the effect of collector aspect ratio on the collector efficiency of flat-plate solar air heaters

7/23/2019 The Effect of Collector Aspect Ratio on the Collector Efficiency of Flat-plate Solar Air Heaters

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ergamon

0360-5442(95)00053-4

Energy Vol 20, No 10, pp 1041-1047, 1995

Printed m

0360-5442/95 S9 50 0 00

T H E E F F E C T O F C O L L E C T O R A S P E C T R A T I O O N T H E

C O L L E C T O R E F F I C I E N C Y O F F L A T - P L A T E S O L A R A I R

H E A T E R S

H O - M I N G Y E H t a nd T O N G - T S H I E N L I N

Department of Chemical Englneenng, Tamkang Umverslty, Tamsul, Talwan, Repubhc of Chma

Recewed 13 December 1994)

Abstract--The effect of col lector aspect rat io of the col lector efficiency of fiat-plate solar air

heaters has been mvesngated theoretically and experimentally. With constant collector area, the

collector efficiency increases when the collector aspect ratio increases. The theoretical predictions

agree reasonably well with experimental results

INTRODUCTION

The m a i n app l i ca t i ons o f a s o l a r a i r hea t e r a r e s pace hea t i ng and d ry i ng . The s o l a r a i r hea t e r occup i es

a n i m p o r t a n t p l a c e a m o n g s o l a r h e a t i n g s y s t e m s b e c a u s e o f m i m m a l u s e o f m a t e r i a l s . F u r t h e r m o r e ,

d i r e c t u s e o f a i r a s t h e w o r k i n g s u b s t a n c e r e d u c e s t h e n u m b e r o f c o m p o n e n t s r e q u i r e d i n t h e s y s t e m .

T h e p r i m a r y d i s a d v a n t a g e o f s o l a r a i r h e a t e r s i s t h e n e e d f o r h a n d l i n g r e l a t i v e l y l a r g e v o l u m e s o f a i r

w i t h l ow t he rm al capac i t y a s work i ng f l u i d .

O u r d e s i g n o f a s o l a r a i r h e a te r h a s a n e x t e n d e d h e a t - t ra n s f e r a r e a , j a n a r r a n g e m e n t f o r p r o d u c i n g

f ree co nvec t i on , z,3 c rea t i on o f a i r t u rbu l enc e pas t t he h ea t i ng s u r f ace , 4 and i nc l u s i on o f i m po r t an t fo rc ed

convec t i on . I t i s we l l known t ha t t he co l l ec t o r con f i gu ra t i on wi l l i n f l uence t he f l u i d ve l oc i t y a s we l l a s

t he s t r eng t h o f fo rced conve c t i on . A s i m p l e p rocedu re fo r chang i ng t he f l u id ve l oc i t y and a l s o t he

s t r eng t h o f fo rced convec t i on i nvo l ves ad j u s t i ng t he a s pec t r a t i o o f a r ec t angu l a r f l a t -p l a t e co l l ec t o r

wi t h cons t an t f l ow ra t e . I t i s ou r pu rpos e i n t he p res en t s t ud i es t o i nves t i ga t e t heo re t i ca l l y and exper -

i m en t a l l y t he e f f ec t o f a s pec t r a t i o o f a r ec t angu l a r f l a t e -p l a t e co l l ec t o r on t he co l l ec t o r e f f i c i ency fo r

cons t an t co l l ec t o r a r ea and cons t an t f l ow ra t e .

THEORY

C o l l e c t o r e f f i c i e n c i e s

T h e c o n v e n i e m r e p r e s e n t a t io n o f e f f ic i e n c y f o r s h ee t a n d t u b e s o l a r e n e r g y c o l l e c t o r

is 5-7

= Q J A ¢ I o

= FR[ap~ g -

U L T r ., - T a ) l l o ] ,

i n w h i c h t h e h e a t - r e m o v a l f a c t o r i s d e f i n e d a s

F R = i n C p / A c U c )

{ 1 - e x p [ - ( U L F A J F n C p ) ] }

E q u a t i o n ( 1 ) w a s d e r i v e d f r o m e n e r g y b a l a n c e s u n d e r t h e f o l l o w i n g a s s u m p t i o n s : t h e t e m p e r a t u r e s o f

t he abs o rb i ng p l a t e and b u l k f l u i d a re m a i n l y func t i ons o f t he f l ow d i r ec t ion and t he r ad i an t ene rg i es

a b s o r b e d b y t h e g l a s s c o v e r a n d f l u i d a r e n e g l i g i b l e .

