International Journal of Energetica (IJECA)
https://www.ijeca.info
ISSN: 2543-3717 Volume 2. Issue 2. 2017 Page 29-37
IJECA-ISSN: 2543-3717. December 2017 Page 29
A parabolic trough solar collector as a solar system for heating water:
a study based on numerical simulation
Mokhtar Ghodbane
1
, Boussad Boumeddane
1
1
Department of Mechanical Engineering, University of Saâd DAHLAB, Blida 1, ALGERIA
ghodbanemokhtar39@yahoo.com
Abstract – This paper is an optical and thermal study of a small model of a parabolic trough
solar collector (CTP), which will be used to heat tap water, in the winter, at Guemar location, (El-
Oued, Algeria). A mathematical model was presented based on the energy balance equation
applied to the absorber tube; this model was solved by the finite difference method. A computer
program based on MATLAB was developed to solve the problem. The results show that the
thermal efficiency of the concentrator can attend a high value of more than 61%, while the fluid
outlet temperature can reach 343 K.
Keywords: Solar thermal, parabolic trough collector, outlet temperature, Tap water, numerical
analysis.
Received: 09/10/2017 – Accepted: 25/12/2017
I. Introduction
The oldest and the greatest source of energy in the
universe is the sun, where an average of 1367 (W/m²)
reached the edge external of the terrestrial atmosphere
according to the world radiometric center of Davos
(Switzerland) [1].
The global solar radiation is the sum of both direct and
diffuse components [2-16]. Algeria has one of the highest
solar radiation in Africa. The sunshine duration on
almost all of the national territory exceeds 2000 hours
annually and can reach 3900 hours in the Highlands and
Sahara [17].
This study deals with the exploitation of solar energy
to produce hot water using parabolic trough concentrator
(PTC) in Guemar region, where the table (1) shows the
meteorological data of this city. In previous studies, we
have studied several models of this system in different
regions in Algeria, where the results were very
encouraging [2-11].
Table 1. The meteorological data of the city of Guemar.
Month
Global
Radiation
(kWh/m²)
Diffuse
Radiation
(kWh/m²)
Beam
Radiation
(kWh/m²)
Monthly average
of ambient
temperature
(°C)
Monthly average
of dew point
(°C)
Monthly average
of wind
speed
(m/s)
1 114 19 211 10,6 4 2,1
2 125 28 184 12,9 3,1 2,5
3 170 48 197 17,8 4,6 3,3
4 207 54 225 21,6 7,1 4
5 234 69 237 26,8 9,6 4,1
6 236 70 228 31,3 11,4 3,6
7 248 66 242 34,7 13,3 3,4
8 219 67 217 33,8 14,6 3,1
9 176 55 187 28,8 15 3
10 144 45 179 23,8 12,7 2,2
11 117 21 200 16,1 7,3 2
12 100 21 187 11,7 5,1 2,3
For the PTC solar concentrator, it gives us a
temperature of fluid that can be used both in industrial
and domestic applications, with a medium- to high range
of [80-160 ° C] [2-6, 9, 11]. According to the size and
position of the PTC collector, this system can obtain a
steam temperature exceeding 1500 °C, according to
mailto:ghodbanemokhtar39@yahoo.com
M. Ghodbane et al.
IJECA-ISSN: 2543-3717. December 2017 Page 30
studies cited in the scientific literature [3-6, 9, 11, 18].
So, the PTC systems are the most currently used
technology by the most powerful solar power plants in
the world, we quote in this context that the solar plant at
Kramer Junction in California represents a total installed
capacity of 354 MW [19]. This kind of solar field is
made up of parallel alignments of long half-cylindrical
mirrors, oriented North-South axis that revolved around
the latter to follow the path of the Sun. The Sun's rays are
concentrated on a horizontal tube, where circulates a heat
transfer fluid.
