~ Pergamon
0960-1481 (95)00007-0
Renewable Eneryy, Vol. 6, No. 7, pp. 73~749, 1995 Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0960-1481/95 $9.50+0.00
D E S I G N C U R V E S F O R C O N V E N T I O N A L S O L A R A I R H E A T E R S
C. C H O U D H U R Y , P. M. C H A U H A N a n d H. P. G A R G
Centre for Energy Studies, Indian Institute of Technology, Hauz Khas, New Delhi-110016, India (Received 30 November 1993 ; accepted 18 December 1994)
Abstract--The objective of this work is to assess the combined effects of fixed pressure drop and specific air mass flow rate on duct dimensions (length and depth) of single-pass-with-bare-plate, single-cover and double-cover solar air heaters, and to obtain the resultant system efficiency that corresponds to a pre-fixed pumping cost and a minimum material cost per unit area of the system. The design selection methodology adopted in this paper will make it feasible for an air-heater designer to construct efficient and economical solar air heaters.
1. INTRODUCTION
The main hindrance to the immediate large-scale introduction of solar air heaters for different practical applications is price. Since the commercial acceptability of any solar device is governed by its cost-effectiveness, efforts must be made to improve the efficiency and simultaneously decrease the cost of previously existing or newly designed collectors if they are to be incorporated into utility systems to satisfy energy need without sacrificing reliability. The cost of air heating by a solar collector is dominated by the dominant values of collector-material cost and air- pumping cost. The material cost (per unit area for a particular configuration) does not depend sig- nificantly on duct depth, whereas the pressure drop, and hence the pumping cost, depends significantly on duct length, depth and air-flow rate. The efficiency advantage to be gained from certain specific design and operational parameters is frustrated by the increase in pumping power (or operational cost) of the system. An ideal way to overcome this problem is to compare system performance for different sets of parameters that correspond to fixed values of pressure drop. Chaterts [1] examined the optimisation of the aspect ratio of the rectangular flow passage from the view point of minimising the cost for a fixed pumping power. Hollands and Shewen [2] studied the effect of the dimensions of the rectangular and triangular air- flow passages on the coefficient of forced convective heat transfer from absorber to flowing air in plate- type air-heating collectors. In recent studies by Choudhury [3] and Choudhury and Garg [4], sugges- tions citing specific examples have been made on the
design selection criteria at a predetermined pressure drop required to obtain design features with mod- erately high efficiency. Hamdan and Jubram [5] have evaluated the cost-effectiveness of bare-, covered- and finned-plate air heaters for the Jordanian climate.
However, this study lacks an investigation of the influence of duct dimensions and air-flow rate (i.e.
pressure drop) on the performance efficiency of the individual systems. This paper deals with a design selection methodology whereby, for combined fixed values of pressure drop, air-flow rate and duct length, duct-depth values and the resultant values of forced convective heat-transfer coefficient, air-temperature increment per unit incident flux and system efficiency for bare-plate, single-cover and double-cover air hea- ters with air-flow beneath the absorber are computed.
2. THEORETICAL ANALYSIS
Figure 1 shows schematic views of the typical solar air heaters considered in this study. Type I (Fig. 1 (a)) is a bare-plate air heater where the upper metallic plate is coated with a black absorbing paint and the rear plate is provided with adequate insulation, Type II (Fig. l(b)), which is a covered air heater, comprises a single sheet glass cover, an absorber and a rear (insulated) plate. Type III is a double-cover air heater with design features as for type II, along with an additional cover sheet on top. In all three types of air heater, the heat-transfer fluid, air, flows through the passage beneath the absorber. Figure 1 depicts the various coefficients of heat transfer occurring in vari- ous components of the air heaters. The heat transfer 739
740 C. C H O U D H U R Y et al.
(a) l h ~
T p Absorber
Ti
~ L ~ hPf 1hbf hP b
mTb ~.N~\\,N.N.\\\\\k\\-N~--N~\\\\\\\\\\\\N~ Back
plate
insulation+ hb.
