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

722

Having obtained such a function we can use it further for

mathematical modelling. This function will definitely

contain some solar collector’s para¬meters, such as, e.g.,

the thickness of the absorber’s plate and the distance

between the tubes (which are ideally connected by

soldering to the absorber), the tube diameter, etc.; by

varying these parameters in our mathematical model we

can calculate the most optimal temperature condition in the

absorber, making it possible to abandon a huge

time-consuming and expensive experimental work for

determination of the heat transfer from the absorber’s plate

to the heat carrier flowing through the tube [1].

The paper presents the mathematical description for the

heat conduction on the plane surface of a solar collector’s

absorber (further in the text absorber). The collector plate’s

cross-section is considered that is perpendicular to the axis

of a tube with liquid. The cross-section is conditionally

divided into three parts. Having chosen one of them, we

will attach to it a corresponding coordinate system.

The temperature [K] on the plate (the O

ABC section) is

designated with T

(x, z), the temperature in the cylindrical

coating – with T

(r, φ), and the temperature of the liquid –

with T

(r, φ).

2. TEMPERATURE FIELD IN COLLECTOR ABS-

ORBER

2.1 The Temperature Field in the Plate Between Tubes

Assuming that the process is stationary, the temperature

field in the O

ABC section in the Descartes coordinate

system O

xz with O

as the initial point is described by the

Laplace equation [4]:

∂

(1)

Fig. 1: Absorber cross-section.

We will introduce dimensionless variables and parameters

[5], the dimensionless temperatures will be described by

the formulae:

=Θ

;

=Θ

;

=Θ

(2)

where T

is the initial temperature, K;

and the dimensionless coordinates and parameters – with

the formulae:

=ξ

;

=ς

()

10 ≤≤ ς

;

−

=ξ

;

=ρ

()

10 ≤≤ ς

;

1>=

;

=η

;

(3)

(4)

(5)

where

λ is the heat conductivity of the collector plate, W/m

q is the density of the solar heat flow, W/m

;

h is the plate’s thickness, m.

2b is the distance between the tubes’ axes, m;

is the inner radius of a tube, m.

The Laplace equation and boundary conditions in the

dimensionless form will be:

∂

Θ∂

∂

Θ∂

ςξ

;

()

∂

Θ∂

ξ 1,

;

()

∂

Θ∂

;

()

∂

Θ∂

;

()

ςξ

Q−=

∂

Θ∂

(6)

(7)

(8)

(9)

(10)

The solution to the problems (6)-(7) is

()

, +−=Θ ςξςξ

(11)

3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS

723

2.2 The Temperature Field in the Tube’S Coating

To describe the temperature fiel d in a tube’s coating we

choose a system of polar coordinates with O as the initial

point and write Laplace’s equation in the polar coordinates

assuming that the process is stationary [7]:

∂

⎟

⎠

⎞

⎜

⎝

⎛

∂

(12)

The Laplace equation and boundary conditions are written

in the dimensionless form:

∂

Θ∂

⎟

⎠

⎞

⎜

⎝

⎛

∂

Θ∂

∂

ϕρ

ρρ

;

()

∂

Θ∂

ϕρ ,

()

ϕπϕϕ −≤≤

;

()

∂

Θ∂

ϕρ

()

2 ϕπϕϕπ −≤≤+

;

()

ϕρς ,, Θ=

⎟

⎠

⎞

⎜

⎝

⎛

−

()

ϕπϕϕπ +≤≤−

;

()

ϕρ

,, Θ

∂

⎟

⎠

⎞

⎜

⎝

⎛

−

∂

()

ϕπϕϕπ +≤≤−

(13)

(14)

(15)

(16)

(17)

Applying the Fourier method of separation of variables [8]

one obtains:

()

⎟

⎠

⎞

⎜

⎝

⎛

−

⎟

⎠

⎞

⎜

⎝

⎛

∑

++=Θ

cosln,

ρρϕρ k

ABA

(18)

where k is a positive integer.

