A solar energy collector for heating air

Solar Energy. Vol. 12. pp. 19-29. PerpmonPress. 1968. Printed in Great Britain

A S O L A R E N E R G Y C O L L E C T O R F O R H E A T I N G A I R *

V. D. BEVILLt and H. BRANDT~;

(Received ! 4 February 1968)

Alntri~ ' t-This paper describes a study of a solar-energy collector that heats air. Solar energy is collected in an absorber consisting of 96 parallel fins of aluminum that are spaced 0.635 cm apart, are 6 i -0 cm long and are 6.35 em high. The absorber is installed in a glass covered box so that air can be pumped past the aluminum fins for heating. One objective of the study is to determine the efficiency that can be obtained with this collector when the absorber fins reflect specularly. A second objective is to evaluate changes in efficiency when different parts of the fins are made diffuse. To determine the performance of the collector, known quantities of air ranging from 65 to 150 g/hr/cm -~ of collector area were passed through the absorber and the temperature rise of the air from the inlet to the outlet of the collector was measured. From these data and a measurement of the solar energy received by the collector, efficiency was calculated. Results indicated that efficiencies of more than 80 per cent could be obtained with an absorber having specular fins when the ambient air was calm, When the fins of the absorber were made diffuse, the collector efficiency decreased by about 50 per cent. This result is in agreement with theory.

R ~ u n ~ - C e t article drcrit une 6tude sur un collecteur d'rnergie solaire qui chauffe I'air. L'Snergie solaire est reccueillie dans un absorbeur qui consiste en 96 ailettes parali~les en aluminium, espacEes de 0,635 cm, de 61 cm de long et de 6,35 cm de haut. L'absorbeur est install6 dans une bo/te h couverture de verre pour permettre de pomper I'air pour le chauffage, au-delh des aillettes d'aluminium. Un premier objectif de 1'6tude est de ddterminer le rendement que I'on peut obtenir h partir de ce collecteur quand la r~fl6xion des aillettes de I'absorbeur devient spE aire. Un deuxi6me objectif est d'Evaluer les modifications de rendement quand les diffErentes parties des aillettes sont rendues diffuses. Pour determiner le rendement du collecteur, on a fait passe des quantit(~s connues d'air variant de 65 ~t 150 g/h cm -2 de la surface du collecteur, :~ travers I'absorbeur et I'EI6vation de la temperature de l'air de I'entrEe h la sortie du collecteur a Et6 mesurEe. A partir de cette donnEe et d'un calcul de I'Energie solaire rerue par le collecteur, on a dvalu6 le rendement. Les r6sultats indi- quent que des rendements de plus de 80 pour cent pourraient Etre obtenus avec un absorbeur h aillettes miroitantes dans un air ambiant calme. Avec les ailettes de I'absorbeur diffuses, on notait une baisse du rendement du collecteur d'environ 15 pour cent. Ce r6sultat s'accorde avecla th6orie.

R e s u m e n - Esta ponencia describe el estudio de un colector de energla solar que calienta el aire. La energla solar es recogida en un absorbedor dorado de 96 aletas paralelas de aluminio, de 61 ,O cm de Iongitud x 6,35 cm de altura, espaciadas a 0,635 cm. El absorbedor va alojado en una caja con tapa de vidrio, bombe~indose el aire a trav6s de las aletas de aluminio para fines de calefacci6n. Una finalidad del estudio consiste en determinar el rendimiento obtenible de este colector cuando las aletas de absorbedor reflejan especularmente. Otra finalidad es la de evaluar los cambios operados en dicho rendimiento al hacer difusas diferentes partes de las aletas. Para determinar la actuaci6n del colector, se hicieron pasar por el absorbedor cantidales conocidas de aire, desde 65 a 150 g/h cm -2 del i rea del colector, midi 6ndose la elevaci6n de la temperatura del aire entre la entrada y la salida del colector. Estos datos, en uni6n de la medici6n de la energia solar captada por el colector, sirvieron para hacer un cilculo de rendimiento. Los resultados indicaron que era posible obtener rendimientos de mils del 80 por ciento con un absorbedor provisto de aletas especulares, en r~gimen de aire ambiental quieto. Sin embargo, al hacer difusas las aletas del absorbedor, el rendimiento del colector dis- minuy6 en un 15 por ciento approximadamente. Este resultado concuerda con la teoria.