Type I
Cover
To D
co)
;;r ,,,,.
T~
m. ~
hpf• r hbf hpb -
T b K\\\\\\\\\\\\\~:t,,\\\\\\\\\\\\\~
hba
Type 1I
(c) Cover I ~ Cover II - Absorber
T i Back plate
insulation ~x,.~,
t hcla
__
1;o,
I T "T.
hb f hp b
ok ~ ' ~ ' ~ ' ~ , ~ Tb
+hba
Type HI Fig. 1. Schematic views of the conventional solar air heaters.in the analysis is assumed to be steady state and the air inlet temperature is assumed to be the same as the ambient air temperature.
The energy-balance equations for the covers, the absorbers and the rear plates of the air heaters can be written as follows.
Type I:
0¢pl = hpa(T p - T~)+ hob(T p - Tb)+hpf(T p - T0;
(1) hM T p - Tb) = hM T b - TO + hM T~-- ~d). (2) Type H:
ucl+hpc(Tp-Tc) = hea(T~- T,,); (3)
~c~pl = hMTp- Tc)+hMTo- T~)+hMT.-- T0;
(4)
hb~( T.-- TO = hM T~-- Tf) + hM T~- ~). (5) Type III:Uc,I+h¢2¢,(T¢2- Tc~) = h~,.(T¢t- Ta); (6) z¢,~.2I+hp¢2(Tp - T~2) = h¢2~l(T~2- T~,); (7) zd z~2c¢pI = hp~z(Tp - T~2) + hpf(Tp - Tf) + hpb(Tp - Tb) ;
(8) h p b ( T p -- Tb) = h b f ( T b - T f ) + hba(T b -- Ta). (9) The energy balance equation for the flowing air in the
air heaters can be written as :
( M C/W)(dTf/dx) = hpf(Tp- Tf)+hbf(Tb-- Tf). (10) Considering the b o u n d a r y conditions as Tf = T~ at x = 0 and Tf = To at x = L, and solving the above equations, the outlet air temperature To for the three configurations can be obtained as follows.
To(type I) = (T~ + KI 2/K13) exp (Kl 3/m C) -- Kl 2/K~3.
(11) To(type II) = (Ti + P, s/P~ 9) exp (P~ 9/rn C)-- P~ 8/Pl 9.
(12) To(type III) = (T~ + R24/R25) exp (R25/rh C)
--R24/R25. (13) The coefficients Ks, Ps and Rs are defined in Append- ices A, B and C, respectively. The efficiency of the collectors can then be calculated as
r l = rh C ( T o - Ti)/l. (14) 2.1. Heat transfer coefficients
The radiative and wind-related convective heat- transfer coefficients hpa , hca and hcl a ; the radiative and natural convective heat-transfer coefficients hpc , h~2~
and hpc 2 ; the radiative heat-transfer coefficient hpb and the conductive heat-transfer coefficient hba w e r e cal- culated by using the standard heat-transfer relations summerised in Duffle and Beckman [6]. The forced
Conventional solar air heaters 741 convective heat-transfer coefficients hpf and hbf were
computed using the relation given by Tan and Char- ters [7] which includes the effects of the entrance and exit length in the air-flow passage, and which is given by
hf = Nu k/D, (15)
where
is presented in Fig. 2. The design curves obtained using this methodology would enable a designer to choose design parameters to suit his specific require- ments with fixed pumping cost, lowest possible material cost, and moderately high performance efficiency. Numerical values of different parameters were computed corresponding to a solar flux of 900 W/m 2, an ambient temperature of 300K and a wind speed of 1.5 m/s.
and
Nu = Nu~j(1 + M D/L), (16) N u ~ = O.O182Re°S pr °4, (17)
Re = 2rhL/~, (18)
M = 14.3 logl0 N--7.9, (19) with N = L / D if 0 < L / D < < . 6 0 , and N = 6 0 if L / D > 60.
