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An experimental check on the weighting factor method of calculating
room cooling load
Mitalas, G. P.
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N 2 1 r 2no.
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NATIONAL RESEARCH COUNCIL OF CANADA CONSEIL NATIONAL DE RECHERCHES D U CANADA
An Experimental Check On The Weighting Factor
Method Of Calculating Room Cooling Load
by G. P. Mitalas Reprinted from A S H R A E T R A N S A C T I O N S Vol. 75, Part 1 1 , 1969 p. 222 - 232
Research Paper No. 453
o f the
Division of Building Research
O T T A W A September 1 9 7 0
VERIFICATION EXPERIMENTALE DE L A METHODE DE PONDERATION POUR LE CALCUL DES CHARGES
THERMIQUES DE CLlMATlSATlON
Le groupe de travail de I'ASHRAE pour les besoins Bnergetiques a adopt6 a titre experimental la methode de ponderation pour le calcul des temperatures ambiantes et du debit de frigories vers une piece dont I'air est climatise. Le present article donne quel- ques resultats experimentaux qui confirment la fiabilite de la nouvelle methode e t montrent quelle est la precision realisable dans le calcul des temperatures ambiantes.
No.
2125
G. P. MITALAS
Member ASHRAE
An Experimental Check on the Weighting Factor
Method of Calculating Room Cooling Load
A new method u s i n g weighting f a c t o r s for room c o o l i n g l o a d and s p a c e temperature c a l c u l a t i o n s w a s d e s c r i b e d i n two p a p e r s p r e s e n t e d a t t h e ASHRAE 1967 w i n t e r meeting. 2 7 3 S u b s e q u e n t l y ,
the ASHRAE T a s k Group on E n e r g y R e q u i r e m e n t s adopted t h i s method (with s o m e s i g n i f i c a n t sim- p l i f i c a t i o n s ) on a t e n t a t i v e b a s i s for t h e c a l c u l a - tion of room a i r temperature a n d r a t e of h e a t ex- t r a c t i o n from air-conditioned rooms.
In t h e development of t h e method a number of a s s u m p t i o n s were i n v e s t i g a t e d by c o m p u t a t i o n s . It w a s difficult, however, t o d e t e r m i n e t h e com- bined effect of a l l a s s u m p t i o n s on t h e a c c u r a c y of t h e p r e d i c t i o n s for r e a l s i t u a t i o n s . An experi- m e n t a l s t u d y w a s therefore i n i t i a t e d t o m e a s u r e h e a t e x t r a c t i o n r a t e a n d a i r t e m p e r a t u r e s for a n air-conditioned room, a l o n g with a s s o c i a t e d out- s i d e w e a t h e r c o n d i t i o n s . In t h i s p a p e r t h e e x p e r i m e n t a l a n d c a l c u l a t e d r e s u l t s a r e compared. T h i s c o m p a r i s o n i n d i c a t e s the a c c u r a c y of t h e w e i g h t i n g f a c t o r method i n a d d i - tion t o , t h e effect on t h e a c c u r a c y of t h e a d d i t i o n a l s i m p l i f i c a t i o n s recommended by t h e T a s k Group.
'
T h e r e s u l t s given in t h i s p a p e r m u s t b e u s e d with c a u t i o n a s t h e comparison b e t w e e n e x p e r i m e n t a l and c a l c u l a t e d r e s u l t s i s m a d e only for o n e t y p e of room, although t h e good a g r e e m e n t a d d s a d d i - t i o n a l c o n f i d e n c e t o the a d e q u a c y of t h e method.G. P. M i t a l a s i s w i t h t h e B u i l d i n g S e r v i c e s S e c t i o n , D i v i - s i o n of B u i l d i n g R e s e a r c h , N a t i o n a l R e s e a r c h C o u n c i l o f Canada, l o c a t e d i n O t t a w o .
SYNOPSIS OF T H E WEIGHTING F A C T O R METHOD Room a i r temperature and t h e r a t e of h e a t pick-up by t h e c o o l i n g s y s t e m c a n b e c a l c u l a t e d by f o l l o w ing t h e s e s t e p s :
1) C a l c u l a t i o n of t h e v a r i o u s c o m p o n e n t s of h e a t g a i n by the room when t h e room a i r is
maintained a t a c o n s t a n t temperature. 2 ) C a l c u l a t i o n of t h e v a r i o u s s e t s of w e i g h t i n g f a c t o r s that r e l a t e h e a t g a i n t o c o o l i n g l o a d for t h e room. 3 ) Combination of t h e w e i g h t i n g f a c t o r s a n d h e a t g a i n c o m p o n e n t s to a s c e r t a i n t h e cool- i n g l o a d t h a t would o c c u r if the room w a s m a i n t a i n e d a t a c o n s t a n t temperature.
4)
Combination of t h e c a l c u l a t e d c o o l i n g l o a d( s t e p 3), t h e h e a t e x t r a c t i o n v s room a i r temperature c h a r a c t e r i s t i c s of the air-condi- tioning unit a n d its c o n t r o l s a n d the weight- i n g f a c t o r s t h a t a c c o u n t for v a r i a t i o n s of room a i r temperature, t o o b t a i n the room a i r temperature and t h e r a t e of h e a t removal from t h e room.
T h i s l a s t s t e p is p a r t i c u l a r l y important b e c a u s e c o n t r o l s y s t e m s a l w a y s h a v e s o m e throttling range and c a n only produce a n i n c r e a s e in t h e r a t e of h e a t removal if t h e room temperature i n c r e a s e s . As a r e s u l t of t h i s r i s e i n room a i r temperature, the maximum r a t e of h e a t removal may b e s u b s t a n - t i a l l y s m a l l e r than it would b e a t c o n s t a n t room a i r temperature.
BASIS O F T H E E X P E R I M E N T T h e e x p e r i m e n t a l program c o n s i s t e d of m e a s u r i n g a n d r e c o r d i n g t h e t e m p e r a t u r e of t h e a i r a n d t h e r a t e of h e a t r e m o v a l in a n a i r - c o n d i t i o n e d o f f i c e for a p e r i o d of s e v e r a l d a y s . D u r i n g t h i s p e r i o d , t h e o u t s i d e a i r t e m p e r a t u r e a n d t h e s o l a r r a d i a t i o n i n c i d e n t o n t h e o u t s i d e w a l l of t h e room w e r e a l s o r e c o r d e d . B o t h room a i r t e m p e r a t u r e a n d h e a t e x t r a c t i o n r a t e w e r e c a l c u l a t e d by t h e w e i g h t i n g f a c t o r m e t h o d a s o u t l i n e d a b o v e a n d c o m p a r e d w i t h t h e m e a s u r e d v a l u e s . T h e c a l c u l a t i o n s w e r e b a s e d h o w e v e r , o n t h e m e a s u r e d r a t e of h e a t r e m o v a l a n d m e a s u r e d a i r t e m p e r a t u r e t o a v o i d a n y e r r o r d u e t o u n c e r t a i n t y r e g a r d i n g t h e c h a r a c t e r i s t i c s of t h e a i r - c o n d i t i o n i n g u n i t s a n d t h e i r c o n t r o l s r e q u i r e d in s t e p
4.