A l t hou gh t he re a re m an y d i f f e ren t des i gns o f f ia t -p l a t e co l l ec t o r s ava i l ab l e , i t i s fo r t una t e l y no t nec es -

s a ry t o deve l o p a new ana l y s i s fo r each s i tua t i on . 6 -s Th e gen era l i zed r e l a t i ons , Eqs . (1 ) and (2 ) , w h i ch

a r e d e v e l o p e d f o r t h e t u b e a n d s h e e t c a se , a p p l y t o m o s t c o l l e c t o r d e s ig n s . I t i s o n l y n e c e s s a r y t o d e r i v e

t h e a p p r o p r i a t e f o r m o f t h e c o l l e c t o r e f f i c ie n c y f a c t o r F , a n d E q s . ( 1 ) a n d ( 2 ) m a y t h e n b e u s e d t o

p r e d i c t t h e t h e r m a l p e r f o r m a n c e .

tTo whom all correspondence should be addressed.

1042 Ho-M ing Yeh and Tong-TshienLin

Acc ordingly , the c ol lector -ef f ic iency factor for the f la t -p la te solar energy c ol lectors show n in F ig . 1

with h = hi = h2 is 9

F = { 1 + U L I { h + [ ( l / h ) + ( l l h r ) ] -I } }-~, (3)

in which the col lector overal l loss coef f ic ient UL is the sum of the top (Ut) and bot tom and edge (Ub)

loss coefficients, i .e.

UL = Ut + Ub. (4)

H e a t - t r a n s f e r c o e f f i c i e n t s

The r es i st ance to ene rgy lo ss t h rough the bo t tom and edges o f t he co l l ec to r is m a in ly the r e s is t ance

to he a t f l ow th rough the in su la t ion by conduc t ion , i .e .

Ub=ks/~ ( 5 )

An empi r i ca l equa t ion fo r Ut was deve loped by Kle in ° f o l lowing the bas i c p rocedure o f H o t t e l and

W oer t z ) I Fo r t he ho r i zon ta l co l l ec to r show n in F ig . 1 ,

(To.m /520 1 t -1

Ut = [

( r p . m / T a )

] o 43o _ lOO/Tp.m+ ~---~w (6 )

1 + (1 + 0.089hw - 0.1166hw%)(1 + 0.0786 6)J

o'(Tp,m + Ta)(7~p,m+ T~a)

(%+0.00591hw)- +[2+(1+0.089hw-0.1166hwep)( 1+0.07866)-1+0.133%]/%-1

The hea t - tr ans f e r coe f f ic i en t s be tween the a i r and tw o duc t wa l l s were a ssumed to be equa l i n Eq . ( 3 ) .

I n t he s tudy o f so l a r a i r hea te r s and co l l ec to r - s to r age wa l l s , i t is necessa ry to know the fo r ced convec t ion

heat - t ransfer coef f ic ient betwee n tw o f la t p la tes . Fo r a i r , the fo l low ing cor re la t ion 12 m ay b e der ived

f rom K ay ' s da t a f o r f u l ly deve loped tu rbu len t f low wi th one s ide hea t ed and the o the r s ide in su la t ed :

N u = h D d k

= 0.0158 Re° 8

The cha rac te r i st i c l eng th i s t he equ iva l en t d i amete r o f t he duc t

D e = 4 H B / 2 ( B + H ) .;

t he Re yno lds num ber fo r t he r ec t angu la r duc t i s t hen de f ined by

I Glass over

bsorbi ng late

: - -h k ' h l

ir low C I Botton late

~ I n s u l a u o n

Fig. 1. Flat-platesolar air heater.

