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Thermal performance of solar air heaters—Experimental correlation
Solar Energy Vol. 55, No. 3, pp. 209-220.1995 Copyright 0 1995 Elsevicr Science Ltd Printed in the U.S.A. All rights resewed 0038~092X/9j $9.50 + 0.00
Pergamon
.
THERMAL
PERFORMANCE EXPERIMENTAL
I
OF SOLAR AIR HEATERSCORRELATION
K. S. ONG Faculty of Mechanical Engineering, University of Malaya, Pantai Valley, 59100 Kuala Lumpur, Malaysia (Communicated by BRIAN NORTON) Abstract-A mathematical model and a solution procedure for predicting the thermal performance of four types of single-pass flat-plate solar air collectors were presented in an earlier paper by Ong (1995). Instead of resorting to complicated algebraic manipulations to solve the energy equations a matrixinversion technique was employed. In this paper, theoretical predictions of surface and air temperatures were obtained for the Types II, III and IV collector designs. In addition, the Type II collector was considered with and without bottom insulation. Experimental data from previous studies were obtained and compared with the present theoretical predictions. Satisfactory qualitative and quantitative agreement was obtained between theoretical predictions and experimental data.
Type IT/ Double channel design with double air flows between top glass and absorber plate and between absorber and bottom plates and with bottom insulation provided.
1. INTRODUCTION
In a series of investigations conducted at the Engineering Faculty of the University of Malaya, much experimental data were obtained with regards to the performance of flat-plate solar air heaters for crop drying. Theoretical models were presented by Than (1980) Gan (1986) and Tan (1986) for predicting the theoretical performance of such solar collectors based on solving the energy balance equations explicitly. In a recent paper, Ong (1995) presented a simple matrix-inversion method of solution which obviated the need for complex algebraic manipulation of the energy equations.
3. HEAT TRANSFER COEFFICIENTS 3.1. Convection heat transfer coeficients 3.1.1. Laminar pow region (Re < 2300). Heaton’s (1964) empirical correlation was employed to determine the Nusselt number for laminar flow between two parallel flat plates with one side insulated and the other subjected to a constant heat flux, a[Re Pr(Dh/L)]” N” = NuW + 1 + b[Re Pr(&/L)]”
2. OBJECTIVES
The objectives of the present paper are twofold, viz: (1) to employ the matrix-inversion solution procedure to obtain theoretical predictions for the performance of solar air heaters, and (2) to compare the predicted results with past experimental data in order to validate the theoretical model. The following types of flat-plate collectors shown in Fig. 1 are considered: Type Zlu. Single channel design with single air flow between absorber and bottom plates with no bottom insulation. Type Ilb. Single channel design with single air flow between absorber and bottom plates with bottom insulation provided. Type III. Double channel design with single air flow between absorber and bottom plates and with bottom insulation provided.
(1)
where the constants a = 0.00190, b = 0.00563, m = 1.71, n = 1.17 and Nu, = 5.4 for Pr = 0.7. 3.1.2. Transition flow region (2300 c Re < 6000). Hausen’s (1943) empirical correlation for the average Nusselt number between the beginning of the heated section and the position L for flow in a tube was employed, Nu = 0.116( Re2/3 - 125) Pr”3 [ 1 + (Lrh/L)2’3] x (lAkv)“.14. (2) 3.1.3. Turbulent flow region (Re > 6000). In the turbulent flow region, Nusselt’s (1931) correlation was employed, Nu = 0.036 Re’.* Pr1’3(Dh/L)0.055.
(3) For flows in-between parallel flat plates, the equivalent diameter D,, is twice the separation distance between the plates. 3.1.4. Natural convection. Holland’s et al. (1976) correlation for free convection between 209
210
K. S. Ong
T
sky
Ta "b
“b
lb)
(4 T
T
sky
sky
Flow #l Flow #2
Flow #2
i “b
“b
(d)
(c)
Fig. 1. Types of solar air collectors
considered:
(a) Type Ha; (b) Type IIb; (c) Type III; and (d) Type IV.
inclined planes lying in the range 0 < Ra < lo5 and 0” I 4 I 60” was employed, Nu,, = 1 + 1.44
l-
1
1708(sin 1.8fj)‘.6 Ra cos 4
a cos f$)‘13_ 1 5830
(4)
The equivalant diameter employed in the above definition for Nusselt number is the separation distance beween the plates. Also the notation Cl + is used to denote that if the quantity in the bracket is negative, it should be set equal to zero. The natural convection coefficient is specified for Type III for the air cavity between the glass and absorber surfaces. Ong (1995) noted that predicted mean temperature results were significantly influenced by the air-surface heat transfer coefficients. In the present paper, all film heat transfer coefficients were multiplied by a factor equal to 0.75. This was found to be most suitable after comparing the experimental results with predicted ones for the wide range of Reynolds number encountered
in the experimental 3300 to 40,000.
investigation,
4. EXPERIMENTAL
from about
DATA
The experimental data in this paper was obtained from investigations conducted by Than (1980), Tan (1986) and Gan (1986). The data is reproduced here in order to compare with the theoretical predictions obtained. 4.1. Than’s investigations In his MEng.Sc. thesis investigations, Than (1980) conducted a series of experiments on the thermal performance of flat-plate solar air heaters with Reynolds number ranging from about 3000 to 40,000. The collectors were of the Types II and III collectors shown in Figs l(a-c). The basic Type IIa collector shown in Fig. l(a) was constructed. By providing thermal insulation on the bottom of the basic Type IIa collector, we obtained the Type IIb collector shown in Fig. l(b). By further providing a glass cover over the top of the Type IIb collector, we end up with the Type III collector. A cross-sectional view of Than’s collector is shown in Fig. 2. It consisted of rivetting two 0.5 mm thick flat
211
Performance of solar air heaters
Absorber plate (0.5 mm AL)
__---------------__
Bottom plate (0.5 mm AL) insulation (Type IIb and III)
Single air channel
Solar
collector
Orifice
plate Centrifugal blower Air out
Air in-
Copper-constantan 12.7 mm
t-9.75 Fig. 2. Details of Than’s Type IIa collector and air circulation arrangement.
