increased because of the vapor transfer and there is a marked deviation from the conditions for the corresponding case of dry materials.

This mechanism and its effects have now been further examined for several combinations of materials and temperatures.

Tests

Samplcs of a number of materials, singly and in combination, 7 in. square and of thicknesses up to 2

Heating, Piping & Air Conditioning, November 1955 137

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heated and cooled plates. Tests were carried out with the materials dry and then with moisture added. Transient conditions were established by suddenly changing the temperature of one plate, and heat flow rates and temperatures were recorded throughout the test period until con- tlilions had substantially "reached steady state.

The materials tested included the follo~ving composite and homoge- neous samples:

Test No. 1: In this test preformed glass wool was placed between two pieces of fiberboard '/z in. thick and with a density of 15.25 Ib per cu ft, or a total weight 1.27 Ib per sq f t of area. T h e glass lvool was 7/8 in. thick and had a density of 11.1 Ib per cu ft, or a total weight 0.81 Ib per sq ft. T h e moisture contents tested were zero and approximately 5.1 percent of the dry weight of fiberboa~d or a total of 0.065 lb per sq ft.

Test No. 2: I n this test preformed glass wool was placed between two sheets of blotting paper 0.023 in. thick and with density 33.1 lb per cu ft. T h e total weight of paper was 0.127 lb per sq ft. T h e glass wool had a thickness of 7/R in. and a density of 12.4 Ib per cu ft. T h e moisture contents were zero, 0.0325 and 0.065 Ib pel sq ft.

Test No. 3: I n this test the material used \\as expanded vermiculite, screened through a 13-mesli screen, having a thickness of 1% in. and a deusity of 16.3 Ib per cu ft, or a weight of 1.70 lb per sq ft. Rloisture contents of zero and 0.065 l b per sq f t of area or 3.8 percent of the dry weight of material were tested.

Test No. 4 : T h e material used was rprrlce sawdust, 2.156 in. thick having a density of 12.0 Ib per cu i t , or a weight of 2.656 Ib per sq ft. The moisture contents were zero and 9 percent of the dry weight or 0.194 Ib per sq f t of area.

Apparatus a i d Test Procedure The testing apparatus developed by Hutcheon and Paxton and modified slightly for these tests, is shown in Fig. 2. It consisted of two 7 - in. square hollow alumillurn plates between which the test samples were placed. Water at a controlled temperature was circulated through a chan- nel in the plates to produce the de- sired plate temperatures. Multiple thermocouple bakelite heat meters 4% in. square by 3/64, in. thick were cemented to the central por- tions of the ~ l a t e s to measure the

~nented to the remaining area of the plates surrounding the meters to provide a guard area around the

Z U-l

~ S 1 ~2 3 O 4 5 6 7 8 9 1 0 X / L

Fig. 1-Temperature, relative humidity, and moisture distribution in wood sawdust w i t h average moisture content of 8

percent for T I T? = 60 F (broken line) and T I = 100 F, T? = 60 F (full line)

h A S A M P L E V Y

I

Fig. 2-Testing apparatus - both liquid reservoirs are provided w i t h electronic temperature control

meters. Thermocouples embedded in the plate surface were used to measure plate temperatures.

The hot plate temperature was maintained by circulating water from an electrically heated 5-gal reservoir. The cold plate was supplied with water from a refrigerated 60-gal reservoir. A valve arrangement permitted either hot or cold water to be circulated through both Heating, Pipin

the other. Water temperatures had to be accurately controlled since a rapid change in water and plate temperature even though of very small amplitude would cause a large change in the heat meter voltage. _-

A commercial electronic temperature controller was adapted to provide a modulatiilg form of control lor boll1 reservoirs.

In tests Nos. 1, 2 a n d 3, samples with thermocouples spaced at intervals as shown in Fig. 2 were sealed in polyethylene bags a n d placed between the plates. Cold water (temperature T , = 6 0

F

approximately) was circulated through both plates until the temperature at all planes reached plate temperature. Hot water (temperature T I = 100

F

approximately) was then substituted for the cold water in the plate at x = 0. Starting at the time of the tempera- ture change ( d = 0) readings of the heat meter voltages a n d of the temperatures were taken a t definite time intervals until very nearly steady state coilditions prevailed. T h e electronic temperature indicator used was suit- ably modified to give heat meter voltages as well as temperatures.

The temperatures T I and T , were maintained for sufficient time to en- sure steady state conditions and the conductallce for the dry sample was obtained. The temperature at the plate x = 0 was then suddenly reduced to T , and heat flows and temperatures again recorded.