T h u s t h e d i f f e r e n c e b e t w e e n m e a s u r e d a n d c o m p u t e d room a i r t e m p e r a t u r e d e p e n d s o n l y o n t h e a c c u r a c y of t h e h e a t g a i n c a l c u l a t i o n s a n d t h e a d e q u a c y of t h e w e i g h t i n g f a c t o r s . T E S T ROOM A t y p i c a l o f f i c e m o d e l 1 2 f t w i d e , 17 ft d e e p a n d9.4
f t h i g h w a s m a d e a v a i l a b l e f o r t h i s s t u d y by t h e D e p a r t m e n t of P u b l i c Works of C a n a d a a t t h e i r h e a d q u a r t e r s b u i l d i n g i n O t t a w a . T h e room h a d a s o u t h w e s t e x p o s u r e w i t h a p p r o x i m a t e l y64
s q ft of d o u b l e - g l a z e d w i n d o w s h a d e d by a n e y e b r o w t y p e s h a d e . T h e f l o o r w a s a n &inch-thick c o n c r e t e s l a b , c o v e r e d by v i n y l - a s b e s t o s t i l e s . T h e c e i l i n g w a s s u s p e n d e d from t h e u n d e r s i d e of t h e f l o o r s l a b a b o v e a n d c o n s i s t e d of s h e e t m e t a l b a c k e d by 1 i n . of m i n e r a l w o o l i n s u l a t i o n . F l u o r e s c e n t l i g h t f i x t u r e s w e r e r e c e s s e d i n t o t h e c e i l i n g ; t h e s p a c e b e t w e e n t h e c e i l i n g a n d t h e f l o o r a b o v e w a s n o t v e n t i l a t e d . T h e w a l l o p p o s i t e t h e o u t s i d e w a l l w a s of 8-in. h o l l o w c l a y t i l e a n d c o n t a i n e d o n e s t a n d a r d size d o o r d i t h a l o u v e r e d a r e a f o r a i r e x h a u s t from t h e room. T h e p a r t i t i o n s w e r e m a d e of s h e e t m e t a l p a n e l s w i t h a p a p e r h o n e y c o m b c o r e . T h e w e i g h t of t h e s e p a n e l s w a s4.5
l b / s q ft. T h e a i r - c o n d i t i o n i n g u n i t s w e r e t h e i n d u c t i o n t y p e a n d w e r e l o c a t e d a l o n g t h e o u t s i d e w a l l b e - l o w t h e w i n d o w s i l l w i t h t h e a i r b e i n g d i s c h a r g e d from t h e t o p of t h e u n i t . T h e h e a t r e m o v a l r a t e of t h e u n i t s w a s m o d u l a t e d by a t h e r m o s t a t i c a l l y c o n t r o l l e d v a l v e o n t h e c h i l l e d w a t e r - l i n e s . T h e w a l l b e h i n d t h e a i r - c o n d i t i o n i n g u n i t s a n d a b o v e t h e w i n d o w w a s 10-in. c o n c r e t e w i t h 1 - i n . i n s u l a - t i o n . T h e d e t a i l s of t h e w i n d o w - w a l l a n d air- c o n d i t i o n i n g u n i t e n c l o s u r e a r e s h o w n i n F i g . 1. I N S T R U M E N T A T I O N T h e room w a s i n s t r u m e n t e d t o m e a s u r e t h e r a t e o f h e a t r e m o v a l by t h e a i r - c o n d i t i o n i n g u n i t s . A i r t e m p e r a t u r e i n t h e room, a i r t e m p e r a t u r e in t h e s p a c e a b o v e t h e c e i l i n g , t h e t e m p e r a t u r e of t h e f l o o r , t h e c e i l i n g , t h e p a r t i t i o n s u r f a c e s , t h e o u t - s i d e a i r t e m p e r a t u r e a w a y from t h e b u i l d i n g , t h e d i r e c t a n d d i f f u s e c o m p o n e n t s of t h e s o l a r r a d i a - t i o n i n c i d e n t o n t h e p l a n e of t h e o u t s i d e w a l l , a n dIl!ldiil
C e i l i n g S p a c e
S C A L E - F E E T F i g . 1 S e c t ~ o r l o / o/t/.sidr wctll.t h e d i r e c t n o r m a l s o l a r r a d i a t i o n w e r e a l s o m e a -
1
C A L C U L A T I O N S s u r e d . T h e o u t p u t s of a l l t h e t r a n s d u c e r s w e r e m e a - s u r e d by a n i n t e g r a t i n g t y p e d i g i t a l v o l t m e t e r a n d t h e v a l u e s w e r e r e c o r d e d i n d i g i t a l f o r m o n m a g - n e t i c t a p e s o t h a t t h e r e s u l t s c o u l d b e p r o c e s s e d a u t o m a t i c a l l y . A l l t h e t r a n s d u c e r o u t p u t s w e r e m e a s u r e d a n d r e c o r d e d 3 0 t i m e s p e r h o u r . A l l h e a t r e m o v e d from t h e room w a s p i c k e d u p by t h e w a t e r f l o w i n g t h r o u g h t h e c o o l i n g c o i l i n t h e a i r - c o n d i t i o n i n g u n i t s . D e t a i l s o f t h e i n s t r u - T h e c a l c u l a t i o n s w e r e d i v i d e d i n t o f i v e s t e p s : 1) C a l c u l a t i o n s of room h e a t g a i n c o m p o n e n t s . 2 ) C a l c u l a t i o n s of room w e i g h t i n g f a c t o r s e t s . 3 ) C a l c u l a t i o n s of room c o o l i n g l o a d * . 4 ) C a l c u l a t i o n s of room a i r t e m p e r a t u r e .5 )
C a l c u l a t i o n of room h e a t e x t r a c t i o n r a t e . T h e h e a t g a i n c a l c u l a t i o n s w e r e b a s e d o n m e a s u r e d v a l u e s of t h e a m b i e n t t e m p e r a t u r e , s o l a r r a d i a t i o n a n d c o r r i d o r . a i r t e m p e r a t u r e . T h e h e a t i t w a s m o u n t e d i n a n i n s u l a t e d b o x w h i c h w a sI
a n g l e s . m e n t a t i o n for m e a s u r i n g t h i s r a t e of h e a t p i c k - u p a r e g i v e n i n A p p e n d i x A. T h e e q u i p m e n t i n t h e room, w i t h t h e e x c e p t i o n of t h e r e c o r d i n g s y s t e m , d i d n o t c o n t r i b u t e t o t h e room h e a t g a i n b e c a u s e c o o l e d by t h e p r i m a r y a i r . T h e t e m p e r a t u r e of t h e p r i m a r y a i r l e a v i n g t h e b o x w a s c o n t r o l l e d s o t h a t i t w a s e q u a l t o t h e t e m p e r a t u r e of t h e a i r l e a v i n g t h e r o o m t h r o u g h t h e l o u v e r s i n t h e d o o r . In t h i s w a y , t h e p r i m a r y a i r p r o v i d e d n e i t h e r c o o l i n g n o r h e a t i n g for t h e room b u t h a n d l e d t h e c o o l i n g l o a d g a i n t h r o u g h t h e w i n d o w w a s c a l c u l a t e d by t a k i n g i n t o a c c o u n t t h e w i n d o w f r a m e , t h e s h a d o w c a s t by t h e e y e b r o w s h a d e , v a r i a t i o n s of t h e t r a n s m i s - s i o n a n d a b s o r p t i o n f a c t o r s f o r d i f f e r e n t i n c i d e n t T h e m o s t p r e c i s e s e t of room w e i g h t i n g f a c - t o r s w a s c a l c u l a t e d u s i n g t h e p r o c e d u r e o u t l i n e d i n r e f .3.