3. COMPUTATION METHODOLOGY If the material cost of any solar air heater is fixed, then for a fixed specific mass-flow rate of air, the economics of the system are governed by the cost of the pumping power expended in the collector, which depends on (increases with) the pressure drop in the air-flow channel. An ideal way of minimising the cost is to place an upper limit on the pressure drop of the system. The procedure adopted in this analysis for design optimisation, therefore, is specification of the value of the pressure drop AP, and then computation of the resultant value of the duct depth (Z) for differ- ent fixed values of the specific mass-flow rate (m) and duct length (L). The equation for AP used in the computation is
A P = f ( m 2 / p ) ( L / Z ) 3, (20) where
f = f o + 7 ( Z / L ) [2, 8], (21) and )co = 24~Re, ? = 0.9 for Re <<. 2550 ; fo = 0.0094, 7 = 2.92 Re -°15 for 2550 < Re <~ 104; andfo = 0.059 Re 02, ? = 0.73 for 104 < Re <~ 105 .
The different values of Z for different fixed values of L and rn thus computed for fixed AP were used as the input to compute the outlet air temperature and the efficiency of the different air heaters individually.
A flow chart showing the computation methodology
4. RESULTS AND DISCUSSION
As discussed in the preceding section, the com- putation of the different parameters of the air heaters was carried out for different groups of design and operational parameters which yield fixed values of the pressure drop AP. Figure 3 shows the four sets of design curves (duct depth vs duct length for different specific mass-flow rates of air) which result in
IAssume PI IRead ,LI Icomput Zl IAs umoTo, Tp I
I Read meteorological data I and thermophysical constants
[ Compute heat transfer coefficients ]
I ompote.ow To,.ew I
N o < Is (new Tp-old Tp)<0.1 >
IComp.teTo, [
Fig. 2. Flow chart showing computation methodology.
742 0.20
0.16 g M 0.12-
~ 0 . 0 8 -
~ 0.04 - 0 0
(a)
C. C H O U D H U R Y et al.
Pressure drop=30.0 Pa[
I
2 4 6 8 I0
Length, L (m)
0•20 ,~ 0.16
~" 0.12 --~o~ 0.08 0.04
(b)
Pressure d r o p ~
--~wmm~F~"''~T I t I
2 4 6 8 10
Length, L (m)
0.20
016
b4 0.12
~0.08 40.04 0
(c)
Pressure drop=90.0 Pa
0 - -
0 2 4 6 8 10
Length, L (m) (d)
0.20 f
~ 0.16
a:~ 0.12
"~ 0,08
~0.04
Pressure drop= 120•0 Pa
0 2 4 6 8 10
Length, L (m)
Fig. 3. Duct depth as a function of duct length for different pressure drops and air mass-flow rates (O m = 50 kg/h m2;+m = 100 kg/h m2; * m = 150 kg/h m2; [] rn = 200 kg/h m2;xrn = 250 kg/h m2;
O m = 300 kg/h m 2 ; A rn = 350 kg/h m2).
A P = 30, 60, 90 and 120 Pa. The curves for any fixed value of A P show that Z is a linear function of L for a particular rh and that Z increases with increase in for any particular value o f L. However, for obvious reasons, for fixed m and fixed L, the Z value decreases with increase in AP.
The resultant values of the forced convective heat- transfer coefficient, hpr, are depicted as a function of L for combinations o f fixed values o f A P and m in Fig. 4. The m o s t i m p o r t a n t features of the curves are the increase in hpf with increase in A P and the very high value o f hvf at small values of L. The relatively lower value o f
hpf at
m = 50 kg/h m 2 and L = 1 m for all the values o f A P is a consequence o f the Re value falling in the laminar (Re <~ 2550) region. This means that for any fixed pressure-drop value, higher efficiency can be obtained at smaller length, which corresponds to smaller duct depth, and hence lower material cost (per unit area) o f the system•The air temperature increment for unit incident flux (To -- Ti)/l for different combinations o f AP, m and L is illustrated in Figs 5, 6 and 7 for the type I, II and III air heaters, respectively. A l t h o u g h the curve shows no visible change in ( T o - T~)/I with change in L, the values show a remarkable rise with increase in A P and substantial fall with increase in m. A comparative analysis of the data in different figures also suggests
that for fixed pumping cost (i.e. fixed A P and fixed
&), the rate o f temperature increment can be i m p r o v e d by increasing the n u m b e r of cover plates over the absorber.
