Труды Всемирного конгресса Международного общества солнечной энергии - 2007. Том 2
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Proceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement
712
In this paper, four different shapes of cavity receivers and
three different glass covers have been proposed. The optical
and thermal performances have been tested and analyzed.
The optical efficiencies of the 16 kinds of cavity receiver
have been calculated using the light tracking method. The
thermal efficiencies of four different shapes of cavities
have been measured in the room and outdoor environments.
At the same time, the thermal efficiency with different
concentrating ratio has been measured, the solar radiation
absorbed by receiver is simulated by heat fluxes produced
by an electrical film heater. Finally, a solar collector based
on linear Fresnel lens and cavity receiver has been
fabricated and its efficiency has been tested.
2. CAVITY RECEIVER DESCRIPTION
Fig. 1 illustrates four types of cavity receivers and three
types of glass covers, the geometrical dimensions have
been marked in Fig. 1 and the unit is millimeter. The
sectional view of four types of cavity is circle, semicircle,
square and triangle respectively. The wall of cavity receiver
is made of circular copper tube or copper plate. Two small
tubes are welded on the receiver, the tubes and wall joint
close and have good heat transfer. The wall operates as both
the receiver and fin, the thermal energy transferred to fluid
media from heat conduction and the temperature difference
between fluid and receiver can be decreased. To decrease
the convection and radiation loss, three kinds of glass
covers have been brought forward. Undoubtedly the glass
Fig. 1: Structure of 4 types of cavities and 3 types of
covers.
cover will decrease the optical efficiency, so the glass
which has high transmission is adopted. The circular glass
cover is produced by borosilicate glass and the V shape and
flat glass is produced by super white glass.
3. OPTICAL PERFORMANCE
The main contribution of cavity receiver to optical
efficiency is that the sunlight can be reflected in the cavity
for several times. The part of solar radiation from the
aperture falls on the copper wall and reflected radiation in a
diffused way both are absorbed. To calculate the optical
efficiency of cavity receiver, the light tracking method is
used. The detailed description on that method can refer to
reference [8]. Here we use formula(1) to describe the
optical performance of cavity receiver.
EEη = (1)
Where the numerator replaces the energy reaches the aperture
and denominator replaces the energy absorbed by cavity wall.
During the calculation, the glass is defined as the super white
glass and its refractive index is 1.52. The absorptivity of
selective coating is 0.9. It is seen in Table1 that the triangle
shape has the best optical efficiency because the sunlight can
be reflected continuously and nearly no sunlight escapes. If the
cover material is the same, the structure will not have
significant influence on the cavity efficiency.
TABLE 1: OPTICAL EFFICIENCY
CAVIT
Y1
CAVIT
Y2
CAVIT
Y3
CAVIT
Y4
NONE 97.3% 90.0% 97.5% 99.0%
COVER1 89.1% 82.4% 89.3% 90.6%
COVER2 89.2% 82.1% 89.1% 90.4%
COVER3 88.6% 82.0% 88.9% 90.2%
4. THERMAL PERFORMANCE
4.1 Thermal Losses of Cavity Receiver
The cavity was coated with black selective coating which is
3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS
713
usually used in flat plate solar collector. Moreover, there
exists an amount of convection loss that can be neglected
for evacuated tube receiver. The shape of solar collector
places an important role in cavity receiver design, and good
design would reduce the thermal loss effectively. In the test,
the inlet temperature of the working fluid is maintained at a
fixed temperature by a thermostat water tank. The ambient
temperature, inlet temperature and outlet temperature are
measured by three PT100 platinum resistance thermometers,
and the flux is measured by a flow meter. The thermal loss
is calculated by such formula.
()
EmcTT=− (2)
Fig. 2: Experimental setup on thermal loss measurement.