As we said earlier, this study focuses on the
conversion of solar energy to thermal energy by using a
parabolic trough solar concentrator in a troubled day of
the winter (Low-temperature weather with some wind).
Tap water was used as the heat transfer fluid. Our aim in
this study is to characterize the optical and thermal
efficiencies of our PTC model based on the geographic
parameters and climatic conditions in Guemar location,
(El-Oued, Algeria). Figure 1 shows the scheme of the
approved water heating system using TRNSYS 16.
Figure 1. Illustrative diagram of the water heater system.
In order to solve to problem, this study will begin with
an optical efficiency analysis using SolTrace software. In
the second step, a mathematical model has been
established with Matlab to calculate the thermal
efficiency, the fluid outlet temperature, the receiver’s
surface temperature, the glass temperature and the
coefficient of thermal losses.
II. Optical simulation
The optical modeling was performed using the
SolTrace; the code is developed by the National Renewable
Energy Laboratory (USA) [20]. The optical system of the
concentrator is composed of the reflecting surface and
absorber tube. The reflecting surface was modeled as a
single mirror of parabolic section. Table (2) shows the
geometric parameters of the PTC concentrator and the
optical parameters are shown in Table (3).
Table 2. Geometrical parameters of the PTC collector.
geometric characteristic Value (mm)
Receiver tube number 1
Absorber length (LA) 12270
outer diameter of the absorber (DA,ext) 22
Inner diameter of the absorber (DA,int) 20
outer diameter of the glass (DV,ext) 26
inner diameter of the glass (DV,int) 23,5
mirror length (L) 12270
mirror width (l) 1100
The absorbent tube dimensions mentioned in the
previous table are the dimensions of a linear Fresnel
receiver that was previously manufactured by H. Chabahi
et al., (2011) [21], but the length of the absorbent tube
here was different.
M. Ghodbane et al.
IJECA-ISSN: 2543-3717. December 2017 Page 31
For the optical simulation, it was assumed that the
reflection coefficient, the absorptivity, and transmissivity
are uniform over the entire reflecting surface. It was
considered that the solar tracking is very accurate and
therefore the concentrator opening is constantly
perpendicular to the rays from the solar disc.
Table 3. Optical parameters of the collector.
parameter Value
optical overall average error (σoptical) 03 mrad
mirror reflection coefficient (ρm) 0,92
Transmissivity of the glass 0,945
Absorption coefficient of the absorber (α) 0,94
The emissivity of the absorber tube (εA) 0,12
There are several models for the simulation of global
direct and diffuse solar irradiance, expressed by semi-
empirical approaches.
For the PTC concentrators, the absorbed solar energy
depends on the beam radiation (DNI) [3-6, 9, 11]. Figure
2 reflects the change in the solar radiation during the day
of 05 December 2016 according to the semi-empirical
model of PERRIN DE BRICHAMBAUT, where M.
Ghodbane et al., (2016), had created a numerical
simulation based on programming using MATLAB for
the calculation of solar radiation (direct, diffuse and
global) [8]. For this model, the different components of
the solar radiation vary according to the height of the
sun, the angle of incidence, the weather condition and the
state of visibility of the atmosphere.
Any application of solar energy in a given site requires
a complete and detailed knowledge of the sunshine of the
site. This is possible if the data are available over a
sufficient period. However, in the majority of cases, there
are no local measurements of solar radiation, and some
approximate methods must be used to predict the
characteristics of solar irradiation.
The total quantity of radiation calculated for a
particular location or area was entered as global
radiation. The calculation radiation (direct, diffuse and
global) was repeated for each entity location or for all
locations of the topographic surface and generates
sunshine maps for an entire geographical area.
8 9 10 11 12 13 14 15 16 17
0
100
200
300
400
500
600
time (hour]
s
o
la
r
ra
d
ia
ti
o
n
[
W
/m
2
]
Global radiation
Direct radiation
Diffuser radiation
Figure 2. Solar radiation evaluation in Guemar area.