I N T R O D U C T I O N

SOLAR ENERGY collection by means of fiat-plate collectors has been studied by several investigators in recent years. These collectors are useful for heating air. water or other

* 1967 Solar Energy Society Conference paper. t Department of Engineering, Fresno State College, Fresno, California. ~t Department of Engineering, University of California, Davis, California.

19

20 V.D. BEVILL and H. BRANDT

fluids when relatively low temperature increases of the fluid are required. Examples are collectors that heat air about 10-2ff'C for drying and dehydrating in agricultural applications, and collectors that are used in saline-water conversion.

Most flat-plate collectors for heating air are made of diffuse surfaces, although in recent years selectively absorbing surfaces are becoming important[I-3]. This paper describes the performance of a flat-plate collector that uses specularly reflecting surfaces. In this respect, the collector is believed to differ from most collectors described in the literature[4, 5].

For this study, two similar collectors were constructed that consist of 96 parallel and uniformly spaced aluminum fins placed below a glass coverplate as shown in Figs. I and 2. Solar energy passing through the glass is incident on the fins where it is partially absorbed and reflected. The absorbed energy raises the temperature of the fins and heats air that is pumped between the fins.

The collector has been designed to attain high collector efficiency, and to require low pumping power to pass air through the collector. High efficiency is obtained because the specular fins capture nearly all the solar energy incident on the collector. Furthermore, the specular absorber is an inefficient emitter of long-wavelength radiation so that heat losses from the collector are kept to a minimum. Consequently, the collector can be thought of as a selective absorber that absorbs incoming energy effi- ciently, but rejects only a small amount of radiative energy of long wavelengths. To verify this behavior, comparison was made with a second collector in which the fins of the absorber were made partially diffuse by sandblasting.

The next section of this paper describes the collector and the experimental equipment. This is followed by sections that present an analysis of the collector system and that discuss the experimental procedure. Results and a discussion of the results are given in the final section.

COLLECTOR DESCRIPTION

Two square collectors, shown in Figs. l and 2, were constructed for the experiments. Each collector measured 61-0 by 61-0 cm which was the smallest size that per- mitted determination of collector efficiency within +_5 per cent. The sides of the collectors were made of 1.9 i cm plywood, and glass plates 0-317 cm thick were used as covers of the collectors.

The absorbers in the collectors consisted of 96 parallel aluminum fins that were spaced 0-635 cm apart and were set in grooves of an aluminum base plate. Before con- structing the collector, a study was made of an optimum fin height that would give maximum collector efficiency and yet would not make the fins unduly high. It was found that a fin height equal to ten times the distance between the fins was found to give high collector efliciency and that additional fin height was not warranted. Con- sequently the exposed height of the fins above the base plate was made 6.35 cm. The fins were made of 24 ST AIclad aluminum and were 0.61 mm thick.

Surfaces of the fins in one of the collectors were made specular by polishing them to a high luster with aluminum polish. The surface roughness of these fins was less than l/~m rms. Fins in the second collector were sandblasted to make portions of these fins diffuse. In one of the experiments, the bottom half of each fin was sandblasted and in another experiment, the fins were sandblasted completely. Sandblasting gave a surface roughness of about 250/~m rms.

Fig. 1. Solar energy collectors with test equipment.

Fig. 2. Solar energy collectors.

[Facing page 20]

A solar energy collector for heat ing air 21

Air was passed through the collector in a direction parallel to the fins. To distribute the incoming air uniformly between all fins, a perforated plate was placed at the collector box entry. A similar arrangement at the exit of the collector provided a uniform distribution to the effluent air. Air was pumped through the collector by means of an air blower as shown in Fig. 1. Orifices were installed in the flow lines to each of the collectors to measure air-flow rates. The orifice and pressure tap arrangements differed slightly from ASME standards. Therefore the orifices were calibrated by means of a Meriam laminar flow meter.

