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Proceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement

592

the emerging rays, an appropriate area near the top of the

paraboloid has to be truncated away so that the light can go

through it. Another way to make a multiplier is to add a

Fresnel prism below the focus F and let its focus on the

point F, as showed in Fig. 4.

Fig. 4: Combined with the Fresnel.

Of course, the concentrator can be combined with other

optical devices when it is used in other purposes. And the

concentrator can be made to be a trough shape one that has

a linear focus.

6. ACKNOWLEDGEMENT

This work is supported by the Natural Scientific

Foundation of China (No. 50576004)

7. REFERENCES

(1) Harald Ries and Jeffrey M. Gordon. Double-tailored

Imaging Concentrators. SPIE Vol. 3781•0277-786X/99/

P.129-134.

(2) Julio Chaves, Manuel Collares-Pereira. New Ideas For

New Solar Concentrators. SPIE Vol. 3781•0277-

786X/99/ P.174-182.

A NEW APPROACH OF THE COLLECTOR AREA IN SOLAR

COLLECTOR TESTING STANDARDS

V. Belessiotis, E. Mathioulakis, G. Panaras

Solar & Other Energy Systems Laboratory - NCSR “DEMOKRITOS”

15310 Agia Paraskevi Attikis – Greece

E-mail: sollab@ipta.demokritos.gr

ABSTRACT

A new approach as regards the presentation of a solar

collector’s characteristic equation and efficiency curve is

described. The proposed approach is based on the

introduction of an effective collector area which is

independent from the geometrical characteristics of the

collector. Based on this new area, two alternative

presentations are examined, whether the collector

performance is presented in terms of energy output or

efficiency. Through the proposed approach, the presentation

of results is simplified to a great extent, based on quantities

objectively measured, thus avoiding the possibility of

results misinterpretation or misuse through subjective

approaches.

1. INTRODUCTION

Nowadays, it is widely accepted that the penetration of

RES depends to a great extent to the trust potential users

would show to the reliability, as well as to the expected

energy output of the products. Focusing on the field of solar

thermal energy, one might observe, during the last years,

intense activities related to the mechanisms of products

quality verification, i.e. testing of products and certification

schemes (Nielsen, 2001). In order for the testing standards

to be in compliance to their role, they have to be based on

scientifically sound models for the product behavior. In

addition, results have to be clearly expressed, thus not

allowing potential misinterpretation.

In the case of solar thermal collectors testing standards, the

energy identity of a collector is described through its

characteristic equation, which provides the instantaneous

efficiency n as a function of the operation conditions (ISO,

1994; CEN, 2006). The issue arising with this approach

refers to the dependence of the collector’s efficiency to the

reference area for the calculation of the incident solar

radiation. If someone considers the fact that every collector

is characterized by three different surfaces (gross, aperture

and absorber area), and that the standard requires

presentation of the efficiency in terms of the temperature in

the inlet of the collector, as well as in terms of the mean

collector temperature, current approach results to six

different energy identities of the same product. In addition,

for some types of collector it is impossible or very difficult

to measure with certainty some of the above mentioned

surfaces. This situation might lead the future users to some

kind of confusion. In addition, and that is the most

important, it allows a situation of results misinterpretation,

especially in cases of energy performance comparison of

different collectors, as well as during the design of solar

thermal energy installations.

The scope of present work is to propose a new approach as

regards the presentation of the characteristic equation and

efficiency curve of a solar thermal collector. Through this

approach, presentation of results is significantly simplified,

while at the same time eventual misinterpretations related

to subjective approach of the used surface are avoided.

Proceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement

594

2. PRESENT SITUATION

The basic target of solar collector testing is the

determination of the collector efficiency by measurements

under specific conditions (Duffie and Beckman, 1991). It is

noted that several models and testing methods have been

proposed by various authors (Perers, 1997). However this

study would concentrate to the testing method defined in

Standard ISO 9806-1, since this method is, at present, the

only acceptable and standardized in an international level.