Fig.3 shows the thermal losses of four kinds of semicircular
cavity receivers (1.5m long) with no cover and three
different kinds of glass cover. The experiment is done in
outdoor conditions and it is operated at night to remove the
influence of sunlight. It can be found that the cover has
good function to reduce the thermal loss. The circular cover
has the smallest thermal losses when the aperture is
downward. Its value is 63.9% of that of no cover’s one with
downward aperture. Whether the direction of aperture is
upward or downward, the thermal losses of three kinds of
cavity receiver are almost the same. The biggest difference
is just 8.7W for a 1.5m receiver. So it can be said that the
thermal loss between different glass covers are nearly the
same.
To study the influence of the aperture angle on thermal loss,
four shapes of cavity (0.5m long) are considered, with
variation of the aperture direction from 0 to 180°. When
the aperture is upward, the angle is 0°. During the experiment,
Fig. 3: Thermal losses of semicircular cavity receiver with
different glass covers.
Fig. 4: Thermal losses of cavity receiver versus different
aperture angle.
the angle is adjusted every 30°. The cavity dimension and
insulation material thickness have been illustrated in Fig.1.
The inlet temperature is fixed at 90 (water as fluid media) ć
and 150ć (water as fluid media) respectively. The
experiment results show that the thermal losses mainly
occurs at cavity aperture, as well as at the top steel wall
close to the aperture. Also found is that the thermal loss
decreases when the aperture angle increases. The best
design is the triangle cavity receiver and its thermal loss is
only 19.7W. If the inlet temperature increases to 150ć, the
insulation material should be enhanced, otherwise some
part of thermal energy would be lost from side walls.
4.2 Thermal Efficiency of Cavity Receiver
To simulate the efficiency of cavity receiver used in linear
concentrating solar collectors and evaluate the thermal
efficiency versus different concentrating ratio, one kind
of film electric heater is utilized and fixed between the
Proceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement
714
cavity wall and the insulation material. The heat flux
provided by electric heater can be thought as solar radiation
falls on cavity wall. Here it is assumed that the beam solar
radiation is 800W/m
2
and the optical efficiency is 0.72. So
the operating voltage is
280UWR= (3)
The thermal efficiency is the ratio of useful energy to
heating power
()
()
mc T T U Rη =− (4)
From Fig.5, it can be found when the aperture width is
larger than 2m, whether the aperture is upward or
downward, the thermal efficiencies are almost the same.
After the width increased to 3m, the thermal efficiency is
more than 94% for triangle cavity receiver. That is to say
the overall collector efficiency will be more than 67%
considering that the collector optical efficiency is 72%.
Fig. 5: Thermal efficiency of cavity receiver versus
different heat flux.
5. SOLAR COLLECTOR BASED ON FRESNEL LENS
AND CAVITY RECEIVER
Fig.6 is a linear concentrating solar collector based on
Fresnel lens and cavity receiver. It tracks the sun by a
stepping motor which is controlled by a single-chip control
system. The beam solar radiation is acquired by a solar
tracker. The fluid flow rate is 290g/s and the inlet water
temperature is near 90ć, and the thermal efficiency of
solar collector is
Fig. 6: Solar collector based on Fresnel lens and cavity
receiver.
()()
mc T T I Aη =− (5)
The results is shown in Fig.7, and the average efficiencies
are 27.2%, 39.4%, 42.4% and 43.4% as the sequence in
Fig. 7.
Fig. 7: Experimental results of Fresnel solar collector.
6. CONCLUSIONS
This paper studies the optical and thermal performance of
four types of cavity receivers. From the experiment and
analysis results, that the following conclusions can be made:
(1) Triangle shape cavity receiver has the best optical
performance which is 99% and the structure of glass cover
will not influence optical efficiency when glass material is
the same;
3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS
715
(2) The minimum thermal losses of triangle cavity are 20W
and 41W when the inlet temperature is 90ć to 150ć;
(3) From the test at outdoor conditions, the triangle cavity
has the best performance and the solar conversion
efficiency can be beyond 67%;
(4) When the concentrator aperture is 0.4m length, the
practical test results show that the collector average
efficiency is more than 40% when
90
in
T = ć.