To minimize heat losses from the collector to the ambient air, the base plate of the absorber assembly was placed on 5.08 cm thick fiberglass insulation. The ends of the collector were covered with aluminum foil to reduce radiative heat transfer from the sun through the end parts of the collector.

To evaluate factors affecting collector efficiency, a number of radiative and other heat-transfer properties were required that could be obtained only from experiment. To measure these properties, thermocouples were installed at various locations in the collector system such as ( l) on the fins, (2) on the bottom of the base plate. (3) on the bottom of the insulation below the plate, and (4) on the cover glass. Thermocouples on the glass cover plate were shielded from the incident solar radiation.

ANALYSIS OF COLLECTOR SYSTEM

To analyze the performance of the collectors, the absorptivity of a set of parallel fins is calculated first[6], in the analysis, the fins are assumed to be infinitely long and end effects are neglected. The ratio of fin length to distance between fins is 96 to I, so that the assumption of infinite length is a relatively good one. A typical path of solar radiation that is reflected from specular fins is shown in Fig. 3(A). The number of

t J ,,

f

r r

....I

t . . ) I.iJ n t. .o

t l g

o =

_5 l B

Fig. 3. Multiple reflections between two fins.


reflections of the incident radiation between two fins of height L and spacing distance a is equal to

n-- 1 + 2Ltan 0. (l) a

When the angle of incidence 0 is zero, the number of reflections reduces to a single reflection from the base plate. On the other hand, when angle 0 approaches 90 °. the number of reflections approaches infinity. In the first case, the sun would be directly overhead, and in the second case the sun would approach the horizon.

The overall absorptivity a of a set of specular fins can be calculated by considering reflections of monochromatic solar radiation and then summing the resulting monochromatic absorptivity a~ over the entire wavelength spectrum, in other words, if an absorber without cover plate is analyzed the absorptivity of the absorber is equal to

p~nG ~ ~=0 (2) c~=l

k = 0

SubstitutiOn of a few typical values for the reflectivity into the above equation shows that high absorptivities can be obtained when the angle of incidence of the solar radiation is greater than about 20 ° .

A less accurate method of calculating absorptivity which nevertheless appears to be followed in the literature is to determine the total reflectivity of the aluminum and to raise this reflectivity value to a power n. Hence,

0e

a = l - = u _ _ . . (3)

k __z0 The difference between the two absorptivities calculated from equations (2) and

(3) depends on the monochromatic reflectivity of the aluminum (see Fig. 7, Appendix) and on the angle of incidence of the solar radiation. This angle affects both the number of reflections and, to a minor degree, the monochromatic radiation transmitted through the glass. Because the angle of incidence of the solar radiation was less than 35 ° throughout the experiments, changes in monochromatic transmittance of the glass were neglected. The difference between absorptivities calculated from Eqs. (2) and (3) is presented in Fig. 4. For this figure the spectrum of direct beam incident solar radiation was obtained from Moon [7].

In the experimental phase of this study, parts of the fins were made diffuse to exa- mine the effect of this change in surface character on collector efficiency, When the bottom halves of the fins are diffuse and the top halves are specular, as shown in Fig. 3(B), the overall absorptivity of the absorber can be calculated from methods described by Wiebelt [8]. When the entire fin surfaces are made diffuse, overall monochromatic absorptivity of the absorber is obtained readily from a simple shape factor relationship [8]. In this case,

l (4) ax = a 1

' +

A solar energy collector for heating air 23

1.0

0.8

>- I--

O.6 I-- Q. n- O ~ 0 4 m

0.2

/ /

, I I 1 J I J 0 20 4 0 60 80

INCIDENT ANGLE , 0 , DEGREES

F i g . 4. Absorptivity of absorber.

The e~iciency of the collector can be expressed in several ways. One way is to consider the heat added to the air and to compare this heat with the incident solar energy. This approach was used in evaluating the test results that are presented in Fig. 5.