The efficiency curves in Figs 8, 9 and 10 for air heater types I, II and III, respectively, quite clearly show that the highest efficiency occurs at lowest material cost (i.e. at smallest length, which cor- responds to smallest Z). Regardless of length L, efficiency can be further increased by increasing the pressure drop, air-flow rate and n u m b e r of cover plates.
Figure 11 is a direct comparison of system efficiency for the three air heater types for different fixed pres- sure drops and air mass-flow rates for duct length L = 1 m. Visibly, the curves show only a small rise in efficiency with increase in pressure drop for fixed air mass-flow rate. However, at fixed pressure drop, with increase in m, the efficiency increases rapidly up to 100 kg/h m 2, after which the rise is almost insig- nificant. This means that too high a pressure drop a n d / o r too large a mass-flow rate should not be pre- ferred as this would increase the pumping cost tremen- dously for only a small benefit in energy gain. F o r fixed pumping cost (i.e. for fixed A P and rh), however, the double-cover air heater seems to be the most efficient. Clear indications of this are the efficiency
55 .~ 45
15 (a)
55 45
15 0 (c)
C o n v e n t i o n a l solar air heaters Pressure drop=30.O Pa ! . ~ 55
~ 4s
e ~
25
2 4 6 8
Length, L (m)
743 Pressure dmp=60.O Pa
-
I I ~ I I
I0 0 2 4 6 8 10
(b) Length, L (m)
I
1 I I I I
2 4 6 8 l0
Length, L (m)
55
35
15 0 (d)
~
. Pressure drop= 120.0 Pa" - - ' ~ O ~ _ ' - - ~ ' ~ "
I I I I
2 4 6 8 10
Length, L (m)
Fig. 4. Heat transfer coefficient as a function of duct length for different pressure d r o p s a n d air mass-flow rates ( Q rn = 50 k g / h m 2 ; + r h = 100 kg/h mZ; * rh = 150 k g / h m2; [ ] rh = 200 kg/h m2; × m = 250 kg/h
m 2 ; ~ m = 300 kg/h m 2 ; /~ n~ = 350 kg/h m2).
0.030 0.025 0.020 0.015 O.OlO
;o
0.005 0 0 (a)
0.030 0.025
~" 0.020 0.015 O.OlO [.., 'o
0.005
(c)
0.030 Pressure drop=30.O P a ]
I
0.025i 0.020
~ ~ ~ 0.015
~ % o.o,o
~ I ~ X I X w X ~ X ~ X I X ~ X I X
12 ~ :- = ~ ~ ~ ~ ' - ' - ' ~ ~ 0.005
l
I I I f / 0
2 4 6 8 10
Length, L (m) (b)
Pressure drop=60.O Pa I I
, x . ~ . X ~ x ~ x ~ x ~ ~ _ _ ~ I~
I I I I I
2 4 6 8 10
Length, L (m) 0.030
Pressure drop=90.O Pa [ ~ 0.025 i
0020
~ o.o15-
~ ~ ~ O.OLO
~ ~ ~ ~ X ~ X ~ X ~ X ~ X
~ ' ° " ~ "c.. ~- ~ ~ ~ 0.005
I I I I [ 0
2 4 6 8 10 0
Length, L (m) (d)
Pressm'e drop= 120.0 Pa I
2 4 6 8 10
Length, L (m)
Fig. 5. Air t e m p e r a t u r e increment per unit incident flux as a function o f duct length for different pressure d r o p s and air mass-flow rates in type I air heater ( 0 m = 50 kg/h m 2 ; + m = 100 kg/h m 2 ; * ~t = 150 kg/h
m2; [ ] m = 200 kg/h m2; × m = 250 kg/h m : ; © rh = 300 kg/h m2; A m = 350 kg/h m2).