7. NOMENCLATURE
F
A Area of Fresnel lens (m
2
)
p
c Thermal capacity (W/m
2
K)
1
E
Energy following on the cavity aperture (V)
2
E
Energy absorbed by the cavity wall (V)
loss
E
Thermal loss energy (W)
b
I
Beam solar radiation (W/m
2
)
L
Cavity receiver length (m)
m Fluid flux (kg/s)
R
resistance of electric heater (Ω)
in
T Inlet temperature (ć)
out
T Outlet temperature (ć)
out
T Outlet temperature (ć)
h
U Electric voltage of electric heater (V)
W Width of concentrator aperture (V)
eff
η Thermal efficiency of collector
opt
η Optical efficiency of cavity receiver
t
η Thermal efficiency of cavity receiver
8. ACKNOWLEDGMENTS
This work was supported by the key project of Science and
Technology Commission of Shanghai Municipality,
Shanghai, PR China(No.06JC14040), the special project of
2010 World Expo, Shanghai, PR China (No.2005BA908B07,
No.05DZ05807), and the project of Ministry of Education,
China ( No. NCET-06-0387: 2007-2009)
9. REFERENCES
(1) M. Li, L.L. Wang, “Investigation of evacuated tube
heated by solar trough concentrating system”, Energy
Conversion and Management 2006, p. 3591-3601.
(2) V. Flores, R. Almanza, “Behavior of the compound
wall copper–steel receiver with stratified two-phase
flow regimen in transient states when solar irradiance is
arriving on one side of receiver”, Solar Energy
2004, p.
195-198.
(3) D.J. Reynolds, M.J. Jance, M. Behnia, G.L. Morrison.
“Thermal Performance of Solar Concentrator/Cavity
Receiver Systems”, Solar Energy
2004, p. 229-234.
(4) N. Sendhil Kumar, K.S. Reddy. “Numerical
Investigat-ion of Natural Convection Heat Loss in
Modified Cavity Receiver For Fuzzy Focal Solar Dish
Concentrator”, Solar Energy
, article in press.!
(5) N.D. Kaushika, K.S.Reddy. “Performance of a Low
Cost Solar Paraboloidal Dish Steam Generating
System”, Energy Conversion and Management
2000, p.
713-726.
(6) D.A. Boyd, R. Gajewski, R. Swift. “A Cylindrical
Blackbody Solar Energy Receiver”, Solar Energy
1976,
p. 395-401.
(7) O.A. Barra, L. Franseschi. “The Parabolic Trough
Plants Using Black Body Receivers: Experimental and
Theoretical Analyses”, Solar Energy
1982, p. 163-171.
(8) W.T Welford, R. Winston “The Optical of Nonimaging
Concentrators”, Science Press
January 1987, p. 8-11.
STUDIES ON TEST RESULTS FOR THERMAL PERFORMANCE
OF SOLAR COLLECTORS IN CHINA
Sun Zhifeng
Institute of Air Conditioning,
China Academy of Building Research, CABR
No.30 Beisanhuan Donglu
Beijing 100013, China
Beijisnow@126.com
Lu Bin, He Tao, Li Zhong, Feng Airong,
Zhang Lei, Huang Zhulian, Deng Yu
Institute of Air Conditioning, CABR
No.30 Beisanhuan Donglu
Beijing 100013, China
IAC@vip.sina.com
ABSTRACT
In this paper, statistical analysis for the thermal
performance of evacuated tube solar collectors and
flat-plate solar collectors is presented respectively
according to the test results by National Center for Quality
Supervision and Testing of Solar Heating Systems (Beijing)
in recent years. It indicates the difference of solar
collectors’ quality, in contrast to the foreign product’s, is
not at zero-loss efficiency but at the heat loss coefficient.
We found that the heat loss coefficient of solar collectors
plays an important role in the aim-assisted space heating or
air-conditioning systems. The ways of improving the solar
collectors’ quality in China are also pointed out.