aluminum sheets together to form a rectangular profile channel 38 mm deep by 0.76 m wide by 9.75 m long through which air could be circulated. The top of the absorber plate was painted with a matt-black paint to increase its absorptivity towards solar radiation. Top cover, when provided, was 3 mm thick plain window glass with a 25 mm air space in-between glass and absorber plate. Insulation when provided, consisted of 25 mm fiberglass wool resting on 25 mm thick expanded foam polystyrene sheets. The collector rested on a supporting structure inclined at 7: degrees to the horizontal in a north-south orientation. Copper-constantan thermocouples were employed to measure absorber plate, bottom plate and air temperature at distances 2.25, 4.50, 6.75 and 9.00 m from the inlet of the collector. Glass cover temperature was not measured. Air circulation was provided by a centrifugal blower and air flowrate was measured with an orifice plate. Flow Reynolds number ranged from 3000 to 40,000.
mance of a double-channel solar air heater of the Type IV collector shown in Fig. l(d). Other than physical constructional details, their collector, shown in Fig. 3 was basically similar to Than’s collector with the exception that air could be circulated in the flow channels created between the absorber plate and the glass cover and between the absorber plate and the bottom plate. The collector measured 0.254 m wide by 6.0 m long. The air flow channels were each 25.4 mm deep. Insulation was 35 mm thick fiberglass wool. Copper-constantan thermocouples at distances 1.5, 3.0, 4.5 and 5.9 m from the inlet of the collector measured the temperatures of the glass, absorber plate, bottom plate, and both air streams. Air circulation was provided with a single centrifugal blower via a manifold at the outlet of the collector. Air flowrates in the flow channels were determined separately by a pitot-static tube located in turn in the air streams at the outlet manifold and connected to an optical manometer.
4.2. Gan’s and Tan’s investigations
Solar radiation was determined with a Kippand-Zonen solarimeter located immediately next to the collector at the same pitch. In the
In their final year project investigations, Gan (1986) and Tan (1986) investigated the perfor-
4.3. Instrumentation and experimental procedure
212
K. S. Ong Absorber plate (0.5 mm AL) ----__---_----__-------------1 25mm
4-i
1 Insulation
25mm
I
25k I’
’
Bottom plate (0.5 mm AL)
, Solar collector
, Outlet
manifold , Centrifugal
‘Copper-constantan TC probe
Fig. 3. Details of Gan and Than’s Type IV collector and air circulation arrangement.
tropics, it is difficult to obtain “steady” radiation levels owing to intermittent and frequent movement of cloud cover. Hence the solarimeter output was connected to a chart recorder and thermocouple readings taken only when the radiation trace showed no signs of rapid fluctuations for about 10 min. Thermocouple readings were taken using a digital-voltmeter via a manually-operated multi-switch box. Data loggers would certainly enable more accurate data to be obtained but they were not available to us then. Hence, at best, it could be assumed that the temperatures taken corresponded to within
about 5 min of the time that the solar radiation readings were noted. Average wind velocities were measured by a cup-type anemometer. In order to avoid inaccuracies in determining ambient temperature, Than measured inlet air temperature with a probe located 12.7 mm from the inlet of the collector. Gan and Tan measured ambient temperature external to the collector and assumed that inlet air temperature was equal to the ambient temperature. In Than’s investigations, preliminary tests conducted showed that the temperature profile across the width of the collector was quite
Table 1. Summary of experimental runs extracted from Than (1980). Gan (1986) and Tan (1986)
H Type
(lcg?-l)
1 2 3
IIa
0.026 0.114 0.315
0 0 0
0.63 0.56 0.27
4 5 6
IIb
0.027 0.132 0.310
0 0 0
7 8 9
III
0 0 0
10 11
IV
0.0129 0.0334
Run
(kgmi-‘)
(m!-l)
&,
(W m-*)
Re( 103)
33.5 32.3 30.0
900 900 9ocl
3.30 14.5 40.0
0.62 0.53 0.61
33.7 31.7 31.5
900 900 900
3.40 16.7 39.3
0.026 0.120 0.307
0.48 1.41 1.26
34.1 33.4 32.8
900 900 900
3.33 15.2 38.9
0.0129 0.0334
0.50 0.40
33.2 34.3
694 700
4.90 12.7
Performance Table 2. Detailed
of solar air heaters
experimental data from Than (1980). Gan (1986) and Tan (1986)
L
Zirl
Kid
Type
Cm)
rY*ss Top (“C) (“C)
Got
Run
(“C)
(“C)
CC)
1
IIa
0.00 2.25 4.50 6.75
33.5 75.8 77.5 79.1
33.5 39.1 42.7 43.7
33.5 41.9 47.8 49.6
2
IIa
0.00 2.25 4.50 6.75 9.00
32.3 61.4 64.0 67.2 68.3
32.2 35.8 39.6 42.4 44.7
32.2 38.0 42.1 45.5 46.3
3
Ha 2.25 4.50 6.15 9.00
30.0 48.5 49.7 51.6 53.2
30.0 32.0 34.5 37.8 40.5
30.0 33.1 35.9 38.1 39.6
4
IIb
0.00 2.25 4.50 6.75 9.00
33.1 15.3 77.3 80.0 80.5
33.7 43.3 49.1 54.3 51.2
33.7 46.9 52.4 56.2 58.9
5
IIb
0.00 2.25 4.50 6.15 9.00
31.7 61.6 64.1 65.6 68.2
31.7 35.5 40.6 45.2 49.0
31.7 37.0 42.8 46.0 49.2
6
IIC
0.00 2.25 4.50 6.75 9.00
31.5 50.7 52.1 53.3 54.4
31.5 33.1 36.1 40.0 42.8
31.5 34.5 37.9 40.6 43.2
1
III
0.00 2.25 4.50 6.15 9.00