⎟

⎠

⎞

⎜

⎝

⎛

−++−=

QBA

ln1 ρ

. (19)

⎟

⎠

⎞

⎜

⎝

⎛

−−−=

sin

2sin

ϕϕϕ

(20)

⎥

⎦

⎤

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛

−++=

2sin

cos

ϕϕϕ

QQA

;

(21)

⎥

⎦

⎤

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛

−+−=

2sin

cos

ϕϕϕρ

ρ QQB

;

(22)

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛

++=

4sin

2sin

ϕϕϕ

πρ h

⎥

⎦

⎤

−+

⎟

⎠

⎞

⎜

⎝

⎛

sin3sin

ϕϕ

; (23)

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛

++−=

4sin

2sin

ϕϕϕ

⎥

⎦

⎤

+−

⎟

⎠

⎞

⎜

⎝

⎛

sin3sin

ϕϕ

; (24)

() () ()

−

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛

−

2sin

cos

2/sin

ϕϕ

ϕπ

cos1

−

b π

() ()

−

⎟

⎠

⎞

⎜

⎝

⎛

−

1sin

sin

ϕϕ

() ()

⎥

⎦

⎤

⎟

⎠

⎞

⎜

⎝

⎛

−

1sin

cos

ϕϕ

; (25)

AB ρ−=

. (26)

2.3 The Temperature Field in the Liquid

The temperature field of the liquid flowing in a tube is

described by the following equation [4, 5, 7, 9]:

c ∇= λ

(27)

The Laplacian in a system of cylindrical coordinates is:

∂

⎟

⎠

⎞

⎜

⎝

⎛

∂

=∇

(28)

Equation (27) in cylindrical coordinates is expressed as

λ=

∂

⎥

⎦

⎤

⎢

⎣

⎡

∂

⎟

⎠

⎞

⎜

⎝

⎛

∂

. (29)

In conformity with Newton’s law, on the contact surface

between the tube and the liquid (r= r

) the following

equality holds:

()

−−=

∂

αλ

(30)

where α is the coefficient of convective heat transfer on the

surface, W/m

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

724

At the fixed points of the tube y = 0 and y = y

we will

determine the temperature as

()

0,, TrT =φ

;

()

,, TyrT =φ

(31)

Having passed in Eq. (29) and boundary conditions (30),

(31) to dimensionless variables (2)–(5), we obtain:

ηϕρ

ρρ

∂

Θ∂

∂

Θ∂

∂

Θ∂

∂

Θ∂

∂

Θ∂

;

()

Θ−Θ−=

∂

Θ∂

;

()

0,, Θ=Θ ϕρ

()

,, Θ=Θ ηϕρ

(32)

(33)

(34)

In order to solve the problem (32)–(34), function is

divided to the components [6, 10]:

()

ηφρηφρηφρηφρ ,,,,,,,, Θ+Θ+Θ=Θ

(35)

each of them satisfying Eq. (32) and the following

boundary conditions:

()

Θ−Θ−=

∂

Θ∂

;

()

00,, =Θ ϕρ

()

0,, =Θ ηϕρ

;

()

0,,1 =Θ ηϕ

;

()

,, Θ=Θ ηϕρ

()

00,, =Θ ϕρ

;

()

0,,1 =Θ ηϕ

(36)

(37)

(38)

(39)

(40)

()

0,, Θ=Θ ϕρ

()

0,, =Θ ηϕρ

(41)

By Fourier’s method of separation of variables [10], using

boundary conditions (37) one obtains:

()

+=Θ

∑

ρμηφρ sin,,

ICe

()

ρμ

φ sin

cos

IkCe

∑∑

⎟

⎠

⎞

⎜

⎝

⎛

−+

(42)

By Fourier’s method of separation of variables [10–12],

using boundary conditions (38) and (39) we obtain:

()

∑

=Θ ηβρμηϕρ shJCe,,

()

ηβρμ

ϕ shJkCe

∑⎟

⎠

⎞

⎜

⎝

⎛

−

∑

cos

(43)

the same manner as it was done for the second component,

we derive:

()

)(

2,,

ρμ

ηβ

ηηβ

ηϕρ

∑

−

=Θ

(44)

3. NOMENCLATURE

The calculations show that in the function describing the

temperature field in the plate section O

ABC (11) the

temperature is directly proportional to the solar energy

density q, which could be expected since the greater the

energy density the greater the temperature in the solar

collector. The plate thickness is inversely proportional to

the temperature, which means that the smaller the plate

thickness the greater the temperature in the plate; however,

if we decrease the plate thickness the angle φ will be

smaller, which means smaller heat flow on chord BC –

the main way through which the heat is flowing from the

plate to the tube’s coating and further to the liquid in this

tube. Considering the temperature function (11) it can be

concluded that the smaller distance b between tubes the

greater the temperature in the plate; this, however,

reduces the area irradiated by sun rays, which would

mean that the collector is more inertial. Even such

simple reasoning about the collector’s parameters allows

for the conclusion that the mathematical description

presented here can help to find the optimal sizes for the

absorber, which, taken for the whole collector, would

provide its maximum efficiency [2,3].