With the sample a t temperature T , throughout, a measured amount of water was introduced near the plate x = 0, without disturbing the plate spacing or the sample in any way, and sufficient time was allowed to permit the water to become distributed. The transient heat flow and temperature relationships for the sample were again recorded.

Test No. 4 was performed using an apparatus similar to that used in tests 1, 2 and 3 but with pro- vision to control the plate temperatures from 1 0 F to 8 0

F.

Heat flow was measured at the x = 0 boundary only. The

late

temperatures f o r this test were T , = 41

F ,

T I in- & Air Conditioning, November 1955

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creased lrom 4 1 F to 79 F ; TI =

79 F, T2 increased from 4f1

F to 79 F ;

and

T ,

= 12 F, T1 increased fro111

12 F to 47 F.

Theoretical Heat Flow

The temperature and heat flow relationships following such sudden boundary temperature changes can be expressed by solutions of the Fourier equation :

sT/se = a (sZT/s,?),

where

T = temperature ( F ) . 8 = time ( h o ~ ~ r s ) .

.z = distance from the reference boundary (feet).

a: = k ~ ' ~ c , the thermal diffllsivity, square feet per hour.

k = thermal conductivity, Btu per ( h o u r ) (square foot) (Fahren- heit degrees per foot).

p = density, pounds per rubic foot. c = specific heat, Btu per (pound)

(Fahrenheit degree).

I l the temperature is initially T, at all planes and at time 0 = 0 the temperature at x = 0 is suddenly increased to TI, while at x

L

the temperature remains at T,, the temperature is given by:

where

z = T'~/L'.

The heat flow at x = 0 will be given by

which can be written

Q, = Q , rl

+

S ( ~ e ) ]

... .

.

.. .

( 2 )

where

Qs the final steady state heat flow wliich is seen to equal K/L ( T I - T , ) .

S (20) = the series,

Similarly at x = 1, the heat flow will he

If after steady state conditions have heen attained with temperatures

TI

at x

-

0 and

I',

at x = I,, i.e.

T T,

+

( T I - T,) ( 1 - x / L ) , the temperature at x = 0 is sud-

I 1 l 1 l l l l l I 1 1 1 1 1 1 1 I i 1 l l l l l l

0.3 0 . 5 1 2 3 4 6 810

VALUES OF z e =J.- e/2

Fig. 3-Theoretical h e a t flow 9 s . s' at/

L2 following sudden temperature changes. a t x = O

clenly reduced to T,, the temperature and heat flow relations are given by:

Q, = - Q , LS ( z e ) ]

... .. .. ...

( 5 ) QL = QI [ B (28) I .

.

. . .

.

. .

. ( 6 )

where

Qs = the steady state heat flow before time 0 = 0.

S

(z0)and B (20) = the series as in Equations 2 and 3.

Typical values of Qo/Qs ancl QL/Qs, which will hereinafter be re- ferred to as the relative heat flows, are plotted against (20 = rrZa0/L' in Fig. 3, using calculated values of

S (20) and tables of

B (20).

Experimental heat flow values may deviate from the theoretical values due to departure from unidirectional heat flow and to the finite time required to produce a boundary temperature change.

The equations may, however, be used as a check on experimental values for dry materials and as a basis of comparison for the corre-

sponding observatioils with mois terials. They may also be use examine the extent to which th with moisture present may be repr sented by the case for the dry material with adjustments to the co- eff icients.

Discussion oP Results

The relative heat flows Qo/Qs ancl QJQs (Qs = the steady state heat flow for d r y material) are presented graphically in Figs. 48, 5, 6 and 7, for tests Nos. 1, 2, 3 and 4 respectively. The temperature rise with time at various planes in test No. 2 is shown i n Fig. 8. A logarithmic time scale is used, in all cases, as a convenient base for plotting.

The presence of moisture, as was expected, very markedly increased the transient heat flows occurring when TI at x = 0 was increased. Ail illcrease in heat flow occurred not only at the x = 0 boundary but also at the x = L boundary. nlaximum relative heat flows QI,/Qs of 1.4 (Fig. 4,), 2.6 (Fig. 5 ) ancl 1.3 (Fig. 6 ) were observed in tests 1, 2 and 3 respectively. These values, according to the theory lor dry materials, (Equation 3 ) shoulcl have ap- proached but not exceeded the final steady state values of 1.05, 1.02 and 1.025 respectively which were found 1% ith moisture present.

The time required to reach a given value of QJQs was considerably reduced with moisture present. Com- parative times. lor example. to reach QJQs = 0.9 were 27/44, 3.5/16 and 15/19 for tests Nos. 1, 2 and 3 respectively.