1. INTRODUCTION
After nearly 20 years of efforts, production and application
of solar collectors in China has been rapidly developed
in recent years. By the end of 2006, 100 million square
meters of solar water heaters have been installed and
used in China. The Productivity of solar heaters has
reached 20 million square meters in 2006. Solar collector
is the key component of solar thermal application and
the core component of solar thermal utilization in
building. The quality of solar collector directly
influenced the development of the solar thermal
utilization industry. Based on test results by National
Center for Quality Supervision and Testing of Solar
Heating Systems (Beijing) (here in after abbr. CTS
(Beijing)) in the last few years, statistical analysis for the
thermal performance of evacuated tube solar collectors
and flat-plate solar collectors has been done respectively
and the solar collector’s thermal performance for space
heating and air-conditioning is also discussed. The
advantages and shortages of the current solar collectors
in China are pointed out and the improvement and
development pattern for solar collector products in the
future is also indicated.
2. EVACUATED TUBE SOLAR COLLECTORS
The main component of evacuated tube solar collectors is
evacuated tube. According to the type of evacuated tube,
evacuated tube solar collectors can be classified into
several main types as all-glass evacuated tube collectors,
heat pipe evacuated tube collectors and U-pipe evacuated
tube collectors.
In early 1980s, many Chinese scholars began to conduct
research on all-glass evacuated tube. The research
established the foundation of industrialization of all-glass
evacuated tube collectors in China. Hereafter, all-glass
evacuated tube collectors had been rapidly spread and
developed in China. Later, new products, such as heat pipe
evacuated tube collector and the U-pipe evacuated tube
collector, are then developed to meet the requirement of
3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS
717
compression resistance, freeze resistance and other aspects.
The field of evacuated tube solar collectors has been
broadening. According to statistics, more than 16 million
square meters of evacuated tube collectors were among 20
million square meters of the solar collectors produced in
China in 2006. At present the output of evacuated tube
solar collectors in China occupies over 90% of total output
of evacuated tube solar collectors in world.
Table 1 shows the statistical results of evacuated tube solar
collectors tested by CTS (Beijing) in recent years. As is
shown in Table 1, average zero-loss efficiency of all-glass
evacuated tube collectors is 69% and the average heat loss
coefficient is 4.43W / ( • ć). The average heat loss
coefficient of heat pipe evacuated tube collectors is smaller
than that of all-glass evacuated tube collectors because the
structure of heat pipe takes a step forward in reducing heat
loss. The average zero-loss efficiency of all-glass evacuated
tube collectors is slightly larger than that of heat pipe
evacuated tube collectors because water is heated indirectly
in heat pipe evacuated tube collectors. Nothing is shown
because there is only one sample of U-pipe evacuated tube
collector in the test results. Three types of collectors’
efficiency curve of evacuated tube solar collectors are
shown in Fig. 1. We can see there is little difference of
thermal performances among three types of evacuated tube
collectors.
TABLE 1: STATISTICAL RESULTS OF EVACUATED
TUBE SOLAR COLLECTORS
Categories Samples
Average
zero-loss
efficiency
(%)
Average
heat loss
coefficient
W / ( •
ć)
all-glass
evacuated tube
collectors
12 69 4.43
heat pipe
evacuated tube
collectors
3 63 2.53
U-tube
evacuated tube
collectors
1 69 4.05
Fig. 1: Efficiency curve of three types of evacuated tube
collectors.
Fig. 2 shows the distribution of zero-loss efficiency and
heat loss coefficient of evacuated tube solar collectors.
Samples 1 ~ 11 are of all-glass evacuated tube collectors,
samples 12 ~ 14 are of heat pipe evacuated tube collectors
and the 15th sample is of U- pipe evacuated tube collectors.
We found that zero-loss efficiency of evacuated tube solar
collectors is similar, whereas heat loss coefficient varies
greatly. Especially for all-glass evacuated tube collector,
heat loss coefficient of the 9th sample and the 4th sample
differs by 5.8W / ( • ). ć
0
10
20
30
40
50
60
70
80
90
100
Samples
Zero-loss efficiency η(%
)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
Heat loss coefficient
U(W/(
•K)
=HURORVVHIILFLHQF\ +HDWORVVFRHIILFLHQW:噝.