744 0.05
~" 0.04 0.03
"- 0.02
~° 0.01 0 (a)
C. C H O U D H U R Y et al.
, 0.05
Pressure drop=30.0 Pa
2 4 6 8 10
Length, L (m)
~" 0.04 0.03 0.02 [~° 0.01
(b)
I
Pressure dmp=60.O Pa I
I
/
!
2 4 6 8 10
Length, L (m) 0.05
~" 0.04 0.03
"" 0.02 [..,
~° 0.01 0 (c)
Pressure drop=90.0 Pa
: : I I 1 I
I I I I
2 4 6 8 10
Length, L (m)
0.05 0.04 0.03
"" 0.02
~° 0.01
Pressure drop=120,O Pa ] I
I
.__+-57:.__:__ :.__
2 4 6 8 10
(d) Length, L (m)
Fig. 6. Air temperature increment per unit incident flux as a function of air-channel length for different pressure drops and air mass-flow rates in type II air heater ( O m = 50 kg/h m ~ ; + r h = 100 kg/h m~;
* rn = 150 kg/h m ~ ; [] rn = 200 kg/h m ~; × rn = 250 kg/h m ~; © rn = 300 kg/h m: ; A rh = 350 kg/h m~).
0.05
~" 0.04 0.03
"- 0.02 ['--' o.oi
(a)
0.05 0.04 0.03 -- 0.02
I o
O.Ol
Pressure drop=30.0 Pa
(c)
0.05 0.04 0.03
"" 0.02
I o
0.01
t I I I I 0
2 4 6 8 10
Length, L (m) (b)
Pressure drop=90.0 Pa
Pressure drop=60.0 Pa
I I I I
2 4 6 8 I0
Length, L (m)
0.05
~ 1 I I I I I I
-r
I I I I |
2 4 6 8 l0
Length, L (m)
~" 0.04 0.03
"- 0.02
I o
b-, 0.01
0 0
(d)
Pressure drop= 120.0 Pa
I I I I
2 4 6 8 10
Length, L (m)
Fig. 7. Air temperature increment per unit incident energy as a function of air-channel length for different pressure drop and air mass-flow rates in type III air heater ( O rh = 50 kg/h m 2 ; + r h = 100 kg/h m2;
* m = 1 5 0 k g / h m 2 ; [ ] m = 2 0 0 k g / h m 2 ; × m = 2 5 0 k g / h m 2 ; ~ m = 3 0 0 k g / h m 2 ; A m = 3 5 0 k g / h m 2 ) .
65 55 g, .~ 45
35 25 (a)
65 ,-, 55
g, 45
(c)
C o n v e n t i o n a l solar air heaters Pressure drop=30.0 Pa
• q P " " • • • • • • • •
I I I I
2 4 6 8 10
Length, L (m)
65
. 55
.~ 45 35 25 0 (b)
745 Pressure drop=60.0 Pa
:-,-:7_2-,-,-"
O ~ O ' ' O ~ O ~ O ~ e ~ O ~ O ~ O ~ 0
I I I I
2 4 6 8 10
Length, L (m)
25 0
65
!
Pressure drop=90.0 Pa [
I
, , ~ A ^ ^ ~ 5 5
45
""~ • ~ o . . . . I ~ 35
I I I I
I
I 252 4 6 8 10
Length. L (m) (d)
O ~ - - , - . O ~ e ~ o ~ o ~ o ~ o ~ o / I
I I I I n
2 4 6 8 10
Length, L (m)
Fig. 8. Efficiency as a function of air-channel length for different pressure d r o p s a n d air mass-flow rates in type I air heater. ( 0 r h = 5 0 kg/h m2; + r n = 100 kg/h m2; * r h = 1 5 0 kg/h m2; [ ] r n = 2 0 0 kg/h
m 2 ; x & = 250 kg/h m 2 ; ~ rn = 300 kg/h m ~" ; /X rh = 350 kg/h m2).
70
.~.
