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Heat Gain Through Transparent Walls
Martorana, S.; National Research Council of Canada. Division of Building
Research
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PREFACE
The contemporary t r e n d t o l a r g e a r e a s o f g l a s s i n t h e o u t s i d e w a l l s of b u i l d i n g s has r e s u l t e d i n very s u b s t a n t i a l i n c r e a s e s i n t h e a i r c o n d i t i o n i n g requirements of t h e s e b u i l d i n g s . In some cases, t h e c o s t of t h e e x t r a c o o l i n g c a p a c i t y n e c e s s i t a t e d by t h e use of g l a s s w a l l s is twice a s much a s t h e c o s t of t h e g l a s s i t s e l f .
It Is, t h e r e f o r e , very important t o be a b l e t o c a l c u l a t e a c c u r a t e l y t h e c o o l i n g loads of b u i l d i n g s with g l a s s c u r t a i n w a l l s o r l a r g e window a r e a s .
This paper by S a l v a t o r e Martorana c o n t a i n s
a
l u c i d summary of t h e h e a t t r a n s f e r phenomena t h a t occur i n a g l a s s wall t h a t i sexposed t o s o l a r r a d i a t i o n . It includes, as an example, an a n a l y s i s of t h e r e d u c t i o n i n h e a t g a i n t h a t can be achieved by u s i n g b l i n d s and h e a t absorbing g l a s s . The example i s f o r a b u i l d i n g in Rome, b u t t h e r e s u l t s a r e p e r t i n e n t f o r southern Ontario and t h e n o r t h e r n s t a t e s of t h e United S t a t e s . This paper h a s been t r a n s l a t e d i n t o English I n t h e hope t h a t i t w i l l h e l p t o propagate t o t h e b u i l d i n g d e s i g n e r s i n t h e English-speaking c o u n t r i e s t h e importance of s o l a r h e a t gain i n b u i l d i n g design.
This t r a n s l a t i o n was prepared by M r .
D.A.
S i n c l a i r of t h e T r a n s l a t i o n s S e c t i o n of the National Research Council t o whom t h e D i v i s i o n r e c o r d s i t s thanks.O t t a w a Robert F. Legget
NATIONAL RESEARCH COUNCIL OF CANADA
Technical T r a n s l a t i o n 1060
T i t l e : Heat g a i n through t r a n s p a r e n t walls
( ~ l i a p p o r t i d l c a l o r e a t t r a v e r s o l e p a r e t i t r a s p a r e n t i ) Author: S a l v a t o r e Martorana
Reference: Termotecnica,
15
( 2 ) :89-100,
1961HEAT G A I N THROUGH TRANSPARENT
WALLS
Genera 1
The e s t i m a t i o n of h e a t g a i n through t r a n s p a r e n t walls has been t h e sub- J e c t , i n r e c e n t y e a r s , of c o n s i d e r a b l e t h e o r e t i c a l and experimental r e s e a r c h .
The most conlplete i n v e s t i g a t i o n s f o r purposes of c a l c u l a t i o n a r e t h e ones d e s c r i b e d i n t h e ASHRAE Guide and t h e one r e p o r t e d by Desplanches i n t h e sec- ond volume of t h e AICVF Guide. However, t h e data of t h e s e two g u i d e s a r e inadequate when i t i s d e s i r e d t o extend t h e i r use t o c a s e s d i f f e r i n g from t h e ones considered e i t h e r f o r t h e c h a r a c t e r i s t i c s o f t h e wall o r f o r t h e c l i m a t i c c o n d i t i o n s .
T h i s i s n o t unexpected i n o u r r e g i o n s where t h e s u p p l i e s of h e a t can be l a r g e even i n autumn and w i n t e r ( ~ i g . 1 ) .
On t h e o t h e r hand t h e complexity of t h e v a r i o u s formulae proposed and t h e d i f f i c u l t y of l o c a t i n g t h e v a l u e s of t h e c o e f f i c i e n t s i n t h e common manuals make i t impossible t o d e a l w i t h such c a s e s with t h e r e q u i r e d d i s p a t c h .
These c o n s i d e r a t i o n s have l e d t o a rearrangement of t h e more s i g n i f i c a n t t h e o r e t i c a l .and e x p e r i m e n t a l m a t e r i a l and t o t h e d e r i v a t i o n o f t a b l e s and e q u a t i o n s w i t h which most of t h e t e c h n i c a l problems can be e a s i l y s o l v e d .
The most convenient scheme of c a l c u l a t i o n appears t o be t h a t i n d i c a t e d i n F i g . 2, which can be extended t o more complex w a l l s and which
i s
t h e one most commonly used; l e t us i l l u s t r a t e b r i e f l y . On t h e wall,5
i s t h e i n t e n s i t y of t h e d i r e c t s o l a r r a d i a t i o n and Id t h a t o f t h e d i f f u s e r a d i a t i o n , b o t h known; o f t h e s e , t h e t r a n s m i t t e d component i s IT = 'CDh+
'CdId, 0 ) t h e absorbed component 'a =%h
+ 'dld t h e r e f l e c t e d component 1, = rD%+
rdIdwhere 7 and
z d ,
ad, rD and rd a r e t h e t r a n s m i s s i o n , a b s o r p t i o n and t o t a l Dr e f l e c t i o n f a c t o r s of t h e w a l l f o r d i r e c t and d i f f u s e r a d i a t i o n .
