Comparison of reflector designs for stationary tubular solar collectors

Solar Energy Vol. 37, No.

3, pp. 195-203, 1986

0038-092X/86 $3.00 + .00 © 1986 Pergamon Journals Ltd.

Printed in the U.S.A.

COMPARISON OF REFLECTOR DESIGNS FOR S T A T I O N A R Y T U B U L A R SOLAR COLLECTORS G. H. DERRICK,I. M. BASSETTand D. R. MILLS School of Physics, The University of Sydney, Sydney, N.S.W. 2006, Australia (Received

31

May

1985;

Accepted 5 March

1986)

Abstract--We consider a number of alternative designs for reflectors which are used in conjunction

with cylindrical tubular solar collectors. The annual relative optical performance of the collectors is assessed, data being presented for a variety of tube absorptances and reflector reflectances. Both North-South (NS) and East-West (EW) orientations of tubes are considered. This performance data may be combined by the reader with his own local tube and reflector unit costs to make cost-effectiveness judgements between rival collector designs. The method is illustrated using some current Sydney prices, on which basis we make the following assessments: A reflector is always cost-effective, the best option being a stainless steel reflector of Winston-Hinterberger type with a geometric concentration ratio (C) of about 1.2, mounted either NS or EW. At higher C values EW is favoured over NS. Back-silvered glass mirrors are not competitive. A plane diffuse reflector with C -> 1.2 is also cost-effective for NS orientation. Since no allowance is made for thermal losses in the present work these conclusions should be regarded as tentative only.

l. T H E PROBLEM

sentative. The reader is invited to use the performance graphs such as Fig. 2 to make his own costeffectiveness estimates (eqn (6)) employing his own values for the unit costs.

We consider a planar array of parallel cylindrical tubular collectors. Because of shading the side of the tubes away from the sun will receive no radiation unless the array is backed by a reflector. We 2. REFLECTORTYPES pose two problems, firstly, that of assessing the Six alternative reflector profile families, denoted relative optical performance of such reflectors and secondly, that of assessing their relative cost-ef- WH(35), WH(60), WH(90), INV, DIF, SPC are fectiveness. We confine our attention to fixed, non- considered. The first three, of type WH(13), are tracking systems. One has the option to use various truncated versions of the Winston-Hinterberger levels of sophistication in the reflector design rang- profile of acceptance half angle 13, modified to allow ing from a cheap coat of white paint on the roof a gap, g (for the cover tube needed for vacuum inbeneath the absorber tubes to carefully contoured, sulation of the absorber tube) between the reflector expensive, high quality specular mirrors based per- cusp and the absorber tube[2]. Parametric equahaps on the profiles proposed by Winston and Hin- tions (see eqn (1) below) and a string construction terberger[1] Further design options are how far for this type of reflector are given by Bassett and apart the tube centres are separated, d, and how Derrick[3]. The reflector is truncated at the half the tubes are oriented, N o r t h - S o u t h (NS) or E a s t - way point between tubes, and overall has periodWest (EW). Here we assume that the tubes are icity d. We take the tubes of unit radius, with a gap mounted in a plane tilted up at the local latitude, g = 4/15 ~ 0.27 radii (the value for the standard NS and E W referring to the orientation of the tube Sydney University absorber tube). Following conaxes within this plane. We calculate the year round ventional usage we refer to the ratio C = (spacing energy collected per tube in each orientation for a of tube centres)/(tube circumference) = d/c as the variety of reflector profiles and for a range of values "geometric concentration ratio." The reflector proof the parameters tube separation, tube absorp- file is completely specified by the family [e.g., tance, reflector reflectivity and diffuse content of WH(60)] and C. INV represents a family of involutes, truncated and repeated periodically. This difthe incident light. Finally, cost-effectiveness is assessed. Natu- fers from WH(90) in that there is no gap at the cenrally the same performance data give rise to differ- tral cusp. ent assessments of relative cost-effectiveness, acThe reflector of the family WH(13) whose concording to the component unit costs which are centration ratio is C has its cartesian equation y = assumed. The cost-effectiveness assessments pre- y(x) determined as follows, y(x) is the even periodic sented here in Fig. 1 are, therefore, merely repre- function of x with period 2~rC whose value in the 195

196

G. H. DERRICKet al.

$~150

TN~

NS

$ 60 Ew

D I F and SPC are families of plane reflectors with equation y = - 3.0, there now being no upper limit on C. This value of y was c h o s e n on the basis of calculations r e p o r t e d in [6] (Fig. 1) which indicate that while the p e r f o r m a n c e i m p r o v e s as [y[ increases, the i m p r o v e m e n t is negligible for ]y[ > 3. Reflectors of the family D I F are assumed to be diffuse, while all those of the families WH(13), I N V and SPC are specular.