According this method, the behavior of the collector can be

described by a 2 or 3-parameter single node, steady state

model n=f (

T ):

nn UT=−

()

nn UT UGT=− − (1)

where

()mC T T

AG AG

−



(2)

The above Eq. (1) as well as the whole analysis presented

in this paper are also valid for reduced temperature

difference

calculated with respect to the mean

collector fluid temperature. In this case the variable

where it appears, must be replaced by

. During the

experimental phase of the test, the output, solar energy and

the basic climatic quantities are measured. During data

analysis, a least square fitting of the model equation is

performed on the measured data, in order to determine

parameters n

and U

or n

, U

and U

As resulting from Eq. (2), the values of the characteristic

equation parameters, as well as the respective efficiency

curves, are strongly dependent to the reference area which

would be selected for the calculations. Moreover it is

possible some confusion to take place, due to the high

number of equations and curves used for the description of

the energy identity of the solar collector. The ISO standard

defines as reference areas the gross area A

and the absorber

area A

, while the respective European Standard defines as

references areas the aperture area Aa and the absorber area

. Through the approach of ISO, the energy performance

of a solar collector is described with 8 equations and 8

curves, combining two surfaces (A

και A

), two

temperatures (

T και T ) and two types of equations (2

and 3-parameter). Taking into account both the ISO and the

EN standard, and despite the fact that they refer to the same

collector model, a total number of 12 equations and 12

efficiency curves result.

Another problem is related to the definition of the reference

area for some types of collectors, which is uncertain and at

the same time different for the two standards, pointing out

the definition of absorber area in the case of collectors with

dewar-type tubes and reflectors.

More specifically, according to the EN standard, absorber

area is equal to the projection of the actual absorber surface

to the collector plane, in other words A

=N×L×D, where Ν,

L and D refer respectively to the number, length and

diameter of the tubes. On the other hand, according to the

ISO standard, the absorber area equals the“…surface area

of the absorber which is designed to absorb solar

radiation…”, that is A

=N×L×π×D. In Fig. 1, the effects of

the surface area definition are clearly depicted through the

comparison of the results of a typical flat-plate collector, a

collector with multiple dewar-type tubes and reflector and a

single vacuum tube collector.

0,5

1,5

2,5

0 0,04 0,08 0,12

T* [Km

w ]

MT-EN

MT-ISO

ST-EN

ST-ISO

FP-EN+ISO

Fig. 1: Efficiency curves for a typical plat-plate collector

(FP), a multi-vacuum-tube collector with reflectors

(MT) and a single-vacuum-tube collector with

reflector (ST). Results are presented according to

both EN and ISO standards considering the

absorber area as reference area.

[Km w ]

3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS

595

On the opposite to the flat-plate collector, presenting the

same results for both standards, the tube collectors present

major deviations with regard to the adopted reference area

definition. One should also note that the results of the EN

approach present efficiencies significantly greater than one.

For some types of collectors, as vacuum tube collectors, the

determination of aperture and absorber area is not possible

to be achieved on an objective basis, at least without

destructing the collector. Typical is the case of dewar type

collectors.

3. USER-ORIENTED PERFORMANCE INDICATORS

WITHOUT USE OF REFERENCE AREA

With regard to the energy performance of the collector, the

user is actually concerned for the useful energy that a

specific collector would produce for specific operation/use

conditions. From this point of view, the characteristic curve

of the collector can be presented as following for a

3-parameter model, without any explicit reference to the

surface A (a similar analysis is possible for the 2-parameter

model):

()

)(

TGAUTAUAn

TTCm

−−=

−



(3)

()

TGPTPS

−−=

(4)

where quantities

=An

, P

i,o

=AU

, P

i,1

=AU

, P

i,2

=AU

(5)

are characteristic constants of the collector.

During the test, the collector is supplied with fluid of

controlled temperature and variables

, G and

are

measured over a range of inlet temperatures. Following, a

least square fitting of the model equation is performed on

the measured data, in order to determine parameters S

, P

i,1

and P

i,2

. Through the examination of Eq. (4) it results that

constant S has surface units. This constant could be

considered as the area the collector would have for

presenting the maximum theoretical performance. An

additional alternative presentation, on the basis of the

reference area S, can be obtained through the division of

both parts of Eq. (4) with S:

()

iiii

TGaTa

−−=

(6)

where

1,i

a =

και

2,i

a =

In this case, one could use the quantity S as the reference

area for presenting the efficiency of the collector. The use

of this reference area, in parallel to the conventional areas

(aperture, absorber, gross) has already been proposed

(Fischer et al., 2002). This solution though can lead to

greater confusion, as it adds an extra area, which even

more does not have physical substance. Thus, the solution

proposed is to use only the reference area, either in terms

of energy output (Eq. 4), or in terms of energy efficiency

(Eq. 6).