The t r a n s m i t t e d component i s transformed i n t o h e a t on t h e f u r n i s h i n g s and i n s i d e s u r f a c e s of t h e room, s o t h a t i t always r e p r e s e n t s a p o s i t i v e h e a t s u p p l y .
The absorbed component i s transformed i n t o h e a t w i t h i n t h e w a l l i t s e l f , which g i v e s i t up by convection and r a d i a t i o n e i t h e r t o t h e i n t e r n a l o r e x t e r n a l environment o r b o t h .
Thus, t h e c a l c u l a t i o n of t h e h e a t g a i n r e q u i r e s a knowledge of t h e
f a c t o r s defined above f o r t h e v a r i o u s walls and a knowledge of t h e h e a t t r a n s - mission r e l a t i o n s h i p s which permit e s t i m a t i o n of t h e q u a n t i t y of h e a t Qi and
Qe exchanged by t h e wall with t h e two environments. Transmission of R a d i a t i o n D i r e c t r a d i a t i o n
The t r a n s m i s s i o n of d i r e c t r a d i a t i o n through any w a l l made up of s e v e r a l absorbing l a y e r s , has been d e a l t w i t h by P r o f e s s o r Bozza i n a monograph of l g j 5 ( ' ) , which has n o t t o t h i s day been superseded.
From t h e normal i n c i d e n c e he determined t h e c o u r s e Of r a d i a t i o n i n t h e i n t e r i o r of t h e wall, assuming t h a t t h i s r a d i a t i o n i s monochromatic, i s
r e f l e c t e d s e v e r a l times on t h e s u r f a c e s of s e p a r a t i o n of t h e d i f f e r e n t l a y e r s and t h a t it i s absorbed i n t h e s e l a y e r s a c c o r d i n g t o an e x p o n e n t i a l l a w .
The formulae o b t a i n e d , extended t o o b l i q u e i n c i d e n c e and s u i t a b l y
modified, lend thenlselves w e l l t o t h e c a l c u l a t i o n of t h e t r a n s m i s s i o n , absorp- t i o n and t o t a l r e f l e c t i o n f a c t o r s of a l a r g e number of t r a n s p a r e n t w a l l s .
For t h e most common of t h e s e , comprising one o r more panes of g l a s s s e p a r a t e d by a t h i n a i r gap, t h e e x p r e s s i o n s f o r t h e above f a c t o r s a r e as
follows: f o r a w a l l c o n s i s t i n g of one pane
2ks r D = p + 2 cs 1
-
p2 exp-
-
(
r ) f o r a w a l l c o n s i s t i n g of two panes T = =DeZDl D ( 1-
p 2 ) 4where s i s t h e t h i c k n e s s of t h e pane, a i s t h e a b s o r p t i o n c o e f f i c i e n t of t h e g l a s s , p i s t h e a i r - g l a s s r e f l e c t i o n f a c t o r and r Is t h e a n g l e of r e f r a c t i o n ; t h e s u b s c r i p t s "el' and "I" r e f e r r e s p e c t i v e l y t o t h e f i r s t and l a s t pane.
The a b s o r p t i o n c o e f f i c i e n t of g l a s s depends on t h e ambient temperature, t h e chernlcal composition of t h e g l a s s and t h e wavelength of t h e i n c i d e n t r a d i a t i o n .
For o r d l n a r y g l a s s e s i t s v a l u e s a r e low i n t h e v i s i b l e range, of t h e o r d e r of 10
-
15
m-', and i n c r e a s e r a p i d l y in t h e v i o l e t d i r e c t i o n and l e s s r a p i d l y in t h e red end of t h e spectrum; above 4.5-
5p, f o r which i t i s 800-
( 2 ) 1500 m-', o r d i n a r y g l a s s of t h e u s u a l t h i c k n e s s i s p r a c t l c a l l y opaque
.
The v a r i a t i o n s o f t h e c o e f f i c i e n t of a b s o r p t i o n with t h e wavelength have been e x p l o i t e d by t h e g l a s s i n d u s t r y t o produce g l a s s e s capable of reducing t h e a c c e s s o f h e a t and l i m i t i n g t h e luminence of windows. Such g l a s s e s ,
c a l l e d athermic, a r e p a r t i c u l a r l y absorbent i n t h e i n f r a r e d r e g i o n and f a i r l y absorbent I n t h e v i s i b l e .