It may be noted that the results just presented for the case of an increase in Tl from 6 0 F to 100 F, T, remaining at 60

F.

a r e for the first such operation, following intro- duction of the water near the x = 0 plate. The corresponding curves obtained for subsequent cycles produced by reducing T, to 60 F a n d then increasing to 100 F a second time did not show exactly the same moisture effects as the initial curves. The in- Heating, Piping & Air Conditioning, November 1955

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f interest also to

eriod. This can be found from the area between the curves for the wet ndition and that for the dry test. e cumulative increase in heat flows at the x = L plate, for various times

I l l l l l l l 1 1 1 I l l 1 1 I l l I F I B E R B O A R D - - - - I ,

1

1 I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I l l 3 4 56 8 10 15 20 ZO40 60 100 200 400 800 TlME IN MINUTES Lcgcnd lo & 11.: M/C = 0 1 30 & 31.: M/C = 0.065 Ib/ft=f T2 = 6 0 F TI ~ncrcased GOF to lOOF at 0 = 0 20 & 21.: M/C = 0 I 40 & 4r.: M/C = 0 065 Ib/ft2[ TZ = GOF T I decreased IOOF to 6 0 F at 0 = 0 F1n.11 Q/Qs for 30 & 31. = 1 05 Q s = 6.72 Btu/hr for A?' = 4 0 F

Fig. 4-Heat flow vs. time for glass wool and fiberboard combination following sudden boundary temperature changes

(test No. 1)

siderable time to seek a uniform distribution was prevented from reach- ing this condition because of the hysteresis effect in adsorption and desorption, so that the first operatio11 following addition of the water always began with a higher moisture content near the x = O side.

The curves presented show the in- slantaneous rates of heat flow. It is

after increase of

T , ,

are given in Table 1 for the case of

T ,

increased

I " ' " '

" ' " '

'

' " I

0 - T H E O R E T I C A L FOR l . 3

#

O L . 0.00725

.

- 1 53 x 0 / 0 5 FOR O R Y M A T E R I A L -2.0 I 5 3 4 6 8 10 20 30 60 100 200 400

J

TlME IN M I N U T E S Legend l o & 11.: Ivf/C = 0 30 & 31.: M/C = 0.0325 Ib/ftZ 50 & 51,: M/C = 0.065 Ib/ft2 T : = 6 0 F T I increased GOF to IOOF at 8 = 0 2u X. 21,: M/C = 0 1 -10 & 41,: M/C = 0.065 Ib/ft2f T : = 6 0 F T I decreased IOOF to 6 0 F at 8 = 0 Final Q/Qs for 50 & 51.

-

1.02 Q = 10.8 Btu/hr for AT = 4 0 F

Fig. 5-Heat flow 1's. time for glass wool and blotting paper combination following s u d d e n boundary temperature changes (test No. 2). L = 0.921 in./12 ft

from 60 F to 100 F. The results for test No. 4 with sawdust are not included since heat flow was metered only a1 x = 0.

It may be noted that the corresponding latent heat transmission, if all the water were evaporated a t x

Table 1-Increase in Heat Flow in Btu at the x = 0 Plate at Various Times Following an Increase in Tl from 60 to 100 F

-

hfo~sture T ~ m e from tncrease of T I ( h r ) Increase at Tcst No.

1

t

1

0.5

I

1

3

I

6

1

20

1

6 hr in % of latent heat value 1. F~berboard

and glass wool 0 0 6 1 0 1 1 7 6.2 10.6 23.7 16 2. Blotting 0.032 6.9 9 6 12.0 13.0 13.9 4 3 paper and

glass wool 0.065 9.2 15 6 24.7 27.9 30 4 4 7 3. Expanded

verrniculitc 0.061 0 64 5 8 9 1 12.7 24.6 3 8

= 0, moved as vapor and condensecl a1 x = L, would be 32 and 65 Btu for the two moisture contents. The increased heat flow at the end of 6 hr varied from 1 6 percent of this lalent heat value for test No. 1 with

he fiberboard and glass wool sample to 47 percent in test No. 2 for the blotting paper and glass wool sample. However, in test NO. 1 the cumulative increase in heat flow was still growing and at the end of 20 h r had amounted to 36 percent of the latent heat value.

The effects of moisture on the heat flows in the cases in which the temperature

T ,

at the x = 0 boundary

0 - T H E O R E T I C A L FOR 0 0101

.

