- Email: [email protected]
Solar air heaters for low and moderate temperature applications
Solar Air Heaters For Low and Moderate Temperature Applications D . J. C l o s e Commonwealth Scientific and Industrial Rese~rch Ol'g~mis~tion, Victoria, Austr~li~ S o l a r air b e a t e r s c a n b e u s e d for m a n y p u r p o s e s , i n c l u d i n g crop d r y i n g , s p a c e h e a t i n g , a n d for regenerating dehumidfying agents. Because of their i n h e r e n t s i m p l i c i t y , t h e y a l s o offer t h e p o s s i b i l i t y of providing cheap, low-grade heat, at temperat u r e s u p to 100 d e g F a b o v e a m b i e n t , T h e r e are m a n y p o s s i b l e d e s i g n s for solar air heaters, from the point of view of both materials a n d c o n f i g u r a t i o n s . T h e s e in t u r n lead to a v a r i e t y of costs and collection eflicieneies, A design study has been made of three basic construction types, to which various modifieat i o n s are m a d e . T h e s e m o d i f i c a t i o n s i n c l u d e various heat-transfer coeficients between the absorber p l a t e a n d t h e air s t r e a m , s e l e c t i v e a n d n o n selective surfaces on the absorber plate, and nat u r a l c o n v e c t i o n barriers b e t w e e n t h e p l a t e a n d a m b i e n t air. C o l l e c t i o n eflLieiencies h a v e b e e n c o m p u t e d for t h e v a r i o u s d e s i g n s for a r a n g e o f operating temperatures. T h e c a l c u l a t i o n s s h o w t h a t t h e s e h e a t e r s c a n be bltilt to p r o v i d e air a t 100 d e g F a b o v e a m b i e n t , at c o l l e c t i o n e f l i c i e n c i e s o f 50 p e r c e n t or m o r e . AT
the present stage of development of solar devices, a major barrier to their increased use is the capital
cost of the absorber itself. In Australia, commercially available solar water heaters are expensive, and although they can be justified on ec
of the absorber plate is also a secondary consideration and light-gauge steel or aluminum are possible plate materials. Hence a solar air heater appears to be inherently cheaper than a water heater. A design study to determine the important factors i~flueneing air heater performance has been made, since there is a wide rauge of applications for w a r m to hot air, including the drying of crops, space heating, and the regeneration of solid absorbents used in dehmnidification. B a s i c T y p e s o f Air H e a t e r s Several interesting air-heater designs are described in the literature, a' 4, a However, since these works were published, a large amount of development s' 7. s has brought spectrally-selective surfaces to the point where they can be u~ed successfully to improve the efficiency and so reduce the cost of solar collectors. The following analysis is, in part, intended to demonstrate the benefits derived from using these surfaces. The basic air-heater types investigated are shown in Fig. l, types I, II, and I I I being grouped according to the location of the air duct. Accepting that an absorber plate and a transparent cover are necessary componellts, then type I is the simplest form of heater as these form the top and b o t t o m of the air duet. T y p e II, with the absorber plate splitting the air stream, is inte~ded to increase the plate to air heat transfer coefticiel~t and to decrease the conduction loss through the heater base, thus reducing the amomlt of r e a r insulatioll required. The type I I I heater employs a stagnant air gap between the ahsorber plate and the cover. The col~vectk)n heat exchaage between the plate aud cover is now small although there is a slight increase in radiation exellange due to the lower cover temperature. Both types I I and I I I are more complicated than type I, but should also achieve higher collection efliciel~cies. All three designs are an a t t e m p t to mimber and complexity of components to a I t is envisaged that for Australia, nmch of close to or within the Tropic. of Capricon L
reduce the miuimum. which lies horizoutal
mounting of the heater would be satisfactory. Incorporation of the heater into a suitably sited roof could also reduce installation costs, although the angle of the absorber might be governed by the seasonal requirements of the task to be performed. 117
#/o5h¢ Cover
'~ l
P/ore
, 4 ~ or/J~
l
/ ,so~ AIR l¢£ArgR
-7~ @ ,.~ ~ ~"
i I
rYP£ Z
Plaalic £over
~-
g
,~// )
,q~¢~,, ~
~
zo,,~,Ai~o.et
t~
h ~_
• o~
/
"t
3"0"
/
A/~ aeArER rmE # m,a,c Co,e~
atolls of tile air heater are determined by the sizes of suitable construction materials, and the air-flow l'e(luirenlents of low power input to the fan and a sarisfa<,tory for('ed <'onve<'tion heat transfer coelfi<'ient. Ele ments three feet wide have been considered as this is a standard size for a wide variety of materials available in A~tstralia. The duet depth is now determined by the air flow requirements, which are discussed in (2) below. The duct length, all other factors being determined, can be fixed by requirements of outlet temperatures and considerations of the overall efficiency of the heater. This factor is also discussed in detail later. through a heater results in higher collection efiieielwies, but also in increased fan running costs. To determine a reasonable compromise point, rough calculations were made involving the effects of various air veh)eities in duets of different depths, assuming the ducts to be three feet wide. With a duct depth of two to three inches and a llleall air velocity of 10 ft per see, the fan running costs are negligible compared to the capital cost oi the heater. The plate to air heat transfer ('oeflieient is quite good, at approximately per ft per hr I:.
/1# Duet ~
I i
~ose ~
d'-o"AVRHiAr£,~ Fro. 1.
NOMENCLATURE ('~
specific h e a t , B t u / l b ° F
1)~ = equiwdent di,tmeter of duet G
rgP£E
C r o s s - s e c t i o n s of t h e t h r e e |taste t y p e s ()f tfir h e a t e r s ,
=
= insolation, Btu/ft2hr e(mveetion |mat
hL = forced
4 X area -
ciremllferenee ' tr'msfer
ft
coefficient,
Btu/ft"' h [ o b, V a r i a b l e s i n Air H e a t e r P e r f o r m a n c e
The main factors determining the efficiency of heat collection of a solar air heater operating at a giveu air inlet t e m p e r a t u r e a r e : 1--Heater configuration; that is the aspect ratio of the duct and the length of duct through which the air passes,
/: = t h e r m a l c o n d u c t i v i t y , B t u / f t ~ h r ( ° F / f t ) K] = grndient of element collection efficiency vs. air t e m p e r a t u r e relation, °F 1 K.2 = i n t e r c e p t "~t ti = 0 of element collection efficiency vs. ,fir t e m p e r a t u r e r e l a t i o n L = l e n g t h of air h e a t e r , ft M = air m a s s flow t h r o u g h - f i r h e a t e r p e r foot w i d t h of
he,tter, lb/hr l/
2--Air-mass flow through heater, 3--Spectral r e f l e c t a n e e - t r a n s r n i t t a n c e
= t e m p e r a t u r e of air at some p o i n t in air he:~ter duct, °F
the absorber cover. 4--Spectral reflectance properties of the absorber plate. 5--Stagnant-air, natural-convection barriers between the absorber plate and ambient air. 6--Heat-transfer coefficient between the absorber
ts0 = t e m p e r a t m ' e of air at e n t r a n c e to air h e a t e r duet, oF V = me.m veh)eity of :dr through duct, ft/see x = length parameter in direction of air fh)w, ft ~, = solar absorptanee of absorber plate ~ = infrtu'ed emitttmee of ,tbsorber plate ~ = o p e n i n g angle of vee c o r r u g a t i o n s , degrees 0 = time, hours
plate and the air stream.
~
7--Insulation 8--Insolation.