F i g u r e
3
shows c l e a r l y how t h e two types of g l a s s vary t h e s p e c t r a l d i s t r i b u t i o n of s o l a r r a d i a t i o n .The a b s o r p t i o n c o e f f i c i e n t of t h e more common g l a s s e s on t h e I t a l i a n market, r e l a t i v e t o t h e s o l a r spectrum a t s e a l e v e l and a i r mass e q u a l t o 2
a s proposed by P. ~ o o n ( ~ ) , h a s an average value of 20
-
22 m-' f o r o r d i n a r y g l a s s e s and 108-
112 m-' f o r atherrnic g l a s s e s , which i s about t h e same as t h e( 5 ) corresponding g l a s s e s produced i n ~ r a n c e ( ~ ) and i n America
For t e c h n o l o g i c a l reasons t h e s e values can vary by 4 t o
5$
f o r o r d i n a r y g l a s s e s and 8 t o 12% f o r athermlc g l a s s e s . Less e a s i l y e s t i m a t e d , however, a r e t h e v a r i a t i o n s a s s o c i a t e d with t h e s o l a r spectrum. J u s t t h e reddening of Moon's spectrum, caused by t h e i n c r e a s e of t h e a i r mass from 2 t o5 ,
reduces t h e t r a n s p a r e n c y f o r normal incidence o v e r a t h i c k n e s s of
6
mrn by 1-
276 f o r t h e o r d i n a r y g l a s s e s and 7-
85 f o r t h e athermic ones.The r e f l e c t i o n f a c t o r depends on t h e a n g l e of incidence, t h e wavelength of t h e i n c i d e n t r a d i a t i o n , i t s s t a t e o f p o l a r i z a t i o n and t h e a b s o r p t i o n c o e f f i c i e n t .
A t ambient temperature, foru o r d i n a r y and athermic g l a s s e s , t h e v a r i a t i o n s with t h e c o e f f i c i e n t of a b s o r p t i o n a r e n e g l i g i b l e ; thus, where n is t h e index of r e f r a c t i o n and I t h e a n g l e of incidence, t h e r e f l e c t i o n f a c t o r can be
expressed by t h e s i m p l i f i e d r e l a t i o n s h i p f o r normal incidence, P =
3
( P '+
P'l) f o r o b l i q u e incidence; where p f =- rl
i s t h e r e f l e c t i o n f a c t o r f o r t h e r a d i a t i o n component s i n 2 ( i+
r ) p o l a r i z e d i n t h e plane of incidence, p"-
-
r, 18 t h e r e f l e c t i o n f a c t o r t a n 2 ( i+
r ) f o r t h e r a d i a t i o n component p o l a r i z e d I n t h e p l a n e p e r p e n d i c u l a r t o t h e p l a n e - 1 s i n i of incidence, and r i s e q u a l t o s i n 7 . Table I g i v e s t h e a n g l e s of r e f r a c t i o n and t h e r e f l e c t i o n f a c t o r s a tv a r i o u s a n g l e s of i n c i d e n c e c a l c u l a t e d with a mean index of r e f r a c t i o n of
( 6 )
1.52 f o r t h e s o l a r spectrum
.
From t h e v a l u e s of p 1 and p " i t i s c l e a r t h a t t h e r e f l e c t i o n f a c t o r s p
can vary widely depending on whether one o r t h e o t h e r component predominates. This happens e i t h e r when t h e i n c i d e n t r a d i a t i o n i s p a r t i a l l y p o l a r i z e d , a s i s o f t e n t h e case f o r s o l a r r a d i a t i o n , o r a f t e r t h e f i r s t r e f l e c t i o n In t h e c a s e of o b l i q u e incidence, because t h e i n c i d e n t r a d i a t i o n i s p o l a r i z e d and t h e t r a n s m i t t e d r a d i a t i o n i s f u r t h e r p o l a r l z e d a t each r e f l e c t i o n of t h e p o l a r i z e d component i n t h e p l a n e p e r p e n d i c u l a r t o t h e p l a n e o f i n c i d e n c e .
A c t u a l l y knowing t h e s t a t e of p o l a r i z a t i o n of t h e s o l a r r a d i a t i o n does n o t permit an e s t i m a t i o n of t h e t r u e v a r i a t i o n s of t h e r e f l e c t i o n f a c t o r s , and
hence of t h e t r a n s m i s s i o n f a c t o r s . Comparison of t h e v a l u e s of t h e l a t t e r f o r n a t u r a l r a d i a t i o n and f o r t h e two l i n e a r l y p o l a r i z e d components as given i n Table 11, s u g g e s t s t h a t l n p r a c t i c e we can eqpect t o f i n d c o n s i d e r a b l e
o s c l l l a t l o n s around t h e mean value.
P o l a r i z a t i o n by r e f l e c t i o n , however, has t h e e f f e c t of p r o g r e s s i v e l y d i m i n i s h l n g t h e r e f l e c t i o n f a c t o r s f o r any given Incidence. I n o r d e r t o t a k e t h i s f a c t i n t o account t h e t r a n s m i s s i o n f a c t o r s a r e c a l c u l a t e d a s t h e mean values of t h o s e assumed f o r t h e two l i n e a r l y p o l a r i z e d components.
Considerable v a r i a t i o n s i n t h e r . e f l e c t i o n f a c t o r s must a l s o be a t t r i b u t e d t o t h e h e t e r o g e n e i t y of t h e s u r f a c e s t a t e of t h e g l a s s e s .
The above e x p r e s s i o n s can a l s o be used In t h e common c a s e where t h e w a l l
is f u r n i s h e d with c u r t a i n s f o r t h e c o n t r o l of t h e s o l a r r a d i a t i o n . However, i t i s p r e f e r a b l e i n p r a c t i c e t o d e r i v e t h i s from t h e o t h e r more g e n e r a l formulae
.