80 60

.......... ~--~

g ~ 4o 20

3. A S S U M P T I O N S O F T H E M O D E L t.O

1.5

1.0

t.5

1.0

1.5

GeometricconcentrationratioC

1.0

1. Hottel's 23 km haze model[4]

1.5

Fig. 1. Comparative cost-effectiveness of some rival collector designs, based on a tube of absorptance a = 0.85 costing either T = $150 or $60 per square metre of tube surface, with orientation NS or EW. The combined initial tube and reflector cost needed for the collection of 1 G J/ year is plotted for the following alternative assumptions about the reflector material, family, reflectance (p), and cost per square meter (M): x x × × × × No reflector, DIF, to = 0.1, M = $0; ...... Silver on glass, WH(35), p = 0.85, M = $60; . . . . . . Stainless steel, WH(35), p = 0.65, M = $25; - Stainless steel, WH(35), to = 0.65, M = $15; . . . . Colorbond, DIF, p = 0.75, M = $5.

-

I(0A = I0[0.1283 + 0.7559exp(

- 0.3878/cos0s)],

(2) w h e r e l(Os) and Io(= 1353 W m -2) are the sea level and extraterrestrial intensities o f b e a m radiation, and Os the angle of the sun from the zenith. We modify eqn (2) so as to m a k e an allowance for a diffuse c o m p o n e n t as follows:

2. Allowance for diffuse light

range 0 _-< x =< ~rC is given parametrically by x = sin0

Our starting point is H o t t e l ' s b e a m radiation f o r mula

A fraction f of the incident light is diffuse, which we define to m e a n the following: The b e a m intensity is now (1 - f)l(OA with l(0s) given by eqn (2), while the whole h e m i s p h e r e emits diffuse light at a radiance B = (f/~r) I(0Acos0~. This means that at each instant, o f the total radiation incident on a horizontal surface, a fraction f is diffuse. H e r e we give results for f = 0.0, 0.3 and 0.5.

l(0)cost~

y = - c o s 0 - l(t~)sin0, 40 =< ~ =< 37r/2 - 13 where 1(0) = t + 0 - qJo,0o~qL-
3. Collector tube absorptance

"rr/2 + 13-<_0--<3~r/2- 13 t = (2g + g2)1/2, cosOo = 1/(1 + g), sin~Jo = t/(1 + g).

(I)

(If a tangent is d r a w n f r o m the central reflector cusp to the absorbing tube it has length t and subtends the angle 00 at the tube centre.) The m a x i m u m allowable value o f C is (1/sin13)[1 + it - 0o)hr], for which value the tangents to the reflector at the rim cusps x = --- 7rC are vertical. In the limit g ~ 0, 13 ~ ~r/2 we obtain the family I N V . Figure 3 illustrates t h e s e profiles, the l o w e r solid line being WH(35) for C = 1.2. The rim height a b o v e the tube centre, h, and the ratio m/c = (reflector length)/ (tube c i r c u m f e r e n c e ) , for WH(35), WH(60), WH(90) and I N V as a function of c o n c e n t r a t i o n ratio C are g i v e n in Table 1. N o t e that the m a x i m u m permissible values o f C for these reflectors, in the listed order, are 1.808, 1.198, 1.037, 1.000.

E a c h point of the collector tube surface absorbs a fraction a of the incident radiation, independent of the angle of incidence at the tube surface, and reflects a fraction (1 - c~) specularly. The values a = 1.0, 0.92 and 0.85 are considered. (It should be noted that the angle of incidence referred to here is that at the a b s o r b e r surface, not the angle of incidence on the collector aperture.)

4. Reflector reflectance E a c h point o f the reflector surface reflects a fraction p of incident radiation, i n d e p e n d e n t of angle of incidence at the reflector surface, and absorbs a fraction (1 - p). W e report results for p = 1.0, 0.95, 0.85, 0.75, 0.65, 0.10.