Discussion
properties of
at the absorber base.
of Variables
p
= = ,~ = n0 =
v
density, l b / f t ~ viscosity, l b / f t / h r collection efficiency of a n Mr h e a t e r e l e m e n t collection efficiency of air h e a t e r -~ssuming h)sses are t h e s a m e as at. inlet s e c t i o n
= over'all efficiency of air heater
1 - - H e a t Configuralion.--The cross-sectional dimen118
Solar Energy
tions on the air heater types the ('over material has been assumed to be polyvinyl fluoride (P.V.F.). If doubts as to its life as a cover material for solar absorbers are excluded, then its ease of mounting and lower first cost make it more attra('tive than glass. Nominally its transmittance to solar radiation is higher than glass 6, being 0.96 against 0.90, but with an allowance for dirt deposition there is probably little difference, l:or these calculations, the transmittance of 1).V.F. has been assumed to bc 0.90. Glass is nearly opaque to long-wave radiation whereas 1).\".l '. has a transmittance of approximately 0.4. This has a minor effect on performance since reradiation from the absorber plate is only part of the total heat
l
~
N
g
eningangle
]oss.
4 Absorber Plate. Absorber plates with highly selective surfaces have been used successfully in solar water heaters 6'~ giving significant improvements in eollection eflieiency and cost. This is because only one transparent cover is re(luired even at faMy high operating temperatures. These improvements cmt be enhanced b y vee corrugating the absorber plate in the east-west direction in the lnamler shown in Fig. 2. Using surfaces with suitable nominal selective properties and b y careful design of the vees, Hollands 9 shows t h a t high selectivity can be obtained, 5 -Natural Convection BarHers.--A stagnant-air gap interposes a high impedenee to convective heat flow between the absorber plate and ambient air. Losses, both radiation and convection can be reduced to low values by multiple covers, but the consequent reduction in transmission of solar radiation makes more than one air gap of doubtful value, li'or this reason and because an ironer cover of plastic, operating at a relatively high temperature, would have a much reduced life, heaters with only one cover have been
hr (,% vo \ k / , ,
\~,,/
(D~Vo) °.~ \ ,b / The subscripts b and w relate the fluid properties to to the bulk temperature and the wall temperature respectively, M a c A d a m s reports coefficients for rectangular duets up to 24 percent below values computed from the above correlation. Voh 7, No. 3, 1963
Fro. 2. Proposed setting of vee-eorrugated absorber plate. E(,kert and Irvine 1~ report experiments on triangular ducts of side length to base length ratio 5 to 1. Again heat-transfer coefficients in fully developed turbulent flow fall 20 percent below those given in the above correlation. However the starting process persisted for a much longer period (60 to 70 diameters) than is the case with circular ducts. Because of the similarity in the mechanisms of boundary-layer growth in the inlet sections of triangular and rectangular ducts, it can be assumed that the starting process is also prolonged in re('tangular ducts. Sehlichting 12 reports starting lengths of at least 25 diameters in circular ducts and Eekert and Irvine, 60 to 70 diameters for their narrow triangular duets. For the absorbers under discussion, ducts of not longer than 25 feet are contemplated, due to the excessive temperature increase with consequent drop in eifieieney encountered if the air makes a long pass through the heater. This length corresponds to approximately 80 diameters for the 36 in. by 2 in. duct and to 60 diameter~ for the triangular duets. It is reasonable to infer then, t h a t the starting process, with its consequent increase in heat-transfer coefficient persists for a large proportion of an air heater of moderate length. For simplicity of comparison, the heat-transfer eoAdams correlation, the heat-transfer rates for a given temperature difference being proportional to the heattransfer areas. 7--[nsulation.--The forced-convection, heat-transfer coefficient between the air stream and the base is cornparatively low. Hence in heater types I I and I I I , there is no need for large amounts of base insulation. The absorber plate of the type I heater, ulrich is 119
the hottest cotnponent of tile absorber, was assumed to
TABI,E 1--Meteorological C(mstanls Vse(l
form the top ground surface. For tile purposes of this analysis, all heaters were assumed to be mounted on the ground. In practice the type I absorber plate would
D'fily dry-bulb telnper'tture ((~ A.M. t o (i P.M.) Averqge hourly insolation (horizonttd surface) l)aily sky ~,emperature (from Holden ~a) Wintt spee(l . . .
be separated from the earth ill IlIOSt places by a small air gap so that calculated conduction losses for this type are higher than would be achieved in an actual installation, To compute the conduction losses, the earth was assumed to provide the same amount of insulation as one inch of mineral wool [k = 0.03 Btu per sq ft p e r d e g p e r ft hr (°F/ft).] The conduction coefficient for earth was taken as 0.54 Btu per sq ft per deg per ft. Studies concernfilg periodic heat flow into a semidnfinite slab confirmed that the conduction losses obtained using the above assumption were of the right order of magnitude, 8 Insolation. For any given air-heater and airstream temperature, the temperature difference betwcen absorber plate and air stream is determined by the heat input to and losses from the heater. Clearly then, insolation affects the element collection efficiency, It is not obvious, especially for the type I and I I heaters, whether or not higher insolation necessarily results in higher collection efficiency. This is demonstrated by detailed calculations, Method
of
Examining
Element
Collection
74.5°1: 160 hltu/ft ~ 46°F 5 mph .
that for t)lack copper-oxide surt'aces, they are the most satisfactory for moderate-temperature ('olle(~tors. (b)--Plale-to-Air Heat Transfer Area. The influence of the heat-transfer area is shown by comparing the results obtained from effect (a) with efliciencies calculated for the same heater, but with double the effectire plate-to-air heat-trallsfer area. The increased heat-transfer area can be achieved by fimfing the absorber plate to give approximately twice the original area. An adjustment is required because of small changes ill the heat-transfer coeiticient. (c)--Vee Covr~tgalion of Absorber Plate. Vee corrugalion of the absort)er plate leads to improvements in performance by effects (a) and (b) above. However, it is essentially a separate study because of its particular application to only certain selective surfaces. The change in performance produced by this technique is shown by comparing rimmed selective and nonselective absorber plates, with roe-corrugated plates having the same nominal spectral-reflectance properties. Both the fins and vee corrugations are assumed to give a heat transfer area double that for the fiat plate, t h e corrugation opening angle q~ being approximately 60 deg. 9 (d)--Natural-Conveclion Barrier. An indication of the effect of the natural-convection barrier can be obrained by examining the performances of the types I I and I I I heaters. A better comparison is made t)y applying a second cover to the types I and I I beaters, but, as was discussed earlier, this is not considered a satisfa('tory design. Hence, this modification was not included in the calculations.
Efll-
eieneies
The factors 4, 5, 6, and 8 constitute the unknowns concerning air-heater performance. Five effects, discussed below, were examined to show their influence on the collection efficiency of an air-heater clement,
(a)--Absorber-Plate Spectral-Reflectance Characleristics. This effect is demonstrated by comparing the performance of each heater type with selective and nonselective absorber plates, The chosen selective properties of a,~ = 0.90, ~, = 0.15, have been used previously a, as calculations showed TABLE
Calculations
in
2--Absorber-Plate Properties as used in Calculations Plate Spectral-Reflectance Properties
Effect 1
a.~ = 0 . 9 0 ,
ER =
eR = 0.90 0.15
Flat Flat
Effect 1 (b) 2
c~, = 0.95, a~ = 0.95,
eR = 0.90 eR = 0.90
Flat Finned to give twice heat
3 4
as = 0.90, a~ = 0.90,
eR = 0.15 eR = 0.15
Flat Finned to
(a)
(~ = 0.95,
Plate Shape
2
transfer give
twice
heat
transfer
Nominal
Effect (c)
1 2 3
a~ = 0 . 9 5 , ,~ = 0.90, as = 0.80,
eR = 0 . 9 0 eR = 0 . 1 5 eR = 0 . 0 5
4
(~ = 0.95,
ere = 0 . 9 0
eR = 0.15
c~, = 0.99,
e~ = 1.00 eR = 0.28
"[ V e e
6
a~ = 0 . 8 0 ,
E~ = 0 . 0 5
a~ = 0 . 9 8 ,
eR = 0 . 1 0
~ ¢ = 60°
5
120
Actual
as = 0.90,
l Finned to give transfer
twice
heat
J a~ =
1.00,
corrugated
Solar Energy
( e ) - - [ n s o l a t i o n . The eflieieneies of all models of all types computed for more than one insolation shows this effect. As described later, the large amount of work required in this comparison was reduced using a summarising teehni(lue.