Collector aspect ratio effect on the co llectorefficiency 1043

H B I 2B + 2 H ) ] [ i n / p BH ) ] p

D e v p l ~

- / x ( B + H )

T h e r a d ia t i on c o e f f i c i e n t b e t w e e n t h e t w o a i r - d u c t s u rf a c e s m a y b e e s t i m a t e d b y a s s u m i n g a m e a n

rad ian t t empera tu re equa l to the mean f lu id t empera tu re , i . e .

h r ~ 4 t r T ~ f. m / [ (l / ) + l / e R ) - 1 ] . ( 1 0 )

Th e co nvec t ive hea t - t rans f e r coe f f i c i en t hw fo r a i r f low ing ov er the ou t s ide s u r f ace o f the g la s s cov er

depends p r imar i ly o n the w ind ve loc i ty V . M cA d am s t3 ob ta ined the exp er imen ta l r e su l t

hw = 5 .7 + 3 .8 V, (11 )

w here the un i t s o f hw and V a r e W /m z °C and m /s ec , r e s pec t ive ly .

M e a n t e m p e r a t u r e s

The t empera tu re d i s t r ibu t ion o f a i r a long the f low d i r ec t ion o f the r ec tangu la r duc t can be ob ta ined

f r o m e n e r g y b a l a n c e s

T y (Z ) - T a - I or g C tp /U L [ A c F U L ( Z / L ) ]

W e - T a - I o T g O l p / U L ex p - ~aCp j . (12 )

The me an f lu id t empera tu re i s then foun d by in teg ra t ing Eq . ( 12 ) f rom z = 0 to z = L , v i z . ,

T f . m = ( 1 / L ) f 2 T f ( z ) d z . ( 1 3 )

P er fo rm ing th i s in t eg ra t ion and s ubs t itu t ing r I and F R f rom Eqs . ( 1 ) and (2 ) , r e s pec t ive ly , the m ean

f lu id t empera tu re i s ob ta ined as

T f . m

Tf .~ + ( ~ l lo / UL F R ) [ 1 - - ( F R / F ) ] . ( 1 4 )

Th i s i s a l s o the p roper t empera tu re fo r eva lua t ion o f the f lu id p roper t i e s .

The mean p la t e t empera tu re w i l l a lw ays be g r ea te r than the mean f lu id t empera tu re due to the hea t -

t r ans f e r r e s i s t ance be tw een the abs o rb ing s u r f ace and the f lu id . The mean p la t e t empera tu re may be

us ed to ca lcu la t e the co l l ec to r e f f i c i ency , i. e .

= T g C t p -- U L ( T p : n - T a ) / l o .

( 1 5 )

I f w e equa te the r e l a t ions fo r ~ g iven in Eqs . ( 15 ) and (1 ) and s o lve fo r the mean p la t e t empera tu re ,

w e f ind

T p m = Tf., + ( * l l o l U L F R ) ( 1 - - F R ) . ( 1 6 )

C a l c u l a t i o n m e t h o d f o r c o l l e c to r e f fi c ie n c i es

Th e p roc edure fo r ca lcu la t ion o f theo re t i ca l va lues o f a9 w i l l now b e des c r ibed . F i r st , w i th kno w n

col l ecto r geo m etr ies (L, B, H ) an d sys te m prop er t ies ( r s , a , Cp, p , /x, k , ks, I s, , eR, eg), as wel l as

the g iven ope ra t ing co nd i t ions ( Io, T~, V , m, Te . ,) , a t em pora ry va lue o f r l i s e s t ima ted f rom Eqs . ( 1 ) -

(11 ) once Tp.m and Tf.m a re a s s umed . Th e va lues o f Tf .m and Tp,m a re then chec ked by us ing Eqs . ( 14 )

and (16 ) , r e s pec t ive ly , and new va lues o f Tf .m and Tp.m ma y be ob ta ined . I f t he ca lcu la t ed va lues o f

T f m and Tp.m a re d i f f e r en t f rom the a s s um ed va lues , con t inued ca lcu la t ions by i t e r a t ion i s need ed un t i l

1044 Ho-M mg Yeh and Tong-Tshien Lin

t h e l a s t a s s u m e d v a l u e s m e e t t h e f in a l l y c a l c u l a t e d v a l u e s , a n d t h u s t h e c o r r e s p o n d i n g v a l u e o f 7 / i s

a l s o f i n a l l y o b t a i n e d .