I 0 0

z . i

o~ 8 0 I.iJ o-

) -

6 0 z hi

,,u_ 4 o w

o

~, 2o hi - J -J 0 U 0

0

I I I l I I [

I I I I I I , I , I , I • I , I , I

2 0 4 0 60 80 I00 120 140 160 180 O0

AIR FLOW RATE, GRAMS PER HOUR CMZOF COLLECTOR AREA

Fig. 5, Efficiency of collector with specular fins.

Another way of calculating efficiency is to consider (1) energy that is absorbed by the collector, (2) energy that is lost to the ambient air, and (3) solar energy that is incident on the collector. The advantage of the second approach is that it expresses the effect of radiation parameters on efficiency and therefore permits better evaluation of the effects of design changes on efficiency.


The equation for the efficiency of the collector with a specular absorber can then be written as

0 = ~. ( 1 - O ~ . , ) G ~ - ~ . p ~ T ~ . G ~ - h . ( T . - T . ) - ~ d ~ r ( T ~ - T ~ ) ~ . (5) k = 0 ~ = 0

The sums in Eq. (5) are to be made for both the direct beam and the diffuse com- ponents of the solar radiation. For the diffuse component a series ofn values need to be considered in accordance with the hemispherical nature of this component.

Radiative emission of energy from the absorber that is transmitted through the glass cover plate is neglected because the wavelength range of the emitted radiation is higher than the wavelength range of energy transmission of the glass cover plate. For example, at wavelengths less than 3/~m, the glass transmissivity is high, as shown in Fig. 8 in the Appendix, but the fraction of energy emitted from a 50°C absorber is less than 0.1 per cent. At wavelengths between 3 and 5/~m the fraction of emitted energy is 2-5 per cent, and the glass transmissivity ranges from 20 per cent to zero. Consequently, the fraction of energy emitted by the absorber that is transmitted through the glass is less than 0-5 per cent. When this energy is compared to the energy incident on the absorber, this percentage becomes insignificant. Another term that has been neglected is the heat losses from the sides and bottom of the collector box. Because the collector box is well insulated, this loss is considered negligible.

To obtain an estimate of collector efficiency, the magnitude of each term in Eq. (5) is determined. The first term is a function of the monochromatic reflectance and the incident solar radiation wavelength spectrum. The reflectance of the glass is approximately 7 per cent, which makes the first term 93 per cent. Other terms in the equation are positive so that they decrease efficiency. Therefore, if the reflectance effect is considered only, the efficiency of this collector can not be greater than 93 per cent.

The second term in Eq. (5) is a function of the monochromatic reflectivity of the aluminum absorber. Figure 4 shows that if the angle of incidence of the solar radiation is greater than 25 °, about 12 per cent of the energy incident on the absorber does not get absorbed. Figure 4 presents only the effect of the direct beam component of the incident solar energy. The absorber absorbs about 94 per cent of the diffuse radiation component so the amount of specular and diffuse radiation that is not absorbed is less than 12 per cent. This percentage is reduced further when the transmittance of the glass cover plate is taken into account. If all these factors are considered, the maximum collector efficiency is found to be about 83 per cent. At angles of incidence greater than 25 ° the efficiency would increase up to a maximum value, and then would decrease with increasing angles of incidence.

The last terms in the brackets represent the convection and the radiation losses from the glass cover plate. The first term is the convection loss which depends on wind speed. If the air is calm, heat transfer takes place by free convection and depends on the difference in the temperatures of the glass and the ambient air. If the wind is blow- ing, heat transfer takes place by forced convection and the heat transfer rate depends on both the heat transfer coefficient and the glass temperature. In the case of a collector with a single cover plate the heat transfer coefficient will be nearly independent of glass temperature, Consequently, with a single cover plate and at a fixed wind speed, the convection losses can be decreased only by decreasing the temperature of the glass.