Efficiency
C o n s t a n t s Used in C a l c u l a t i o n s o f E l e m e n t Col lection Meteorological data as given in Table 1, was used to compnte heater collection eificiencies. The conditions are fairly typical of the Northeast coast of Australia. The cross-sectional dimensions of the three air-heater types are shown in Fig. 1. Theys were o arranged . that flow through each at an average velocity of l0 ft per sec was the same, being 510 c u f t per lniu per duct. Because of the low latitude of Townsville, the absorbers were assumed to be mounted horizontally on the ground. No conventional insulation is inehtded. As well as the average insolation of 160 Btu per sq ft per hr, a figure of 300 Btu per S{l ft per hr was chosen as being the maximum value to be expected under most conditions. The spectral reflectance properties and physical shapes of the absorber plates, as used in the performance calculations are given in Table 2. The cover material is P.V.F., with an assumed transmittance to solar radialion of 0.90, and to long wave radiation, of 0.40. The spectral-reflectance properties of vee-corrugated absorber plates, quoted as the actual values for effect (c) above are derived by Hollands 9. The nominal values of the selective surfaces quoted are from actual measurements 6. C a l c u l a t e d A i r - H e a t e r Efliciencies Data assembled by Tabor ~4' ~', was used to plot the element eollectioueflieielwies m., shown in Figs. 3, 4, 5, and 6. The insolation value of 160 Btu pet' sq ft per hr was used to ot)tain these curves, where collection etficiencies are shown as functions of air-stream ternperature, t/. Each modification in the form of a suitable selective surface, finned absorber plate or vee-corrugated absorber plate, provides some improvement in collection etficieney as shown in Figs. 3, 4, and 5. Benefits are most marked for the type III heaters, for the following reason, In the case of the types I and II heaters, the forcedconvection heat exchange between the air stream and cover is the principal source of heat loss. Devices such as the selective surface and finned or corrugated absorber plate have reduced effect, hnprovements in efficiency due to these are made by reducing the radialion heat transfer from the plate, and the base conduetion losses. These reductions are unimportant due to the dominance of the forced-convection term. An examination of Fig. 4(a), (b) and (c) illustrates particularly this effect, For the models examined, those with the vee-corruVol. 7, No. 3, 1963
,oo
----~-
~pe I ' } "~pe I 7~e$
ao =
~
~"
f~,pe
~Jl
" \'"
/
.. ~ : ' ~ , ", \\ ~,'% \~ .a, \
~a~ *, ,~o g o
% = 0.90, ~ = o.15
i \\
~ ~ ,,o
%
Po,,,t
,
.5¥,,ppeeZl } ) 5 e / e c h v e 5 u , ' / a c e
-~~6o~ ~ ~
I
--,-,,["~lock
\
•
\ 70
9o
. ~ . ~ \~,~ , "\,
Jlo J3o Air Tempel'at~,re
j'"--, /.~o
/to
-t F of
Fro. 3.--Element collection efficiency lines showing relative performance of selective trod non-selective '~t)sorber plates, G = 160 Btu per sq ft per hr. gated absorber plate, nominal selective properties a.~ = 0.80, ek = 0.05 gave the best performance while those with the flat absorber plate painted black gave the poorest. To show effect (d) and compare the three types, Fig. 6 was plotted by using the best and poorest model of each type and shading the region between these two " b o u n d a r y " lines, according to the heater type. Hence any model investigated lies somewhere in the appropriate region, its more exact position being obtained by refeyence to Figs. 3, 4, and 5. The general superiority of the type II[ heater, using the natural convection barrier is shown by Fig. 6. The advantage is most marked at the higher operating temperatures, from 120 deg F upwards, t)ut is inarginal for lower temperatm'es. The bast type i i heater has a somewhat better performance than the best type III, at temperatm'es below 100 deg F, an operating level that is quite satisfactory for space heating and some types oferopdrying. The variation of perfonnanee with insolation, effect (e), is denmnstrated by comparing Figs 6 and 7. these figures being the same in all respects except that Fig 7 was plotted for an insolation of 300 Btu per sq ft per hi'. The higher insolation yields higher eiticiencies for all models, especially at elevated operating temperatures. This is explained by the relatively higher coefficient of heat transfer between the air-heater absorber plate and the air stream as compared to the over-all coefficient of loss, referred to the absorber-plate temperature. To summarize the calculations exhibited in Figs. 3 to 7, t:ig. 8 has been plotted. This shows constant-eflieieney curves as functions of insolation and air-stream temperature for the best and poorest models of each type. For the types I and II heaters, straight lines were drawn through the computed values for 160 and 300 121
/.i~; ,o/oi~ )
........
~1~
~'\I
,~ ,'0
S,~{echve
~urioce
% = o.9o.,2,~=o.,'-s" ~
:
90
#0
I$0
ISO
Vee Co"r"ga/ed ~
70
_ _ i - 7o
90
"~
SO
II0
Air
61oc,~ Po,;~t ,~/ech~'e~Su,.,~c¢
%~
1;
/30
/$0
70
7~mpe~,+ure- e f °F
9o
II0
130
150
,~//" ~mperc~fu~ - ~ °F
( o..90,=¢~,=,o.L~ ~'~ned P/ale ~lac.A P~wnt . . . . . . . . . . . . 8elective Ou,'/ece %= 0.9o £,~=o./s ~,el¢chve Sue/ace %=o.8o,~=o.os ............................. ,3e/ec,%,¢ ,3u,'/ace %=o.¢~o,~,=o.~;
~,
i 0
I 8/oc~ P~.,>-,/
Pl~fe)
~°
~l/r Temperotur~ - t/ OF
Plate
:-/~:P/~,'~ ~ne::
~'x
i",
\'%
20
---
:,~...:,edPl~te
".\~"
_\
I
~ /10
0 130
150
%
I
I
"
o
"
70
90
~l/r T e m F r o / u r e -~( ~F
,air [ ~ m p a r o / ~
i
0 130
//0
70
/5o
- ~ or
90
I/0
/30
1~'0
Air 7~m/~.rcz/#re - ~/ " F
E l e m e n t collection efficiency lines showing relative performance of flat, "rod finned absorber plates; G - 160 Btu per sq ft per hr. FI(~. 5. E l e m e n t collection efficiency lines showing relative performance of finned and vee corrugated absorber plates; G 150 Btu per sq ft pet' hr. FIG. 4.
/o~
/oo
Typ~[
/I/
1// 6':':
\ \ \\" °
7~
,.
,,o ~lie" , ~ F r ~ l ' ~ w
/'30
,,~"
,Z
-
~"
•
- ~ °#
F,(;. 6. Relative element collection efficiency i'anges covered by three heater types G = I00 Btu per sq ft per hr.
122
~4 °,;
,,
,~ . . . . . . . R/r Te~wperoture- t,
~o
FIG. 7.--Relative element co]]ecthm efficiency ranges covered by three heater types G = 300 Btu per sq ft, per hr.
Solar Energy
15o _
~
f/O/" ~/Qck Po,k~d Pl~t*
Q
/80.
--
Vee Coreoqated Plate J
~ = ~a
[ ~
I
/~
? ~
50
IoO
~
80
I yFE CORg,UOkTF-D PLATE. ~=~° i
I FLAT BLAC~ P~|NTEO PLA.T
-
1oo Z5
8°
0
100
~00
I00
200
] n E o l a h ~ n - G 8/u/ft/3hr
Zn~olaflbn- G
200
~$tu/ft*hr 0 I000
0600
/St r l a t ~ l a c l ( P o i n l e d P/ale
- v ¢ e 6=# t u go a t e d P / a l e ~ L ~ L
Z, A
'*s
Fiat ~i~¢k ~
I
Ztl.~o~/b~ - G ~tu/~tfa~lr
/
_
~o ¢4
E/ao
ZO
/oo
~oo
/
Z
IlJ I .J
/.
30O
o
~tu//#=h¢
//////
i2/k..