T h e b a s e s of t h e m a t h e m a t i c a l m o d e l u s e d t o r e p r e s e n t t h e r o o m a r e . g i v e n i n A p p e n d i x B. T h e w e i g h t i n g f a c t o r s w e r e c a l c u l a t e d f o r a t i m e i n t e r v a l of 2 0 min. T h e f a c t o r s l i s t e d i n c a u s e d b y s o m e of t h e t e s t a p p a r a t u s . T h e p o w e rI
T a b l q 1 a r e , h o w e v e r , f o r t i m e i n t e r v a l s of 1 hr. d r a w n by t h e r e c o r d i n g s y s t e m w a s c o n s t a n t a t 2 9 7 w a t t s . T h e h e a t p i c k - u p b y t h e c h i l l e d w a t e r l i n e s i n t h e c e i l i n g s p a c e w a s e s t i m a t e d a t 4 8 w a t t s . B o t h t h e 2 9 7 - w a t t h e a t g a i n a n d 4 8 - w a t t h e a t l o s s w e r e t a k e n i n t o a c c o u n t i n c o m p u t i n g t h e room a i r t e m p e r a t u r e . T h e s e w e r e o b t a i n e d by c o m b i n i n g 20-min. t i m e i n t e r v a l f a c t o r s .I
' T h e t e r m " c o o l i n g l o a d " is d e f i n e d a s t h e r a t e of h e a t re- m o v a l from t h e r o o m t h a t is r e q u i r e d t o k e e p t h e room a i r1
t e m p e r a t u r e a t 70 P . TABLE IWEIGHTING FACTORS FOR TIME INTERVAL O F 1 HR
(by "accurate" procedure )
0 1 2 3 4 5 6 7 8 9 10 11 12 13 S a t i o of s u c c e s s i v e t e r m s Room a i r ( Watt/deg F / I Solar Radiation I Air condi- tioning unit top cover
I
Dimensionless ~ a t t / d e g F 6q ft Floor Partitions Inside windowT A B L E !I
WEIGHTING FACTORS FOR TLME INTERVAL O F 1 HR
( b y T a s k Group P r o c e d u r e ) Outside a i r t e m p . T h e s a m e a s t h e " a c c u r a t e " weighting f a c t o r s ( s e e T a b l e I) Ratio of s u c c e s a i v e t e r m s
A s e c o n d s e t of the weighting f a c t o r s , which are l i s t e d in T a b l e 11, w a s c a l c u l a t e d by the pro- cedure adopted by the T a s k Group on Energy Re- quirements for Heating and Cooling.
'
In t h i s pro-Watt/deg F s q ft I i I I C o r r i d o r t e m p .
I
0 . 9 2 11
0 . 9 2 1c e d u r e , a l l s o l a r heat gain components a r e
lumped in a s i n g l e input. A s an example, the t o t a l s o l a r h e a t g a i n i s the s u m of the d i r e c t s o l a r radi-
Out. wall s o l - a i r t e m p .
!
ation i n c i d e n t on air-conditioning unit c o v e r ; direct s o l a r radiation on partitions and on the floor; d i f f u s e s o l a r radiation transmitted through windows, the fractions of s o l a r radiation that are a b s o r b e d by inner and o u t e r p a n e s of g l a s s and transmitted to the i n s i d e ; t h e fraction of s o l a r radiation t h a t i s incident on the window frame -and i s transmitted t o the i n s i d e .
T h e computation of the weighting factor s e t for the t o t a l s o l a r heat g a i n , RMRG, w a s b a s e d on the composition of t h i s t o t a l s o l a r g a i n at i t s peak v a l u e , i.e. 60 p e r c e n t e n t e r s the room, a s d i f f u s e radiation, and 30 p e r c e n t , a s the d i r e c t incident on partitions and air-conditioning c o v e r s ; 10 p e r c e n t a s the d i r e c t i n c i d e n t on floor s u r f a c e .
T h e s e t of room a i r weighting f a c t o r s w a s c a l - c u l a t e d by a procedure s i m i l a r to that outlined in ref. 1, i . e . ,
RMRTj = F l o o r Area (x - y); [IOOC-ceiling
+
C e i l i n g Area ( 2 - y)j ~ I O O ~ . C ~ ~ I ; ~ ~+
P a r t i t i o n Area ( x-
y),-
Window Area xi ,;,do,+ Instrument Box Area xi b,,
+ Corridor Wall Area x i where ,
RMRT = weighting factor s e t relating room
c o o l i n g l o a d , r a t e of h e a t re- moval from the room and room a i r temperature
xi, yj and z i = thermal r e s p o n s e factors for t h e
room e n v e l o p e components where the s u r f a c e r e s i s t a n c e i s a c - c o u n t e d for by the combined s u r f a c e h e a t transfer c o e f f i c i e n t ; s u b s c r i p t j i n d i c a t e s time. T h i s e q u a t i o n differs from the one given in ref.