Virtually, it was in the regions for which we had the
least solar radiation measurements that the projects of
implantation of the solar energy systems for water
pumping, desalination, or the decentralized electric
power supply are the most important and the most
demanding. Direct radiation (DNI) is solar radiation
reaching the earth's surface directly from the sun. It
depends on the thickness of the atmosphere that the solar
radiation must cross, as well as the inclination of the rays
relative to the ground. The PYRHELIOMETER is the
instrument for measuring the intensity of direct radiation.
The PYRHELIOMETER must be equipped with a device
to direct it permanently towards the sun. Through Figure
2, it was noticeable that the maximum radiation value is
the true solar noon, which can reach 585 (W/m²), despite
the bad weather on this day, the amount of solar radiation
was considered.
Figure 3 illustrates the captured solar energy by the
collector, as presented in SolTrace. We tried to show the
importance and effectiveness of parabolic trough
collector in the field of solar concentrate.
Figure 3. Schema parabolic trough concentrator as it appears in
SolTrace.
III. Thermal simulation
This section treats the thermal analysis and numerical
modeling of a PTC concentrator. This modeling was used
to predict the change in the outlet temperature of the heat
transfer fluid (water) versus the beam radiation. The
thermal exchanges are between the heat transfer fluid, the
absorber tube and the glass tube. The temperature
modeling was based on the energy balances characterized
by the differential equations of the three temperatures: TF
(for the fluid), TV (for glass tube) and TA (for the
absorber tube), these equations will vary depending on
M. Ghodbane et al.
IJECA-ISSN: 2543-3717. December 2017 Page 32
two parameters, namely the time (t) and the length (x) of
the absorber tube. In calculating the energy balances, we
have assume that [9, 13]:
The heat transfer fluid is incompressible;
The parabolic shape is symmetrical;
The ambient temperature around the concentrator is
uniform;
The shadow effect of the absorber tube on the mirror
is negligible;
The solar flux at the absorber is uniformly
distributed;
The glass is considered opaque to infrared radiation;
The exchanges by conduction in the absorber and the
glass are negligible.
III.1. Energy balance for the fluid
The energy balance for the heat transfer fluid that
circulates in the absorber tube was expressed by the
following relationship [2, 5, 7, 10, 11]:
X
(X,t)T
..Q.Cρq
t
(X,t)T
..A.Cρ
F
vFFu
F
A,FF
int
(1)
The initial conditions and the boundary conditions of
equation (1) are [2, 5, 10, 11]:
(0)T=(t)T=t)(X,T
(t)T=(t)T=t)(0,T
ambinitialF,F
ambentryF,F
(2)
qu is the heat flow transmitted to the fluid [W]; it was
given by the following relationship [3, 10, 14]:
)T(T.Ahq
FAA,Fu
int
(3)
III.2. Energy balance for the absorber tube
The energy balance for the absorber was given by the
following equation [2, 5, 7, 10, 11]:
Figure 4. Thermal balance on a surface element of the parabolic
cylindrical concentrator [3].
(X,t)(X,t)-qq(t)q
t
(X,t)T
..A.Cρ
uexitabsorbed
A
AAA
(4)
The initial conditions for the equation (4) are [5, 10,
11]:
)((t)=T(X,t)=TT
ambA,initialA
0
(5)
III.3. Energy balance of the glass
Similarly, the energy balance for the glass was given
by [2, 5, 7, 10, 11]:
(X,t)(X,t)-qq
t
(X,t)T
..A.Cρ
ext
V
VV V
int
(6)
The initial condition of equation (6) is [5, 10, 11]:
)((t)=T(X,t)=TT
ambV,initialV
0 (7)
To solve this problem, we chose the finite difference
method. A calculation program Matlab was established,
after the discretization of non-linear equations that
allowed us to obtain a set of numerical results.