,~
/oo ]n,~o/Otl'Oll
laodels
~5f
o~oo
,ooo
i,ioo
,~o
c
o~oo
~0O
1400
~ -
T
,ooo
,,too
~) TYPE ii
I~00
,~o
...o., , . o . , ,
BLkCK PAIN'W-D
I
VEF_ COP~U6.~,TE.D PLATE ~-(oC,°l
it]
" Btu//lt~ht
of e,tch type
I
i I000
2
8
50
t}o = &O%:
~ ~
-
of }]eater
~li
I
are
°o~oo
BLu per sq f t per hr insolation. Some points were c~]cul ~ t e d for a n i n s o l a t i o n of 50 B t u p e r sq ft per hr, w h i c h eollfirmed t h e s t r a i g h t - l i n e r e l a t i o n s . Values computed for the type i I I heaters at, 50 Btu per s(t ft, p e r hr gave t h e curves as shown in Figs. 8 (e)
0
~oo
TIME,
tjo=8OiOO,lZO 4o°r '
~s
I
i00o
inchided.
So
-
j ~
~s [ / /
"
and poorest
Ioo
1
F~,. 9.--Curves showing overall he~ter collection efteieneies during a tvpie,d d'w. l)otted lines indicate corresponding daily • Best
q
2£
o
0600
~i~ T'f'PE. =
"
FI(L 8.--Constant element-eolleeti(m efficiency curves for v:trying insolations and air strean~ teinperatures. Best and poorest models of each type are shown.
efficieneies.
r
"'=|
%°_
In~olat/on-
r
IbO0
U- 75~
fn~/ohbn- G ~fu/(tm~lr
i~o
Z[10o F
I~0
15oo
OF
0~o
DAY
--
iooo
,aoo
laeo
FIOUR.S
Let ,, -Kill + K2 [2] This is a straight-line relation obtained from Figs 3, 4 .~nd 5. Solving Eqs. [1] and [2] above, with the boundary conditions =
a n d (f).
Overall Air-Heater Performance
0 =
K.
+
x = 0, (K,
b = t,>, )[(-GKI~,~
,,o Lexpk
)j
[31
T o t h i s stage, all v ~ r i a b l e s h a v e b e e n d e a l t w i t h except the air-heater length,
The over-all collection efficiency of the heater is the ratio of the total heat collected to the total insolation. Thus
The temperature v'~riation in the direction of air flow is given hy the haste relation:
~ = ']lCs,(ts - t.o)/GL Substituting from [3]
assuming an element (if unit width:
n
i.e. dtl dx Vol. 7, No. 3, 1963
n+G JlCp
1]
= ~-
\ K1 + tfo
exp \
MOp
/
-- 1
[4]
This derivati(m assumes that there is no longitudinM conduction, and that temperatures in the lateral direction are unifl'om. 123
The efficiency 7o of the inlet element, which is the limiting case of L tending to zero, is determined by the insolation and inlet air temperature. Thus:
7 v0
exp \
:IlCj, ,/
:I( ,,
With inlet air temperature 140°F, and air heater of length 40 ft 7o = --K1
+ lfo
[5]
L / M C , = 0.252,
From [4] and [5]
and
- = -- 1 ~' , [6] r>, \ MCp / ,'ICp This relation is fundamentally of similar form to that derived t)y Buelow 16. A curve can now be plotted of 7~no as a function of - G K ~ L / MCv which is applicable to all air heaters where the air flow is parallel to the absorber plate.
Values for K1 carl be computed from Fig. 8. Tbus - G K ~ L / M C , = -0.217. Hence 7/70 = 0.899. From Fig. S, 70 = 0.58. Therefore 7 = 0.52.
T o i l l u s t r a t e t h e use of t h i s a n a l y s i s , c u r v e s of collec-
use". C.S.I.R.O. Engineering Section, Report E.I).5., September 1957. Bliss, R. W. Jr. "The derivation of several plate efficiency factors useful in the design of fi'~t plate solar collectors". Solar Energy III (4), ])ecember 1959. L6f, (L O. G. "Solar house heating A panel discussion". Proc. World Syrup. on Applied Solar Energy, November 1955. Bliss, R. W. Jr. "Solar house heating--A panel discussion". Proc. World Syrup. on Applied Solar Energy, Novelnt)er, 1955. Shoemaker, M. J. "Notes on a solar collector with unique air permea/)le media". Solar Energy V (4), Octoi)er-Decem-
t i o n efficiency t h r o u g h o u t
a d a y a r e s h o w n in Fig. 9.
To ('ompute them, an idealized insolation rate througho u t t h e d a y G = (300 sin I I 0 / 1 2 ) w~s a s s u i n e d . T h i s c o r r e s p o n d s f a i r l y closely t o a c l e a r d a y of t w e l v e horn's d u r a t i o n , w i t h a p e a k i n s o l a t i o n of 300 B t u p e r sq ft p e r h r a t noon. A g a i n o n l y t h e b e s t a n d p o o r e s t m o d e l s of e a c h t y p e w e r e c h o s e n , for a h e a t e r l e n g t h of 40 ft. A v e r a g e eflic i e n e i e s b a s e d on t h e t o t a l i n s o l a t i o n r e c e i v e d d u r i n g t h e d a y a r e also s h o w n , T h e m e t h o d u s e d to p l o t t h e s e c u r v e s is i l h l s t r a t e d by the Appendix. Conclusions S o l a r air h e a t e r s , of s i m p l e c o n s t r u c t i o n a n d erap l o y i n g c h e a p m a t e r i a l s , c a n be p r o d u c e d t o s u p p l y air a t t e m p e r a t u r e s a b o v e 150 d e g F, a n d
w i t h g o o d effi-
ciency. Selective surfaces and vee-corrugated and finned a b s o r b e r p l a t e s are b e n e f i c i a l t o a i r - h e a t e r p e r f o r m a n c e , b u t t h e i m p r o v e m e n t s are e n h a n c e d b y t h e use of t h e natm'al
convection barrier.
The
type
III
h e a t e r in-
c o r p o r a t e s t h i s f e a t u r e a n d for t e m p e r a t u r e s a b o v e 100 (leg F is c l e a r l y s u p e r i o r t o T y p e s I a n d I I . I t is h o p e d t h a t e x p e r i e n c e o b t a i n e d w i t h t e s t h e a t e r s will s h o w t h e m to be e c o n o m i c a l l y C o l u p e t i t i v e w i t h other
forms
of air
heating
even
including
oil-fired
e(luipmeut.
A P P E N D I X - - C A L C U L A T I O N OF O V E R A L L A I R HEATER COLLECTION EFFICIENCY T-tke the best type I I I heater incorporating the vee-corrugated (¢ = 60 °) absorber plate and the a., = 0.80, en = 0.05 selective surface. 110 G = 300 sin 12' at 1000 hours, 0 = 4 Thus G = 260 B t u / f C h r . Now
124
K~ = 0.00331
REFERENCES 1. Morse, R. N. "Solar water heaters for domestic "rod farm
2.
3. 4.
5.
ber, 1961. 6. Close, D. J. "Flat-plate solar al)sorbers: The production and testing of a selective surface for COl)per absorber plates", C.S.I.R.O. Enginccring Section, Report E.D.7., June 1962. 7. Edwards, E. K.; Gier, J. T.; Nelson, K. E . ; a n d Roddick, R. 1). "Spectral and directional therlnal r-tdiation characteristics of selective surfaces for solar collectors." Sol, r E,~ergy VI (1), January 1962 8. Tabor, H.; Harris, J.; Weinbergcr, H.; and l)or(m, B. " F u r t h e r studies on selective [)lack coatings", U.N. Conf. on New Sources of Energy, florae, Aug., 19(il. 9. Hollands, K. G. T. "l)irectional selectivity; Emitl.mce and absorption properties of three corrug'ttcd specular surfaces", Solar En~rfly, 7, no. 3, I). 108. 10. MacAd.tms, W. J. " H e a t Transmission", Mc(h'aw-Hill Book Co. New York, N. Y., 1954. 11. Eckert, E. I~. G.; and Irvine, T. F. Jr. "l)rcssurc dr(q) and heat tr.msfcr in a duct with triangular cross-section". Trans. A.S.M.E., 82, 1960. 12. Schlichting, H. "l~,oundary L:tyer Theory", l)crg:m)on Press, 1955. 13. Holden, T. S. "Calculation of incident low temperature radiation upon building surfaces". A . S . H . R . A . E . Jo,r~al, April 1961. 14. Tabor, H. "Sol'tr energy collector design", Bull. of the Res. Council of lsr:ml, 5C, No. 1. Nov. 1955. 15. Tab(),', H. "Radiation, convection and conduction eoeflicients in solar collectors". Bull. of the Res. Council of Israel, 6C, No. 3. Aug. 1958. 16. Buelow, F. H.; and Boyd, J. S. "Heating air by solar energy", Agricult~o'al Engineering, 38 (1) : 1957.