For t h i s puprose n o t e t h a t c u r t a i n s a r e d e v i c e s f o r i n t e r c e p t i n g d i r e c t r a d i a t i o n , t o which, t h e r e f o r e , t h e y a r e opaque, and t o c o n t r o l t h e transmls- s i o n of t h e luminous f l u x , and hence a l s o t h e d i f f u s e r a d i a t i o n , t o which t h e y
may be considered p a r t i a l l y t r a n s p a r e n t . T h e i r s u r f a c e s a r e i n g e n e r a l ( 7
p a r t i a l l y . d i f f u s i n g
.
Of t h e i n t e r c e p t e d r a d i a t i o n a p o r t i o n i s r e f l e c t e d and a p o r t i o n i s
absorbed and transformed i n t o h e a t e i t h e r o u t s i d e o r i n s i d e o r w i t h i n t h e w a l l , depending on whether t h e c u r t a i n s a r e l o c a t e d o u t s i d e o r i n s i d e , o r a r e i n c o r p o r a t e d i n t h e w a l l i t s e l f . In t h e l a t t e r arrangement t h e r e f l e c t e d energy, b e f o r e r e t r a v e r s i n g t h e g l a s s , i s r e f l e c t e d and absorbed a number of times by t h e g l a s s panes and by t h e c u r t a i n s .
We a r e n o t f a r wrong, t h e r e f o r e , i n assunling t h a t t h e c u r t a i n s a r e opaque t o t h e d i r e c t and d i f f u s e r a d i a t i o n s and t h a t t h e t r a n s m i s s i o n occur8 a c c o r d i n g t o t h e mechanism r e p r e s e n t e d i n Fig. 4, where f o r convenience t h e i n t e n s i t y of t h e i n c i d e n t r a d i a t i o n i s assumed e q u a l t o u n i t y and t h e w a l l i s
assumed t o c o n s i s t of two panes with an i n s i d e c u r t a i n .
On t h i s b a s i s , s i n c e t h e c u r t a i n r e c e i v e s t h e r a d i a t i o n T~ i n a d d i t i o n
t o t h e group o f r a d i a t i o n s R r d r e f l e c t e d by t h e g l a s s panes and r e t u r n s t h e r a d i a t i o n R t o t h e g l a s s while a b s o r b i n g and transforming t h e f r a c t i o n T~~
i n t o h e a t , which f o r t h i s s i t u a t i o n c o i n c i d e s with t h e t r a n s m i s s i o n f a c t o r , we may w r i t e
T D 1 = ( T ~ + R r d ) a
R = ( T
+
~ F t r d ) ( l-
a ) ,where a i s t h e a b s o r p t i o n f a c t o r of t h e c u r t a i n .
Now, s o I v i n g t h e system and o b s e r v i n g t h a t t h e o u t s i d e g l a s s and t h e i n s i d e g l a s s r e s p e c t i v e l y absgrb t h e f r a c t i o n a,,e and aDi of t h e i n c i d e n t r a d i a t i o n a s w e l l a s t h e f r a c t i o n s R a d l and Rade of R, and t h a t tvro g l a s s e s r e f l e c t t h e f r a c t i o n rD o f t h e foriiler and t r a n s m i t t h e f r a c t i o n R T ~ o f t h e l a t t e r , we d e r i v e t h e d e s i r e d r e l a t i o n s h i p s
where aDi and rD1 a r e r e s p e c t i v e l y t h e a b s o r p t i o n f a c t o r s f o r t h e o u t - s i d e g l a s s , t h e i n s i d e g l a s s and t h e t o t a l r e f l e c t i o n f a c t o r .
Equation ( 7 ) holds a l s o f o r w a l l s c o n s i s t i n g of a s i n g l e pane where t h e magnitudes which appear t h e r e a r e replaced by t h o s e corresponding t o t h e s i n g l e pane and t h e a b s o r p t i o n f a c t o r s a r e p u t e q u a l t o 0 and t o a D 1 , r e s p e c t i v e l y .
For w a l l s with c u r t a i n s i n c o r p o r a t e d between t h e two panes aDel = aD1, aDif = 0, =
8 ~ ~ ' ;
i n t h i s case t h e energy absorbed by t h e c u r t a i n i stransformed I n t o h e a t w i t h i n t h e w a l l s and n o t w i t h i n t h e w a l l s and n o t w i t h i n t h e room.
I f t h e c u r t a i n s a r e e x t e r n a l i t i s obvious t h a t t h e y absorb t h e f r a c t i o n a of t h e energy of i n c i d e n t u n i t i n t e n s i t y and do n o t r e f l e c t t h e f r a c t i o n
1-a.
F i n a l l y , we n o t e t h a t t h e r e l a t i o n s obtained hold s t r i c t l y f o r p a r a l l e l c u r t a i n s very c l o s e t o t h e g l a s s panes, 1 . e . f o r c o n d i t i o n s o f maximum
e f f i c i e n c y .
D i f f u s e r a d i a t i o n
The t r a n s m i s s i o n of t h e d i f f u s e r a d i a t i o n czn be d e a l t w i t h v e r y slmply by imagining t h a t t h e r a d i a t i o n impinges on t h e w a l l from a l l d i r e c t i o n s con- t a i n e d w i t h i n t h e s o l i d a n g l e 27c w i t h i n t e n s i t y d i s t r i b u t e d e i t h e r uniformly o r a c c o r d i n g t o Lambertls l a w .