4. IMPLEMENTATION TO EXPERIMENTAL TEST

RESULTS

Following, the results of real tests of 3 typical commercial

collectors are presented. The analysis of results has been

based on the basic aforementioned approaches. The

characteristics of the collectors used are the following:

A typical flat-plate collector with selective absorber surface,

presenting absorber area of 2.05 m

A collector with 12 vacuum tubes and reflector. Tubes are

of dewar-type with absorbing glass tube diameter of

0.033 m and 1.45 m length (selective coating).

A collector consisting of a vacuum tube of 0.15m diameter,

absorbing glass tube diameter of 0.12 m and 1.47 m length

(selective coating).

In Table 1, the coefficients of the characteristic curve are

presented for each approach, on absorber area basis

(3-parameter model), while Figs. 2, 3 and 4 present the

respective efficiency curves. It has to be noted that for the

calculation of the absorber area for the tube collectors the

ISO approach has been selected.

Proceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement

596

TABLE 1: EFFICIENCY TEST RESULTS FOR DIFFER-

ENT TYPES OF COLLECTORS AND DIFFERENT

CALCULATION APPROACHES

Efficiency

approach (Eq. 1)

Alternative ref. area

(Eq. 6)

Wm K

2,i

Wm K

Flat-plate

selective

0.76

3.72

0.019 1.57 4.87 0.025

Dewar-type

tubes,

reflector

0.42 0.57 0.012 1.14 1.39 0.029

Single vacuum

tube, reflector

0.66 2.49 0.014 0.37 3.77 0.021

Useful energy approach (Eq. 4)

1,i

2,i

Flat-plate selective

collector

1.57 7.64 0.039

Dewar-type tubes,

reflector

1.14 1.58 0.034

Single vacuum tube,

reflector

0.37 1.41 0.008

0,2

0,4

0,6

0,8

0 0,02 0,04 0,06 0,08 0,1 0,12

Ti* [Km w ]

Flate plate

Multiple tubes

Single tube

Fig. 2: Efficiency curves for different types of collectors,

according to ISO standard, with the absorber area as

reference area.

0,2

0,4

0,6

0,8

0 0,03 0,06 0,09 0,12

Ti* [Km

-1

]

Qu/(GS )

Flate plate

Multiple tubes

Single tube

Fig. 3: Efficiency curves for different types of collectors,

using alternative reference area (Eq. (6)).

0,4

0,8

1,2

1,6

0 0 ,03 0,06 0,09 0,1 2

Ti* [Km w ]

Qu/G [m ]

Flate plate

Multiple tubes

Single tube

Fig. 4: Useful energy curves for different types of

collectors (Eq. (4)).

5. CONCLUSIONS

Standardized methods for the estimation of actual energy

performance of solar thermal collectors present nowadays a

useful tool, not only for the manufacturer who wants to

have detailed knowledge of his product, in order to improve

it, but for the future user as well, who needs to know the

actual energy efficiency achieved by his investment.

Standardized methods are also considered the keystone of

the certification schemes and of any actions that aim to

support the penetration of solar thermal products in the

market. Basic conditions for the effectiveness of the used

testing methods refer to reliability, explicitness and

avoidance of misinterpretations that would affect their

general acceptance by all interesting parties. Proposed

[Km w ]

[m ]

/(GS )

3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS

597

approach for the presentation of testing results gives a clear

answer to the ambiguous points that have been emerged

during last years, mainly due to the appearance in the

market of new design concepts for collectors, for which the

used approaches have not anticipated satisfying answers.

6. NOMENCLATURE

A, S

Surface [m]

1,i

Coefficient [Wm

-1

]

2,i

Coefficient [Wm

-2

]

Cp Specific heat [JK

-1

]

G Solar radiation [Wm

-2

]



Mass flow-rate [kgs

-1

]

Maximum efficiency [-]

1,i

Coefficient [WK

-1

]

2,i

Coefficient [WK

-2

]

Useful energy [W]

T Temperature [K]

T* Reduced temperature [Km

-1

]

7. REFERENCES

(1) CEN (2006), EN 12975-1: Thermal solar systems and

components - Collectors - Part 1: General requirements,

CEN ed., Brussels

(2) CEN (2006), EN 12975-2: Thermal solar systems and

components - Collectors - Part 1: Test Methods, CEN

ed., Brussels

(3) Duffie J.A. and Beckman W.A. (1991), Solar

engineering of thermal processes, 2nd edn, Willey, New

York.