- I 12 ~ o / a , F O A M / C : o 2 3 6 8 10 002- 400 T l M E IN MINUTES Legend lo & 1 1 . M/C = 0 3u & 31'~: M/C = 0.06s Ib/ft2] Tz = 60F T I increased GOF to IOOF at 0 = 0 20 & 21.: M/C = 0 1 4u & 4 ~ : M/C = 0.065 Ib/ftZf T : = GOF T I decreased IOOF to 6 0 F at 0 = 0 F ~ n a l Q/Qs for 30 & 31, = 1.025 Q = 11.2 Btu/hr for AT = 4 0 F

Fig. &-Heat flow 0s. time for expanded vermiculite following sudden boundary temperature changes (test No. 3)

was reduced from 1 0 0

F

to 60

F,

T 2

at x = L remaining constant at 60 F, were of the same order as those occurring upon an increase in

T ,

lrom 6 0 F to 100 F as just discussed. The heat flow out at x = 0 following a decrease of

T ,

was increased by the presence of moisture. The heat flow out at x =

L,

which in the dry case decreased gradually from the steady state value to zero, was caused by the presence of moisture to decrease much more rapidly, then to

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ture present, heat flowed out at both sides, gradually reducing to zero as temperatures equalize. However, with

by rise to the first maximum indicates which is followed by drop indicating re- reached values of evaporation and finally a slow rise e value for the dry material as the evaporation is com-

is being condensed and again by conduction to the cold boundar Thus, in effect, the heat flow can b THEORETICAL H E A T FLOW F O R

-

: 0 . 0 0 7 9 0 the evaporating and condensing r

gions.

Fig. 7-Heat flow or.

During part of the transient wit

time for spruce saw-

dust following sudden moisture present the heat flow at b o u n d a r y temperature = 0, appears, in some of the tests, changes (test N o . 4 ) to be a constant multiple of the heat flow for the dry material. Points have been plotted in Figs. 5 and G showing

1.53 and 1.12 times the heat flow fo

the dry material. These agree fair1 TIME IN M I N U T E S material for the time from 0 = 0

During the transient period, the _{1 1 0 2} ₃ ₄ ₆ _{8 10} ₂₀T I M E _{30 40}IN M I N U T E S _{60 80 I00} ₂₀₀ _{400 600}

moisture present, which was redistributed by a process of evaporation, vapor flow and condensation as the temperatures equalized, heat had to be provided for the evaporation and absorbed upon condensation. The net heat flow out at both sides must

always equal the difference in heat _{I O O -} stored in the material between initial

95 and final conditions. Without mois-

heat of evaporation was supplied partly from the plate at n- =

L

and partly by coliduction from the condensing region. The balance of the heat liberated upon condensation moved by conduction to the plate at

x = 0. The heat required for evapo-

ration was first drawn from the sen- sible heat in the material, but as the evaporation colltiliued, the ternpera- ture was reduced below 60 F, result- ing ill a heat flow i r ~ at x = L.

During the redistribution, moisture evaporated at one plane need not necessarily migrate to another plane

I I I I I

, X = 0 0 0 0 800

/

4

__---

-

5;

~Toy7-

_-

ancl remain there: but may succes- sively be condensed and re-evaporated at several intermediate planes. This pheliomenon is illustrated by the temperature curves for test No.

2 (Fig. 8 ) . The rapid temperature

L E G E N D

-

MOISTURE C O N T E N T = 0

---

M O I S T U R E C O N T E N T = 0 065 L B / F T ' T2= 60 F , T, I N C R E A S E D 60 F T O I00 F A T 8 = 0

Fig. 8-Temperature rise us. time at various planes for glass wool blot- ting paper combination (test N o . 2)

pleted. The amount of moisture pres- until steady state conditions were ent in this test was more than could

be absorbed hygroscopically, leading to rather high humidities, so that this effect was more pronounced than ~vould normally be expected.

A mathematical treatment of the case with moisture present would 11e complicated since the conductive heat

reached with the dry material. The x = 0 heat flow with moisture can be represented approximately by equation 2 using a lower value for a.

This device does not, however, use- fully describe the heat flow a t x =

L

since Q L / Q s (Equation 3 ) can still only equal unity, while in the actual flow and the latent heat flow are so case a value greater than unity is inter-related. The latent heat flow found.

must operate both in series and in While no simple correlation be- parallel with the co~iductive heat flow, tween heat flow and moisture move- since lieat must flow by conduction ment is evident, the magnitude of the to the plane at which water is being increase in heat flow observed in the

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tests with moisture does illdicate some of the factors involved.