34.1 107.0 113.3 122.3 127.0
34.1 53.3 67.5 78.6 86.5
34.1 55.8 JO.9 80.0 87.8
8
III
0.00 2.25 4.50 6.75 9.00
33.4 71.7 76.8 80.9 86.2
33.4 38.9 45.7 52.2 58.0
33.4 40.3 41.9 52.7 57.7
32.8 54.3 56.0 57.5 59.1
32.8 34.6 38.0 42.1 45.1
32.8 35.8 39.8 42.6 45.6
213
showed non-uniform temperature profiles from the absorber plate to the bottom plate. A temperature gradient existed across each collector section. The shape of each profile varies, depending upon air flowrate and distance from the collector inlet. As a result, mean air stream temperatures were assumed to be represented by the arithmetic average of the three probes in the air stream. In Gan’s and Tan’s investigations, air stream temperatures were measured using single probes located in the center of the air streams along the collector centerline. Gan and Tan measured the temperatures at the surfaces of the glass, absorber plate, and bottom plate, and also of the two air streams. Than did not measure glass temperature. Than obtained a substantial amount of data. He resorted to obtaining linear regressions between air temperature and radiation intensity with regression coefficients greater than 0.95 in most cases. Gan and Tan, not having as much time with their investigations as Than, presented non-linearized data. Than’s data covered the Reynolds number range of 3300-40,000, while Gan and Tan covered the Reynolds number range of 4900-12,700. In this paper, some experimental data are extracted from the above works in order to correlate the theoretical predictions made. A summary of the experimental runs from which experimental data are extracted from is listed in Table 1. Detailed experimental data are shown tabulated in Table 2. 5. COMPARISON BETWEEN EXPERIMENTAL AND THEORETICAL RESULTS
9
III
0.00 2.25 4.50 6.15 9.00
10
IV
0.00 1.50 3.00 4.50 5.90
33.2 43.2 46.2 47.6 52.9
33.2 64.9 68.3 73.8 76.1
33.2 41.6 48.8 53.8 57.3
33.2 44.2 51.7 60.3 63.0
33.2 38.4 48.5 56.8 58.9
11
IV
0.00 1.50 3.00 4.50 5.90
34.3 39.1 40.0 41.9 44.2
34.3 46.2 52.7 56.1 60.3
34.3 36.3 41.2 44.2 47.4
34.3 35.2 41.9 46.9 48.8
34.3 34.9 40.5 44.2 48.1
uniform. However, thermocouples placed across sections of the collector (one each on the absorber and bottom plates, and three in the air stream) located along the collector centerline
Values of absorptivity, emissivity and transmissivity for the various surfaces are assumed values taken from generally accepted figures and not measured values. These values are similar to the values employed in the previous paper by Ong (1995). Previous results have shown that small temperature differences of the order of 1°C or less were obtained by modifying these values and that the predictions were not heavily dependent upon these values. 5.1. Temperature
cariation alongflow
direction
In order to compare experimental data with theoretical predictions, wall and air stream/s temperatures were plotted in Figs 4-14 for the different experimental runs. The range of Reynolds numbers from 3300 to 40,000 correspond to flows usually encountered in solar
214
K. S. Ong
0
1
2
3
4 Distance
I
+
f
Tabsorber(theory)
Tbottom(theory)m
5 along collector
X
Tairl (theory)
Fig. 4. Temperature
variation
along
: :
: :
: :
6
7
6
(m)
Tabsorber(expt)
+ Tbottom(expt)
Type IIa collector
A Tairl (expt)
: :
: :
: :
: :
: :
,100 -/ _I
60
60
-......I
20
I
at Re = 3300.
100,
t t
9
. . . . . . . .. . . . . . . . ____...:
. ..___..
_.__.
. ..I
__...
__; ______.:
-20
““l”“I,,,,I,,,,I,,~~I~~,~l~~~~I,~~~r~~~~.o
o
0
1
2
3
4 Distance
-Tabsorber(theory)
fTbottom(theory)
Fig. 5. Temperature
mTair1
variation
5 along collector
(theory)
along
X
6
7
6
9
(m)
Tabsorber(expt)
Type IIa collector
+ Tbottom(expt)
at Re = 14,500.
A Tairl (expt)’
I
Performance
0
1
2
of solar air heaters
3
4
5
215
6
7
6
9
Distance along collector (m)
I
+Tabsorber(theory)
+Tbottom(theory)
%Tairl
Fig. 6. Temperature
X
(theory)
variation
Tabsorber(expt)
along Type IIa collector
+ Tbottom(expt)
A Tairl (expt)
at Re = 40,000.
100,
20-
,100
.
.
.
.
+Tabsorber(theory)
.
..
.
.
.
.
.
.
.
. .
.
.
.
.
+Tbottom(theoty)
Fig. 7. Temperature
.
.
.
.
.
.
.
.
.
. . .
.
.
.
mTair1 (theory)
variation
.
.
X
.
.
;......:
Tabsorber(expt)
along Type IIb collector
.
.
.
.
.
.
.
.
+ Tbottom(expt)
at Re = 3400.
-20
A Tairl (expt)
I
216
K. S. Ong
0
1
2
3
4
5
6
7
6
9
Distance along collector (m)
+Tabsorber(theory)
+Tbottom(theory)
XTairl
(theory)
X Tabsorber(expt)
+ Tbottom(expt)
A Tairl (expt)
Fig. 8. Temperature variation along Type IIb collector at Re = 16,700.
0
1
2
3
4
5
6
7
6
9
Distance along collector (m)
+Tabsorber(theory)
fTbottom(theory)
m Tairl (theory)
X Tabsorber(expt)
+ Tbottom(expt)
Fig. 9. Temperature variation along Type IIb collector at Re = 39,300.
A Tairl (expt)
Performance of solar air heaters
217 140
140
-0
1
2
3
4 Distance
-o- Tglass(theory)
f
+ Tabsorber(expt)
A Tbottom(expt)
5
6
along collector
Tabsorber(theory)
m Tbottom(theory)
X
7
6
(m)
*
1
TairP(theory)
TairP(expt)
Fig. 10. Temperature variation along Type III collector at Re = 3300.
,100
100,
t
:
:
:
:
:
:
1
:
40
40
20-
.
.
.
.
.
..
.
.
.
.
.
.
.
. ___....i__..
: .
.
.
.
.._..
.
.
.
.
.
.
:...