1 b e c a u s e i t i s a s s u m e d that the thermal condi- tions in the t e s t room and surrounding rooms a r e i d e n t i c a l .
* * An a c c u r a t e s e t of room \i,eighting f a c t o r s i s the s e t of
f a c t o r s b a s e d on a m a t h e m a t i c a l model of the room where only the n e c e s s a r y s i m p l i f y i n g a s s u m p t i o n s a r e u s e d , s u c h a s a linear h e a t transfer by c o n v e c t i o n and r a d i a t i o n , one- d i m e n s i o n a l h e a t flow through room e n v e l o p e c o m p o n e n t s , and uniform room a i r rcmperature.
T h e room c o o l i n g l o a d w a s d e t e r m i n e d by com- b i n i n g t h e room h e a t g a i n c o m p o n e n t s w i t h a p p r o - p r i a t e w e i g h t i n g f a c t o r sets. T h e room a i r t e m p e r - a t u r e c a l c u l a t i o n w a s b a s e d o n t h e c a l c u l a t e d c o o l i n g l o a d a n d t h e m e a s u r e d r a t e of h e a t re- m o v a l from t h e room. T h e r o o m ' s h e a t e x t r a c t i o n r a t e w a s c a l c u l a t e d u s i n g t h e c a l c u l a t e d c o o l i n g l o a d a n d t h e m e a s u r e d room a i r e x h a u s t t e m p e r a - ture. R E S U L T S F i g . 2 s h o w s t h e r e s u l t s o f t h e m e a s u r e m e n t s , for t h e t e s t p e r i o d 2 9 , A u g u s t 1967 t o 5 , S e p t e m b e r 1 9 6 7 , a s w e l l a s t h e c a l c u l a t e d c o o l i n g l o a d , t o t a l room h e a t g a i n w h e n room a i r t e m p e r a t u r e i s 7 0 F , a n d t h e room a i r t e m p e r a t u r e . T h e room a i r t e m p e r - a t u r e a n d c o o l i n g l o a d c u r v e s w e r e c a l c u l a t e d u s i n g t h e " a c c u r a t e " w e i g h t i n g f a c t o r s . F i g .
3
s h o w s t h e r e s u l t s of t h e m e a s u r e m e n t s , o n a 1 - h r i n t e r v a l b a s i s , f o r t h e s a m e p e r i o d a n d t h e c a l c u l a t e d room a i r t e m p e r a t u r e a n d c o o l i n g l o a d b a s e d on t h e f a c t o r s c a l c u l a t e d by t h e pro- c e d u r e r e c o m m e n d e d by t h e T a s k G r o u p on E n e r g y R e q u i r e m e n t s for H e a t i n g a n d C o o l i n g . ' T h e d i f f e r e n c e s b e t w e e n t h e m e a s u r e d a n d c a l - c u l a t e d h e a t e x t r a c t i o n r a t e s from t h e room a n d t h e m e a s u r e d room a i r e x h a u s t a n d c a l c u l a t e d room t e m p e r a t u r e s a r e p l o t t e d i n F i g s . 4 a n d 5. C a l c u l a t e d r e s u l t s a r e i n e r r o r f o r a p p r o x i - m a t e l y t h e f i r s t 2 4 h r s . o f t h e t e s t p e r i o d b e c a u s e t h e c o n d i t i o n s a s s u m e d f o r t h e s t a r t of t h e c a l - c u l a t i o n s ( a l l t e m p e r a t u r e s e q u a l t o 7 0 F a n d s o l a r h e a t g a i n s e q u a l z e r o ) w e r e n o t t h e s a m e a s a c t u a l c o n d i t i o n s . DISCUSSION Among t h e s e v e r a l v a r i a t i o n s of t h e room m a t h e - m a t i c a l m o d e l t h a t w e r e c h e c k e d w e r e t h e f o l l o w - ing: t h e room e n c l o s u r e w a s d i v i d e d i n t o 7 a n d 13 s u r f a c e s ; n o a l l o w a n c e w a s m a d e f o r l o n g - w a v e r a d i a t i o n a b s o r p t i o n by t h e room a i r ; t h e h e a t s t o r a g e by p a r t i t i o n s , s u s p e n d e d c e i l i n g a n d in- s t r u m e n t box w e r e n e g l e c t e d . Of t h e s e v a r i a t i o n s , o n l y t h e d i v i s i o n of t h e room i n s i d e s u r f a c e i n t o 13 s u r f a c e s a n d a n a l l o w a n c e for h e a t s t o r a g e by t h e p a r t i t i o n s , s u s p e n d e d c e i l i n g a n d i n s t r u m e n t box n o t i c e a b l y i m p r o v e d t h e m a t c h b e t w e e n t h e c a l c u l a t e d a n d t h e m e a s u r e d room a i r t e m p e r a t u r e s . T h e c u r v e s i n F i g . 4 s h o w f a i r l y g o o d a g r e e - m e n t b e t w e e n t h e m e a s u r e d a n d c a l c u l a t e d room a i r t e m p e r a t u r e s a n d h e a t e x t r a c t i o n r a t e s . T h e < 1 a c c u r a t e " w e i g h t i n g f a c t o r s w e r e u s e d for t h e s e c a l c u l a t i o n s . T h e l a r g e s t d i s a g r e e m e n t ( a b o u t 2 0 0 w a t t s i n h e a t e x t r a c t i o n r a t e s a n d a b o u t 2.5 d e g i n room a i r t e m p e r a t u r e s ) o c c u r r e d i n t h e a f t e r n o o n p e r i o d of 31 A u g u s t . T h i s may b e d u e p a r t l y t o t h e o c c u r r e n c e of s h o w e r s a n d h i g h w i n d s ( m e a n w i n d s p e e d a p p r o x i m a t e l y 1 5 mph). T h e h i g h w i n d may h a v e i n d u c e d s i g n i f i c a n t in- f i l t r a t i o n of o u t s i d e a i r t h a t i s n o t a c c o u n t e d f o r i n t h e c a l c u l a t i o n s . T h e c a l c u l a t e d h e a t e x t r a c t i o n r a t e s for t h e a f t e r n o o n p e r i o d s a r e l o w e r t h a n t h e m e a s u r e d o n e s ( F i g . 