5. Latitude W e give results for the three latitudes h = 0 °, 35 ° , 50 ° and ignore any a s y m m e t r y b e t w e e n the northern and southern hemispheres. The assumptions 3 and 4 of angle i n d e p e n d e n c e

197

Reflector designs for stationary tubular solar collectors

N S 1.0

E

0.92

0.85

1.0

W

0.92

0.85 10.0

8.0 1.0

6.0 4.0 I

I

I

I

I

I

I

I

I

I

I ~

/

0.95

10.0~

SI" 8.0

~

6.o 4.0

o

i

I

i

I

t

I

i

I

I

I

i

I

I

/ / ..•___ 8.0

0.8E

l" I

I

I

- 6.0

-

~.

4.0

a

I

6.0

:).7~

4.0 ""

71

l

6.0 ~).6~= I

(

t

I

~

~

"

"

.'1

L

-':'::-=~ 2.0 1.0 ,

i

1.o 1.5

1.o 1.s

~omotric

1.o 1.s

1.o 1.5

conc~tration

J

1.o 1.s

l

,

1.o 1.s

ratio C

Fig. 2. D e p e n d e n c e of the annual energy collection at latitude 35 ° and diffuse fraction 0.3 on the tube spacing for a range o f values o f the reflector reflectance (p) and tube absorptance (a), with orientation NS or EW. Solid c u r v e - - s p e c u l a r family WH(35): Broken curve--diffuse family DIF. The total annual insolation on a horizontal plane is 5.682 GJ m -2.

reduce the problem effectively to a 2-dimensional one. More realistic angle dependent absorptances and reflectances may be included at the cost of greatly increased computing time, but the results are substantially the same. See Table 3 of [6] and also Section 6.

4. YEARLYENERGYCOLLECTIONPER TUBE Let us fix cartesian axes to the collector with X, Y as in Fig. 3 and the Z axis along that of the tube. The yearly energy absorbed from the direct

beam per m 2 of collector aperture is

JB = f K(t)'q(+)dt

(3)

where K(t) = (1 - f)l(0s)sin0sind~. Here 0,~b are the polar angles defining the sun's direction cosines (sin0cosd~, sin0sin~b, cos0) relative to XYZ. These angles and the angle of the sun from zenith, 0s, are functions of the time t which are calculated from sun-earth geometry[5]. -q(~b) is the absorption efficiency for light entering the collector from direction

198

G. H. DERRICKet al. I

35 8.0

6.0

i 4.0

60

I

2.0

I

90

i

- 2.0 ,

i o.o

,

21o

,

4;o

'

6 n.v

x

Fig. 3. Reflector geometry. The curves labelled 35, 60, 90 are Winston-Hinterberger (WH) profiles for these respective half angles of acceptance, with a gap 0.267. INV is the no-gap involute. The lower solid curve represents the WH profile with acceptance half angle 35° truncated at the geometric concentration ratio C = !.2.

0,~b and depends only on ~b. We approximate eqn (3) by

JB = 2x1(0-30) fo < , < 3oK ( t ) d t + 2"q(30-60) f30 < 4>< 60K(t)dt

(4)

+ 2"q(60-90) f60 < ~ < 90K(t)dt, where the factors 2 come from symmetry and ~q(030), ~q(30-60) and 0(60-90) are the mean efficiencies for light incident respectively from the "orange slices" 0 < ~b < 30, 30 < ~b < 60 and 60 < d~ < 90. One obtains a similar expression for the yearly diffuse energy contribution J o as a weighted sum analogous to eqn (4). The total yearly energy collection per m 2 of collector aperture, J = JB + JD, then assumes the form J = c:q(0-30) + c~-q(30-60) + c3-q(60-90).

(5)

The weights c~, C 2 and c3 depend only on the latitude, orientation (NS or EW) and diffuse fraction f , and may be evaluated numerically once and for all since they do not depend on the reflector profile or the tube absorptance et, reflector reflectance p