Fig. 2: The distribution of zero-loss efficiency and heat
loss coefficient of evacuated tube solar collectors.
Fig. 3 indicates the recent test results of evacuated tube
solar collectors in CTS (Beijing) and in SPF. As can be
seen, the average zero-loss efficiency is equal. However,
the average heat loss coefficients differ in 2.4 times. This
shows that the difference of thermal performance is at the
heat loss coefficients between Chinese evacuated tube solar
Proceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement
718
collectors’ thermal performance and similar foreign
products’. Therefore, for further improvement of evacuated
tube solar collectors, the focus is to reduce the collector
heat loss coefficient.
68 68
4.03
1.68
0
10
20
30
40
50
60
70
80
90
100
&76%HLMLQJ 63)
Average zero-loss efficienc
y
η(%)
0
1
2
3
4
5
6
7
8
Average heat loss coefficien
t
U(W/(
•K)
$YHUDJH]HURORVVHIILFLHQF\
$YHUDJHKHDWORVVFRHIILFLHQW:噝.
Fig. 3: Zero-loss efficiency and heat loss coefficient of
evacuated tube solar collectors in CTS (Beijing)
and in SPF.
3. FLAT-PLATE SOLAR COLLECTORS
In the past flat-plate solar collectors’ development was slow
in China. At present, with improvement of production
process and further demand of energy saving in building in
China, particularly the gradually spread of centralized hot
water system, solar space heating systems and solar
air-conditioning system, flat-plate solar collectors’
production and application have also developed rapidly.
Definitely that flat-plate collectors’ share will grow larger
and larger in China.
Statistical analysis of the thermal performance of flat-plate
solar collectors tested by National Center for Quality
Supervision and Testing of Solar Heating System (Beijing)
in the last few years has been done. Average zero-loss
efficiency is 75%, the highest is 88%, and the smallest is
66%. Average heat loss coefficients is 7.6 W / ( • ), ć
the maximum reached 16.7 W / ( • )ć , and the
minimum is 5.4 W / ( • ). ć The difference of heat loss
coefficient is very significant. This shows that the
difference of flat-plate solar collectors is big. The
distribution of zero-loss efficiency and heat loss coefficient
of flat-plate solar collectors are shown in Fig. 4.
0
10
20
30
40
50
60
70
80
90
100
Samples
Zero-loss efficiency η(%
)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
Heat loss coefficient U(W/(
•K)
=HURORVVHIILFLHQF\ +HDWORVVFRHIILFLHQW:噝.
Fig. 4: The distribution of zero-loss efficiency and heat loss
coefficient of flat-plate solar collectors.
Fig. 5 shows the zero-loss efficiency of flat-plate solar
collectors is similar among them, nevertheless heat loss
coefficient in CTS(Beijing) is larger 3.56 W / ( • )ć
than that in SPF, larger 2.39 W / ( • ) ć than that in
SRCC. It is similar to evacuated tube solar collectors. The
difference of thermal performance is also heat loss
coefficient. Therefore, reducing heat loss coefficient is an
important way of Chinese flat-plate solar collectors’
products reaching the international level.
75
79
75
7.57
4.01
5.18
0
10
20
30
40
50
60
70
80
90
100
&76%HLMLQJ 63) 65&&
Average zero-loss efficienc
y
η(%)
0
1
2
3
4
5
6
7
8
Average heat loss coefficien
t
U(W/(
•K)
$YHUDJH]HURORVVHIILFLHQF\
$YHUDJHKHDWORVVFRHIILFLHQW:噝.
Fig. 5: Zero-loss efficiency and heat loss coefficient of
flat-plate solar collectors in CTS (Beijing), in SPF
and in SRCC.