4 ) . T h i s d i f f e r e n c e i s p r o b a b l y d u e t o a n u n d e r - e s t i m a t e of t h e room h e a t g a i n for t h e mid-day p e r i o d of 5 t o 1 0 p e r c e n t . In g e n e r a l , t h e m a t c h b e t w e e n t h e c a l c u l a t e d a n d m e a s u r e d a i r t e m p e r a t u r e s a n d t h e h e a t e x t r a c t i o n r a t e s i s f a i r l y g o o d . T h i s i n d i c a t e s t h a t t h e s i m p l i f y i n g a s s u m p t i o n s u s e d i n s e t t i n g u p t h e room m a t h e - m a t i c a l m o d e l d o not i n t r o d u c e s e r i o u s e r r o r s . T h e s a m e c o m m e n t s a p p l y t o t h e r e s u l t s c a l - c u l a t e d by t h e p r o c e d u r e r e c o m m e n d e d by t h e A S H R A E T a s k G r o u p ( F i g s .3
a n d 5) e x c e p t t h a t in t h i s c a s e t h e c u r v e s d o n o t c h a n g e a s r a p i d l y a s t h e o n e s c a l c u l a t e d u s i n g t h e " a c c u r a t e " w e i g h t i n g f a c t o r s b e c a u s e t h e t i m e i n t e r v a l u s e d w a s 1 h r i n s t e a d of 1/3 h r . T h e c a l c u l a t i o n p r o c e d u r e s a r e b a s e d o n a n a s s u m p t i o n of a uniform room a i r t e m p e r a t u r e ( i . e . z e r o s p a c e g r a d i e n t s ) . b u t t h e a i r t e m p e r a t u r e i n t h e t e s t room w a s n o t uniform. T h e d i f f e r e n c e b e - t w e e n t h e t e m p e r a t u r e m e a s u r e d a t t h e c e n t e r of t h e room a n d t h a t of t h e e x h a u s t a i r w a s a s h i g h a s3
d e g F w h e r e s o l a r h e a t g a i n of t h e room w a s a t i t s p e a k , ( F i g . 4). T h e e x h a u s t a i r t e m p e r a t u r e w a s u s e d in t h e c a l c u l a t i o n s b e c a u s e i t w a s a s - s u m e d t o b e a b e t t e r r e p r e s e n t a t i o n of t h e a v e r a g e a i r t e m p e r a t u r e of t h e room. T h e e x h a u s t a i r tem- p e r a t u r e v a r i e d r a p i d l y d u r i n g p e r i o d s w h e r e h e a t g a i n i n t h e room w a s h i g h a n d t h e s e v a r i a t i o n s a r e t h e c a u s e of r a p i d v a r i a t i o n s i n t h e c a l c u l a t e d a n d m e a s u r e d h e a t e x t r a c t i o n d i f f e r e n c e s ( F i g . 4 ) .1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 l , l 1 1 1 1 1 1 1 l l l l l l l l l l l l l l l i 1 1 1 1 1 1 1 1 1 1 1 , 1 , 1 , 1 1 1 1 1 1 1 1 12 24 12 24 12 24 12 24 12 24 12 24 k 29 30 31
*
1 2 3 A u q 6 7 14224
Sept 6 7 TlMEFig. 2 O u t s i d e c o n d i t i o n s , air temperatures, h e a t gain, cooling load and heat extraction rate; c a l c u l a - tion by "accura;e" weighting factors.
- D i f f u s e S o l a r R a d . / M e a s u r e d A i r Temp ( c e n t e r o f t h e r o o ~ n ) 4 R o o m H e a t G a i n a t C a l c u l a t e d R o o m C o o l i n g L o a d a t 1 5 0 0 1000 + +
f
5 0 0 0 - 5 0 0 1 2 24 1 2 24 1 2 24 1 2 24 1 2 24 1 2 24 It 29 3 0 3 1-
1 2 3 A u g 6 7 S e p t 67 T l M EFig. 3 O u t s i d e c o n d i t i o n s , room air temperatures, heat gain, cooling load and heat e x t r a c t i o n rate; c a l - c u l a t i o n s by T a s k Group procedure.
I I I I I I l I l I I l I I I l I I I I I I I I I I I I I I I I I ~ ~ I I I I I ~ ~ I I ~ ~ , i I I ~ ~ l l l 1 I I I l I f 1 l i l ~
-
'5.0- C e n t e r M i n u r Exhaust Room A l r Temp 3
'2
x--- Wb *--/-d+?//-- ,---
-5.0 - \Calculal;d M i n u s M e a s u r e d l e x h a u s l ) Room A i r Temp
/ C a l c u l a t e d M i n u s M e a s u r e d Heat E x l r a c l i o n
Fig. 4 D i l l e r e n c e s b e t w e e n t h e c a l c u l a t e d and measured roonl air temperatures and heat extraction r n t e s using "accz~rnte" weighting l a c t o r s method.
Calculated r d i n u l M e a r u r r d l e r h a u s l l Room A l r Temp
- 5 . 0
- 4 0 0
Fig. 5 D i l l e r e n c e s b e t w e e n t h e c a l c u l a t e d and measured room air temperatures and heat extraction r a t e s using A S H R A E T a s k Group procedure.
-
200-
..