In t h e f i r s t case t h e t r a n s m i s s i o n , a b s o r p t i o n and r e f l e c t i o n f a c t o r s a r e given by t h e a r i t h m e t i c mean of t h e v a l u e s which each of t h e s e have
between 0 and
d2
f o r d i r e c t r a d i a t i o n ; i n t h e second c a s e , however, t h e y a r e given by t h e weighted means of t h e s e v a l u e s i n which t h e weights a r e t h e r a d i a t i o n i n t e n s i t i e s a t each a n g l e of i n c i d e n c e .We have based o u r c a l c u l a t i o n s , the r e s u l t s of which we shall p r e s e n t below, on t h e l a t t e r hypothesis, which appeared p h y s i c a l l y more r e l i a b l e .
In p r a c t i c e , t h e overhangs of t h e favade reduce t h e above-mentioned s o l i d a n g l e . However, even w i t h a cone a n g l e r e s t r i c t e d t o 150
-
160°, t h i s make8l e s s t h a n 1% d i f f e r e n c e i n t h e r e s u l t and Is t h e r e f o r e n e g l i g i b l e .
The d i s t r i b u t i o n of i n c i d e n t energy i n t h e s o l i d a n g l e s under c o n s l d e r a - t i o n , assumed u n i t a r y , was found t o be a s f o l l o w s :
Thus 76.6% of t h i s energy i s found w i t h i n t h e s o l i d a n g l e between 20 and 70°
.
Hcnce t h e d i f f i c u l t y of p r o t e c t i n g t h e w a l l from d i f f u s e r a d i a t i o n and of e s t i m a t i n g t h e f r a c t i o n i n t e r c e p t e d by v a r i o u s p r o t e c t i v e d e v i c e s w i t h a s i n g l e v a l u e .
Venetian b l i n d s , c l o s e t o t h e g l a s s and with t h e vanes t u r n e d s o as t o produce i n t e g r a l r e f l e c t i o n of t h e d i r e c t r a d i a t i o n * , i n g e n e r a l i n t e r c e p t
v2
-
of t h e d i f f u s e r a d i a t i o n , i. e . a l l o r p a r t of t h a t coming from above.The t r a n s m i s s i o n of t h e i n t e r c e p t e d f r a c t i o n through walls w i t h c u r t a i n s can a g a i n be i n v e s t i g a t e d w i t h t h e a i d of e q u a t i o n ( 7 ) where t h e t r a n s m i s s i o n , a b s o r p t i o n and t o t a l r e f l e c t i o n f a c t o r s a r e now t h o s e r e l a t i v e t o t h e d i f f u s e rad l a ti o n .
Experimental r e s u l t s and p r a c t i c a l v a l u e s f o r t h e t r a n s m i s s i o n , a b s o r p t i o n and r e f l e c t i o n f a c t o r s
The mentioned i n v e s t i g a t i o n c a r r i e d o u t i n t h e ASHRAE l a b o r a t o r y in
Cleveland, Ohio, secms t o be among t h e n o s t s u i t a b l e f o r t e s t i n g t h e r e l i a b i l - i t y of t h e c a l c u l a t i o n s t h a t can be c a r r i e d o u t w i t h t h e e q u a t i o n s and methods t h a t have been d e s c r i b e d .
In
Table 111 a r e shown, f o r a g l a s s w i t h ks-
0.05 and n = 1.52, t h e v a l u e s c a l c u l a t e d by u s and t h o s e p u b l i s h e d on page 312 of t h e ASHRAE Guide, 1957.The agreement, as i s a p p a r e n t , i s extremely good. I f we had n e g l e c t e d t h e p o l a r i z a t i o n due t o r e f l e c t i o n t h e t h e o r e t i c a l v a l u e s f o r t h e t r a n s m i s s i o n f a c t o r s would have been s m a l l e r from 110
-
50° o r by3
-
5:; f o r t h e wall made of s i n g l e g l a s s and 8-
lo$
f o r t h t c o n s i s t i n g of two panes.Encouraged by t h i s r e s u l t we have c a l c u l a t e d and p r e s e n t i n Table
N
t h e t r a n s n ~ i s s i o n and a b s o r p t i o n f a c t o r s and t h e t o t a l r e f l e c t i o n f a c t o r s f o r d i r e c t and d i f f u s e r a d i a t i o n f o r t h e main combinations t h a t can be r e a l i z e d w i t h t h e more colnmon o r d i n a r y and athermic g l a s s e s o b t a i n a b l e i n t h e I t a l i a n market, and with c u r t a i n s havlng a n a b s o r p t i o n f a c t o r e q u a l t o 0.5.The l a t t e r depends, as i s known(7), on t h e c o l o u r of t h e c u r t a i n s o t h a t when c o n s i d e r a b l e v a r i a t i o n s a r e f o r e s e e n w i t h r e s p e c t t o t h e assumed value
i t w i l l be n e c e s s a r y t o t a k e t h e s e i n t o account w i t h c o r r e c t i o n f a c t o r s t h a t can be derived from e q u a t i o n , ( 7 ) .