Solar Energy
the present stage of development of solar devices, a major barrier to their increased use is the capital
cost of the absorber itself. In Australia, commercially available solar water heaters are expensive, and although they can be justified on ec
of the absorber plate is also a secondary consideration and light-gauge steel or aluminum are possible plate materials. Hence a solar air heater appears to be inherently cheaper than a water heater. A design study to determine the important factors i~flueneing air heater performance has been made, since there is a wide rauge of applications for w a r m to hot air, including the drying of crops, space heating, and the regeneration of solid absorbents used in dehmnidification. B a s i c T y p e s o f Air H e a t e r s Several interesting air-heater designs are described in the literature, a' 4, a However, since these works were published, a large amount of development s' 7. s has brought spectrally-selective surfaces to the point where they can be u~ed successfully to improve the efficiency and so reduce the cost of solar collectors. The following analysis is, in part, intended to demonstrate the benefits derived from using these surfaces. The basic air-heater types investigated are shown in Fig. l, types I, II, and I I I being grouped according to the location of the air duct. Accepting that an absorber plate and a transparent cover are necessary componellts, then type I is the simplest form of heater as these form the top and b o t t o m of the air duet. T y p e II, with the absorber plate splitting the air stream, is inte~ded to increase the plate to air heat transfer coefticiel~t and to decrease the conduction loss through the heater base, thus reducing the amomlt of r e a r insulatioll required. The type I I I heater employs a stagnant air gap between the ahsorber plate and the cover. The col~vectk)n heat exchaage between the plate aud cover is now small although there is a slight increase in radiation exellange due to the lower cover temperature. Both types I I and I I I are more complicated than type I, but should also achieve higher collection efliciel~cies. All three designs are an a t t e m p t to mimber and complexity of components to a I t is envisaged that for Australia, nmch of close to or within the Tropic. of Capricon L
reduce the miuimum. which lies horizoutal
mounting of the heater would be satisfactory. Incorporation of the heater into a suitably sited roof could also reduce installation costs, although the angle of the absorber might be governed by the seasonal requirements of the task to be performed. 117
#/o5h¢ Cover
'~ l
P/ore
, 4 ~ or/J~
l
/ ,so~ AIR l¢£ArgR
-7~ @ ,.~ ~ ~"
i I
rYP£ Z
Plaalic £over
~-
g
,~// )
,q~¢~,, ~
~
zo,,~,Ai~o.et
t~
h ~_
• o~
/
"t
3"0"
/
A/~ aeArER rmE # m,a,c Co,e~
atolls of tile air heater are determined by the sizes of suitable construction materials, and the air-flow l'e(luirenlents of low power input to the fan and a sarisfa<,tory for('ed <'onve<'tion heat transfer coelfi<'ient. Ele ments three feet wide have been considered as this is a standard size for a wide variety of materials available in A~tstralia. The duet depth is now determined by the air flow requirements, which are discussed in (2) below. The duct length, all other factors being determined, can be fixed by requirements of outlet temperatures and considerations of the overall efficiency of the heater. This factor is also discussed in detail later. through a heater results in higher collection efiieielwies, but also in increased fan running costs. To determine a reasonable compromise point, rough calculations were made involving the effects of various air veh)eities in duets of different depths, assuming the ducts to be three feet wide. With a duct depth of two to three inches and a llleall air velocity of 10 ft per see, the fan running costs are negligible compared to the capital cost oi the heater. The plate to air heat transfer ('oeflieient is quite good, at approximately per ft per hr I:.
/1# Duet ~
I i
~ose ~
d'-o"AVRHiAr£,~ Fro. 1.
NOMENCLATURE ('~
specific h e a t , B t u / l b ° F
1)~ = equiwdent di,tmeter of duet G
rgP£E
C r o s s - s e c t i o n s of t h e t h r e e |taste t y p e s ()f tfir h e a t e r s ,
=
= insolation, Btu/ft2hr e(mveetion |mat
hL = forced
4 X area -
ciremllferenee ' tr'msfer
ft
coefficient,
Btu/ft"' h [ o b, V a r i a b l e s i n Air H e a t e r P e r f o r m a n c e
The main factors determining the efficiency of heat collection of a solar air heater operating at a giveu air inlet t e m p e r a t u r e a r e : 1--Heater configuration; that is the aspect ratio of the duct and the length of duct through which the air passes,
/: = t h e r m a l c o n d u c t i v i t y , B t u / f t ~ h r ( ° F / f t ) K] = grndient of element collection efficiency vs. air t e m p e r a t u r e relation, °F 1 K.2 = i n t e r c e p t "~t ti = 0 of element collection efficiency vs. ,fir t e m p e r a t u r e r e l a t i o n L = l e n g t h of air h e a t e r , ft M = air m a s s flow t h r o u g h - f i r h e a t e r p e r foot w i d t h of
he,tter, lb/hr l/
2--Air-mass flow through heater, 3--Spectral r e f l e c t a n e e - t r a n s r n i t t a n c e
= t e m p e r a t u r e of air at some p o i n t in air he:~ter duct, °F
the absorber cover. 4--Spectral reflectance properties of the absorber plate. 5--Stagnant-air, natural-convection barriers between the absorber plate and ambient air. 6--Heat-transfer coefficient between the absorber
ts0 = t e m p e r a t m ' e of air at e n t r a n c e to air h e a t e r duet, oF V = me.m veh)eity of :dr through duct, ft/see x = length parameter in direction of air fh)w, ft ~, = solar absorptanee of absorber plate ~ = infrtu'ed emitttmee of ,tbsorber plate ~ = o p e n i n g angle of vee c o r r u g a t i o n s , degrees 0 = time, hours
plate and the air stream.
~
7--Insulation 8--Insolation.
Discussion
properties of
at the absorber base.
of Variables
p
= = ,~ = n0 =
v
density, l b / f t ~ viscosity, l b / f t / h r collection efficiency of a n Mr h e a t e r e l e m e n t collection efficiency of air h e a t e r -~ssuming h)sses are t h e s a m e as at. inlet s e c t i o n
= over'all efficiency of air heater
1 - - H e a t Configuralion.--The cross-sectional dimen118
Solar Energy
tions on the air heater types the ('over material has been assumed to be polyvinyl fluoride (P.V.F.). If doubts as to its life as a cover material for solar absorbers are excluded, then its ease of mounting and lower first cost make it more attra('tive than glass. Nominally its transmittance to solar radiation is higher than glass 6, being 0.96 against 0.90, but with an allowance for dirt deposition there is probably little difference, l:or these calculations, the transmittance of 1).V.F. has been assumed to bc 0.90. Glass is nearly opaque to long-wave radiation whereas 1).\".l '. has a transmittance of approximately 0.4. This has a minor effect on performance since reradiation from the absorber plate is only part of the total heat
l
~
N
g
eningangle
]oss.