4 0 r - 2 0 0 - 4 0 0 - - - ?. - Calculated M l n u S Measured H e a l E r l r a c l ~ o n A* J-,
,,\,r, ,,-A iv '---9<kAvao-,/, 1 7 I f' - 1 \ I -f,
;,/
l/l,,
:-'
I f - I 1 I I I 't ' r " 11 I I f ' ' I - I ;J '4I
I'',I
- k 11 - - J-
1 J I ~ i I I I ~ ~ ~ I ~ ~ ~ ~ I I ~ I I I ~ ~ I ~ I I ' ~ I ~ U L l l L L W ~ I I I I I ~ I I ' I I I I - ~ ~ ~ ~ ~ I I 12 24 12 24 12 24 I2 24 12 24 12 24 F 29 30 31-
1 2 3 S e p l 67 Aug 67 T I M ET h e d i f f e r e n c e s b e t w e e n t h e c a l c u l a t e d a n d m e a s u r e d t e m p e r a t u r e s may h a v e b e e n d u e , i n p a r t , t o d i f f e r e n c e s b e t w e e n t h e c o n d i t i o n s i n t h e s u r r o u n d i n g r o o m s a n d t h e room u n d e r t e s t . T h e m o s t u n c e r t a i n p a r t o f t h e c a l c u l a t i o n is t h e e s t i m a t e of h e a t g a i n t h r o u g h t h e w i n d o w , c a u s e d by i n s i d e a n d o u t s i d e t e m p e r a t u r e differ- e n c e s . T h i s is b a s e d on t h e o u t s i d e a i r t e m p e r a - t u r e m e a s u r e d a b o u t 100 ft i n front of t h e b u i l d i n g . D u r i n g s u n n y p e r i o d s , s i g n i f i c a n t a m o u n t s of s o l a r r a d i a t i o n a r e a b s o r b e d by t h e e y e b r o w s h a d e a n d o p a q u e p a r t s of t h e o u t s i d e w a l l ; t h i s w i l l a f f e c t t h e t e m p e r a t u r e of t h e a i r l a y e r t h a t is a d j a c e n t t o t h e b u i l d i n g . T h u s t h e t e m p e r a t u r e t h a t g o v e r n s t h e h e a t t r a n s f e r t h r o u g h w i n d o w s m a y b e c o n s i d - e r a b l y h i g h e r t h a n t h e t e m p e r a t u r e r e m o t e from t h e b u i l d i n g . T h e o p p o s i t e e f f e c t m a y o c c u r at n i g h t d u e t o s k y c o o l i n g . I t . i s d i f f i c u l t t o e s t i m a t e t h e s e e f f e c t s s i n c e t h e r e is n o i n f o r m a t i o n o n t h i s s u b - j e c t i n t h e l i t e r a t u r e . T h e c o m p a r i s o n of t h e room a i r w e i g h t i n g f a c - t o r s e t s l i s t e d i n T a b l e s I a n d I1 a n d c a l c u l a t e d room a i r t e m p e r a t u r e s u s i n g t h e s e s e t s ( F i g s . 2 a n d
3)
i n d i c a t e s t h a t r e l a t i v e l y l a r g e v a r i a t i o n s i n t h e v a l u e s of w e i g h t i n g f a c t o r s d o n o t i n t r o - d u c e c o r r e s p o n d i n g l y l a r g e v a r i a t i o n s i n c a l c u - l a t e d room a i r t e m p e r a t u r e s . T h i s s u g g e s t s t h e p o s s i b i l i t y t h a t o n l y a f e w s e t s of w e i g h t i n g f a c t o r s m a y b e s u f f i c i e n t t o c o v e r a l l t h e c o m - mon t y p e s of room c o n s t r u c t i o n . T h i s m a y e l i m i - n a t e t h e n e e d f o r t h e c a l c u l a t i o n of f a c t o r s f o r e a c h p a r t i c u l a r c a s e . F u r t h e r i n v e s t i g a t i o n s h o u l d b e c a r r i e d o u t i n t h i s d i r e c t i o n . C O N C L U S I O N S T h e t e s t a n d c a l c u l a t i o n r e s u l t s i n d i c a t e t h a t t h e w e i g h t i n g f a c t o r m e t h o d , r e c o m m e n d e d by t h e A S H R A E T a s k G r o u p o n E n e r g y R e q u i r e m e n t s , g i v e s r e s u l t s w i t h r e a s o n a b l e a c c u r a c y . A r e l a t i v e l y c r u d e , m a t h e m a t i c a l m o d e l of a room is a d e q u a t e f o r e v a l u a t i n g w e i g h t i n g f a c t o r s , i.e. a p p r o x i m a t e a l l o w a n c e f o r l o n g - w a v e r a d i a - t i o n e x c h a n g e w i t h i n a r o o m , a s s u m p t i o n of c o n - s t a n t s u r f a c e c o n v e c t i o n c o e f f i c i e n t s a n d a s s u m p - t i o n of uniform a i r t e m p e r a t u r e t h r o u g h o u t a room d o n o t i n t r o d u c e l a r g e e r r o r s . A t i m e i n t e r v a l of I h r is a d e q u a t e for t h e s e t y p e s of c a l c u l a t i o n s . F u r t h e r r e s e a r c h s h o u l d b e c a r r i e d o u t t o p r o v i d e : 1 ) B e t t e r d a t a o n h e a t t r a n s f e r by c o n v e c t i o n of t h e i n s i d e s u r f a c e s of a room. 2 ) D a t a o n t h e e f f e c t of s o l a r r a d i a t i o n a b - s o r b e d by o p a q u e p a r t s of o u t s i d e w a l l s a n d t h e h e a t t r a n s f e r t h r o u g h w i n d o w s , p a r t i c u - l a r l y i n t h e c a s e o f h i g h - r i s e b u i l d i n g s .3)
A c h e c k o n t h e a d e q u a c y of p r e t a b u l a t e d room w e i g h t i n g f a c t o r sets c o v e r i n g a r a n g e of room c o n s t r u c t i o n f e a t u r e s . A C K N O W L E D G E M E N T S T h e a u t h o r w i s h , e s t o r e c o r d h i s a p p r e c i a t i o n t o Dr. D . G . S t e p h e n s o n for h i s m a n y h e l p f u l s u g g e s - t i o n s , a n d t o a c k n o w l e d g e t h e a s s i s t a n c e of Mr. G. A r s e n e a u l t i n t h e p r e p a r a t i o n of c o m p u t e r p r o g r a m s . A l s o , Mr. R . J a e k e l i n r u n n i n g t h e t e s t s . T h i s p a p e r is a c o n t r i b u t i o n from t h e D i v i s i o n of B u i l d i n g R e s e a r c h , N a t i o n a l R e s e a r c h C o u n c i l of C a n a d a a n d is p u b l i s h e d w i t h t h e a p p r o v a l of t h e D i r e c t o r of t h e D i v i s i o n . R E F E R E N C E S1. P r o p o s e d P r o c e d u r e for Determining H e a t i n g and Cooling L o a d s for Energy C a l c u l a t i o n s , compiled a n d p u b l i s h e d by the T a s k Group o n Energy Require- ments for H e a t i n g and Cooling, ASHRAE, 1968. 2. D. G. S t e p h e n s o n and G. P . Mitalas, Cooling L o a d
C a l c u l a t i o n s by Thermal R e s p o n s e F a c t o r Method, ASHRAE T r a n s a c t i o n s , VoI. 73, P a r t 1 , 1967. 3. G. P . M i t a l a s and D. G. S t e p h e n s o n , Room Thermal
R e s p o n s e F a c t o r s , ASHRAE T r a n s a c t i o n s , Vol. 7 3 , P a r t 1 , 1967.