or concentration ratio C. F o r each of the 6 reflector families and a range of the parameters a , p , C we have calculated the efficiencies -q(0-30), -q(30-60), -q(60-90) by a matrix method adapted from heat transfer theory. The technique is a non-ray tracing one which allows for all multiple reflections from and between the absorbing tubes and the reflector by summing a matrix geometric series. The details of the method are reported elsewhere[6]. We present our data in terms of E = C J, the yearly energy collected per m 2 o f tube selective absorbing surface. The reasons for this choice are given in Section 7 where it is shown that E is more closely related to cost-effectiveness than is J, the annual energy collected p e r m 2 o f aperture. Figure 2 plots E in GJ m 2 (year)- ~ against C for tube absorptances a = 1.0, 0.92, 0.85 and reflector reflectances p = 1.0, 0.95, 0.85, 0.75, 0.65, 0.10 for latitude h = 35 ° and diffuse fractions f = 0.3 for WH(35) (full curves) and D I F (broken curves). The following points may be noted: (1) F o r the specular family WH(35), E W gives better energy collection than NS at higher C values. (2) F o r the diffuse family DIF, NS is better than E W at all C. (3) Too big an aperture actually decreases energy collection in NS orientation for WH(35). (4) F o r realistic absorptances and reflectances the reflectors INV, WH(90), WH(60) yield curves close to those of WH(35), except that they necessarily terminate at the smaller C values 1.0, 1.037, 1.198, respectively. (5) SPC has curves almost indistinguishable from D I F for NS, and inferior to D I F for EW. Points 4 and 5 are illustrated in Figs. 4 and 5. Figure 4 compares E for INV, WH(90), WH(60), WH(35) at latitude 35 ° and diffuse fraction 0.3 for the ideal system (a = 1.0, p = 1.0, upper curves) and a more realistic collector (a = 0.85, p = 0.65, lower curves). While the idealized collectors show some dispersion, the more realistic parameter values yield curves which differ little from one another except when the performance drops as C approaches the limiting values. Energy is then dissipated between excessively high reflector walls, particularly in NS orientation. That these features persist at other parameter values is shown by Fig. 5 which compares the performance of WH(35), WH(60), DIF, SPC for a = 0.85, p = 0.65 at the three latitudes 0 °, 35 °, 50 ° and the three diffuse fractions 0.0, 0.3, 0.5. Contrast the relative performance of D I F and SPC for NS and EW. F o r comparison of rival designs what matters are relative performance figures rather than absolute ones. Nevertheless if one needs an estimate of the annual energy collection but has no detailed weather information the figures presented here give an average figure for a site at the specified latitude. If the total annual insolation incident per square metre of a horizontal plane surface is known then its ratio to the corresponding quantity in our model

Reflector designs for stationary tubular solar collectors

199

Table 1. Reflector parameters for modified involute reflectors

Rim height above tube centre, h

(Reflector length)/(tube circum.), m/c

WH(35)

WH(60)

WH(90)

I.~m

WH(35)

WI-I(60)

~-I(90)

0.6

-1.462

-1.462

-1.462

-1.330

0.650

0.650

0.650

0.687

0.8

-1.017

-0.982

-0.982

-0.806

0.896

0.903

0.903

0.949

1.0

-0.379

0.037

0.149

1.000

1.181

1.286

1.319

1.570

1.2

0.500

3.321

1.525

2.357

1.4

1.740

1.968

1.6

3.653

2.610

1.8

8.471

4.158

I

.

.

.

.

'

*

'

NS

EW 35

8.0

o" lID

6,.0,/

35

e.o

///

]

a

i

_

e

.=

| 1.0

1.5

1.0

1.5

Geometric concentration ratio C Fig. 4. Comparison of the annual energy collection by the Winston-Hinterberger families at latitude 35°, diffuse fraction 0.3, orientation NS or EW. INV denotes the involute family, while the curves labelled 35, 60, 90 correspond respectively to the WH families with these half angles. The upper curves are for the ideal system with tube absorptance a = 1.0 and reflector reflectance p = 1.0, while the lower curves correspond to the more physical values ~t = 0.85, p = 0.65. The total annual insolation on a horizontal plane is 5.682 GJ m -2.

200

G. H. DERRICK et al.

EW

NS 0.0

0.3

0.5

0.0

0.3

0.5 6.0

4.0

0

s'

,llz¢ ~ ~ X X

f

2.0

@ 0 tg m @ ,,Q

I

I

I

I

I

t

',

',

',

1

',

',

@

4.0

I !35

@

E @

2.0

o' m a,

I

I

I

I

I

I

:

:

:

',

:

r,,5

:

i e, e,,

4.0

,<

50

1'.o;.5

11o'1.s

¢.,,'.s

Geometric

1.ol.5

~.o

1.ol.5

concentration ratio C

Fig. 5. Comparison o f the annual energy collection by the Winston-Hinterberger families WH(35) (full curve), WH(60) (dotted curve), the plane diffuse family DIF (broken curve) and the plane specular family SPC (crosses), for different values of latitude (h) and diffuse fraction (f) and orientation (NS or EW). The tube absorptance and reflector reflectance are respectively c~ = 0.85, p = 0.65. The total annual insolation on a horizontal plane is 7.309, 5.682, 4.235 GJ m -2 at h = 0 °, 35 °, 50 ° respectively.