(4) Fischer S, Heidemann W. and Muller-Steinhagen H.

(2002), The definition of an alternative reference area

for representation of collector efficiency, Eurosun

Conference, Bologna, Italy

(5) ISO (1994), Standard 9806-1. Test methods for solar

collectors - Part 1: Thermal performance of liquid

heating collectors including pressure drop, ISO ed.,

Switzerland

(6) Klein S., Duffie J.A. and Beckman W.A (1974),

Transient considerations of flat-plate solar collectors,

Journal of Engineering for Power, pp 109-113

(7) Nielsen, J.E. (2001), CEN Certification of Solar

Thermal Products: The Solar Keymark, ISES

Conference 2001, Adelaide, Australia

(8) Mathioulakis E., Voropoulos Κ., Belessiotis V. (1999),

Assessment of uncertainty in solar collector modelling

and testing, Solar Energy, Vol. 66(5), pp.337-347

CONVECTIVE HEAT TRANSFER FROM EXPOSED FLAT HORIZONTAL

SURFACE IN OUTDOORCONDITIONS AT LOW WIND SPEEDS: AN APPLICATION TO

FLAT PLATE SOLAR COLLECTOR

Suresh Kumar

Centre for Energy Studies,

Indian Institute of Technology, Delhi

Hauz khas, New Delhi- 110016, India

skjesm@yahoo.co.in

S. C. Mullick

Centre for Energy Studies,

Indian Institute of Technology, Delhi

Hauz khas, New Delhi- 110016, India

subhash_cmullick@yahoo.com

ABSTRACT

Estimation of various heat losses in flat plate solar

collectors is important for their thermal performance

evaluation under different operating conditions. Upward

heat losses have a major contribution in the total heat losses

in flat plate collectors (FPC). Equations for estimation of

top heat loss coefficient for single and double glazed FPC

have already been proposed [1-2]. Top heat loss coefficient

is a function of wind heat transfer coefficient. Different

forced convection studies [3-6] conducted in indoor and

outdoor conditions have been reported for estimation of

wind heat transfer coefficient. At sites/locations with very

low wind, use of different velocity based correlations [3-6]

would give a wrong estimation of wind heat transfer

coefficient. In present work wind heat transfer coefficient is

estimated by employing an exposed blackened test plate (of

size 925mm x 865mm x 2mm) in outdoor conditions.

Experiments have been conducted on rooftop of a building

in IIT Delhi. Delhi, in general, has low wind throughout the

year [9]. From experimental data of test plate, mixed

convection effects have been observed at very low wind

speeds.

1. INTRODUCTION

Estimation/measurement of various heat losses in flat plate

solar collectors is important for design and thermal

performance evaluation of these collectors under different

operating conditions. The major part of overall heat loss

factor is top heat loss factor. Detailed equations for

estimation of upward heat losses for single glazed and

double glazed FPC have already been proposed [1-2]. Top

heat loss coefficient is a function of wind induced

convective heat transfer from upper outermost surface of a

solar collector. It becomes necessary to choose appropriate

values of wind induced convective heat transfer coefficient

in order to minimize error in computed values of top heat

loss coefficient in FPC.

Solar collectors are always exposed to natural environment

for solar thermal applications. The convective heat transfer

from the upper outer most cover a flat plate collector is

influenced by wind flowing over the surface of a collector.

High wind speeds results in forced convection and at times

when there is low wind or no wind; heat transfer could be

by mixed convection/natural convection. Different forced

convection studies have been reported in literature for

estimation of wind induced heat transfer coefficient [3-6].

These studies predict different values of wind heat transfer

coefficient at same wind speed. Different experimental

conditions and different sizes of plates used for

experiments may be responsible for differences between

these studies. Also at sites/locations with low wind, the

results of forced convection studies [3-6] if used would

give wrong estimation of wind induced heat transfer

coefficient. Duffie and Beckman [7] have quoted that

3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS

599

free convection data for hot inclined plates facing upward

are not available. They have reported that at very low wind

speeds, wind induced convective heat transfer coefficient

can be estimated by using a correlation between Nusselt

number and Rayleigh number for flat horizontal plates[8].