4 Absorber Plate. Absorber plates with highly selective surfaces have been used successfully in solar water heaters 6'~ giving significant improvements in eollection eflieiency and cost. This is because only one transparent cover is re(luired even at faMy high operating temperatures. These improvements cmt be enhanced b y vee corrugating the absorber plate in the east-west direction in the lnamler shown in Fig. 2. Using surfaces with suitable nominal selective properties and b y careful design of the vees, Hollands 9 shows t h a t high selectivity can be obtained, 5 -Natural Convection BarHers.--A stagnant-air gap interposes a high impedenee to convective heat flow between the absorber plate and ambient air. Losses, both radiation and convection can be reduced to low values by multiple covers, but the consequent reduction in transmission of solar radiation makes more than one air gap of doubtful value, li'or this reason and because an ironer cover of plastic, operating at a relatively high temperature, would have a much reduced life, heaters with only one cover have been
hr (,% vo \ k / , ,
\~,,/
(D~Vo) °.~ \ ,b / The subscripts b and w relate the fluid properties to to the bulk temperature and the wall temperature respectively, M a c A d a m s reports coefficients for rectangular duets up to 24 percent below values computed from the above correlation. Voh 7, No. 3, 1963
Fro. 2. Proposed setting of vee-eorrugated absorber plate. E(,kert and Irvine 1~ report experiments on triangular ducts of side length to base length ratio 5 to 1. Again heat-transfer coefficients in fully developed turbulent flow fall 20 percent below those given in the above correlation. However the starting process persisted for a much longer period (60 to 70 diameters) than is the case with circular ducts. Because of the similarity in the mechanisms of boundary-layer growth in the inlet sections of triangular and rectangular ducts, it can be assumed that the starting process is also prolonged in re('tangular ducts. Sehlichting 12 reports starting lengths of at least 25 diameters in circular ducts and Eekert and Irvine, 60 to 70 diameters for their narrow triangular duets. For the absorbers under discussion, ducts of not longer than 25 feet are contemplated, due to the excessive temperature increase with consequent drop in eifieieney encountered if the air makes a long pass through the heater. This length corresponds to approximately 80 diameters for the 36 in. by 2 in. duct and to 60 diameter~ for the triangular duets. It is reasonable to infer then, t h a t the starting process, with its consequent increase in heat-transfer coefficient persists for a large proportion of an air heater of moderate length. For simplicity of comparison, the heat-transfer eoAdams correlation, the heat-transfer rates for a given temperature difference being proportional to the heattransfer areas. 7--[nsulation.--The forced-convection, heat-transfer coefficient between the air stream and the base is cornparatively low. Hence in heater types I I and I I I , there is no need for large amounts of base insulation. The absorber plate of the type I heater, ulrich is 119
the hottest cotnponent of tile absorber, was assumed to
TABI,E 1--Meteorological C(mstanls Vse(l
form the top ground surface. For tile purposes of this analysis, all heaters were assumed to be mounted on the ground. In practice the type I absorber plate would
D'fily dry-bulb telnper'tture ((~ A.M. t o (i P.M.) Averqge hourly insolation (horizonttd surface) l)aily sky ~,emperature (from Holden ~a) Wintt spee(l . . .
be separated from the earth ill IlIOSt places by a small air gap so that calculated conduction losses for this type are higher than would be achieved in an actual installation, To compute the conduction losses, the earth was assumed to provide the same amount of insulation as one inch of mineral wool [k = 0.03 Btu per sq ft p e r d e g p e r ft hr (°F/ft).] The conduction coefficient for earth was taken as 0.54 Btu per sq ft per deg per ft. Studies concernfilg periodic heat flow into a semidnfinite slab confirmed that the conduction losses obtained using the above assumption were of the right order of magnitude, 8 Insolation. For any given air-heater and airstream temperature, the temperature difference betwcen absorber plate and air stream is determined by the heat input to and losses from the heater. Clearly then, insolation affects the element collection efficiency, It is not obvious, especially for the type I and I I heaters, whether or not higher insolation necessarily results in higher collection efficiency. This is demonstrated by detailed calculations, Method
of
Examining
Element
Collection
74.5°1: 160 hltu/ft ~ 46°F 5 mph .
that for t)lack copper-oxide surt'aces, they are the most satisfactory for moderate-temperature ('olle(~tors. (b)--Plale-to-Air Heat Transfer Area. The influence of the heat-transfer area is shown by comparing the results obtained from effect (a) with efliciencies calculated for the same heater, but with double the effectire plate-to-air heat-trallsfer area. The increased heat-transfer area can be achieved by fimfing the absorber plate to give approximately twice the original area. An adjustment is required because of small changes ill the heat-transfer coeiticient. (c)--Vee Covr~tgalion of Absorber Plate. Vee corrugalion of the absort)er plate leads to improvements in performance by effects (a) and (b) above. However, it is essentially a separate study because of its particular application to only certain selective surfaces. The change in performance produced by this technique is shown by comparing rimmed selective and nonselective absorber plates, with roe-corrugated plates having the same nominal spectral-reflectance properties. Both the fins and vee corrugations are assumed to give a heat transfer area double that for the fiat plate, t h e corrugation opening angle q~ being approximately 60 deg. 9 (d)--Natural-Conveclion Barrier. An indication of the effect of the natural-convection barrier can be obrained by examining the performances of the types I I and I I I heaters. A better comparison is made t)y applying a second cover to the types I and I I beaters, but, as was discussed earlier, this is not considered a satisfa('tory design. Hence, this modification was not included in the calculations.
Efll-
eieneies
The factors 4, 5, 6, and 8 constitute the unknowns concerning air-heater performance. Five effects, discussed below, were examined to show their influence on the collection efficiency of an air-heater clement,
(a)--Absorber-Plate Spectral-Reflectance Characleristics. This effect is demonstrated by comparing the performance of each heater type with selective and nonselective absorber plates, The chosen selective properties of a,~ = 0.90, ~, = 0.15, have been used previously a, as calculations showed TABLE
Calculations
in
2--Absorber-Plate Properties as used in Calculations Plate Spectral-Reflectance Properties
Effect 1
a.~ = 0 . 9 0 ,
ER =
eR = 0.90 0.15
Flat Flat
Effect 1 (b) 2
c~, = 0.95, a~ = 0.95,
eR = 0.90 eR = 0.90
Flat Finned to give twice heat
3 4
as = 0.90, a~ = 0.90,
eR = 0.15 eR = 0.15
Flat Finned to
(a)
(~ = 0.95,
Plate Shape
2
transfer give
twice
heat
transfer
Nominal
Effect (c)
1 2 3
a~ = 0 . 9 5 , ,~ = 0.90, as = 0.80,
eR = 0 . 9 0 eR = 0 . 1 5 eR = 0 . 0 5
4
(~ = 0.95,
ere = 0 . 9 0
eR = 0.15
c~, = 0.99,
e~ = 1.00 eR = 0.28
"[ V e e
6
a~ = 0 . 8 0 ,
E~ = 0 . 0 5
a~ = 0 . 9 8 ,
eR = 0 . 1 0
~ ¢ = 60°
5
120
Actual
as = 0.90,
l Finned to give transfer
twice
heat
J a~ =
1.00,
corrugated
Solar Energy
( e ) - - [ n s o l a t i o n . The eflieieneies of all models of all types computed for more than one insolation shows this effect. As described later, the large amount of work required in this comparison was reduced using a summarising teehni(lue.