3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS

725

4. REFERENCES

(1) Shipkovs P., Esbensen T., Kashkarova G., Lebedeva K.,

Shipkovs J. Solar energy use in Latvian conditions.

North Sun Conference 2005, Vilnius, Lithaunia, May

25-27, 2005, CD

(2) Shipkovs P., Kashkarova G., Lebedeva K., Shipkovs J.

Prespectives for solar termal energy in Baltic states.

Solar World Congress 2005, Orlando, Florida, USA,

August 8–12, 2005, CD.

(3) Shipkovs P., Kashkarova G. Solar Termal Systems for

Energy Conservation in Latvia. Proceedings of the

International Conference EUROSUN 2002, the Fourth

ISES Congress, Italy, 2002, 65 p.

(4) Исаченко В.П., Осипова В.А., Сукомел А.С. (1969)

Теплопередача Москва: Энергия 724 стр.

(5) Лыков А.В. (1972) Тепломассообмен Москва: Энергия

560 стр.

(6) Тихонов А.Н., Самарский А.А. (1956) Уравнения

математической физики Москва: Наука 724 стр.

(7) Лыков А.В. (1967) Теория теплопроводности

Москва: Высшая школа 600 стр.

(8) Riekstiņš E.(1969) Matematiskās fizikas metodes Rīga:

Zvaigzne 620 lpp.

(9) Исаев С.И., Кожинов И., Кофанов В.И.и др. (1979)

Теория тепломассообмена Москва: Высшая школа

496 стр.

(10) Будак Б.М., Самарский А.А., Тихонов А.Н. (1972)

Сборник задач по математи¬ческой физике

Москва: Наука 688 стр.

(11) Янке Е., Эмде Ф., Леш Ф. (1968) Специальные

функции Москва: Наука 344 стр.

(12) Градштейн И.С., Рыжик И.М. (1963) Таблицы

интегралов, сумм, рядов и произведений Москва:

Физматгиз 1100 стр.

MEASURING ENERGY EFFICIENCY FROM A 4 kW DISH CONCENTRATOR SYSTEM

USING OLDER PARABOLIC ANTENNA TECHNOLOGY

Rafael E. Cabanillas L

Universidad de Sonora

Rosales y Luis Encinas, Col. Centro

Hermosillo, Sonora, 83000 México

Tel.-Fax: +52 (662) 259-21-05

rcabani@iq.uson.mx

Joseph Kopp

University of Nevada, Las Vegas

Graduate College

josephkopp@gmail.com

ABSTRACT

A fiberglass parabolic dish with a diameter of 2.44 m and

focal length of 0.92 m, used for telecommunication in

decades past, has been converted into a parabolic solar

concentrator. In previous work a solar tracking system

was developed and a vinyl-aluminum film was applied to

the receiver to make it reflective. Current studies began

with the analysis of the optical properties of the

vinyl-aluminum film after three years of exposure to the

elements; subsequently a new film was tested and applied.

A receptor, serving as a heat exchanger, was constructed

from carbon steel in order to measure the energy efficiency

and net energy gain of the system. A cost analysis is

reported for the entire system. The average net energy

gain for the 4.68 m

receiver was 2.18 kJ when normal

direct irradiance averaged 950 W/ m

. With thermal

efficiency measured to be 48%, capable of reaching 53%, a

Stirling engine is proposed to generate electricity.

1. INTRODUCTION

The need to pursue renewable energy sources has greater

acceptance today than ever before. Every ecosystem must

recognize its own potential for clean energy. In the

Sonoran Desert and encompassing areas of northwestern

Mexico and southwestern United States of America, the sun

is the strongest and most ample natural resource.

Therefore solar energy for electricity generation is and

should be capitalized even more by photovoltaic cells and

solar concentrating technologies.