4. G. P . Mitalas, An A s s e s s m e n t of Common Assump- t i o n s i n E s t i m a t i n g Cooling L o a d s and S p a c e Tem- p e r a t u r e s , ASHRAE T r a n s a c t i o n s , Vol. 7 1 , P a r t 11, 1965.
APPENDIX A
I N S T R U M E N T A T I O N A r e l i a b l e s y s t e m f o r a p r e c i s e m e a s u r e m e n t of t h e r a t e of h e a t r e m o v a l by t h e a i r c o n d i t i o n i n g u n i t s w a s a b a s i c r e q u i r e m e n t f o r t h i s s t u d y . T h e f i n a l d e s i g n of t h e s y s t e m is s h o w n s c h e m a t i c a l l y i n F i g . A - I . T h e w a t e r t e m p e r a t u r e is m e a s u r e d a t t h r e e p o i n t s i n t h e s y s t e m . T h e t e m p e r a t u r e r i s e ,P l a t i n u m R e s i s t a n c e P e r a t u r e S e n s o r P l a t i n u m ~ e s i s t a n c e i T e m p e r a t u r e S e n s o r s W a t e r L i n e s . P r e s s u r e R e l i e f V a l v e
Fig. A-1 S c h e m a t i c diagram of n s y s L e m Lo m e a s u r e t h e c o o l i n g rate of air c o n d i t i o n i n g unirs.
A d , , b e t w e e n t h e f i r s t a n d s e c o n d p o i n t i s d i r e c t l y p r o p o r t i o n a l t o t h e h e a t i n g r a t e by t h e room a i r , Q , w h i l e t h e t e m p e r a t u r e r i s e , A d 2 , b e t w e e n t h e s e c - o n d a n d t h i r d p o i n t i s d i r e c t l y p r o p o r t i o n a l t o t h e h e a t i n g r a t e , P , by t h e w a t e r h e a t e r . T h u s , w h e n s t e a d y - s t a t e c o n d i t i o n s p r e v a i l i n t h e s y s t e m . T h e s p e c i f i c h e a t of w a t e r , u n i t s of t e m p e r a - t u r e a n d t h e w a t e r f l o w r a t e d o n o t e n t e r i n t h i s e q u a t i o n . P r e c a u t i o n s w e r e t a k e n , h o w e v e r , t o e n s u r e ( a ) t h a t t h e m e a s u r e d t e m p e r a t u r e s a r e t h e b u l k m e a n t e m p e r a t u r e s of t h e w a t e r flow- i n g p a s t t h e t h e r m o m e t e r s . T h i s w a s a c h i e v e d by p a s s i n g t h e w a t e r t h r o u g h c c m i x e r s " t h a t w'ere 2 - i n . d i a m e t e r c o p p e r t u b e s a b o u t
9
i n . l o n g a n d p a c k e d w i t h c o p p e r w o o l ; ( b ) t h a t t h e i n l e t w a t e r t e m p e r a t u r e v a r i a t i o n s a r e s l o w s o t h a t t h e a s s o c i a t e d h e a t s t o r - a g e by t h e s y s t e m b e t w e e n t h e t e m p e r a t u r e m e a s u r i n g p o i n t s a n d t h e t r a n s p o r t d e l a y s d o n o t i n v a l i d a t e E q . A-1. F o r t h i s p u r p o s e , a r o u n d 30-gal. w a t e r t a n k w a s c o n n e c t e d a t t h e i n l e t t o t h e s y s t e m . T h e w a t e r i n t h e t a n k w a s m i x e d by t h e t a n g e n t i a l i n l e t f l o w d i r e c t i o n ; (c) t h a t t h e w a t e r f l o w i s c o n s t a n t . A p o s i t i v e d i s p l a c e m e n t w a t e r p u m p w a s u s e d t o m a i n t a i n c o n s t a n t w a t e r f l o w a t a p p r o x i - m a t e l y 1 . 2 g a l / m i n . A w e l l r e g u l a t e d D . C . p o w e r s u p p l y w a s u s e d t o s u p p l y p o w e r t o t h e w a t e r h e a t e r . A s t e a d y v o l t a g e a l l o w e d a p r e c i s e d e t e r m i n a t i o n of t h e h e a t e r i n p u t p o w e r r a t e , P , ( a p p r o x i m a t e l y 4 0 0 w a t t s ) by m e a s u r i n g t h e v o l t a g e a c r o s s , a n d t h e c u r r e n t t h r o u g h t h e h e a t e r . A c o n s i s t e n c y c h e c k w a s m a d e a t t h e s t a r t of t h e test t o g u a r d a g a i n s t p o s s i b l e d r i f t i n t h e t e m p e r a t u r e s e n s o r s a n d i n t h e a s s o c i a t e d e l e c t r i c c i r c u i t . T h e m a n u a l v a l v e a t t h e o u t l e t o f t h e a i r - c o n d i t i o n i n g u n i t w a s c l o s e d t o s t o p t h e w a t e r flow t h r o u g h t h e u n i t s a n d t h e p o w e r t o t h e w a t e r h e a t e r w a s t u r n e d off. C o n s e q u e n t l y , t h e t e m p e r a t u r e s a t a l l t h r e e p o i n t s s h o u l d b e e s s e n t i a l l y t h e s a m e . T h e s m a l l t e m p e r - a t u r e d i f f e r e n c e s ( u s u a l l y l e s s t h a n 0 . 0 1 F d e g ) n o t e d a t t h e s t a r t of t h e t e s t w e r e u s e d t o c o r r e c t t h e c a l i b r a t i o n c o n s t a n t s f o r t h a t t e s t . T h i s pro- c e d u r e e l i m i n a t e d m o s t of t h e e r r o r i n t h e m e a s u r e - m e n t s from t h e h e a t g e n e r a t e d by t h e w a t e r f r i c t i o n l o s s e s a n d l o n g - t e r m d r i f t s in e l e c t r i c a l c i r c u i t . T h e e r r o r c o u l d n o t b e e l i m i n a t e d e n t i r e l y b e c a u s e t h e f r i c t i o n l o s s e s in t h e b y p a s s v a l v e w e r e n o t e x a c t l y e q u a l t o t h e l o s s e s w h e n t h e w a t e r flowwas divided between air-conditioning units and bypass valve.
The measurement accuracy of the heat pick-up rate was checked a t s e v e r a l different water flow and heat pick-up rates. For these c h e c k s , the air- conditioning units were replaced by electric water heaters and the power input to these heaters was measured. T h e s e c h e c k s indicated that, a t steady- s t a t e conditions, this system i s able to measure heat pick-up rate with an accuracy better than ? 10 watts in the range of heat pick-up r a t e s 0 to 800 watts.