50
4O (a)
7O
~
6o50
40 (e)
Pressure drop=30.0 Pa
• - . - . - . _ . . . i i 1
70
~'60
40 I I I I I I
2 4 6 8 10 2 4 6 8 10
Length, L (m) (b) Length, L (m)
70 ure drop=90.0 Pa ]
~ * . . . . " ~ , ~ ~" 60
- ~...~ ~ ~ ' u d
I
I I I I I 40
2 4 6 8 10
Length, L (m) (d)
I I I I
I
I2 4 6 8 10
Length, L (m)
Fig. 9. Efficiency as a function o f air-channel length for different pressure d r o p s and air mass-flow rates in type II air heater ( 0 rh = 50 kg/h m : ; + m = 100 kg/h m2; * rn = 150 k g / h m2; [ ] rh = 200 k g / h m2;
x m = 250 k g / h m2; ~ rn = 300 k g / h m2; / k m = 350 kg/h m2).
746 75 70 65
• ~ 60 55 50 (a)
C. C H O U D H U R Y et al.
Pressure drop = 30.0 P a
I I I I
2 4 6 8 10
Length, L (m)
75
~, 70
55 50 (b)
I
Pressure drop=60 0 Pa[
~ ~ ~_~__~__^,.._.^_.~',
II I I I
2 4 6 8
Length, L (m)
71i .o rop:9o.oPa 75 I
70 , . . . ~ 70
2 4 6 8 10 0
(c) Length, L (m) (d)
Pressure drop= 120.0 Pa
I I I I
2 4 6 8 10
Length, L (m)
F i g 10 Efficiency as a function o f air-channel length for different pressure drops and air mass-flow rates in type III air heater ( O m = 50 kg/h m 2 ; + m = 100 kg/h m2; * rn = 150 kg/h m2; [] m = 200 kg/h
m 2 ; x m = 2 5 0 k g / h m 2 ; ~ m = 3 0 0 k g / h m 2 ; A m = 3 5 0 k g / h m 2 )
100 /
] Pressure drop=30 0 Pa
8 0 E ~ l
60 * - - ' - - - ~
o I I I I I
50 (a)
100 / Pressure drop=60 0 Pa
80 I-- - ~
40 ~ 0 ~.~.~,,0.__..~. 0 --O--.---e - - t
0 1 I I I
100 150 200 250 300 350 50 100 150 200 250 300 350
Air mass flow rate, • (kg/h m 2) (b) Air mass flow rate, ~ (kg/h m 2)
100 ] Pressure drop=90 0 Pa
80 ~
2---.---"
0 I I I I I
50 (c)
100 l
l Pressure drop= 120.0 Pa
80 [ - !
60 ~ ~.~-,"r- _ . _ _ _ _ ~ " ' " " r - - ~ o _ ~ . , . . o " o.--- • ~ • o ~ , ~
40 ° ~ ' ~ ° ' ~ °
0 I I I I I
100 150 200 250 300 350 50 100 150 200 250 300 350
• 2
Air mass flow rate, m (kg/h m ) (d) Air mass flow rate, • (kg/h m 2) Fig. 11. Efficiency as a function o f air mass-flow rate for fixed length L = 1 m and different pressure drops
for the three air heaters ( O b a r e - p l a t e ; + single-cover; * double-cover).
Conventional solar air heaters 1oo
. ~ ~ Pumping power=2.5 kW/m 2 80
6 0 I I ... +
• • .
20 t
o 5o (a)
1oo
!~_...__ P u m p i 80
4 0 0 ~
Io I I I
lpmg power=5.0 kW/m 2
48 • • ' •
I I I I I I I
100 150 2 0 0 2 5 0 3 0 0 3 5 0 5 0 100 150 2 0 0 2 5 0 3 0 0 3 5 0
Air mass flow rate, ~ (kg/h m 2) (b) Air mass flow rate, ~ (kg/h m 2)
7 4 7
Pumping power=7.5 kW/m 2 80
60~ I I - ~ - I "
- 5 • •
40q ~ ° ~ ' • ' - ' - ' - ' ° -
20
0 I I I I
50 (c)
100 8O 6O 4o
20
Pumping power= 10.0 kW/m 2
I 0 I I I I I
100 150 200 250 300 350 50 100 150 200 250 300 350
Air mass flow rate, ~ (kg/h m 2) (d) Air mass flow rate, m (kg/h m 2) Fig. 12. Efficiency as a function of air mass-flow rate for fixed length L = 1 m and different pumping power
for three air heaters (Q bare p l a t e ; + single cover; * double cover).