While solar concentrating technologies are emerging as

macro-scale power plants for on-grid electricity

generation, photovoltaic cells still have market

domination on the micro-scale. Only very recently have

companies begun to publicize future micro-scale solar

concentrators for electricity generation. Infinia

Corporation in conjunction with Open Energy Corporation

plan to market a 1 kW Stirling engine in Asia, and Europe

[1]. Solarsphere will sell 8 kW systems [2] and Infinia

also plans to sell 3 kW systems in the United States [3].

Major advantages of solar concentrating technologies

compared to photovoltaic cells include greater

cost-electricity ratios and they physically occupy less

space than cells for equal amounts of electricity. To

further improve the cost-electricity ratio, either the cost

can go down or the efficiency can increase.

With the intention of creating a practical and economical

solar concentrator, a fiber-glass parabolic dish that was

developed to collect radio transmissions from cable

television satellites in decades past has been converted into

a highly reflective receiver. Utilizing telecommunication

dish technology has been studied by Estrada [4], Cabanillas

[5], and Palavras [6]; both Estrada and Palavras used

metallic dishes. Recycling old dishes and treating their

imperfections or manufacturing new dishes utilizing a

known industry could dramatically reduce costs.

3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS

727

Furthermore, existing industries could provide all required

materials up to the specific application of the dishes. This

study concludes by proposing integration with a 1 kW

Stirling engine.

2. PROGRESS REPORT

2.1 Optical Properties of Reflective Films

The vinyl-aluminum reflective film that served as the

reflective surface for the dish was removed after four years

of exposure to the elements and its optical properties were

retested. The original results reported in Cabanillas et. al

[1] showed the mean value of reflectance to be 85% and a

mean value of transmittance to be 1%. The mean values

of reflectance and transmittance after four years are 40.4%

and 1% respectively. The new vinyl-aluminum reflective

film was found to have a mean value of reflectance of 82.3

% and a mean value of transmittance of 1.5 %, within the

accepted range for receiver reflectivity. Both spectral

studies are shown in the Figure 1, the weather degradation

is evident on the old film.

Fig. 1: The spectral studies of the reflective films.

2.2 Establishing Focus

In previous experiments, it was established that 90% of the

light rays hit a 0.15 m surface at 0.92 m from the center of

the dish. While 0.92 m is the theoretical focal point, a

new experiment found that the focus of the dish differs

slightly. The dish was positioned perpendicular to the

ground and a light source was set a distance such that at

night all light rays would hit the receiver in parallel. The

experiment showed that the true focal point was found at

0.95 m and slightly off center.

3. CONSTRUCTION OF HEAT EXCHANGER

The receptor portion of the heat exchanger has three primary

components all made from carbon steel. The base that

receives the focused light is a 0.18 m diameter disk 0.025 m

thick. The disk that faces the sun is identical in shape and

had a carbon steel spiral soldered to its lower half and this

spiral was then soldered to the base disk creating a spiral path

for fluid to flow through. Apertures were made at the center

and at the edge of the top disk, located at the two ends of the

spiral. Above the top disk and connected to each aperture is

a thermocouple type K and tubing for fluid flow. Water was

chosen as the fluid for its thermodynamic properties and

abundance.

Fig. 2: (a) Heat exchanger apertures are visible in the center

and top of left disk, (b) Drawing of heat exchanger

and supporting arms, (c) Fixed to the heat exchanger

are the thermocouples and the hoses, (d) Heat

exchanger with supporting arms and attachments.

4. EXPERIMENTAL SET UP

A water pump was utilized to direct water through the heat

exchanger. It is common for the heat differential to vary

depending on the direction of the fluid flow. Therefore,

Wavelength (nm)

Reflectance

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

728

the first column of Table 2 specifies which direction the

water flowed. The direction “e” signifies that the water

entered the cavity from the edge and flowed towards the

center, and inversely “c” signifies that the water entered

from the center and flowed towards the edge. In addition,

two flow speeds were selected for each direction, denoted

by subscripts 1 and 2.

A datalogger was used to measure the temperatures of the

thermocouples placed at the apertures of the heat exchanger.

For every flow velocity several minutes of data was taken;

the temperatures were measured every second then

averaged and recorded in ten second intervals. The

datalogger also recorded the global radiation, diffuse

radiation, and normal direct irradiance via a pyranometer.

This data was measured every ten seconds and then

averaged and recorded every minute.