Efficiency
C o n s t a n t s Used in C a l c u l a t i o n s o f E l e m e n t Col lection Meteorological data as given in Table 1, was used to compnte heater collection eificiencies. The conditions are fairly typical of the Northeast coast of Australia. The cross-sectional dimensions of the three air-heater types are shown in Fig. 1. Theys were o arranged . that flow through each at an average velocity of l0 ft per sec was the same, being 510 c u f t per lniu per duct. Because of the low latitude of Townsville, the absorbers were assumed to be mounted horizontally on the ground. No conventional insulation is inehtded. As well as the average insolation of 160 Btu per sq ft per hr, a figure of 300 Btu per S{l ft per hr was chosen as being the maximum value to be expected under most conditions. The spectral reflectance properties and physical shapes of the absorber plates, as used in the performance calculations are given in Table 2. The cover material is P.V.F., with an assumed transmittance to solar radialion of 0.90, and to long wave radiation, of 0.40. The spectral-reflectance properties of vee-corrugated absorber plates, quoted as the actual values for effect (c) above are derived by Hollands 9. The nominal values of the selective surfaces quoted are from actual measurements 6. C a l c u l a t e d A i r - H e a t e r Efliciencies Data assembled by Tabor ~4' ~', was used to plot the element eollectioueflieielwies m., shown in Figs. 3, 4, 5, and 6. The insolation value of 160 Btu pet' sq ft per hr was used to ot)tain these curves, where collection etficiencies are shown as functions of air-stream ternperature, t/. Each modification in the form of a suitable selective surface, finned absorber plate or vee-corrugated absorber plate, provides some improvement in collection etficieney as shown in Figs. 3, 4, and 5. Benefits are most marked for the type III heaters, for the following reason, In the case of the types I and II heaters, the forcedconvection heat exchange between the air stream and cover is the principal source of heat loss. Devices such as the selective surface and finned or corrugated absorber plate have reduced effect, hnprovements in efficiency due to these are made by reducing the radialion heat transfer from the plate, and the base conduetion losses. These reductions are unimportant due to the dominance of the forced-convection term. An examination of Fig. 4(a), (b) and (c) illustrates particularly this effect, For the models examined, those with the vee-corruVol. 7, No. 3, 1963
,oo
----~-
~pe I ' } "~pe I 7~e$
ao =
~
~"
f~,pe
~Jl
" \'"
/
.. ~ : ' ~ , ", \\ ~,'% \~ .a, \
~a~ *, ,~o g o
% = 0.90, ~ = o.15
i \\
~ ~ ,,o
%
Po,,,t
,
.5¥,,ppeeZl } ) 5 e / e c h v e 5 u , ' / a c e
-~~6o~ ~ ~
I
--,-,,["~lock
\
•
\ 70
9o
. ~ . ~ \~,~ , "\,
Jlo J3o Air Tempel'at~,re
j'"--, /.~o
/to
-t F of
Fro. 3.--Element collection efficiency lines showing relative performance of selective trod non-selective '~t)sorber plates, G = 160 Btu per sq ft per hr. gated absorber plate, nominal selective properties a.~ = 0.80, ek = 0.05 gave the best performance while those with the flat absorber plate painted black gave the poorest. To show effect (d) and compare the three types, Fig. 6 was plotted by using the best and poorest model of each type and shading the region between these two " b o u n d a r y " lines, according to the heater type. Hence any model investigated lies somewhere in the appropriate region, its more exact position being obtained by refeyence to Figs. 3, 4, and 5. The general superiority of the type II[ heater, using the natural convection barrier is shown by Fig. 6. The advantage is most marked at the higher operating temperatures, from 120 deg F upwards, t)ut is inarginal for lower temperatm'es. The bast type i i heater has a somewhat better performance than the best type III, at temperatm'es below 100 deg F, an operating level that is quite satisfactory for space heating and some types oferopdrying. The variation of perfonnanee with insolation, effect (e), is denmnstrated by comparing Figs 6 and 7. these figures being the same in all respects except that Fig 7 was plotted for an insolation of 300 Btu per sq ft per hi'. The higher insolation yields higher eiticiencies for all models, especially at elevated operating temperatures. This is explained by the relatively higher coefficient of heat transfer between the air-heater absorber plate and the air stream as compared to the over-all coefficient of loss, referred to the absorber-plate temperature. To summarize the calculations exhibited in Figs. 3 to 7, t:ig. 8 has been plotted. This shows constant-eflieieney curves as functions of insolation and air-stream temperature for the best and poorest models of each type. For the types I and II heaters, straight lines were drawn through the computed values for 160 and 300 121
/.i~; ,o/oi~ )
........
~1~
~'\I
,~ ,'0
S,~{echve
~urioce
% = o.9o.,2,~=o.,'-s" ~
:
90
#0
I$0
ISO
Vee Co"r"ga/ed ~
70
_ _ i - 7o
90
"~
SO
II0
Air
61oc,~ Po,;~t ,~/ech~'e~Su,.,~c¢
%~
1;
/30
/$0
70
7~mpe~,+ure- e f °F
9o
II0
130
150
,~//" ~mperc~fu~ - ~ °F
( o..90,=¢~,=,o.L~ ~'~ned P/ale ~lac.A P~wnt . . . . . . . . . . . . 8elective Ou,'/ece %= 0.9o £,~=o./s ~,el¢chve Sue/ace %=o.8o,~=o.os ............................. ,3e/ec,%,¢ ,3u,'/ace %=o.¢~o,~,=o.~;
~,
i 0
I 8/oc~ P~.,>-,/
Pl~fe)
~°
~l/r Temperotur~ - t/ OF
Plate
:-/~:P/~,'~ ~ne::
~'x
i",
\'%
20
---
:,~...:,edPl~te
".\~"
_\
I
~ /10
0 130
150
%
I
I
"
o
"
70
90
~l/r T e m F r o / u r e -~( ~F
,air [ ~ m p a r o / ~
i
0 130
//0
70
/5o
- ~ or
90
I/0
/30
1~'0
Air 7~m/~.rcz/#re - ~/ " F
E l e m e n t collection efficiency lines showing relative performance of flat, "rod finned absorber plates; G - 160 Btu per sq ft per hr. FI(~. 5. E l e m e n t collection efficiency lines showing relative performance of finned and vee corrugated absorber plates; G 150 Btu per sq ft pet' hr. FIG. 4.
/o~
/oo
Typ~[
/I/
1// 6':':
\ \ \\" °
7~
,.
,,o ~lie" , ~ F r ~ l ' ~ w
/'30
,,~"
,Z
-
~"
•
- ~ °#
F,(;. 6. Relative element collection efficiency i'anges covered by three heater types G = I00 Btu per sq ft per hr.
122
~4 °,;
,,
,~ . . . . . . . R/r Te~wperoture- t,
~o
FIG. 7.--Relative element co]]ecthm efficiency ranges covered by three heater types G = 300 Btu per sq ft, per hr.
Solar Energy
15o _
~
f/O/" ~/Qck Po,k~d Pl~t*
Q
/80.
--
Vee Coreoqated Plate J
~ = ~a
[ ~
I
/~
? ~
50
IoO
~
80
I yFE CORg,UOkTF-D PLATE. ~=~° i
I FLAT BLAC~ P~|NTEO PLA.T
-
1oo Z5
8°
0
100
~00
I00
200
] n E o l a h ~ n - G 8/u/ft/3hr
Zn~olaflbn- G
200
~$tu/ft*hr 0 I000
0600
/St r l a t ~ l a c l ( P o i n l e d P/ale
- v ¢ e 6=# t u go a t e d P / a l e ~ L ~ L
Z, A
'*s
Fiat ~i~¢k ~
I
Ztl.~o~/b~ - G ~tu/~tfa~lr
/
_
~o ¢4
E/ao
ZO
/oo
~oo
/
Z
IlJ I .J
/.
30O
o
~tu//#=h¢
//////
i2/k..
,~
/oo ]n,~o/Otl'Oll
laodels
~5f
o~oo
,ooo
i,ioo
,~o
c
o~oo
~0O
1400
~ -
T
,ooo
,,too
~) TYPE ii
I~00
,~o
...o., , . o . , ,
BLkCK PAIN'W-D
I
VEF_ COP~U6.~,TE.D PLATE ~-(oC,°l
it]
" Btu//lt~ht
of e,tch type
I
i I000
2
8
50
t}o = &O%:
~ ~
-
of }]eater
~li
I
are
°o~oo
BLu per sq f t per hr insolation. Some points were c~]cul ~ t e d for a n i n s o l a t i o n of 50 B t u p e r sq ft per hr, w h i c h eollfirmed t h e s t r a i g h t - l i n e r e l a t i o n s . Values computed for the type i I I heaters at, 50 Btu per s(t ft, p e r hr gave t h e curves as shown in Figs. 8 (e)
0
~oo
TIME,
tjo=8OiOO,lZO 4o°r '
~s
I
i00o
inchided.