_-20
1
it,,,
nL~~““““““‘~‘~“‘~““~““‘,“” -0
1
2
3
4 Distance
5 along collector
6
7
(m)
+Tglass(theory)
+Tabsorber(theory)
*
Tbottom(theory)
6 Tabsorber(expt)
A Tbottom(expt)
X
TairP(expt)
*
Tairl(theory)
Fig. 11. Temperature variation along Type III collector at Re = 15,200.
6
o
9‘
K. S. Ong
218
0
1
2
3
4 Distance
*
Tglass(theory)
* Tabsorber(expt)
+
6
along collector
Tabsorber(theory)
7
9
*
TairP(theory)
Tair2(expt)
along Type III collector
variation
0
(m)
+f Tbottom(theory)
X
A Tbottom(expt)
Fig. 12. Temperature
5
at Re = 38,900.
00
70 -1
, :--rs” p??.
20t”““““““““““““““““““““““““““““.’ 0 0.5 1
.:
:
.‘.
:
.:.
.:.
.:.
2.5
3
3.5
4
4.5
5
5.5
*
TairP(theory)
.-j4(J
20 1.5
2
Distance
along collector
*
Tglass(theory)
+Tabsorber(theory)
x
X
Tglass(expt)
0
v Tbottom(expt)
Tabsorber(expt)
Fig. 13. Temperature
Tbottom(theory)
variation
(m)
*
Tairl (theory)
F% Tairl (expt)
along Type IV collector
?? TairP(expt)
at Re = 4900.
6
Performance
of solar air heaters
219 80
80
2.
,,,,,,,,,,,,,,,,,,,1,,,,~11111,1 0
0.5
1
Illllll/‘llllllllljllllll 1.5
2
2.5 Distance
3
along collector
+
Tglass(theory)
+
Tabsorber(theory)
x
X
Tglass(expt)
0
Tabsorber(expt)
v Tbottom(expt)
Fig. 14. Temperature
Tbottom(theory)
variation
3.5
5
5.5
4.5
-) Tairl (theory)
*
Tair2(theory)
Z% Tairl (expt)
?? TairP(expt)
6
(m)
along Type IV collector
air heaters operation. The Reynolds number extended over both transition and turbulent flow regimes. From the results, it can be seen that, generally as expected, temperatures decrease as air flowrate increases. Also, in all the results, it was observed that the absorber plate exhibited the highest temperature, with glass being at the lowest. Further, as air flowrate increases, the temperature difference between the air streams and the bottom plate become less. The results showed that agreement between experimental data and predicted results was to within 5°C. In most cases, differences were much less, about 3°C for Types IIa, IIb and III collectors. For the Type IV collector, agreement was slightly less satisfactory. In this case, for air temperatures, differences of as much as 8°C were obtained. Also, it was observed that the theory over-predicted towards the outlet end of the collector and under-predicted at the inlet end. This was attributed to the fact that while the inlet air temperature was measured just after the inlet to the collector in Than’s case, in Gan’s and Tan’s investigation, ambient temperature was recorded outside the collector. The copperconstantan thermocouples were constructed by twisting the bared ends together and welded.
‘-20
4
at Re = 12,700.
They were connected to a digital multimeter via a multi-point selector switch. The thermocouples were calibrated against high-precision thermometers, accurate to within +0.2”C. The cold junction temperature varied by +l”C during the testing. Hence it could be said that the temperature readings were accurate to within + 1°C. In Than’s investigations, the mean air temperatures were averaged using three probes at each station. In Gan’s and Tan’s investigations, only a single probe located in the middle of the air stream at an accuracy of + 2 mm were employed. This could perhaps account for the poor correlation of theory to experiment. From Than’s work, deviations of 2-3°C could result especially when there was a steep temperature distribution across the depth of the airstream. However, qualitative agreement could be said to be have been obtained for this case. It should be reiterated here that it was extremely difficult to obtain true “steady” ambient conditions in the tropics and especially without the use of data-loggers. 6. CONCLUSIONS
Predicted temperatures for Types II, III and IV solar air heaters were presented and com-
220
K. S. Ong
pared with experimental results. Satisfactory qualitative and quantitative agreement was obtained. The mathematical model could be deemed to be satisfactory for predicting the thermal performance of flat-plate type solar air heaters. NOMENCLATURE D, equivalent diameter = 4 x flow area/wetted perimeter (m)
H incident solar radiation intensity (W m-r)
L m,,2 T. V W
length of collector (m) mass flow rate of air streams 1 and 2 (kg s-‘) ambient temperature (K) wind velocity (m s-i) width of collector (m)
Dimensionless Nu Nusselt number
Pr Re Ra Gr
Prandtl number Reynolds number Rayleigh number Grashof number
Greek symbols p dynamic viscosity of air (kg m-’ s-‘)
pewdynamic viscosity of air at wall temperature -1 s-I (kgm ) $ collector slope angle (degrees)
REFERENCES Gan C. K. Double-channel flow flat-plate solar air heater, Part II. Final Year Project, B.Eng., Engineering Faculty, Univ. Malaya (1986). Hausen H. Darstellung des warmenberganges in rohren VDIZ 4, durch verallgemeinerte potenzbeiziehungen. 91-98 (1943). Heaton H. S., Reynolds N. C. and Kays W. M. Heat transfer in annular passages, simultaneous development of velocity and temperature fields in laminar flow. Int. J. Heat and Mass Transfer 7, 763 (1964).
Hollands K. G. T., Unny T. E., Raithby G. D. and Konicek. L. Free convection heat transfer across inclined air layers. Trans. ASME, J. Heat Transfer 98, 189-193 (1976).
McAdams W. H. Heat Transmission, 3rd edn. McGraw-Hill, New York (1954). Nusselt W. Der warmeaustatsch zwischen wand und wasser im rohr. Forsch. Geb. Ingenieurwes 2, 309 (1931). Ong K. S. Thermal performance of solar air heaters-mathematical model and solution procedure. Solar Energy. Submitted for publication. Tan H. M. Double-channel flow flat-plate solar air heater, Part I. Final Year Project, B.Eng., Engineering Faculty, Univ. Malaya (1986). Than C. F. Experimental and theoretical evaluation of a flat-plate solar air heater. MEng.S. thesis, Engineering Faculty, Univ. Malaya (1980).