The glass temperature depends on (1} the type of absorber that is used, (2) the air flow rate through the collector and (3) the temperature of the air entering and leaving the collector. The temperature of the absorber is low compared to other collectors because the absorber has a large surface area to heat air. For example, the present absorber has 21 times the area of a flat plate collector of the same size. Radiative emission in the long-wavelength region is low because the emissivity of the specular aluminum at long wavelengths is about 0.05. If emission from the specular fins is assumed to occur diffusely, the emissivity of the absorber would be about 0-5. Eckert and Sparrow[9] have shown that the effective emissivity is less for a cavity with specular surfaces than for a cavity with diffuse surfaces. Consequently, the effective emissivity of the absorber with specular fins is less than 0.5. As a result of both low absorber emissivity and temperature, the glass temperature remains low and both the convection and radiation losses to the outside environment are reduced.

When the fins of the collector are sandblasted to make them diffuse, the emissivity of the abosrber approaches unity. As shown in Eq. (4), fin emissivities of 0.5 or higher cause the emissivity of the absorber to be greater than 0.95, which is sub- stantially higher than the emissivity of the specular absorber.

Although heat convection losses from the collector during windy days are significant, on calm days the convection losses were found to be about one-third of the radiation losses.

The reason for the high efficiency obtained with the present collector can then be summarized as follows. The absorber of the collector is essentially a selective surface that is a highly efficient collector of incident solar radiation and an inefficient emitter of long-wavelength radiation, in the case of long-wavelength emission, the specular collector emits less radiation than the diffuse collector.

EXPERIMENTAL PROCEDURE The experimental procedure can be divided into two parts, in the first part, the

performance of the solar energy collector having an absorber with specular fins was evaluated. Measurements were made over a range of air flow rates and at different angles of incidence of the solar radiation. In the second part of the experiments, two collectors were run simultaneously. One of the collectors had an absorber with specular fins and the second collector had an absorber with fins that were partially specular and partially diffuse. The purpose of these experiments was to evaluate the effect on collector efficiency of making portions of the specular fins diffuse.

During the experiments, the collectors and associated equipment such as pumps and pipes with orifices were located about 150 m from a building. Therefore, the collectors had a slightly restricted view of the sky's diffuse radiation. The pyrhelio- meter was placed close to the collector boxes. The collectors were operated horizontally with the fins perpendicular to the direction of the projection of the Sun's rays on a horizontal plane. During all of the experiments the sky was free of clouds.

Sky temperature was not measured but was assumed to be 5°C below ambient temperature. In theory, the incident solar radiation changes continuously during the day and therefore the collector temperature changes continuously. However, in prac- tice, temperatures varied slowly and recording of data was delayed for each run until absorber temperatures and air temperatures had stabilized to within_+_ 0-2°C.

The air rate to the collectors was measured by means of sharp-edged orifices. The


air flow rate ranged from 65 to 150 g/hr cm -2 of collector area and the air rate was measured with an accuracy of about_+ 2 per cent.

To determine the temperature rise of air passing through the collector, average air temperatures at the inlet and outlet of the absorber were measured by means of five thermocouples that were connected in parallel.

In the determination of the theoretical efficiency of the collector, the monochromatic reflectivity of the aluminum fins is needed. This reflectivity was measured with a Beckman DK-2 spectrophotometer with an integrating sphere. A graph of the monochromatic reflectivity vs. wavelength is shown in Fig. 7 in the Appendix. The transmittance of the glass cover plate was measured with a Perkin-EImer light source and monochromater unit. The results of the transmittance measurements are shown in Fig. 8 in the Appendix. Changes in monochromatic transmittance of radiation incident at angles of 0 ° and 20 ° were found to be within the experimental limits. Consequently only one curve of transmittance is plotted in Fig. 8.

R E S U L T S A N D D I S C U S S I O N

Figure 5 shows the efficiency of the collector with specular fins as a function of air flow rate. The efficiency varies from a low value of about 75 per cent to more than 80 per cent over an air flow range 65-150 g/hr cm -z of collector area. These efficiencies are obtained on calm days when convection losses from the collector are small and when the efficiency of the collector closely approximates the theoretical efficiency discussed in the Analysis section. The efficiency increases with increasing air flow rate. The increase is attributed to the decrease in absorber temperature at the higher flow rates. This decrease consists of a reduction in the heat emitted by the absorber to the glass cover plate and therefore from the glass cover plate to the ambient air. As discussed in the Analysis section, high collector efficiencies are obtained because the absorber has a high absorptivity for solar radiation and has a low rate of radiative emission. The low radiative losses are attributed to the low effective emissivity in the long wavelength region of the specular absorber and the low mean temperature of the absorber. The temperature rise of the air flowing through the collector ranges from about 12 to 20°C. At the higher flow rates the temperature increase of the air is about 12°C and at the low air flow rates the temperature increase is about 20°C.