(given with each graph) may be used to rescale all curves.

5. REFLECTOR COST-EFFECTIVENESS

The above graphs together with the relative cost of absorber tubes and reflectors enable us to rank the cost-effectiveness of the various designs. Consider the cost of collecting a fixed amount of energy per year, say 1 GJ. The cost may be divided into tube costs, reflector costs and fixed costs. " T u b e

costs" refers to all costs proportional to the number of tubes and we include the heat transfer fin and connection costs in this category. The reflector costs will be proportional to the reflector area rather than to the aperture area. "Fixed costs" refers to those related to the heat transfer and storage elements of the full system which are not greatly affected by the substitution of one type of collector for another. To collect 1 GJ per year we need an area 1/E m 2 of tube absorbing surface and an area m/c times this amount of reflector. See Table 1. For

Reflector designs for stationary tubular solar collectors

201

(2) Those predictions which hold over a wide range of model parameters are likely to be valid. F o r example, Fig. 2 and similar results at other latitudes indicate that for a planar diffuse reflector, $/(annualGJ) = [ T + ( m / c ) M ] / E (6) energy collection per tube may be increased by about 20% by increasing the tube spacing from C where T is the cost per m 2 of tube absorbing surface = .6 to C = 1.2. This conclusion seems likely to and M the cost per m 2 of reflector. be valid since it holds for the whole range of asLet us illustrate the method for latitude 35 ° for sumptions about reflectivity p, absorptivity a, latthe case a = 0.85, f = 0.30 and the three designs: itude, fraction of diffuse light and collector orienWH(35) in stainless steel, M = $15 to $25 per m 2, tation (NS or EW). p = 0.65; WH(35) in glass and silver, M = $60 per (3) A companion calculation, Mills et al.[9], m2, 9 = 0.85; D I F in Colorbond[7], M = $5 per which includes the glass cover tube, the angle dem 2, p = 0.75. The Sydney tube has an absorbing pendence of et (though not of p), makes an allowarea 0.13 m 2 and will probably cost between $8 and ance for energy losses after absorption, is based on $20 per tube, the former figure being an optimistic local (Sydney, Australia) light data, and employs a estimate for very large scale production. Thus T = more refined angular integration, provides some $60 to $150 per m 2. Figure 1 graphs the $/(annual support for points (1) and (2) above. Typical results GJ) against concentration ratio C for these three of the two calculations are shown together in Fig. competing designs. Clearly the glass-silver WH(35) 6. The dashed curves represent the results of the is eliminated. The best choice is WH(35) in stainless present calculation, from Fig. 2, reduced by 9% to steel in EW orientation with C = 1.1 to 1.5. Next make a rough allowance for the glass cover tube ranks D I F in NS orientation with large C. These are (our ray trace simulations showed this figure to be both cost-effective compared with the no reflector appropriate) and further scaled by the factor 5.84/ option. The curve for the latter is taken as a D I F 5.68 to match the observed figure 5.84 GJ m -2 for with p = 0.1 which corresponds to an average the total annual horizontal insolation in Sydney. weathered tile roof. To have no reflector at all is The full curves represent the results of correspondthus a poor design. ing ray trace calculations[9]. That such disparate We emphasize that the above assessments are models should yield agreement to 2% or better is made on the basis of current prices in Sydney, remarkable. where silver mirrors are relatively expensive, and (4) Simplification can be an advantage. After all, will not necessarily hold e l s e w h e r e - - t h e reader the ideal Winston-Hinterberger reflector profile should insert his own local values for the unit costs. turns out to be useful for collecting sunlight onto a Note also that the present results apply only to tubular absorber even though it is based on a much absorbers of circular cross section. Some results on more extreme simplification of the collecting situthe effect of side mirrors on the performance of fiat ation than has been adopted in the present model. plate absorbers are given by Bannerot and HowThe W H reflector profile is optimal if it is assumed ell[8]. that, not only is there no cover tube and no losses after absorption, but also the absorber and reflector 6. VALIDITY OF THE MODEL are perfect, and the incident light falls with uniform The model is simpler than reality in a number of time averaged radiance within the acceptance half angle of the reflector. The present model attempts ways. (1) The reflectivity p and absorptivity et are as- a compromise between such an extremely simple sumed to be independent of angle of incidence and picture and the full complexity of the real situation, wavelength (and polarization). in the hope of being realistic enough to be predictive (2) Any concentric glass cover tube (to contain and yet simple enough to be comprehensible and a vacuum around the tubular absorber) is omitted rapidly computable; and therefore useful as an aid from the optical calculation. in the design of reflectors for tubular collectors. (3) Only the optical performance is e s t i m a t e d - no allowance is made for energy losses after the 7. INADEQUACY OF EFFICIENCY AS A DESIGN light is absorbed at the surface of the absorber tube. CRITERION (4) The assumptions about the distribution of incident light are unlikely to match any actual local We have chosen to represent collector performlight distribution accurately. ance by the annual energy E collected per square (5) The angular integration over the incident metre of tube surface, rather than the more conhemisphere is rather crude. ventional annual energy per square metre of aperThe following considerations tend to justify the ture, J, a quantity closely related to the efficiency. adoption of a model of such simplicity. Of course J and E are simply related; J = E / C . We (1) Our aim is to predict the r e l a t i v e performance would like to use a cost free performance measure of various reflector configurations, and this is likely which has a closer relationship to the power per to be insensitive to the factors neglected. dollar than has J or efficiency. The power per unit