Pergamon
.
THERMAL
PERFORMANCE EXPERIMENTAL
I
OF SOLAR AIR HEATERSCORRELATION
K. S. ONG Faculty of Mechanical Engineering, University of Malaya, Pantai Valley, 59100 Kuala Lumpur, Malaysia (Communicated by BRIAN NORTON) Abstract-A mathematical model and a solution procedure for predicting the thermal performance of four types of single-pass flat-plate solar air collectors were presented in an earlier paper by Ong (1995). Instead of resorting to complicated algebraic manipulations to solve the energy equations a matrixinversion technique was employed. In this paper, theoretical predictions of surface and air temperatures were obtained for the Types II, III and IV collector designs. In addition, the Type II collector was considered with and without bottom insulation. Experimental data from previous studies were obtained and compared with the present theoretical predictions. Satisfactory qualitative and quantitative agreement was obtained between theoretical predictions and experimental data.
Type IT/ Double channel design with double air flows between top glass and absorber plate and between absorber and bottom plates and with bottom insulation provided.
1. INTRODUCTION
In a series of investigations conducted at the Engineering Faculty of the University of Malaya, much experimental data were obtained with regards to the performance of flat-plate solar air heaters for crop drying. Theoretical models were presented by Than (1980) Gan (1986) and Tan (1986) for predicting the theoretical performance of such solar collectors based on solving the energy balance equations explicitly. In a recent paper, Ong (1995) presented a simple matrix-inversion method of solution which obviated the need for complex algebraic manipulation of the energy equations.
3. HEAT TRANSFER COEFFICIENTS 3.1. Convection heat transfer coeficients 3.1.1. Laminar pow region (Re < 2300). Heaton’s (1964) empirical correlation was employed to determine the Nusselt number for laminar flow between two parallel flat plates with one side insulated and the other subjected to a constant heat flux, a[Re Pr(Dh/L)]” N” = NuW + 1 + b[Re Pr(&/L)]”
2. OBJECTIVES
The objectives of the present paper are twofold, viz: (1) to employ the matrix-inversion solution procedure to obtain theoretical predictions for the performance of solar air heaters, and (2) to compare the predicted results with past experimental data in order to validate the theoretical model. The following types of flat-plate collectors shown in Fig. 1 are considered: Type Zlu. Single channel design with single air flow between absorber and bottom plates with no bottom insulation. Type Ilb. Single channel design with single air flow between absorber and bottom plates with bottom insulation provided. Type III. Double channel design with single air flow between absorber and bottom plates and with bottom insulation provided.
(1)
where the constants a = 0.00190, b = 0.00563, m = 1.71, n = 1.17 and Nu, = 5.4 for Pr = 0.7. 3.1.2. Transition flow region (2300 c Re < 6000). Hausen’s (1943) empirical correlation for the average Nusselt number between the beginning of the heated section and the position L for flow in a tube was employed, Nu = 0.116( Re2/3 - 125) Pr”3 [ 1 + (Lrh/L)2’3] x (lAkv)“.14. (2) 3.1.3. Turbulent flow region (Re > 6000). In the turbulent flow region, Nusselt’s (1931) correlation was employed, Nu = 0.036 Re’.* Pr1’3(Dh/L)0.055.
(3) For flows in-between parallel flat plates, the equivalent diameter D,, is twice the separation distance between the plates. 3.1.4. Natural convection. Holland’s et al. (1976) correlation for free convection between 209
210
K. S. Ong
T
sky
Ta "b
“b
lb)
(4 T
T
sky
sky
Flow #l Flow #2
Flow #2
i “b
“b
(d)
(c)
Fig. 1. Types of solar air collectors
considered:
(a) Type Ha; (b) Type IIb; (c) Type III; and (d) Type IV.
inclined planes lying in the range 0 < Ra < lo5 and 0” I 4 I 60” was employed, Nu,, = 1 + 1.44
l-
1
1708(sin 1.8fj)‘.6 Ra cos 4
a cos f$)‘13_ 1 5830
(4)
The equivalant diameter employed in the above definition for Nusselt number is the separation distance beween the plates. Also the notation Cl + is used to denote that if the quantity in the bracket is negative, it should be set equal to zero. The natural convection coefficient is specified for Type III for the air cavity between the glass and absorber surfaces. Ong (1995) noted that predicted mean temperature results were significantly influenced by the air-surface heat transfer coefficients. In the present paper, all film heat transfer coefficients were multiplied by a factor equal to 0.75. This was found to be most suitable after comparing the experimental results with predicted ones for the wide range of Reynolds number encountered
in the experimental 3300 to 40,000.
investigation,
4. EXPERIMENTAL
from about
DATA
The experimental data in this paper was obtained from investigations conducted by Than (1980), Tan (1986) and Gan (1986). The data is reproduced here in order to compare with the theoretical predictions obtained. 4.1. Than’s investigations In his MEng.Sc. thesis investigations, Than (1980) conducted a series of experiments on the thermal performance of flat-plate solar air heaters with Reynolds number ranging from about 3000 to 40,000. The collectors were of the Types II and III collectors shown in Figs l(a-c). The basic Type IIa collector shown in Fig. l(a) was constructed. By providing thermal insulation on the bottom of the basic Type IIa collector, we obtained the Type IIb collector shown in Fig. l(b). By further providing a glass cover over the top of the Type IIb collector, we end up with the Type III collector. A cross-sectional view of Than’s collector is shown in Fig. 2. It consisted of rivetting two 0.5 mm thick flat
211
Performance of solar air heaters
Absorber plate (0.5 mm AL)
__---------------__
Bottom plate (0.5 mm AL) insulation (Type IIb and III)
Single air channel
Solar
collector
Orifice
plate Centrifugal blower Air out
Air in-
Copper-constantan 12.7 mm
t-9.75 Fig. 2. Details of Than’s Type IIa collector and air circulation arrangement.