In the present study, an exposed blackened test plate (of

size 925mm x 865mm x 2mm) has been employed in

outdoor conditions for measurement of wind induced

convective heat transfer coefficient. The experimental site

is on the rooftop of a building in premises of IIT Delhi.

Delhi is situated in plain terrains of northern part of India

which is a low wind region [9]. Therefore Delhi, in general,

has low wind over major parts of year except monsoon

season when wind speeds are comparatively higher. Present

study was conducted in the months of December and

January and very low wind speeds were observed during

experimental runs.

2. EXPERIMENTAL SET UP

The outermost cover of a flat plate collector is represented

by black painted aluminum test plate (2mm thick) having

dimensions 0.92m x 0.86 m. At the bottom of unglazed

aluminum test plate, a composite slab consisting of 3mm

thick asbestos sheet, 50 mm thick fibre glass wool slab and

45 mm thick thermocole slab were fixed, to reduce the

bottom heat losses(Composite slabs were made slightly

larger as compared to aluminum test plate, so as to reduce

the side heat loss). Temperatures at different points were

measured with the help of calibrated Chromel Alumel

thermocouples. Three thermocouples were fixed at the

center of test plate assembly at different locations for the

measurement of test plate temperature, insulation top

temperature and insulation bottom temperature. A three cup

anemometer of G. Lufft make (kept beside the plate) was

used for the measurement of the wind speed. The

anemometer used was sensitive enough to respond to wind

gusts of short duration (in seconds). The anemometer cup

was kept a level of 150 mm higher than top surface of test

plate. Solar radiation was measured with the help of a

pyranometer. Solar radiation and ambient temperature were

measured at the site of experiments.

The prepared test plate was exposed to solar radiation for

the determination of wind heat transfer coefficient. The

test plate temperature, insulation top temperature,

insulation bottom temperature, ambient temperature, wind

speed and solar radiation were recorded at an interval of 1

second on different days by using data-logger. The

observed data was averaged over a time period of ten

minutes for calculation of wind heat transfer coefficient by

applying heat balance for test plate. Each ten minutes

corresponds to one data point.

= 0.45

0.00 0.08 0.16 0.24 0.32 0.40

V (m/s)

( W/m

-K)

Fig. 1: Plot of wind heat transfer coefficient at different

wind speed.

3. HEAT BALANCE FOR UNGLAZED TEST PLATE

The wind heat loss coefficient was calculated by applying

heat balance for the test plate. Heat balance for the test

plate is given by

= Q"

+Q"

(1)

Where,

= αI (2)

And

= k(T

-T

)/t

(3)

Radiation heat exchange flux between test plate and

external environment is found as

= σ ε

- T

) (4)

V=0to0.37m/s

Proceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement

600

Swinbank correlation [10] is used for estimation of

effective black body sky temperature

= 0.0552(T

)

1.5

(5)

Now,

= m c

dT/dt (6)

where, dt = Time interval during which test plate

temperature rises by an amount dT.

Now wind heat loss coefficient is given by

= Q"

/(T

-T

) (7)

The experimental data used in the calculation of h

is that

for one and half hours at around solar noon where the

conditions are close to steady state.

4. RESULTS AND DISCUSSIONS

In present study it has been observed that the average

values of wind speed obtained at the site of experiments (on

different days) were in the range 0 to 0.37 m/s.

It is noted that for unglazed test plate, variation in values of

wind heat loss coefficient could be due to both wind

speed and temperature difference (between test plate

temperature and ambient temperature) at low values of

wind speed (0 to 0.37m/s). The experimental results are

presented in Fig. 1 and Fig. 2.

Chen et al. [11] has reported that Nusselt number in mixed

convection can be correlated by combining the Nusselt

number for pure forced convection and Nusselt number for

pure natural convection in an equation of the form

= Nu

+ Nu

(8)

Where, n is a constant exponent.

Equation (8) can be written as

/ Nu

= 1+ Nu

(9)

= 0.27

21 22 23 24 25 26 27 28 29 30 31 32 33

-T

) K

( W/m

-K)

Fig 2: Variation of wind heat transfer coefficient with

temperature difference.