EXPERIMENTAL STUDIES

Apparatus and procedure

F o u r s o l a r a i r h e a t e r s w i t h t h e s a m e c o l l e c t o r s u r f a c e a r e a A c o f 0 . 4 2 1 3 5 m 2 b u t w i t h d i f f e re n t a s p e c t

r a t i o s L/B) w e r e b u i l t . T h e L / B r a t i o s a r e 6 : 1 ( 1 . 5 9 m x 0 . 2 6 5 m ) , 3 : 2 ( 0 . 7 9 5 m x 0 . 5 3 m ) , 2 : 3

( 0 . 5 3 m x 0 . 7 9 5 m ) , a n d 1 : 6 ( 0 . 2 6 5 m x 1 . 5 9 m ) . I n o r d e r t o m a i n t a i n s t e a d y c l i m a t i c c o n d i t i o n s , e x p e r -

i m e n t s w e r e c a r r i e d o u t w i t h a n a r t if i c ia l s i m u l a t o r , a s s h o w n i n F i g . 2 . O n e s e t o f h e a t s o u r c e s c o n s i s t s

o f 8 4 e l e c t ri c a l e n e r g y s u p p l i e s ( 1 1 0 V , 1 2 5 W ) . D u r i n g o p e r a t i o n s , t h e s t r e n g th s o f h e a t s o u r c e s w e r e

a d j u s t e d b y u s i n g a se t o f o n - o f f s w i t c h e s . T h e i n s o l a t io n s Io w e r e m e a s u r e d a n d r e c o r d e d w i t h a n E p p l y

L a b o r a t o r y p y r a n o m e t e r . W i n d w a s p r o v i d e d b y a f a n a n d t h e w i n d v e l o c i t y V w a s s e t a t 1. 0 m / s e c ( a s

i n d i c a t e d b y a C h i c a g o C e n c o a n e m o m e t e r ) . T h e t e m p e r a t u r e s w e r e m e a s u r e d a t b o t h t h e o u t s i d e g l a s s

c o v e r a n d t h e a b s o r b i n g s u r f a c e a t s e v e r a l p o i n t s w i t h a N o . 7 0 9 p r o b e f r o m t h e Y e l l o w S p r i n g s I n s t r u -

m e n t C o . , w h i l e th e a m b i e n t t e m p e r a t u r e T a w a s c o n t r o l l e d b y a n a ir c o n d i t i o n e r a n d w a s m e a s u r e d a t

a p o s i t i o n 1 5 c m a b o v e t h e o u t s i d e g l a s s c o v e r w i t h a N o . 7 0 5 p r o b e . I n a d d i t i o n , e i g h t m e r c u r y t h e r -

m o m e t e r s w e r e e m p l o y e d t o m e a s u r e t h e a i r t e m p e r a t u r e s w i t h i n t h e h e a te r , a s w e l l a s a t th e i n l et

a n d o u t l e t .

E x c e p t f o r t h e g l a s s c o v e r , a l l p a r t s o f t h e s o l a r a i r h e a t e r w e r e w e l l i n s u l a t e d t h e r m a l l y t o m a k e

t h e e n e r g y l o s s a s s m a l l a s p o s s i b l e . F o r e a c h h e a t e r , a n a i r b o x w i t h a p r e h e a t e r w a s u s e d f o r a ir

d i s t r i b u t io n a n d t e m p e r a t u r e c o n t r o l a t th e i n l e t. A i r t o b e h e a t e d w a s s u p p l i e d s t e a d i l y b y a b l o w e r

( R e d m o n d C o . M o d e l B L M o d e l 5 5 2 ) a n d t h e f lo w r a te w a s c o n t r o l l e d b y a t r a ns f o rm e r , w h i l e th e

f l o w ra t e w a s m e a s u r e d w i t h a N o . 3 1 3 2 T a y l o r a n e m o m e t e r f r o m F i s h e r S c i en t i fi c C o .

Experimental results

A t t h e e n d o f e a c h e x p e r i m e n t a l r u n , t h e a i r t e m p e r a t u r e s i n t h e in t e r io r , a s w e l l a s a t th e i n l e t a n d

o u t l e t o f th e c o l l e c t o r , t h e a m b i e n t t e m p e r a t u r e , a n d t h e m a s s - f l o w r a t e w e r e m e a s u r e d . I t w a s f o u n d

t h a t th e t e m p e r a t u r e s o f t h e a b s o r b i n g p l a t e a n d b u l k f l u id a r e m a i n l y f u n c t i o n s o f t h e f l o w d i r e c t io n .