So
-
j ~
~s [ / /
"
and poorest
Ioo
1
F~,. 9.--Curves showing overall he~ter collection efteieneies during a tvpie,d d'w. l)otted lines indicate corresponding daily • Best
q
2£
o
0600
~i~ T'f'PE. =
"
FI(L 8.--Constant element-eolleeti(m efficiency curves for v:trying insolations and air strean~ teinperatures. Best and poorest models of each type are shown.
efficieneies.
r
"'=|
%°_
In~olat/on-
r
IbO0
U- 75~
fn~/ohbn- G ~fu/(tm~lr
i~o
Z[10o F
I~0
15oo
OF
0~o
DAY
--
iooo
,aoo
laeo
FIOUR.S
Let ,, -Kill + K2 [2] This is a straight-line relation obtained from Figs 3, 4 .~nd 5. Solving Eqs. [1] and [2] above, with the boundary conditions =
a n d (f).
Overall Air-Heater Performance
0 =
K.
+
x = 0, (K,
b = t,>, )[(-GKI~,~
,,o Lexpk
)j
[31
T o t h i s stage, all v ~ r i a b l e s h a v e b e e n d e a l t w i t h except the air-heater length,
The over-all collection efficiency of the heater is the ratio of the total heat collected to the total insolation. Thus
The temperature v'~riation in the direction of air flow is given hy the haste relation:
~ = ']lCs,(ts - t.o)/GL Substituting from [3]
assuming an element (if unit width:
n
i.e. dtl dx Vol. 7, No. 3, 1963
n+G JlCp
1]
= ~-
\ K1 + tfo
exp \
MOp
/
-- 1
[4]
This derivati(m assumes that there is no longitudinM conduction, and that temperatures in the lateral direction are unifl'om. 123
The efficiency 7o of the inlet element, which is the limiting case of L tending to zero, is determined by the insolation and inlet air temperature. Thus:
7 v0
exp \
:IlCj, ,/
:I( ,,
With inlet air temperature 140°F, and air heater of length 40 ft 7o = --K1
+ lfo
[5]
L / M C , = 0.252,
From [4] and [5]
and
- = -- 1 ~' , [6] r>, \ MCp / ,'ICp This relation is fundamentally of similar form to that derived t)y Buelow 16. A curve can now be plotted of 7~no as a function of - G K ~ L / MCv which is applicable to all air heaters where the air flow is parallel to the absorber plate.
Values for K1 carl be computed from Fig. 8. Tbus - G K ~ L / M C , = -0.217. Hence 7/70 = 0.899. From Fig. S, 70 = 0.58. Therefore 7 = 0.52.
T o i l l u s t r a t e t h e use of t h i s a n a l y s i s , c u r v e s of collec-
use". C.S.I.R.O. Engineering Section, Report E.I).5., September 1957. Bliss, R. W. Jr. "The derivation of several plate efficiency factors useful in the design of fi'~t plate solar collectors". Solar Energy III (4), ])ecember 1959. L6f, (L O. G. "Solar house heating A panel discussion". Proc. World Syrup. on Applied Solar Energy, November 1955. Bliss, R. W. Jr. "Solar house heating--A panel discussion". Proc. World Syrup. on Applied Solar Energy, Novelnt)er, 1955. Shoemaker, M. J. "Notes on a solar collector with unique air permea/)le media". Solar Energy V (4), Octoi)er-Decem-
t i o n efficiency t h r o u g h o u t
a d a y a r e s h o w n in Fig. 9.
To ('ompute them, an idealized insolation rate througho u t t h e d a y G = (300 sin I I 0 / 1 2 ) w~s a s s u i n e d . T h i s c o r r e s p o n d s f a i r l y closely t o a c l e a r d a y of t w e l v e horn's d u r a t i o n , w i t h a p e a k i n s o l a t i o n of 300 B t u p e r sq ft p e r h r a t noon. A g a i n o n l y t h e b e s t a n d p o o r e s t m o d e l s of e a c h t y p e w e r e c h o s e n , for a h e a t e r l e n g t h of 40 ft. A v e r a g e eflic i e n e i e s b a s e d on t h e t o t a l i n s o l a t i o n r e c e i v e d d u r i n g t h e d a y a r e also s h o w n , T h e m e t h o d u s e d to p l o t t h e s e c u r v e s is i l h l s t r a t e d by the Appendix. Conclusions S o l a r air h e a t e r s , of s i m p l e c o n s t r u c t i o n a n d erap l o y i n g c h e a p m a t e r i a l s , c a n be p r o d u c e d t o s u p p l y air a t t e m p e r a t u r e s a b o v e 150 d e g F, a n d
w i t h g o o d effi-
ciency. Selective surfaces and vee-corrugated and finned a b s o r b e r p l a t e s are b e n e f i c i a l t o a i r - h e a t e r p e r f o r m a n c e , b u t t h e i m p r o v e m e n t s are e n h a n c e d b y t h e use of t h e natm'al
convection barrier.
The
type
III
h e a t e r in-
c o r p o r a t e s t h i s f e a t u r e a n d for t e m p e r a t u r e s a b o v e 100 (leg F is c l e a r l y s u p e r i o r t o T y p e s I a n d I I . I t is h o p e d t h a t e x p e r i e n c e o b t a i n e d w i t h t e s t h e a t e r s will s h o w t h e m to be e c o n o m i c a l l y C o l u p e t i t i v e w i t h other
forms
of air
heating
even
including
oil-fired
e(luipmeut.
A P P E N D I X - - C A L C U L A T I O N OF O V E R A L L A I R HEATER COLLECTION EFFICIENCY T-tke the best type I I I heater incorporating the vee-corrugated (¢ = 60 °) absorber plate and the a., = 0.80, en = 0.05 selective surface. 110 G = 300 sin 12' at 1000 hours, 0 = 4 Thus G = 260 B t u / f C h r . Now
124
K~ = 0.00331
REFERENCES 1. Morse, R. N. "Solar water heaters for domestic "rod farm
2.
3. 4.
5.
ber, 1961. 6. Close, D. J. "Flat-plate solar al)sorbers: The production and testing of a selective surface for COl)per absorber plates", C.S.I.R.O. Enginccring Section, Report E.D.7., June 1962. 7. Edwards, E. K.; Gier, J. T.; Nelson, K. E . ; a n d Roddick, R. 1). "Spectral and directional therlnal r-tdiation characteristics of selective surfaces for solar collectors." Sol, r E,~ergy VI (1), January 1962 8. Tabor, H.; Harris, J.; Weinbergcr, H.; and l)or(m, B. " F u r t h e r studies on selective [)lack coatings", U.N. Conf. on New Sources of Energy, florae, Aug., 19(il. 9. Hollands, K. G. T. "l)irectional selectivity; Emitl.mce and absorption properties of three corrug'ttcd specular surfaces", Solar En~rfly, 7, no. 3, I). 108. 10. MacAd.tms, W. J. " H e a t Transmission", Mc(h'aw-Hill Book Co. New York, N. Y., 1954. 11. Eckert, E. I~. G.; and Irvine, T. F. Jr. "l)rcssurc dr(q) and heat tr.msfcr in a duct with triangular cross-section". Trans. A.S.M.E., 82, 1960. 12. Schlichting, H. "l~,oundary L:tyer Theory", l)crg:m)on Press, 1955. 13. Holden, T. S. "Calculation of incident low temperature radiation upon building surfaces". A . S . H . R . A . E . Jo,r~al, April 1961. 14. Tabor, H. "Sol'tr energy collector design", Bull. of the Res. Council of lsr:ml, 5C, No. 1. Nov. 1955. 15. Tab(),', H. "Radiation, convection and conduction eoeflicients in solar collectors". Bull. of the Res. Council of Israel, 6C, No. 3. Aug. 1958. 16. Buelow, F. H.; and Boyd, J. S. "Heating air by solar energy", Agricult~o'al Engineering, 38 (1) : 1957.
Solar Energy