APPENDIX 0
THE BASIS O F ROOM UATHEMATICAL MODEL The inside surface o f the room was divided into 1 3 surfaces consisting of the window, top cover of air-conditioning units, front cover of air- conditioning units, corridor wall, instrument box and two s u r f a c e s each for the ceiling, floor and partitions. The constants used for these s u r f a c e s were:
(1) emissivity for long-wave radiation for all the surfaces = 0.9;
(2) absorption coefficient for solar radiation: ceiling = 0.50, floor = 0.35, and the re- maining surfaces except window = 0.8; (3) convection coefficient = 0.8 ~ t u / h r s q f t
deg F except for window and air-condition- ing unit top cover. The higher value of 1.5 ~ t u / h r s q f t deg F was used for t h e s e
two s u r f a c e s s i n c e the cooled air i s dis- charged through the top cover of air- conditioning units adjacent to the g l a s s . The absorption of long-wave radiation by room air was accounted for by the reduction of the long-wave radiation interchange factors of room surfaces. T h i s reduction was made accord- ing to the relative position of the two surfaces and, for example, i t was a s high a s 0.25 in c a s e of window-corridor wall interchange factors.
The sol-air temperature calculations for out- s i d e surfaces of window and wall were based on a value of 3.0 Btu/hr s q f t deg F for the combined heat transfer coefficient for outside surface, and 0.9 for the solar absorption factor for opaque surfaces.
The heat conduction through floor s l a b , out- s i d e wall and corridor wall was calculated using thermal response factors.
The convection heat transfer coefficient was 0.25 Btu/hr s q f t deg F for the ceiling air s p a c e and 0.22 Btu/hr s q f t deg F for window air s p a c e .
The heat storage of partitions, instrument box and suspended ceiling was calculated using a lumped thermal resistance-capacitance network; the heat storage by the room air was neglected.
It was assumed that the thermal conditions in the adjacent rooms, in the rooms below and above the t e s t room, and in the test room were identical.
DISCUSSION
T. KUSUDA, (Wash. D.C.): As the Chairman of theSubcommittee for Heating and Cooling L o a d s of the ASHRAE T a s k Group on Energy Requirements, I am very much encouraged to know that the load calcu- lated by the procedure recommended by the Subcom- mittee agreed well with that experimentally measured a s well a s that calculated by the "accurate" method.
I would like to take this opportunity to clarify the procedure adopted by the Task Group. The weighting factors concept adopted by the T a s k Group applied to t h e instantaneous heat gains whereas t h e weight- ing factors calculated by the " accurate" method in
this particular paper applies to fundamental excita- tions such as s o l a r radiation, outdoor air temperature, lighting power and e t c . When the "accurate" method i s employed, the instantaneous cooling load can be obtained directly from the excitation component and the "accurate" weighting factor (which are room response factors). The T a s k Group procedure i s , however, to calculate the instantaneous heat gain first and apply the weighting factors to the heat gain t o obtain the cooling load, a procedure similar to Carrier's storage load factors. The T a s k Group recommends this two s t e p procedure because the
< 1
accurare" mcrhod i s very complicaced ( r e q u i r e s solucion of s i m u l r a n c o u s equacions) and may noc be n e c e s s a r y for convenrional rooms a s long a s [he ~veighcing facrors for [he heac g a i n s a r e relatively
unaffecred by [ h e varier!, ot che rooms.
I would like co report chac Mr. hiicalas, upon the rcquesr of [he T a s k Group, is currencly invescigac- ing [he lpar iec}, of room conscruccions, furnishings and oriencacions co arrive ac a cypical s e c of n e i g h r i n g faccors for heac g a i n s u s i n g [ h e room r e s p o n s e faccor compucer program developed ac the Nacional R e s e a r c h Council of C a n a d a .
F i n a l l y , I would like co a s k a question. Am I corrrcc in s a y i n g [he f o l l o n ~ i n g : In F i g s . 2 and
3
you h a v e calculaced [he cooling load b a s e d upon o conscanc room air cemperacurc, 7 0 F and found chc d i s c r e p a n c i e s b e c ~ e e n [he c a l c u l a r e d and ob- s e r v e d cooling load. Then u s i n g [he d i f f e r e n c e s b r c n ~ e r n [ h e calculncrd and observed cooling l o a d ,you have recalculaced che room air cemperacure which agreed very well wirh che measured room a i r cemperacure.
I a s s u m e ic i s p o s s i b l e wirh [he u s e of RMRT chac you could have c a l c u l a r e d [ h e cooling load directly by caking inro accounr the room air tern- peracure variation. If you had done chac, whac kind of agreement would you have e x p e c t e d between [he calculaced and observed cooling l o a d ?
MR. MITALAS: T h e calculaced room air cemperacure c u r v e s shown in F i g s . 2 and
3
were obtained by t h e procedure you d e s c r i b e d .T h e heac excraccion from the room c a n be c a l c u - laced directly u s i n g the measured room air tempera- cure a n d RMRT faccors. T h e calculation approach u s e d co obcain [he c u r v e shown in F i g .
5
w a s b a s e d on t h i s d i r e c t c a l c u l a t i o n .This publication i s being distributed by the Division of Building Research of the National Research Coun- cil of Canada. I t should not be reproduced in whole or i n part without permission of the original pub- lisher. The Division would be glad t o be of assistance i n obtaining such permission.
Publications of the Division may be obtained by mailing the appropriate remittance, (a Bank, Express, or Post Office Money Order, or a cheque made pay- able at par in Ottawa, t o the Receiver General of Canada, credit NRC) t o the National Research Coun- cil of Canada, Ottawa. Stamps are not acceptable. A list of all publications of the Division is available and may be obtained from the Publications Section, Division of Building Research, National Research Council of Canada, Ottawa 7, Canada.
REPRINTED FROM ASHRAE TRANSACTIONS VOL. 75, PART 11, 1969, BY PERMISSION OF THE AMERICAN SOCIETY OF HEATING, REFRIGERATING AND AIR- CONDITIONING ENGINEERS, INC. ASHRAE DOES NOT NECESSARILY AGREE WITH THE STATEMENTS OR OPINIONS HEREIN. THIS ARTICLE IS NOT TO BE RE- PRINTED OR USED FOR PROMOTION. A L L ARTICLES PUBLISHED I N ASHRAE TRANSACTIONS ARE ACCEPT- ED ON A N EXCLUSIVE BASIS AND ARE COPYRIGHTED BY THE SOCIETY.