4. ANALYSIS FOR THERMAL PERFORMANCE OF
SOLAR COLLECTORS USED IN SPACE HEATING
AND AIR-CONDITIONING
With rapid development in China, the annual new housing
3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS
719
in city has reached 1 billion square meters. And with the
improvement of people’s living and the process of
urbanization speeding up, Rapid growth trend of housing
will continue in 15 years. It will also bring on gradually
increase of energy consumption in building. According to
related report, energy consumption in building has
presently been 27.6% of social total terminal energy
consumption. Reference to the experience of developed
countries, energy consumption in building will gradually
increase to 35% of social total terminal energy
consumption. And the majority of energy consumption in
building is mainly for space heating and air-conditioning
which accounts for 65% of them. Therefore, if sharing of
solar energy for space heating and air-conditioning in
building would be vigorously promoted, it will have a
tremendous impact on saving energy in building and
reducing conventional energy consumption,
At present, solar collectors are mainly concentrated on the
supply of hot water. Along with the development of
technology and the demand of renewable energy in
building, solar collectors will be used in large-scale space
heating and air-conditioning for building. If the solar
collectors were used in space heating system in building,
the requirement of water temperature for floor radiant
heating system is about 40ćin order to make space heating
system in better working conditions. When air temperature
outdoor is about 0ć and solar irradiance is about 800W/,
reduced temperature difference of Solar collectors should
be about 0.05 (m
2
•k)/W. At this time instantaneous
efficiency should be no less than 40% in order that the
fraction of solar energy will be higher in space heating
system. If solar collectors were used in air-conditioning
system, the requirement of water temperature for
refrigeration Unit is about 85ć for ensuring that the
air-conditioning system can be effectively work. When air
temperature outdoor is about 30ć and solar irradiance is
about 800W/, reduced temperature difference of Solar
collectors should be about 0.07(m
2
•k)/W. The instantaneous
efficiency at this time should not be less than 30% to be
sure that the fraction of solar energy is bigger in system.
Fig. 6 is the distribution of instantaneous efficiency of
evacuated tube solar collectors at reduced temperature
difference of 0.05 and 0.07(m
2
•k)/W. Fig. 7 is the
distribution of instantaneous efficiency of flat-plate solar
collectors at reduced temperature difference of 0.05 and
0.07(m
2
•k)/W.
6DPSOHV
,QVWDQWDQHRXV
HIILFLHQF\
,QVWDQWDQFRXVHIILFLHQF\DW7RI噝N:
,QVWDQWDQFRXVHIILFLHQF\DW7RI噝N:
Fig. 6: The distribution of instantaneous efficiency of
evacuated tube solar collectors at reduced
temperature difference of 0.05 and 0.07(m
2
•k)/W.
,QVWDQWDQHRXV
HIILFLHQF\
,QVWDQWDQFRXVHIILFLHQF\DW7RI噝N:
,QVWDQWDQFRXVHIILFLHQF\DW7RI噝N:
Fig. 7: The distribution of instantaneous efficiency of
flat-plate solar collectors at reduced temperature
difference of 0.05 and 0.07(m
2
•k)/W.
According to the test results, the number of instantaneous
efficiency of evacuated tube solar collectors in samples
meeting the working conditions of heating (not less than
40%) is 11, the number of instantaneous efficiency meeting
the needs of air-conditioning conditions(not less than 30%)
is 10. For flat-plate solar collectors in samples, the number
of instantaneous efficiency meeting the heating needs(not
less than 30%) is 12, the instantaneous efficiency meeting
the needs of air-conditioning conditions(not less than 40%)
is only 9. And especially there are three samples of
flat-plate solar collectors whose instantaneous efficiency
reduce to negative in heating or air-conditioning conditions.
This shows that it is impossible for these to use in space
heating or air-conditioning.
If current average heat loss coefficient of solar collectors
could be reduced 1W/ (m
2
•ć), the instantaneous efficiency
of solar collectors at reduced temperature difference equal
Proceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement
720
to 0.05(•k)/W could be raised by 5% and that at reduced
temperature difference equal to 0.07(•k)/W could be
raised by 7%. So heat loss coefficient of solar collectors
should also be given adequate attention and various
measures should be taken to reduce heat loss coefficient of
solar collectors.