curves in Fig. 12, w h i c h c o r r e s p o n d to a n a i r - h e a t e r l e n g t h o f 1 m. A t different fixed p u m p i n g p o w e r values, the curves show the d o u b l e - c o v e r air h e a t e r to h a v e the highest, a n d the b a r e - p l a t e air h e a t e r to h a v e the lowest efficiency at all the air-flow rates. However, since the cost o f the systems increases w i t h increase in the n u m b e r o f c o v e r plates, the d a t a are quite inad- e q u a t e to e s t a b l i s h w h i c h air h e a t e r type is the m o s t cost-effective c o r r e s p o n d i n g to a n y p a r t i c u l a r set o f air-flow rate a n d d u c t d i m e n s i o n s o f the systems. N o n - etheless, the m e t h o d o l o g y a n d the design curves dis- cussed a b o v e are certainly ideal for the design opti- m i s a t i o n o f a n y p a r t i c u l a r type o f air h e a t e r with either n o cover, a single c o v e r or a d o u b l e cover a b o v e the a b s o r b e r .
5. CONCLUSIONS
It is e v i d e n t f r o m the a b o v e discussion t h a t the c o m p u t a t i o n m e t h o d o l o g y a n d the design curves pre- sented in this p a p e r c a n be successfully used to con- s t r u c t solar air h e a t e r s w i t h p r e - d e t e r m i n e d a c c e p t a b l e values o f pressure d r o p ( A P = 30 to 120 Pa) w i t h the r e q u i r e d rate o f air flow (i.e. fixed p u m p i n g power), m i n i m u m m a t e r i a l cost a n d highest possible efficiency.
H o w e v e r , if c o n c e n t r a t i o n is focussed o n the relative
cost-effectiveness o f the bare-plate, single-cover a n d d o u b l e - c o v e r air heaters, one m a y realise t h a t since the m a t e r i a l cost increases with increase in the n u m b e r o f cover sheets, the i n f o r m a t i o n p r e s e n t e d in this p a p e r is quite i n a d e q u a t e to establish w h i c h air h e a t e r type h a s the highest c o s t - b e n e f i t ratio for a n y par- ticular practical application. F u r t h e r studies in this r e g a r d are p l a n n e d as s e p a r a t e p u b l i c a t i o n s by the a u t h o r s .
Acknowledgements--The authors would like to thank MNES for funding this project.
NOMENCLATURE C specific heat capacity of air (W h/kg K) D equivalent diameter of air channel (m)
f friction factor
h heat transfer coefficient (W/m 2 K)
I solar radiation incident on the collector (W/m 2) k thermal conductivity of air (W/m K)
L length of air heater (m) M mass flow rate of air (kg/h)
m specific mass flow rate of air (kg/h m 2) M constant dependent on N
N number of equivalent diameters Nu Nusselt number for any N
Nu,~ Nusselt number for fully developed thermal flow P pumping power (W/m 2)
Pr Prandtl number
748
R e Reynolds number W width o f absorber (m)
Z duct depth (m) Greek letters
c¢ solar absorptance r solar transmittance p density of air (kg/m 3) r 1 efficiency of system
p dynamic viscosity of air (kg/m s) AP pressure drop (Pa)
Subscripts a ambient b back plate
c cover cl cover I c2 cover II
f fluid i inlet o outlet p absorber plate.
C. C H O U D H U R Y et al.
R E F E R E N C E S
1. W. W. S. Charters, Some aspects of flow duct design for solar air heater applications. Solar Energy 13, p. 283 (1971).