The second part of the experiment consisted of evaluating the effect of sandblasting of the absorber fins on efficiency. Fins of the absorber were made diffuse for two reasons. First, to verify the theoretical result that a collector with diffuse fins would have lower efficiency than a similar collector with specular fins. Second, during actual operation of a specular collector the fins would become less specular because dust particles would collect on the fins.

Figure 6 shows the effect of sandblasting of the absorber fins on efficiency, in this figure an efficiency ratio is plotted versus air flow rate. The ratio is the efficiency of a collector in which fins have been made partially diffuse to the efficiency of a collector having all specular fins. It is evident from the data shown in the figure that an increase in the amount of diffuse surface of the fins decreases overall efficiency of the collector. Data points indicated by circles are for a collector that has specular fins but has a diffuse bottom plate, in this case, an average decrease of 5-10 per cent is observed. When the lower halves of the fins are diffuse the efficiency decreases by about


er

o ,20

8~ -, .~ I00 ~ ° - - dl[ ¢'~ ,-I ~.~ 80

i.I ...1 uJ

~ 6o

0

F -

n- 40 >-

' I ' I I ' 1 I

A (3

1 0 SPECULAR FINS & DIFFUSE BOTTOM SPECULAR FINS & BOTTOM

- ~ [3 DIFFUSE LOWER FIX HALVES & BOTTOM SPECULAR FINS & BOTTOM

/ ~ DIFFUSE FINS & BOTTOm SPECULAR FINS & BOTTOM

Z /a.J

2 0 ~ I i I i I I I i - - 5 0 6 0 7 0 8 0 9 0 I00 h I, w AIR FLOW RATE,GRAMS PERHOUR CMZOF COLLECTOR AREA

Fig. 6. Efficiency ratio of collectors. This figure compares efficiencies of collectors with fins that are made partially or totally diffuse with the efficiency of a collector having specular fins.

10 per cent and when the fins are made completely diffuse the efficiency decreases by about 15 per cent. These latter data are shown by the curve with triangles in Fig. 6.

The decrease in collector efficiency observed with an increase in the amount of diffuse surface area is in harmony with theory. Only in a special case when the angle of incidence of the solar radiation is very small would the diffused collector be more efficient than the specular collector. In this case, the Sun would be nearly overhead and the number of reflections would approach one with a specular absorber.

Although an increase in diffuse areas of the fins decreases efficiency, the decrease is not sufficiently large to make a diffuse collector impractical. Consequently, although high efficiencies would be obtained with a specular collector, the difficulty of making and maintaining the fins specular is probably not warranted for actual operations. If the sandblasting can be considered to be representative of collection of dust on the fins, it would indicate that a significant amount of diffuseness of the fins would be acceptable.

The data presented in Figs. 5 and 6 were obtained on calm days when there was esentially no air movement over the collector cover plate. On windy days the collector efficiency decreases. For example, with a wind speed of 10 km/hr the efficiency decreases from 80 to about 70 per cent, and when the wind speed increases to 30 km/hr the efficiency decreases further to about 50 per cent. No accurate data were obtained to correlate collector efficiency with wind speed. Nevertheless, the data indicate that wind speed has a significant effect on efficiency, and that heat losses from the glass cover plate should be reduced. This may be accomplished by installing additional cover plates over the collector.

The experimental data were taken at different times of the year. However . because time was required to set up the equipment, most of the data were taken from late morning through early afternoon. As a result, the angle made by the Sun from the

28 V.D. BEVILL and H. B R A N D T

vertical ranged from about 25 to 35 ° . In spite of the changes in output of the collector as the incident solar radiation angle changed, the efficiency was affected less than 5 per cent by the incident solar radiation angle. Data in Fig. 5 are average data taken at different angles of incident solar radiation and each data point represents the average of about three or four test runs.