In the present study from experimental data of unglazed

test plate, values of Reynolds number were calculated

and found to be less than 2.1 x 10

. By using these values

of Reynolds number, values of Nu

were calculated from

the laminar forced convection correlation for flat

horizontal plate[12] given as

= 0.664 Re

1/2

1/3

(10)

For all experimental runs, values of Rayleigh number were

calculated and found to be varying from 1.5x10

2.03x10

. Now, the values of Nu

were calculated by

using turbulent natural convection correlation for flat

horizontal plate [13] given as

= 0.14Ra

1/3

for 2x10

< Ra

<3x10

(11)

The values of Nu

have been calculated by using the

experimental values of h

for unglazed test plate.

Linear regression plot between Nu

/ Nu

and Nu

has been made and a value of R

equal to 0.99 has

been obtained as shown in Fig. 3. It indicates strong

presence of mixed convection phenomenon at very low

values of wind speed (less than 0.4 m/s). Therefore, at very

low values of wind speed as observed in present study, the

convective heat transfer from upper outermost surface of a

flat plate collector cannot be well treated by forced

convection or natural convection alone.

V=0 to 0.37m/s

3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS

601

Fig. 3: Plot of Nu

/ Nu

against Nu

5. NOMENCLATURE

= plate area(m

)

= specific heat of aluminium plate(J/kg-K)

= wind heat transfer coefficient(W/m

.K)

I = solar radiation (W/m

)

k = thermal conductivity of plate(W/m.k)

m = mass of plate per unit area(kg/m

)

L = length of unglazed test plate (m)

= average Nusselt number for pure forced convection

based on L

= average Nusselt number for pure free convection

based on L

= average Nusselt number for mixed convection based

on L

= rate of heat absorbed by test plate per unit area

(W/m

)

= rate of heat loss through insulation by conduction per

unit area (W/m

)

= rate of convective heat loss per unit area of test plate

(W/m

)

= rate of radiative heat loss per unit area of test plate

(W/m

)

= rate of sensible heat absorbed to raise temperature of

test plate per unit area (W/m

)

= Rayleigh number based on L

= Reynolds number based on L

= ambient temperature (K)

= thickness of insulation(m)

= test plate temperature (K)

= insulation top temperature (K)

= insulation bottom temperature (K)

= thickness of plate(m)

= effective black body sky temperature (K)

V= wind speed (m/s)

α = absorptivity of plate =0.9

= emissivity of plate= 0.9

6. REFERENCES

(1) S.C. Mullick and S. K Samdarshi, “An improved

technique for computing the top heat loss factor of a

flat plate collector with a single glazing”, ASME J.

Solar Energy Engg., vol. 110, 1988, p. 262-267.

(2) S.K Samdarshi, S.C. Mullick, “Analytical equation for

the top heat loss factor of a flat plate collector with

double glazing”, ASME J. Solar Energy Engg. Vol. 113,

1991, p. 117-122.

(3) W. H. McAdams, “ Heat Transmission”, 3

edition,

McGraw-Hill, 1954, New York.

(4) J.H. Wattmuff, W.W.S. Charters and D.Proctor, “Solar

and wind induced external coefficients for solar

collectors”, Int. revue d’ Hellio-technique 2, 1977, pp.

56.

(5) F. L. Test, R. C. L. Lessman and A. Johary, Heat

transfer during wind flow over rectangular bodies in

natural environment. ASME J. Heat Transfer, 103, 1981,

p. 262-267.

(6) Subodh Kumar, V. B. Sharma, T.C. Kandpal, and S.C.

Mullick, “Wind induced heat losses from outer cover of

solar collectors”, Renewable Energy, vol.10, no.4, 1997,

p. 613-616.

(7) J.A. Duffie, W. A. Beckman, Solar Engineering of

Thermal Processes, 2

edition, 1991, Wiley Interscience,

New York.

(8) J.R. Lloyd and W. P. Moran, “Natural Convection

Adjacent to Horizontal Surface of Various Planforms”,

ASME J. Heat Transfer 96, 1974, p .443 .

(9) Mani, Anna, “Wind Energy: Resource Survey in India

III”, 1994, Allied Publisher, New Delhi.

(10) W.C. Swinbank, “Long-wave radiation from clear

skies”, Quarterly J. Royal Metrological Soc. 89, 1963,

p. 339.

(11) T. S. Chen, B. F. Armaly and N. Ramachandran,

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