2. K. G. T. Hollands and E. C. Shewen, Optimization o f flow passage geometry for air heating plate type solar collectors. J. Solar Energy E n y n y , Trans. A S M E 103, p.
323 (1981).
3. C. Choudhury, A corrugated plate solar air heater : trade- otis between efficiency and pressure drop. Report 88-15, ISSN 0332-5571, Institute o f Physics, University o f Oslo, Norway (1988).
4. C. Choudhury and H. P. Garg, Design analysis of cor- rugated and flat plate solar air heaters. R e n e w a b l e E n e r g y 1, p. 595 (1991).
5. M. A. H a m d a n and B. A. Jubram, Thermal performance of three types of solar air collectors for the Jordanian climate. Energy 17, p. 173 (1992).
6. J. A. Duffle and W. A. Beckman, Solar Engineering Ther- m a l Process. Wiley, New York (1980).
7. H. M. Tan and W. W. S. Charters, Effect o f thermal entrance region on turbulent forced convective heat trans- fer for an asymmetrically heated rectangular duct with uniform heat flux. Solar E n e r g y 12, p. 513 (1969).
8. W. M. Kays and H. C. Perkins, Forced convection inter- national flow in ducts, Handbook.
A P P E N D I X A
K~ = hpa q-hpfq-hpb 1(2 = hpb/k, K3 = K2hp~ + hb~
K 4 = K2hpf+hbf Ks = hpb + hpf+ hb~
K6 = hZb/K, Kv = K5 - - K 6
K 8 = hbf+ hpfhpb/K]
K ~ = h~f/ K l - (hof+ hbO
KL o = hpf(%l+ hp~ Ta)/KI K~, = Ks~K7
K12 = KIo + KL t K~T~ + K~ ~Ke%I KI3 = K g + K I I K 4
A P P E N D I X B P~ = hc~ + hp~
P2 = hpc + hpb + hpf P3 = h~c/P~
P4 = h p j P I Ps = P4 h~.
P6 = hpb q- hba q- hpf P7 = hpb/(P2-- P3)
P8 = P7 hpb P9 = P7 hpf Plo = P6 P8 PI I = PsP7 + hba
P~2 = Pg+hpf
P l 3 = hpf(zc ep I + ~c I P4 + TaPs)/(P2 - P3) P~4 = Pg+hpf
Pl 5 = h~f/(P2 - P3)-- (hpf+ hbf ) P16 = P I 4 ( r o % I P 7 + c c c l P 4 P 7 + T a P I O / P l o
P~7 = P~2 P l 4 / P l o Pl8 = P I 3 - ~ - P I 6 Pt9 = P I s + P I 7
A P P E N D I X C
R~ = h~,+hc2cl R2 = hpc2 + hc2~t
R 3 = hc2cl/Ri R4 = hc2¢t/Rl R5 = Ro h~a R6 = hp~2 + hof + hpb R7 = h ~ 2 / ( R 2 - g3) R8 = h p d ( R 2 - R3)
R9 = R4R8
RLo = RsR8 R l l = hpbq-hbf+hba R,2 = h~b/(R6 R7)
R13 = R i i - - R i 2 e l 4 = hpb/(R6--R7)
R I s = RsRI4 Rl6 = R9RI4 Rt7 = RloRl4+hba
RIB = R~4hpr+hbf
C o n v e n t i o n a l s o l a r a i r h e a t e r s 749
R L 9 = hbf(Trcl l"c2 ~p I + Zci ~ 2 1 R8 + ~cl I Rq
+ TaRIo)/(R 6 - R 7 ) R20 = hp~pb/(R6 - R7) q'- hbf q- hpr
R21 = h~f/(R6 R7)-(hb¢+hpf) R22 = R20(z~t r~2 o:p l R]4 + 7:cl 0~c21R~5 + o~l 1Rl 6
+ 72. RI7)/Rt3 R23 = Rzo RIs/RI3
R24 = R I g + R 2 2 Rz5 = R21+ R23