For t h e w a l l s w i t h c u r t a i n s t h e d a t a of t h e t a b l e a r e a p p l i e d t o t h e d i r e c t and d i f f u s e r a d i a t i o n f r a c t i o n s which a r e presumed i n t e r c e p t e d .
T r a n s l a t o r ' s Note:
*
T h i s probably means t h a t t h e b l i n d i s a d j u s t c d t o i n t e r c e p t a l l of t h e d i r e c t s o l a r beam.Heat Transmi3sion B a s i c r e l a t i o n s
The t r a n s m i s s i o n o f h e a t by convection, conduction and r a d i a t i o n between two environments a t d i f f e r e n t t e m p e r a t u r e s , s e p a r a t e d by a w a l l i n t h e i n t e r i - o r of which h e a t i s generated a c c o r d i n g t o some law, h a s been t r e a t e d s e v e r a l times by r i g o r o u s methods.
These methods, however, have n o t been widely used i n o u r c a s e because t h e u n c e r t a i n t i e s I n h e r e n t i n t h e very n a t u r e o f t h e problem w i t h which we a r e concerned a r e s o g r e a t t h a t r e c o u r s e t o very r e f i n e d c a l c u l a t i o n s i s n o t j u s t i f i e d , and because t h e frequency with which t h e problem comes up i n e n g i n e e r i n g o f f i c e s r e n d e r s i t p r e f e r a b l e t o employ approximate and r a p i d s o l u t i o n s
.
I n an a t t e m p t t o r e c o n c i l e s c i e n t i f i c p r e c i s i o n w l t h r a p i d i t y of c a l c u - l a t i o n Desplanches h a s r e c e n t l y proposed ( 4 ) a s t u d y of h e a t t r a n s m i s s i o n under t h e above c o n d i t i o n s , ansunling i n f i n t e t h e r m a l c o n d u c t i v i t y o f t h e g l a s s and uniform d i s t r i b u t i o n o f t h e h e a t generated i n t h e i n t e r i o r o f t h e w a l l .
The two hypotheses, which f o r p r a c t i c a l purposes do n o t change t h e f i n a l r e s u l t s in view o f t h e small t h i c k n e s s o f t h e g l a s s panes, are b o t h u s e f u l . The second however i s t o o r e s t r i c t i v e , because when t h e w a l l c o n s i s t s o f s e v e r a l panes o f d i f f e r e n t a b s o r p t i o n c h a r a c t e r i s t i c s we cannot assume u n i - form d i s t r i b u t i o n of h e a t and i n f a c t Desplanches a p p l i e s t h e method t o a wall
comprising o n l y one pane o r two non-absorbing panes.
When we wish t o s t u d y t h e behavlour o f w a l l s made w i t h panes o f d i f f e r - e n t a b s o r p t i o n , It w i l l be n e c e s s a r y t o r e s t r i c t t h e hypotheses t o each pane;
In t h i s way, t h e method r e t a i n s a l l i t s good q u a l i t i e s .
On t h i s b a s i s l e t u s c o n s i d e r a w a l l ( ~ i g .
5 )
comprising t h r e e panes o f I n f i n i t e t h e r m a l c o n d u c t i v i t y , i n which i s generated t h e q u a n t i t y o f h e a t qe, qc and ql; l e t te and ti be t h e t e m p e r a t u r e s of t h e two environments, Se, 5,and t h e t e m p e r a t u r e s of t h e panes and ae, ai, ace, aci t h e c o e f f i c i e n t s o f h e a t t r a n s f e r .
Now, choosing any c o n d i t i o n o f regime, f o r example t c c 3, c 3, > >
ti, we may w r i t e
whence we d e r i v e
where 1
i s t h e t o t a l c o e f f i c i e n t of t r a n s m i s s i o n and
i s t h e temperature d i f f e r e n c e between t h e o u t s i d e and i n s i d e environments.
The h e a t exchanged with t h e two environments i s c a l c u l a t e d a s u a u a l w i t h
which, t a k i n g i n t o account e q u a t i o n ( g ) , become
The exchange of h e a t w i t h t h e i n s i d e can be t a b u l a t e d , i f r e q u i r e d ; f o r t h i s purpose t h e e x p r e s s i o n
Q,
= K ( t , *-
t i ) i s convenient, wherei s t h e "imaginary s o l a r temperature".
For w a l l s comprising two panes we p u t qc = 0 and aci = a c e = 2aC, and f o r t h a t c o n p r i s l n g one pane q = qi = 0 , qe = q and aci = a = m .
None of t h e hypotheses p r e s e n t e d was based on t h e r c ~ i m e which becomes s t a b i l i z e d i n t h e w a l l ; f o r t h e one comprlslnp, a s i n g l e pane i t i s t r e a t e d a s
a s p e c i a l regime which some h e a t e n g i n e e r s have d e f i n e d a s "permanent
i n s t a n t a n e o u s rcgirne". Since t h e therillal c o n d u c t i v i t y and hence t h e c a p a c i t y f o r d i f f u s i o n i s i n f i n i t e , t h e wall i n s t a n t a n e o u s l y asswnes t h e regime
temperature.