the purpose of rankings of cost-effectiveness we may ignore the fixed costs and write for the tube + reflector costs per G J/year

G. H. DERRICK et al.

202 .... ,

t

t

i

!

i

!

/

NS

EW

//

/

I

iI

/ill

5.0

JI ll/ i II • 1I / ~ IIt

/ I//

/ / / 1 1 i// II II i/ ,,

4.0

ii/I / t

II

iIJ ! i

I

/

/ I

s

i

(.'1

,' 0 . 6 5

m

/ i

O3 !-

/

.{

/

r.

3.0 ~ ; '

/

,I

I

I i t I I /

Q,

/

,

/

I

i

iI

Ii

// I

I

,"0.65

J

I

/11

/I

eI I

I ii

/

ii I

/

iI ,

/~'

/

/

/

I

i

,

J

1.0

,

l

,

I

i

_l

t

1.5 Geometric

1.0 concentration

ratio

1.5 C

Fig. 6. Comparison of the ray trace results for Sydney light data, ambient temperature (full curves) and results of the present calculations (dashed curves) for the two values of the reflector reflectance, O = 0.85 (upper curves) and p = 0.65 (lower curves). The dashed curves are for latitude 35 °, diffuse fraction 0.3 and tube absorptance a = 0.85 (the hemispherical average of the angle-dependent a of [9]). They correspond to the results of Fig. 2, reduced by 9% to allow for the cover tube and scaled by (5.84/5.68) to match Sydney's observed annual total horizontal insolation.

area of tube is such a measure. Of the three elements, tube, mirror and aperture, it is the tube which dominates the cost. It must be admitted that where space is at a premium high efficiency can be essential. However efficiency is still not a suitable quantity to maximize; optical efficiency is always maximized by placing the tubes as close as possible together, an arrangement which obviously does not maximize the power per dollar if the tubes are expensive.

8. VALIDITY OF THE COMPUTER PROGRAMS

The computer program proved correct in two cases where an analytic result is available (a) A plane (imperfect) specular reflector and a perfect absorber (for given geometry) (b) A perfect specular WH reflector and an imperfect absorber. Again, where the companion program[9] was specialized so that its model of the physical situation agreed with that of the present program, the results were concordant (to 1 or 2%).

Reflector designs for stationary tubular solar collectors REFERENCES

1. R. Winston and H. Hinterberger. Solar Energy 17, 255 (1975). 2. R. Winston. Applied Optics 17, 1668 (1978). 3. I. M. Bassett and G. H. Derrick, Optical and Quantum Electronics 10, 61 (1978). 4. H. C. Hottel. Solar Energy 18, 129 (1976). 5. W. T. Welford and R. Winston, The Optics of NonImaging Concentrators, Section 8.2. Academic Press, New York (1978).

203

6. G. H. Derrick and I. M. Bassett, Optica Acta 32, 937 (1985). 7. ®, John Lysaght (Australia) Ltd., Sydney, Australia. Colorbond is a proprietary white baked enamel on a metal substrate and is predominantly diffusely reflecting. 8. R. B. Bannerot and J. R. Howell. Solar Energy 19, 549 (1977). 9. D. R. Mills, I. M. Bassett and G. H. Derrick. Solar Energy, (in press).