The efficiency of the collector was also found to be nearly independent of the ambient air temperature. Some of the data were taken during the month of August when the average air temperature was about 35°C and other data were taken during the month of January when the temperature was about 16°C.

C O N C L U D I N G R E M A R K S

In this study a solar energy collector for heating air was designed and tested. In one design, the absorber consisted of 96 parallel specular aluminum fins that were placed in a box with a glass cover plate. With the specular fins efficiencies of more than 80 per cent were obtained when air was heated from 12 to 20°C. In the second design the fins were made diffuse and the efficiencies of the two collectors were compared. It Was found that the collector with a diffuse absorber had about 15 per cent lower efficiency.

Wind velocity had a severe effect on collector efficiency. The efficiency was about 50 per cent at a wind speed of 30 km/hr. It is recommended that a second cover plate be installed in future designs of collectors of this type to decrease heat loss through the cover plate to the ambient air.

Acknowledgement-This research was supported in part by a grant from the National Science Foundation.

N O M E N C L A T U R E

G~ monochromatic energy of incident radiation L absorber fin height

T~ temperature of ambient air T o temperature of glass cover plate T~ temperature of sky a distance between fins

h,, coefficient of heat convection for heat transfer from glass cover plate to ambient air n number of reflections

absorptivity of absorber ~, emissivity of glass cover plate r/ efficiency of specular collector 0 angle of incidence of solar radiation ~. wavelength

• ,o reflectivity p~ monochromatic reflectivity of aluminum fins

p u monochromatic reflectance of glass cover plate o- Stefan-Boltzmann constant

~'~ monochromatic transmittance of glass cover plate.

R E F E R E N C E S

[ l ] F .E. Edlin, Plastic glazing for solar energy absorption collectors, Solar Energy 2, 3 (1958). [2] H. C. Hottel and T. A. Unger, The properties of a copper oxide-aluminum selective black surface

absorber of solar energy, Solar Energy 3, 10 ( 1959). [3] R. A. Solomon, The properties and performance characteristics of selective tin oxide films deposited

on glass for use in solar energy collection, M.S. thesis, p. 32. University of Arizona (1963). [4] Y. H. Liu and R. C. Jorden, The long term average performance of flatplate solar energy collectors,

Solar Energy 7, 53 (1963).


[5] A. Whillier, Black-painted solar air heaters of conventional design, Solar Energy 8, 3 i (1964). [6] V. D. Bevill, A solar energy collector for heating air, M.S. thesis, University of California, Davis (1965). [7] P. Moon, J. Franklin inst. 604 (1940). [8] J. H. Wiebelt, Engineering Radiation Heat Transfer, pp. 88. ! 44- i 50. Holt. New York (1966). [9] E. R. G. Eckert and E. H. Sparrow, Radiative heat exchange between surfaces, Int. J. Heat Mass Trans-

fer3,42(1961).

A P P E N D I X

To determine the efficiency of the collector from equation (5), the monochromatic reflectivity of the aluminum fins and the monochromatic transmittance of the glass cover plate are needed. Measurement of these material properties were described in the Experimental Procedure and the results are presented in Figs. 7 and 8.

1.0

0.9

z ,T ,, 0.8 o )-

N o.7 I--- L) W _J ~ 0.6

l I I I [ I I I I

FIN MATERIAL 24 ST ALCLAD ALUMINUM

U 3

<~ _J

L L o l.¢J (J z

l -

z

I---

IO0

8 0 -

60

40

20

0 0

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 WAVELENGTH, MICRONS

Fig. 7. Monochromatic reflcctivity of aluminum fins.

1.8 2.0

i I 1 I

I /

/ i

I

I I I 2 3 4 5

WAVELENGTH, MICRONS

Fig. 8. Monochromatic transmittance of glass cover plate of collector.

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A solar energy collector for heating air