I n p r a c t i c e o r d i n a r y g l a s s e s e s t a b l i s h t h e regime i n
5
-
10 minutes and athermic g l a s s e s i n 15-
20 minutes.A p p l i c a t i o n t o a s p e c i f i c c a s e and s u g ~ c s t i o n s f o r c a l c u l a t i ? n and f o r p l a n n i n g of w a l l s
I n Table V we have c o r r e c t e d t h e d a t a and e s s e n t i a l c a l c u l a t i o n r e s u l t s on t h e s u p p l i e s of h e a t which w i l l presumably be found i n Rome on t h e 23rd of J u l y a t 4:00 p.m. through a number of t r a n s p a r e n t w a l l s with western exposure, made o f o r d i n a r y g l a s s and of a t h e r m l c g l a s s and f u r n i s h e d with v e n e t i a n
b l i n d s of p a i n t e d a l u n i n i u n ~ .
The i n t e n s i t y of t h e d i r e c t s o l a r r a d i a t i o n was d e r i v e d from t h e s u n s h i n e t a b l e s e d i t e d by Termotecnica. The i n t e n s i t y o f t h e d i f f u s e r a d i a t i o n was o b t a i n e d from Elvegard and bloloerlcoferfa c u r v e s ( l i ) . The f l n a l value o b t a i n e d , which Is t h e annual rnaximun f o r Rome, may a p p e a r h i & , b u t i t has t o be
accepted I n t h e absence of tnore r e l i a b l e d a t a f o r t h e n a t i o n a l t e r r i t o r y t h a n t h o s e c o r r e l a t e d by Moon, a s t h e e x t e n s o r s of t h i s t a b l e , moreover, show.
I n c a r r y i n g o u t t h e c a l c u l a t i o n we t r i e d t o s a t i s f y t h e c o n d i t i o r ~ a t t h e boundaries of t h e v a r i o u s s t r a t a w i t h a view t o b e t t e r e s t i m a t i n e t h e i n t e r d e - pendence of t h e d i f f e r c n t v a r i a b l e s and t h e p r a c t i c a l v a l u e s of t h e h e a t
t r a n s f e r c o e f f i c i e n t t h a t can be used under s i m i l a r c o n d i t i o n s .
F o r n a t u r a l convection we employed t h e c o r r e l a t i o n s o f Wcise and
~ a u n d e r s ' ~ ) , and f o r f o r c e d convection t h e c o r ~ e l a t i o n s of ~ o l b u r n ' ~ ) , a l s o adopted i n t h e ASHRAE Guide, and f o r convection i n t h e a i r gaps, t h o s e o f Mull and
elh her'^)
a s v e r i f i e d and modified by Llnke ( 1 0 )The f i r s t two c o r r e l a t i o n s a r e taken w i t h c a u t i o n because t h e y have been e x t r a p o l a t e d up t o s u r f a c e s of 2 m high, considered by u s ; more r e l i a b l e , however, a r e t h e c o r r e l a t i o n s of Linke who r e c e n t l y experimented on a i r gaps between g l a s s with height/width r a t i o s up t o 112.
The o u t s i d e h e a t t r a n s f e r c o e f f i c i e n t w i t h a wind o f 2.5 d s e c i s alnlost always found t o be e q u a l t o
15
kcal/m2 hr°C; i n c a s e s no. 1 4 and15
t h i s reaches r e s p e c t i v e l y 43 and 20 kcal/m2 hr°C because t o t h e c o n v e c t i o n i s added I n t h e f i r s t c a s t t h e i r r a d i a t i o n of t h e o u t s i d e g l a s s , 1 . e . of av i r t a u l l y b l a c k body and i n t h e second c a s e t h e i r r a d l a t i o n of t h e p a i n t e d aluminium, 1 . e . a body of low enlission c a p a c i t y .
The i n s i d e h e a t t r a n s f e r c o e f f i c i e n t i s g e n e r a l l y 7
-
9 kcal/m2 hr°C, except when t h e c u r t a i n i s i n s i d e . I n t h i s c a s e i t may drop t o 2-
5.5
k c a l / m2 hr°C, because t h e g l a s s g i v e s up h e a t t o t h e a i r by convection and r e c e i v e s h e a t from t h e c u r t a i n s by i r r a d i a t i o n .I n u n v e n t i l a t e d a i r gaps t h e thermal conductance Is 15
-
18 kcal/m2 hr°C. However, when t h e c u r t a i n i s i n s i d e t h e gap t h i s i s reduced t o 9-
1 0 kcal/m2 hr°C f o r t h e low enlission c a p a c i t y of t h e p a i n t e d aluminium.U n f o r t u n a t e l y t h e temperatures a r e always h i g h . Cold a i r a g a i n s t t h e g l a s s i s advantageous, because i t reduces t h e temperature
3
-
5OC w i t h o u t a p p r e c i a b l y i n c r e a s i n g t h e h e a t g a i n .I n s o l u t i o n s concerned e x c l u s i v e l y w i t h g l a s s t h e s e g a i n s can be reduced by more than 50
-
GO$.