T h e e x p e r i m e n t a l v a l u e s o f t h e c o l l e c t o r e f f i c ie n c y w e r e t h e n c a l c u l a t e d f r o m

r l = m C p / A J o ) T f , o - T f , , ) .

( 1 7 )

T h e r e s u l t s a r e p l o t t e d i n F i g s . 3 a n d 4 .

\ \ ~ \ \ \ \ \

\ \ \ x x \ x

\ \ \ \ \ \ \ \

N \ \ \ \ N \ \ \

\ \ \ \ , k \ \ \ x ,

C ' , .

\ \ \ X \ \ \ \ \ \ \

F~g. 2. Schem atic dmgram o f a solar air heater w ith amficlal s~mulation. A = a~r heater, B = artificial sun;

C = b lower; D = air m ixer; E = differential manom eter, F = air conditioner, G = temperature indicator; H = fan;

I =a tr box; J thermocouples; K = transformer

C o l l e c t o r a s p e c t r a t m e f f e c t o n t h e c o l l e c t o r e f f i c i e n c y 1 0 45

I= 0 .4

F i g 3

E X ~ T H E O. L ~

+ . . . . . 3 / 2

O 2 /3

1o 15 20 25

x 1 0 3 k g l s e c )

E f f e c t o f c o l l e c t o r a s p e c t r a t i o o n c o l l e c t o r e f f i c i e n c y , 1 o = 8 3 0 W / m 2

¢ 0 4

E X E T H E O . L ~

4- 3 /2

0 . . . . . . . 2 / 3

° ° ° °° °° °°

0 . o I I I I

5 1 0 1 5 2 0 2 5

x 1 0 3 ( k s / s e e )

F i g 4 . E f f e c t o f c o l l e c t o r a s p e c t r a U o o n t h e c o l l e c t o r e f f i c ie n c y , I o = 1 1 0 0 W / m 2

T h e o r e t i c a l p r e d i c t i o n

The m et hod fo r t heo re t i ca l p red i c t i on o f t he co l l ec t o r e f f i c i enc i es was des c r i bed i n t he l a s t pa rag raph

o f t h e s e c t i o n o n t h e o r y . T h e f o l l o w i n g a n d T a b l e 1 a r e t h e e x p e r i m e n t a l c o n d i t i o n s a n d p h y s i c a l

p rope r t i e s em p l o ye d i n th i s s t udy : Ac =

= 0 .42132 m2; L = 1 .59 , 0 .795, 0 .53 , and 0 .265 m; B = 0 .265,

0 .53 , 0 . 795 , and 1 .59 m ;

= 6 / 1 , 3 / 2, 2 / 3 , a n d 1 /6 ; H = 5 . 5 c m ; z g = 0 . 8 7 5 ; a p = 0. 95 ; e R = 0 . 9 4 ;

eg = 0.94; Ub =

ks~Is ~

0; Io = 830 and 1100 W /m2; Ta = 30°C; Tf.~= 35 -+ 0 .1) °C; V = 1 .0 m /se c;

t h = 0 .0107 , 0 . 0161 and 0 .0214 kg / s ec .

B y s ubs t i t u t i ng t he s pec i f i ed va l ues i n t o t he app rop r i a t e equa t i ons , t heo re t i ca l p red i c t i ons were

ob t a i ned . The r e s u l t s a re a l s o p l o t t ed i n F i g s . 3 and 4 fo r com par i s on .

Ho-Ming Yeh and Tong-Tshien Lin

Table 1. P hysical properties of air at 1 atm.

T p Cp p~x l0 s

(°C) (kg/ms) (kJ/kg.K) (kg/m.sec)

10.0 1 246 1.0048 1.78

37.8 I. 137 1.0048 1.90

65.6 1.043 1.0090 2.03

93.3 0.964 1.0090 2 15

DISCUSSION AND CONCLUSIONS

T h e e f f e c t o f c o l l e c t o r a s p e c t r a t i o o n t h e c o l l e c t o r e f f i c i e n c y o f f l a t- p l a te s o l a r a i r h e a t e r s h a s b e e n

i n v e s t i g a t e d b o t h t h e o r e t i c a l l y a n d e x p e r i m e n t a l l y . I t is s e e n i n F i g s . 3 a n d 4 t h a t t h e t h e o r e t ic a l p r e d i c -