5. CONCLUSION AND SUGGESTION
(1) Both for evacuated tube solar collectors and for
flat-plate solar collectors, the main difference of thermal
performance in contrast to oversea product is at heat loss
coefficient. How to reduce heat loss coefficient of solar
collector is the key to solar collectors’ industries.
(2) Research and application of flat-plate solar collectors
must be vigorously promoted. Improving on technology
and production, especially vigorously improving insulated
measures and the application of selective absorbing coating
in flat-plate solar collectors, playing to the advantage of its
more applicable to the construction, are all paid more
attention.
(3) Further strengthening quality supervision and testing of
solar collectors, ensuring the quality of solar collectors,
perfecting the construction of the survival of the fittest in
Chinese market, all result in making better technical
services for the promotion of Chinese large-scale
applications of solar energy.
6. REFERENCES
(1) Zheng Ruicheng, “Technical Guidebook for Solar
Water Heating System of Civil Buildings”, 2006,
Chemical Industry Press.
(2) Energy Bureau of National Development and Reform
Commission etc, “The Report of China Renewable
Energy Industry Development (2006)” 2007.
(3) Zhao Jiarong, " ‘11th Five-Year Plan’ 10 Energy-saving
Major Project View" Reading, Beijing, 2007. China
Development Press
(4) Test Methods for Thermal Performance of Flat-plate
Solar Collectors. GB/T 4271-2000
(5) Evacuated Tube Collectors. GB/T 17581-1998
(6) Lu Weide, “Solar Collectors and Solar Water
Heaters/System”, 1999, 14-21, Acta Energiae Solaris
Sinica (Special Issue of China Solar Energy Society
20th Anniversary).
THE MATHEMATICAL DESCRIPTION FOR THE HEAT CONDUCTION PROCESS ON
PLANESURFACES OF A SOLAR COLLECTOR’S ABSORBER
Peteris Shipkovs
Institute of Physical Energetics
Aizkraukles Street 21
Riga LV-1006, Latvia
shipkovs@edi.lv
Martinsh Vanags
Institute of Physical Energetics
Aizkraukles Street 21
Riga LV-1006, Latvia
galina.k@edi.lv
Voldemars Barkans
Latvian Maritime Academy
Kronvalda Boulevard 6
Riga, LV-1206, Latvia
Abrams Temkins
Riga Technical University
Kronvalda Boulevard 1
Riga, LV-1010, Latvia
Kristina Lebedeva
Institute of Physical Energetics
Aizkraukles Street 21
Riga LV-1006, Latvia
Kristina.Lebedeva@edi.lv
Galina Kashkarova
Institute of Physical Energetics
Aizkraukles Street 21
Riga LV-1006, Latvia
galina.k@edi.lv
Janis Shipkovs
Institute of Physical Energetics
Aizkraukles Street 21
Riga LV-1006, Latvia
ABSTRACT
The paper gives a mathematical description for the heat
conduction proceeding on the plane surface of a solar
collector’s absorber divided into three parts for each of
which the Laplace equation with boundary conditions is
formed. Applying definite approximations the authors have
completely described mathematically the heat conduction
process initiating in the plane part of a collector’s absorber,
then passing to a tube and from the tube to the liquid
flowing through it. In all the three absorber’s parts the
process is considered stationary, independent of time, and,
therefore the temperature field is obtained in spatial
coordinates.
1. INTRODUCTION
The heat flow in the absorber of a solar collector, which
occupies there a definite space and in which this heat
spreads by conduction, is now being studied intensively
[1–3]. The process can be considered mathematically if we
know the temperature at any time and any point of this
space. There are cases when it is sufficient to measure the
temperature at separate points and to tabulate the data
obtained. However for a solar collector it is advantageous
to preliminarily analyze the heat conduction thus
considering the problem theoretically. Besides, the
temperature not always can be measured at all points. The
challenge is therefore to obtain the temperature function
theoretically, depending on the time and spatial coordinates.