The larger of the two moisture con- telits iu test No. 2 is seen to produce a much larger increase in heat flow. Comparing tests Nos. 1 and 2, with equal total amounts of moisture, a much greater increase in heat flow resulted in test No. 2. This can be attributed to the lower thermal resistance between the heat source and the moisture source and also between the moisture sink and the heat sink. The expanded vermiculite (test No. 3 ) exhibited a relatively smaller increase in heat flow. I t is thought thal the water present was more intimate- ly bound in this material and permitted a much lower rate of evaporation.

I n test No. 4 the higher tempera- lure level test procluced a larger increase in heat flow. The 9 percent moisture content at 4 1 F indicates a relative humidity of 47.5 percent or a vapor pressure of 0.122 in. Hg. Upon increasing the temperature a1

x = 0 to 7 9

F

the vapor pressure could rise momentarily to approximately 0.500 in. Hg, producing a l a p o r pressure difference of 0.378 in. Hg. The corresponding vapor pressure difference produced by in- creasilig T, from 12 F to 47

F

woulcl only be 0.124, in. Hg, res~llting in the smaller increase in heal flow. Tests at a 2 0 F temperature difference

(TI

= 60,

T?

= 4 0 not s h o ~ v r ~ here) produced practically the same relative heat flow as a 4 0 deg temperature difference

(TI = 80, T2

= 4'0). With one-half the temperature difference, very nearly one-half the initial vapor pressure difference results and hence he same relativc heat flows. Since a vapor flow is necessary to produce the increased heat flows il- lustraled, the vapor permeability of

the materials can be expected to have a marked influence on the increase in heat flow.

The transient conditiolls selected for study were chosen to facilitate the testing. They do, however, give some indication of the probable im- portance of moisture in cases of periodic heat flow such as are involved in the determination of air. conditioning loads from walls and roofs. I n these studies the temperature changes were created suddenly while in periodic heat flow they oc- cur gradually. The rapid and substantial increase in heat transmissiori attributable to the presence of moisture in certain of the transient cases indicates that similar substantial effects may be expected in periodic flow. The maximum periodic flow, the total flow o r both may be increased. Sirice the moisture may be regarded as providing a mechanism which can, b y providing for latent heat transfer, by-pass part of the resistance to conduction provided by a vapor permeable insulation, it may be expected also that in certain cases the time lag for maximum heat flow will be substantially decreased.

The cases studied were for closed systems, whereas in walls moisture can enter and leave at the boundaries. However. the amounts of moisture introduced in these tests of 0.032 and 0.065 lb per sq ft are relatively small and well within the amounts which might be expected in any hygroscopic materials regardless of moisture lransfer at the boundaries. Built-up roofs will usually ~ r o v i d e a close approximation to a closed system and may at times contain considerably greater qualitities of water than those studied.

C o l ~ c l u s i o l ~

It Ilna been shown that moderate aznounts of moisture present in por- ous samples capable of providing moisture storage can modify greatly the transient heat flow conditions from

duced corresponding vapor press changes and led to evaporation, va flow, and condellsation. This con tuted an additional nlechanism for th transmission of heat in the form o latent heat, operating i n conjunctio with the usual mechanisms of hea trnnsmission in dry materials. The e feet of the moisture upon the stead state heat transmission in the sampl studied was shown to he small.

The magnitude of the variation i the heat flow puttern produced by th preaence of moisture in an actual wa or roof construction would appear to depend on: (n) the arnount of mois- ture present; ( b ) the imposed tem- peratures and vapor pressures; ( c )

the moisture-sorbing and moisture transmission properties of the mate- rials; and ((1) the heat transmission properties of the materials and the arrangement of the materinls.

The results indicate that substantial en'ects lnay also he foulid in many cases of periodic heat flow in walls :and roofs. Further experimental work allould I,e undertaken to determine how estensive these effects may be in

practice.

Acknowledgment

The experimental work was done b y the author while on the staff of t h e Prairie Regional Station of the Di- vision of Buildilig Research, National Research Council, at Saskatoon, Can- ada. I t formed the basis for a thesis submitted, under a cooperative a r - rangement, to the Department o l Mechanical Engineering, University of Saskatchewan, in partial fulfillment of the requirements for the degree of

Master of Science. The author is in- debted to members of t h e staff of the College of Engineering of the Uni- versity of Saskatchewan, to

N.

B.

Hutcheon, assistant director of the Division of Building Research, a n d to

G. 0. Handegord, officer.in-charge

of the Prairie Regional Station, f o r assistance and encouragement in the prosecution of this project.

This paper is a contribution from the Division of Building Research, National Research Council, Canada, and is published with the approval of the director.

-