t i o n s a g r e e r e a s o n a b l y w e l l w i t h t h e e x p e r i m e n t a l r e s u l t s . T h e t h e o r e t i c a l v a l u e s a r e g e n e r a l l y l o w e r

t h a n t h e e x p e r i m e n t a l d a t a , e x c e p t f o r t h e h i g h e s t a s p e c t r a t i o ( 6 : 1 ) . P e r h a p s t h e t h e o r e t i c a l p r e d i c t io n s

a r e g r e a t e r th a n t h e e x p e r i m e n t a l r e s u l ts f o r h i g h e r a s p e c t ra t i o s b e c a u s e o f t he a s s u m p t i o n w e m a d e

t h a t t h e l o ss c o e f f i c i e n t U b f r o m t h e s u r f a c e s o f e d g e s a n d t h e b o t t o m o f t h e s o l a r c o l l e c t o r t o t h e

a m b i e n t i s n e g l i g i b le . T h i s a s s u m p t i o n i s o b v i o u s l y u n r e a s o n a b l e w h e n t h e c o l l e c t o r a s p e c t r a t io i s

l a r g e s i n c e t h e s u r f a c e a r e a o f th e e d g e s f r o m w h i c h p a r t o f t h e e n e r g y i s lo s t b e c o m e s l a r g e a n d t h is

e n e r g y l o s s b e c o m e s s i g n if i c an t a l t h o u g h t h e s u r f a ce s a r e s o m e w h a t i n s u la t ed .

W e a l s o f o u n d f r o m F i g s . 3 a n d 4 t h a t th e c o n s t a n t c o l l e c t o r a r e a A c, t h e c o l l e c t o r e f f i c i e n c y in c r e a s e s

w h e n t h e c o l l e c t o r a s p e c t ra t i o i n c re a s e s . T h i s r e s u l t i s o b t a i n e d b e c a u s e i n c r e a s i n g t h e a s p e c t r a t io

d e c r e a s e s t h e c r o s s - s e c t i o n a l a r e a o f t h e a i r d u c t a n d t h u s i n c r e a s e s t h e v e l o c i t y o f a i r fl o w a n d a l s o

t h e c o n v e c t i v e h e a t - t r a n s f e r r a t e f r o m t h e s u r f a c e o f t h e a b s o r b i n g p l a t e t o t h e f lo w i n g a i r. H o w e v e r ,

i n c r e a s i n g t h e a s p e c t r a t i o a l s o i n c r e a s e s t h e f a n p o w e r a n d t h e r e b y l e a d s t o i n c r e a s e d o p e r a t i n g c o s t .

C o n s e q u e n t l y , a p r o p e r i n c r e a s e o f t h e c o l l e c t o r a s p e c t r a ti o s h o u l d b e e c o n o m i c a l l y f e a s i b l e in th e

d e s i g n o f a s o l a r a i r h e a t e r .

REFERENCES

1. M. K. Seluck,

Solar Air Heaters and Their Applications

pp . 155 -182 , A . A . M. Say igh ed ., Acad emic Press ,

N ew Y o rk , N Y (1 9 7 7 ) .

2. F. Kreith and J. F. Kreider, Principles of Solar Engineering Chap. 4 , pp. 20 3-3 09, M cGraw-Hill , New Yo rk,

NY (1978) .

3 . H. M. Yeh and Y. C. Ting, Appl. Energy 22, 145 (1985).

4 . H . M. Yeh and Y . C . T ing ,

Energy-The International Journal

13, 543 (1988).

5 . A. Whil l ier, S olar Energy Collect ion and Its Uti lization for House Heating, ScD Thesis, M IT (1953).

6 . H. C. Hottel and A. Whil l ier,

Transactions of the Conference on the Use o f Solar Energy

2, Part I , 74,

Univers i ty o f Ar izona Press (1958 ) .

7. A. Whillier, Applicat ions of Solar Energy for Heating and Cooling of Buildings A S H R A E , N e w Y o r k, N Y

(1977).

8 . R . W. Bhss , Sol . Energy 3, 55 (1959).

9 . J . A. Duffle and W. A. Beckman,

Solar Engineering of Thermal Processes

3rd edn., pp. 238, 245, Wiley,

New York , NY (1980) .

10. S. A. Klein, Sol . Energy 17, 79 (1979).

11. H. C. Hottel and B. B. Woetz,

Trans. Am. Soc . Mech. Engnrs 64

91 (1942).