Preliminary tests showed water in the heat exchanger

increased by approximately 30 ºC. It was determined to

use water at roughly 5 ºC as the source fluid in order for the

heat exchanger’s temperature to be comparable to the

ambient temperature, thus reducing heat loss to the

environment. With

ambient temperatures ranging

between 30-34 ºC, the heat transfer with the environment

was negligible.

Fig. 3: Solar concentrator in foreground. Solar radiation

data was recorded by equipment with solar panel in

background.

5. RESULTS

5.1 Net Heat Measurements

The calculations for determining the heat gain and

efficiency are those fundamental to thermodynamics. The

solar heat gained can be expressed by the following

expressions.

By the equation,

QmCT=⋅ ⋅Δ



, (1)

where

⋅

m is the change in mass density, Cp is the specific

heat (4.186 J/gK), and ΔT is the change in temperature.

The heat exchanger absorbed some direct light from its

portion facing the sun and this heat had to be eliminated in

order to interpret only the heat gained from the receiver.

So,

QIAη=⋅ ⋅ , (2)

where I is the normal direct irradiance, A is the area of the

heat exchanger (0.1 m

), and η

rec

is the absortance of the

receptor, estimated to be 70 %. The complete experiment

was conducted three times in two weeks. The averages of

the three days’ measurements are presented in Table 1.

TABLE 1: MEASUREMENTS AND CALCULATIONS

FOR NET HEAT ACQUIRED

5.2 Thermal Efficiency and Projected Electrical Efficiency

After obtaining the net heat collected by the heat exchanger,

we then calculated the thermal efficiency of the entire

system. Using

3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS

729

()QIAη =÷⋅ (3)

where Q

net

is found in Table 2, I is the direct normal

irradiance and A is 4.68 m

. The relatively high thermal

efficiency of this low cost solar concentrator, as shown in

Table 2, has many possible applications. This report

focuses on electricity generation using the estimated

efficiency of a solar Stirling engine suggested by scholars

and corporations. United Stirling A.B. reported in the

early 1980s that Stirling engine efficiency exceeded 40%

(7), though Infinia Corporation reports 24% efficiency for

their 3 kW engine [8]. Therefore engine efficiencies of

30% and 40% have been projected. As mentioned in prior

studies, only 90% of the receiver accurately reflects light

onto the receptor. The average heat gained was 2.18 kJ,

but this could rise to 2.48 kJ with the additional 10%

accurately reflecting light. Therefore the column furthest

to the right uses a projected thermal efficiency of 53%.

TABLE 2: DIRECT NORMED IRRADIANCE AND

ANALYSIS OF EFFICIENCY

Plow

velocities

W/m Qnet J η η η η

B1 969.911 2267.942 0.50 0.15 0.20 0.22

B2 970.056 2365.066 0.52 0.16 0.21 0.23

C1 962.157 2067.905 0.46 0.14 0.18 0.20

C2 970.611 2023.746 0.45 0.13 0.18 0.20

Average 968.186 2181.164 0.48 0.14 0.19 0.21

6. CONCLUSIONS

6.1 Potential System for Electricity Generation

Great strides have been made to create a solar concentrator

from basic and recycled materials. By using an old

telecommunication antenna many basic business questions

are known such as how to create the dishes and how much

they cost. Another option would be to recycle the old

antennas by testing and reforming the curvature of the

receivers. The application of the vinyl-aluminum film

proves the materials and manpower are easily accessible.

It is also important to keep in mind that the low cost of the

materials could offset a reduction in efficiency.

We determined how much energy would be available for a

single day by analyzing the total solar insolation for

October 16, 2006 and this data is presented in Appendix 1.

Currently the solar concentrator tracks the sun from

9:00-15:00. The total heat focused onto the heat

exchanger was 12.7 kWh. Were the system to follow the

sun all day, this value would increase to 19.8 kWh.

Since only 90% of the current dish area reflects onto the

receiver these values could increase to 14.1 kWh and 22.0

kWh. With a Stirling engine operating at 30% efficiency,

4.23 kWh and 6.59 kWh of electricity would be generated,

for six hours and all-day respectively. If the Stirling

engine efficiency were 40%, up to 8.75 kWh could be

generated on a typical day in mid October. These values

would certainly increase during summer months when air

conditioning demands are at a maximum.