aluminum sheets together to form a rectangular profile channel 38 mm deep by 0.76 m wide by 9.75 m long through which air could be circulated. The top of the absorber plate was painted with a matt-black paint to increase its absorptivity towards solar radiation. Top cover, when provided, was 3 mm thick plain window glass with a 25 mm air space in-between glass and absorber plate. Insulation when provided, consisted of 25 mm fiberglass wool resting on 25 mm thick expanded foam polystyrene sheets. The collector rested on a supporting structure inclined at 7: degrees to the horizontal in a north-south orientation. Copper-constantan thermocouples were employed to measure absorber plate, bottom plate and air temperature at distances 2.25, 4.50, 6.75 and 9.00 m from the inlet of the collector. Glass cover temperature was not measured. Air circulation was provided by a centrifugal blower and air flowrate was measured with an orifice plate. Flow Reynolds number ranged from 3000 to 40,000.
mance of a double-channel solar air heater of the Type IV collector shown in Fig. l(d). Other than physical constructional details, their collector, shown in Fig. 3 was basically similar to Than’s collector with the exception that air could be circulated in the flow channels created between the absorber plate and the glass cover and between the absorber plate and the bottom plate. The collector measured 0.254 m wide by 6.0 m long. The air flow channels were each 25.4 mm deep. Insulation was 35 mm thick fiberglass wool. Copper-constantan thermocouples at distances 1.5, 3.0, 4.5 and 5.9 m from the inlet of the collector measured the temperatures of the glass, absorber plate, bottom plate, and both air streams. Air circulation was provided with a single centrifugal blower via a manifold at the outlet of the collector. Air flowrates in the flow channels were determined separately by a pitot-static tube located in turn in the air streams at the outlet manifold and connected to an optical manometer.
4.2. Gan’s and Tan’s investigations
Solar radiation was determined with a Kippand-Zonen solarimeter located immediately next to the collector at the same pitch. In the
In their final year project investigations, Gan (1986) and Tan (1986) investigated the perfor-
4.3. Instrumentation and experimental procedure
212
K. S. Ong Absorber plate (0.5 mm AL) ----__---_----__-------------1 25mm
4-i
1 Insulation
25mm
I
25k I’
’
Bottom plate (0.5 mm AL)
, Solar collector
, Outlet
manifold , Centrifugal
‘Copper-constantan TC probe
Fig. 3. Details of Gan and Than’s Type IV collector and air circulation arrangement.
tropics, it is difficult to obtain “steady” radiation levels owing to intermittent and frequent movement of cloud cover. Hence the solarimeter output was connected to a chart recorder and thermocouple readings taken only when the radiation trace showed no signs of rapid fluctuations for about 10 min. Thermocouple readings were taken using a digital-voltmeter via a manually-operated multi-switch box. Data loggers would certainly enable more accurate data to be obtained but they were not available to us then. Hence, at best, it could be assumed that the temperatures taken corresponded to within
about 5 min of the time that the solar radiation readings were noted. Average wind velocities were measured by a cup-type anemometer. In order to avoid inaccuracies in determining ambient temperature, Than measured inlet air temperature with a probe located 12.7 mm from the inlet of the collector. Gan and Tan measured ambient temperature external to the collector and assumed that inlet air temperature was equal to the ambient temperature. In Than’s investigations, preliminary tests conducted showed that the temperature profile across the width of the collector was quite
Table 1. Summary of experimental runs extracted from Than (1980). Gan (1986) and Tan (1986)
H Type
(lcg?-l)
1 2 3
IIa
0.026 0.114 0.315
0 0 0
0.63 0.56 0.27
4 5 6
IIb
0.027 0.132 0.310
0 0 0
7 8 9
III
0 0 0
10 11
IV
0.0129 0.0334
Run
(kgmi-‘)
(m!-l)
&,
(W m-*)
Re( 103)
33.5 32.3 30.0
900 900 9ocl
3.30 14.5 40.0
0.62 0.53 0.61
33.7 31.7 31.5
900 900 900
3.40 16.7 39.3
0.026 0.120 0.307
0.48 1.41 1.26
34.1 33.4 32.8
900 900 900
3.33 15.2 38.9
0.0129 0.0334
0.50 0.40
33.2 34.3
694 700
4.90 12.7
Performance Table 2. Detailed
of solar air heaters
experimental data from Than (1980). Gan (1986) and Tan (1986)
L
Zirl
Kid
Type
Cm)
rY*ss Top (“C) (“C)
Got
Run
(“C)
(“C)
CC)
1
IIa
0.00 2.25 4.50 6.75
33.5 75.8 77.5 79.1
33.5 39.1 42.7 43.7
33.5 41.9 47.8 49.6
2
IIa
0.00 2.25 4.50 6.75 9.00
32.3 61.4 64.0 67.2 68.3
32.2 35.8 39.6 42.4 44.7
32.2 38.0 42.1 45.5 46.3
3
Ha 2.25 4.50 6.15 9.00
30.0 48.5 49.7 51.6 53.2
30.0 32.0 34.5 37.8 40.5
30.0 33.1 35.9 38.1 39.6
4
IIb
0.00 2.25 4.50 6.75 9.00
33.1 15.3 77.3 80.0 80.5
33.7 43.3 49.1 54.3 51.2
33.7 46.9 52.4 56.2 58.9
5
IIb
0.00 2.25 4.50 6.15 9.00
31.7 61.6 64.1 65.6 68.2
31.7 35.5 40.6 45.2 49.0
31.7 37.0 42.8 46.0 49.2
6
IIC
0.00 2.25 4.50 6.75 9.00
31.5 50.7 52.1 53.3 54.4
31.5 33.1 36.1 40.0 42.8
31.5 34.5 37.9 40.6 43.2
1
III
0.00 2.25 4.50 6.15 9.00