12 W. M. Kays , Convective Heat and Mass Transfer McGraw-Hi l l , New York , NY (1966) .

13 . W. H . McAdams,

He at Transmission

3rd edn . , McGraw-Hi l l , New York , NY (1954) .

14 . J . A . Duff le and W. A . Beckman ,

Solar Engineering of Thermal Processes

3rd edn., p . 223, W iley, New

York , NY (1980) .

NOMENCLATURE

A~ = Surface area o f the collector, LB

B = Col lec to r w id th (m )

Cp = Specific heat o f air at c onstant

pressure (kJ kg I K I)

De = Equ ivalen t d iameter o f the condu i t

F = Effic iency fac to r o f the so lar a i r

heater

Collector aspect ratio effe ct on the collector efficiency 1047

F R = H e a t - r e m o v a l f a c t o r f o r t h e s o l a r

a i r h e a t e r

H = H e i g h t o f t h e a i r t u n n e l i n t h e s o l a r

c o l l e c to r ( m )

h h I h E = C o n v e c u v e h e a t - t r a n s f e r c o e f f i c i e n t

fo r f l u i d f l o win g o v er a f l a t p l a t e

(1 0 h - I m -2 )

h r = Rad i an t h ea t - t r an s fe r c o ef f i c i en t

b e t w e e n t w o p a r a l l e l p l a t e s

(1 0 h - I m -2 K )

h w = C o n v e c t i v e h e a t - t ra n s f e r c o e f f i c i e n t

f o r m r f t o w m g o v e r t h e o u t s i d e

su r f ace o f g l as s co v er (1 0 h -~ m -2 )

l o = In c id en t so l a r r ad i a t i o n (1 0 m -2 h -~ )

k , k , = T h e r m a l c o n d u c u w t y o f a i r ,

insu la tor (10 h -~ m -2 K)

L = C o l l e c t o r l e n g t h ( m )

l , = T h i c k n e s s o f t h e i n s u l a t o r ( m )

rh = Mas s - f l o w r a t e o f m r (k g h -~ )

Q u = U s e f u l g a i n o f e n e r g y c a r d e d a w a y

b y a i r p e r u m t t i m e ( k g h - I )

R e = R e y n o l d s n u m b e r

T a = A m b i e n t t e m p e r a t u r e ( K )

T f z ) = F l m d t e m p e r a t u r e ( K )

Tf,, Tf,o = T f a t th e i n l e t an d o u t l e t o f t h e

s o l a r a i r h e a t e r ( F )

E g , e p , E R =

Tf.m = A v er ag e v a lu e o f T f (K)

Tp, TR = Tem p era tu re o f t h e ab so rb in g p l a t e ,

b o t t o m p l a t e ( K )

Tp.m = A v er ag e v a lu e o f Tp (K )

U b = L o s s c o e f f i c i e n t f r o m t h e s u r f a c e s

o f e d g e s a n d t h e b o t t o m o f t h e

s o l a r c o l l e c t o r to t h e a m b i e n t

(1 0 h - m 2 K)

U L = O v e r a l l l o s s c o e f f i c i e n t

( l d h - I m e K )

U , = L o s s c o e f f i c i e n t f r o m t h e t o p o f t h e

so l a r co l l ec to r t o t h e am b ien t (1 0

h -~ m -2 K )

v = A i r v e lo c i t y i n t h e t u n n e l (m h -~ )

V = W i n d v e l o c i t y ( m h - ~ )

z = A x i a l c o o r d i n a t e a l o n g t h e f l o w

d i r e c t i o n ( m )

¢tp = Ab s o rp t i v i t y o f t h e ab so rb in g p l a t e

C o l l e c t o r e f f i c i e n c y

T r a n s m i t t a n c e o f t h e g l a s s c o v e r

E m i s s i v i t y o f t h e g l a s s c o v e r ,

ab so rb in g p l a t e , b o t t o m p l a t e

p = A i r d e n s i t y ( k g m - 3

/ ~ = A i r v i sco s i t y (k g m -~ h - l )

ty = S t e f a n - B o l t z m a n n c o n s ta n t ,

2 .0 4 x 1 0 7 1 0 h - I m -2 K -4

the effect of collector aspect ratio on the collector efficiency of flat-plate solar air heaters

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