Present efficiency levels would create a product that is as

efficient as standard photovoltaic modules and known

improvements can be made. Companies are announcing

plans to provide micro-scale solar concentrators for heating

and electricity because they have several advantages over

photovoltaic systems. Solar Energy Systems states net

solar-to-electric conversion efficiencies are reaching 30

percent [9], and this system is not far below. Also this

system may present an economical alternative to high

efficiency-high cost solar concentrators.

6.2 Future Improvements and Research

Future studies will involve investigating the benefits of a

protective film applicable to the vinyl-aluminum film,

enhancing the knowledge of the heat exchanger and optical

efficiency, research into the benefits of recycling old dishes

or manufacturing new dishes, integrity studies to ensure the

dish will support the weight demands of a Stirling engine,

and a new electronic (cheaper) tracking system.

Appendix 1: Data analysis for solar irradiance for a

complete day

TABLE 3: SOLAR INADIANCE AND EFFICIENCY

PROJECTIORS USING 53% THENNAL EFFICIENCY

Tracking

Time

KW/m

Energy

Potential

kWh

6peak hours 5.64 14.11 4.23 5.64

All day 8.78 22.0 6.59 8.78

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

730

Fig. 4: Solar irradiance for a complete day.

7. ACKNOWLEDGMENTS

This work was financed partly by University of Sonora and

partly by CIBNOR. We gratefully acknowledge the valuable

help on heat exchanger design of Mr. Claudio Delgadillo.

8. REFERENCES

(1) Open Energy, 2006. www.openenergycorp.com/ news/-

pressreleases/11132006.php

(2) Solarsphere, 2006. www.seao2.com/solarsphere/tech-

nology.htm.

(3) ZDNet News, 2006. http://news.zdnet.com/2100-

9596_22-6129168-2.html.

(4) Estrada, C.A., et. al. 1998. A Parabolic Dish Concentrator

From A Telecomunication Antenna. In: Campbell-

Howe, et. al. (Eds.), Proceedings of the1998 Annual

American Solar Energy Society, Albuquerque, NM, US,

Vol. 1 pp267-270

(5) Cabanillas, R.A., et. al. 2005. Construction of a 4kWt

dish concentrator system using older parabolic antenna

technology. ISES 2005 Solar World Congress, Orlando,

FL, US. pp.

(6) Palavras, I., Bakos, G.C., 2006 Development of a

low-cost dish solar concentrator and its application in

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COLLECTOR EFFICIENCY TESTING – REDUCTION OF TEST DURATION BY

USING A 2-NODE COLLECTOR MODEL

Stephan Fischer, Hans-Müller Steinhagen

Universität Stuttgart

Institute for Thermodynamics and Thermal Engineering (ITW)

Pfaffenwaldring 6, 70550 Stuttgart, Germany

fischer@itw.uni-stuttgart.de

ABSTRACT

Up to now all national and international standards prescribe

certain boundary conditions like ambient air velocity, level

of solar irradiance, etc. for the efficiency test of solar

collectors. Although the boundary conditions vary between

standards, one requirement is common for all of them: Only

measured data with a positive collector output are allowed

to be used to determine the collector efficiency. For outdoor

tests, this requirement may lead to long test periods due to

unfavourable weather conditions. Against the background

of a possible reduction of testing costs and the wish to

satisfy the increasing demand for collector tests a reduction

of the test duration is a desirable option.

One possibility to reduce the test duration is the use of a so

called 2-node numerical collector model. In contrast to a

1-node model, the 2-node model takes into account the

temperature difference between the absorber and the fluid

temperature using two heat capacities C

abs

and C

as well as

a heat transfer capacity rate (UA) combining the two

capacities. This differentiation allows for the use of

measured data with negative collector output as long as the

heat transfer capacity rate is independent of the direction of

heat transfer.

The paper describes a possible method for efficiency

testing of solar thermal collectors using the 2-node

collector model.

1. INTRODUCTION

The most common Standards for collector testing, e. g. ISO

9806 /1/ or EN 12975 /2/ use a 1-node model to describe

the thermal performance of a solar thermal collector.

However, in order to separate the fluid from the absorber

temperature a 2-node model is necessary.

1.1 One-Node-Model

In the case of a 1-node model (see figure 1) all the thermal

capacities of the various components of the collector are

lumped together into one capacity node. The temperature of

this node is represented by the fluid temperature.

Fig. 1: One-Node-Model.

Труды Всемирного конгресса Международного общества солнечной энергии - 2007. Том 2

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