34.1 107.0 113.3 122.3 127.0
34.1 53.3 67.5 78.6 86.5
34.1 55.8 JO.9 80.0 87.8
8
III
0.00 2.25 4.50 6.75 9.00
33.4 71.7 76.8 80.9 86.2
33.4 38.9 45.7 52.2 58.0
33.4 40.3 41.9 52.7 57.7
32.8 54.3 56.0 57.5 59.1
32.8 34.6 38.0 42.1 45.1
32.8 35.8 39.8 42.6 45.6
213
showed non-uniform temperature profiles from the absorber plate to the bottom plate. A temperature gradient existed across each collector section. The shape of each profile varies, depending upon air flowrate and distance from the collector inlet. As a result, mean air stream temperatures were assumed to be represented by the arithmetic average of the three probes in the air stream. In Gan’s and Tan’s investigations, air stream temperatures were measured using single probes located in the center of the air streams along the collector centerline. Gan and Tan measured the temperatures at the surfaces of the glass, absorber plate, and bottom plate, and also of the two air streams. Than did not measure glass temperature. Than obtained a substantial amount of data. He resorted to obtaining linear regressions between air temperature and radiation intensity with regression coefficients greater than 0.95 in most cases. Gan and Tan, not having as much time with their investigations as Than, presented non-linearized data. Than’s data covered the Reynolds number range of 3300-40,000, while Gan and Tan covered the Reynolds number range of 4900-12,700. In this paper, some experimental data are extracted from the above works in order to correlate the theoretical predictions made. A summary of the experimental runs from which experimental data are extracted from is listed in Table 1. Detailed experimental data are shown tabulated in Table 2. 5. COMPARISON BETWEEN EXPERIMENTAL AND THEORETICAL RESULTS
9
III
0.00 2.25 4.50 6.15 9.00
10
IV
0.00 1.50 3.00 4.50 5.90
33.2 43.2 46.2 47.6 52.9
33.2 64.9 68.3 73.8 76.1
33.2 41.6 48.8 53.8 57.3
33.2 44.2 51.7 60.3 63.0
33.2 38.4 48.5 56.8 58.9
11
IV
0.00 1.50 3.00 4.50 5.90
34.3 39.1 40.0 41.9 44.2
34.3 46.2 52.7 56.1 60.3
34.3 36.3 41.2 44.2 47.4
34.3 35.2 41.9 46.9 48.8
34.3 34.9 40.5 44.2 48.1
uniform. However, thermocouples placed across sections of the collector (one each on the absorber and bottom plates, and three in the air stream) located along the collector centerline
Values of absorptivity, emissivity and transmissivity for the various surfaces are assumed values taken from generally accepted figures and not measured values. These values are similar to the values employed in the previous paper by Ong (1995). Previous results have shown that small temperature differences of the order of 1°C or less were obtained by modifying these values and that the predictions were not heavily dependent upon these values. 5.1. Temperature
cariation alongflow
direction
In order to compare experimental data with theoretical predictions, wall and air stream/s temperatures were plotted in Figs 4-14 for the different experimental runs. The range of Reynolds numbers from 3300 to 40,000 correspond to flows usually encountered in solar
214
K. S. Ong
0
1
2
3
4 Distance
I
+
f
Tabsorber(theory)
Tbottom(theory)m
5 along collector
X
Tairl (theory)
Fig. 4. Temperature
variation
along
: :
: :
: :
6
7
6
(m)
Tabsorber(expt)
+ Tbottom(expt)
Type IIa collector
A Tairl (expt)
: :
: :
: :
: :
: :
,100 -/ _I
60
60
-......I
20
I
at Re = 3300.
100,
t t
9
. . . . . . . .. . . . . . . . ____...:
. ..___..
_.__.
. ..I
__...
__; ______.:
-20
““l”“I,,,,I,,,,I,,~~I~~,~l~~~~I,~~~r~~~~.o
o
0
1
2
3
4 Distance
-Tabsorber(theory)
fTbottom(theory)
Fig. 5. Temperature
mTair1
variation
5 along collector
(theory)
along
X
6
7
6
9
(m)
Tabsorber(expt)
Type IIa collector
+ Tbottom(expt)
at Re = 14,500.
A Tairl (expt)’
I
Performance
0
1
2
of solar air heaters
3
4
5
215
6
7
6
9
Distance along collector (m)
I
+Tabsorber(theory)
+Tbottom(theory)
%Tairl
Fig. 6. Temperature
X
(theory)
variation
Tabsorber(expt)
along Type IIa collector
+ Tbottom(expt)
A Tairl (expt)
at Re = 40,000.
100,
20-
,100
.
.
.
.
+Tabsorber(theory)
.
..
.
.
.
.
.
.
.
. .
.
.
.
.
+Tbottom(theoty)
Fig. 7. Temperature
.
.
.
.
.
.
.
.
.
. . .
.
.
.
mTair1 (theory)
variation
.
.
X
.
.
;......:
Tabsorber(expt)
along Type IIb collector
.
.
.
.
.
.
.
.
+ Tbottom(expt)
at Re = 3400.
-20
A Tairl (expt)
I
216
K. S. Ong
0
1
2
3
4
5
6
7
6
9
Distance along collector (m)
+Tabsorber(theory)
+Tbottom(theory)
XTairl
(theory)
X Tabsorber(expt)
+ Tbottom(expt)
A Tairl (expt)
Fig. 8. Temperature variation along Type IIb collector at Re = 16,700.
0
1
2
3
4
5
6
7
6
9
Distance along collector (m)
+Tabsorber(theory)
fTbottom(theory)
m Tairl (theory)
X Tabsorber(expt)
+ Tbottom(expt)
Fig. 9. Temperature variation along Type IIb collector at Re = 39,300.
A Tairl (expt)
Performance of solar air heaters
217 140
140
-0
1
2
3
4 Distance
-o- Tglass(theory)
f
+ Tabsorber(expt)
A Tbottom(expt)
5
6
along collector
Tabsorber(theory)
m Tbottom(theory)
X
7
6
(m)
*
1
TairP(theory)
TairP(expt)
Fig. 10. Temperature variation along Type III collector at Re = 3300.
,100
100,
t
:
:
:
:
:
:
1
:
40
40
20-
.
.
.
.
.
..
.
.
.
.
.
.
.
. ___....i__..
: .
.
.
.
.._..
.
.
.
.
.
.
:...