For g r e a t e r r e d u c t i o n s , i n l i n e w i t h t h e g e n e r a l c r i t e r i o n t h a t t h e s o l a r r a d i a t i o n must be i n t e r c e p t e d b e f o r e r e a c h i n g t h e s u r f a c e of s e p a r a t i o n between t h e two environments, r e c o u r s e must be had t o i n s i d e c u r t a i n s , c u r t a i n s i n c o r p o r a t e d w i t h i n t h e w a l l and o u t s i d e c u r t a i n s o r c u r t a i n s i n c o r p o r a t e d i n v e n t i l a t e d a i r gaps.I n t h i s r e g a r d t h e l a s t column of t h e t a b l e , where t h e r a t i o C between t h e t o t a l h e a t t r a n s m i t t e d by each wall and t h a t t r a n s m i t t e d under t h e same c o n d i t i o n s by walls c o n s i s t i n g of a s i n g l e g l a s s a r e recorded, i s s u f f i c i e n t l y i n d i c a t i v e .
The c u r t a i n s r~lust be c l o s e t o t h e g l a s s , p o s s i b l y f l a t , and must have a
1ow.absorption f a c t o r and h i g h d i f f u s e r e f l e c t i o n f a c t o r , s i n c e g l a s s i s t o o t r a n s p a r e n t t o t h i s type of r a d i a t i o n . The r e g u l a r r e f l e c t i o n may r e f l e c t energy a t a n g l e s f o r which g l a s s i s v e r y r e f l e c t i v e .
The e n l i s s i v i t y of t h e c u r t a i n s should, f i n a l l y , be h i g h . When t h e c u r t a i n s a r e placed i n s i d e , however, low e r n i s s i v i t y on t h e room s i d e may be s u i t a b l e .
The w i n t e r behaviour of t h e w a l l s i n q u e s t i o n should be s u b j e c t e d t o a
s i m i l a r i n v e s t i g a t i o n because t h e y p r e s e n t some i n t e r e s t i n g a s p e c t s . F o r t h e p r e s e n t , however, t h e f i g u r e s given a r e s u f f i c i e n t .
I wish t o thank P r o f e s s o r Gino Bozza f o r h i s v a l u a b l e s u g g e s t i o n s made
References
Bozza, G. Trasniissione d e l c a l o r e e assorbimento d l r a d l a z l o n e I n p a r e t i t r a s p a r e n t l . 1st. Lomb. S c l e n . e L e t t . 68 (16-18 and 19-20), 1935. The I n s t i t u t e of S i l i c a t e Research. Thermal t r a n s m i s s i v ~ t y by r a d i a t i o n ,
t h e g l a s s i n d u s t r y , 36 (11): 575, 1955.
Moon, P. Proposed standard s o l a r - r a d i a t i o n curves f o r e n g i n e e r i n g u s e . J. F r a n k l i n I n s t . 230:
583,
1940.Desplanches, A . Guide de chauffage, v e n t i l a t i o n , condltlonnement d l a i r .
E d . A . I . C . V . F . 1959. p.123.
Watkins, George B. F l a t and laminated
8:"""
.
Engineering M a t e r i a l sHandbook. E d . Mantell, 27-44, 195
Morey, G.W. The p r o p e r t i e s o f g l a s s . Ed. Reinhold, 1954. p.386. Del Monaco, A . Un metodo p e r l a misura d e l c o e f f l c i e n t i d l r l n v i o d l
s u p e r f i c i p a r z i a l n e n t e d l f f o n d e n t l . Termotecnlca, ( 1 0 ) : 494, 1957. McAdams. Heat t r a n s m i s s i o n . McGraw-Hill, 1954. p.172 and 249
Jacob. Heat t r a n s f e r . Wiley and Sons, 1: 534, 1950.
Llnke W . ~ g l t e t e c h n i k , 8: 378-384, 1956; Krings and Olink i n "Transmis- ? i o n de c h a l e u r t r a v e r s des p a n n e a u 6 t a n c h e s doubles ou m u l t i p l e s a remplissage gazeux", S i l i c a t e s I n d u s t r i e l s , 11: 595, 1957, do n o t g i v e a f u l l r e p o r t . Table I Angles of r e f r a c t i o n and a i r - g l a s s r e f l e c t i o n f a c t o r s c a l c u l a t e d f o r n = 1.52
Table I1 Transmission f a c t o r s of g l a s s e s having k s 0.05 f o r n a t u r a l r a d i a t i o n (1) and f o r t h e l i n e a r l y p o l a r i z e d components i n t h e plane of i n c i d e n c e ( 2 ) and i n t h e p l a n e p e r p e n d i c u l a r t o t h e p l a n e of Incidence
( 3 )
AngLcs One glass
of incidence 1 2 3 W 1 .875 375 875 20" 373 360 885 40" 8 6 1 302 .918 so" a41 ,745 .938 60" .794 .619 .939 70" .678 A91 36.4 8(P .419 261 .576 Table I11
Values given i n ASHRAE ( 1 ) and v a l u e s c a l c u l a t e d by u s ( 2 )
of t h e t r a n s m i s s i o n and a b s o r p t i o n f a c t o r s f o r w a l l s comprising one o r two g l a s s e s having
ks
-
0.05 and n = 1.52 Angleso f
in cidcnec
-
Onc glass Two qlesscs
T~ a~ -- a,i 1 2 1 2 1 2 1 2 1 2 (r 2U 40' Lhrect radiation -- - - - - -- --. - . . - - At A75 .05 .048 -76 .767 .06 .052 .04 .043
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