_-20
1
it,,,
nL~~““““““‘~‘~“‘~““~““‘,“” -0
1
2
3
4 Distance
5 along collector
6
7
(m)
+Tglass(theory)
+Tabsorber(theory)
*
Tbottom(theory)
6 Tabsorber(expt)
A Tbottom(expt)
X
TairP(expt)
*
Tairl(theory)
Fig. 11. Temperature variation along Type III collector at Re = 15,200.
6
o
9‘
K. S. Ong
218
0
1
2
3
4 Distance
*
Tglass(theory)
* Tabsorber(expt)
+
6
along collector
Tabsorber(theory)
7
9
*
TairP(theory)
Tair2(expt)
along Type III collector
variation
0
(m)
+f Tbottom(theory)
X
A Tbottom(expt)
Fig. 12. Temperature
5
at Re = 38,900.
00
70 -1
, :--rs” p??.
20t”““““““““““““““““““““““““““““.’ 0 0.5 1
.:
:
.‘.
:
.:.
.:.
.:.
2.5
3
3.5
4
4.5
5
5.5
*
TairP(theory)
.-j4(J
20 1.5
2
Distance
along collector
*
Tglass(theory)
+Tabsorber(theory)
x
X
Tglass(expt)
0
v Tbottom(expt)
Tabsorber(expt)
Fig. 13. Temperature
Tbottom(theory)
variation
(m)
*
Tairl (theory)
F% Tairl (expt)
along Type IV collector
?? TairP(expt)
at Re = 4900.
6
Performance
of solar air heaters
219 80
80
2.
,,,,,,,,,,,,,,,,,,,1,,,,~11111,1 0
0.5
1
Illllll/‘llllllllljllllll 1.5
2
2.5 Distance
3
along collector
+
Tglass(theory)
+
Tabsorber(theory)
x
X
Tglass(expt)
0
Tabsorber(expt)
v Tbottom(expt)
Fig. 14. Temperature
Tbottom(theory)
variation
3.5
5
5.5
4.5
-) Tairl (theory)
*
Tair2(theory)
Z% Tairl (expt)
?? TairP(expt)
6
(m)
along Type IV collector
air heaters operation. The Reynolds number extended over both transition and turbulent flow regimes. From the results, it can be seen that, generally as expected, temperatures decrease as air flowrate increases. Also, in all the results, it was observed that the absorber plate exhibited the highest temperature, with glass being at the lowest. Further, as air flowrate increases, the temperature difference between the air streams and the bottom plate become less. The results showed that agreement between experimental data and predicted results was to within 5°C. In most cases, differences were much less, about 3°C for Types IIa, IIb and III collectors. For the Type IV collector, agreement was slightly less satisfactory. In this case, for air temperatures, differences of as much as 8°C were obtained. Also, it was observed that the theory over-predicted towards the outlet end of the collector and under-predicted at the inlet end. This was attributed to the fact that while the inlet air temperature was measured just after the inlet to the collector in Than’s case, in Gan’s and Tan’s investigation, ambient temperature was recorded outside the collector. The copperconstantan thermocouples were constructed by twisting the bared ends together and welded.
‘-20
4
at Re = 12,700.
They were connected to a digital multimeter via a multi-point selector switch. The thermocouples were calibrated against high-precision thermometers, accurate to within +0.2”C. The cold junction temperature varied by +l”C during the testing. Hence it could be said that the temperature readings were accurate to within + 1°C. In Than’s investigations, the mean air temperatures were averaged using three probes at each station. In Gan’s and Tan’s investigations, only a single probe located in the middle of the air stream at an accuracy of + 2 mm were employed. This could perhaps account for the poor correlation of theory to experiment. From Than’s work, deviations of 2-3°C could result especially when there was a steep temperature distribution across the depth of the airstream. However, qualitative agreement could be said to be have been obtained for this case. It should be reiterated here that it was extremely difficult to obtain true “steady” ambient conditions in the tropics and especially without the use of data-loggers. 6. CONCLUSIONS
Predicted temperatures for Types II, III and IV solar air heaters were presented and com-
220
K. S. Ong
pared with experimental results. Satisfactory qualitative and quantitative agreement was obtained. The mathematical model could be deemed to be satisfactory for predicting the thermal performance of flat-plate type solar air heaters. NOMENCLATURE D, equivalent diameter = 4 x flow area/wetted perimeter (m)
H incident solar radiation intensity (W m-r)
L m,,2 T. V W
length of collector (m) mass flow rate of air streams 1 and 2 (kg s-‘) ambient temperature (K) wind velocity (m s-i) width of collector (m)
Dimensionless Nu Nusselt number
Pr Re Ra Gr
Prandtl number Reynolds number Rayleigh number Grashof number
Greek symbols p dynamic viscosity of air (kg m-’ s-‘)
pewdynamic viscosity of air at wall temperature -1 s-I (kgm ) $ collector slope angle (degrees)
REFERENCES Gan C. K. Double-channel flow flat-plate solar air heater, Part II. Final Year Project, B.Eng., Engineering Faculty, Univ. Malaya (1986). Hausen H. Darstellung des warmenberganges in rohren VDIZ 4, durch verallgemeinerte potenzbeiziehungen. 91-98 (1943). Heaton H. S., Reynolds N. C. and Kays W. M. Heat transfer in annular passages, simultaneous development of velocity and temperature fields in laminar flow. Int. J. Heat and Mass Transfer 7, 763 (1964).
Hollands K. G. T., Unny T. E., Raithby G. D. and Konicek. L. Free convection heat transfer across inclined air layers. Trans. ASME, J. Heat Transfer 98, 189-193 (1976).
McAdams W. H. Heat Transmission, 3rd edn. McGraw-Hill, New York (1954). Nusselt W. Der warmeaustatsch zwischen wand und wasser im rohr. Forsch. Geb. Ingenieurwes 2, 309 (1931). Ong K. S. Thermal performance of solar air heaters-mathematical model and solution procedure. Solar Energy. Submitted for publication. Tan H. M. Double-channel flow flat-plate solar air heater, Part I. Final Year Project, B.Eng., Engineering Faculty, Univ. Malaya (1986). Than C. F. Experimental and theoretical evaluation of a flat-plate solar air heater. MEng.S. thesis, Engineering Faculty, Univ. Malaya (1980).