The thermal power emitted by the sun and received by
the concentrator is therefore [5, 10, 11, 22]:
.DNI.KA=q
camcmabsorbed
.. (8)
Where Kcam is Angle of incidence correction factor
modified, is the intercept factor.
We can express the optical efficiency ( optη ) of the
concentrator [5, 10, 11, 15]:
camopt
K=η ..α.ρ
m
(9)
The thermal efficiency ( η ) was calculated as follows [2,
M. Ghodbane et al.
IJECA-ISSN: 2543-3717. December 2017 Page 33
5, 10, 11, 15]:
C
ambAAL
opt
ADNI
)T.(T.AU
ηη
(10)
III.4. The coefficient of thermal losses
The coefficient of thermal losses (UL) was expressed
as [2, 5, 7, 10, 11]:
VVA,ext
A,A
AA
ambAambA
vA,ext
A,
ambA
L
ε
f
εD
DT
εε
)T).(TTσ(T
hD
D
f
TT
C
U
1
450
104.0
1
1
int
1
22
1
int
25.0
1
(11)
Where the factor (f) takes into account the loss ratio
resulting from the wind, it can be obtained by the
following equation [5, 10, 11]:
27300325.0exp
3.161.1
9.04.0
int
A
-
vA
-
A,
T
h εDf
(12)
C1 was given by the following empirical expression
[5, 10, 11]:
251
6.06.0
int
int
2
1
1
5.096.045.1
,
A,extA,
A,
A
DD
D
ε
C
(13)
The term (hv) is the wind convection coefficient, it can
be obtained by the following equation (according
McAdams (1954)) [5, 10, 11, 15, 23]:
Wv
Wh 8.37.5 (14)
IV. Results and discussion
The PTC concentrators can offer an opportunity to
sunny countries such as Algeria for investment and
construction of solar central.
The right choice of the studied site is very important
because each site is characterized by its direct
illumination, the ambient temperature, the speed of the
wind, the latitude, and the elevation compared to the
level of the sea, which play a significant role on the
profitability of the solar concentrator. These factors were
quite apparent in the results obtained where the energy
production vary when moving the solar collector in
different sites. We selected Guemar city to conduct this
study, it is located at an altitude of 62 meters with a
latitude and longitude of 33°29'24'' N north and
06°47'50'' East respectively. PTC concentrator had
headed south. We chose tap water as the working fluid
with a flow rate of 0.015 [kg/s].
The absorber was the seat of the thermal conversion
(from concentrated solar radiation into high temperature
heat sensitive). On wall of the absorber tube, the thermal
energy acquired from the sun has propagated by direct
contact of the particles without appreciable displacement
of the latter. Figures 5a and 5b reflect the average
intensities contours of heat flux on the absorber surface
based on the direct solar radiation (DNI).
a) DNI= 1000 [W/m²]
b) DNI= 500 [W/m²]
Figure 5. Flux intensity contour at the absorber tube [W/m²].
This assessment can approach the actual values of
thermal flow influencing absorbers with a reflectivity of
the mirrors equal to 92% and real illumination values.
The main objective of the optical characterization have
known the concentration of solar power on the surface
absorber tube, and the evolution of the maximum value
of thermal flow depending on the incidence angle of
solar radiation.
Figures 6a and 6b illustrate the average heat flow
distributions. We observe a good distribution of heat flux
M. Ghodbane et al.
IJECA-ISSN: 2543-3717. December 2017 Page 34
at the surface level of the absorber. We can say that our
concentrator has a good overall optical behavior. Thus,
we can conclude that the average distributions of heat
flux provided the software ray tracing issues
representative of real flux distributions by the parabolic
trough concentrator.
a) DNI= 1000 [W/m²]
b) DNI= 500 [W/m²]
Figure 6. Flux intensity distribution at the absorber tube [W/m²].
Now we turn to the thermal analysis, the finite
difference method was chosen to solve the non-linear
equations of thermal balance. A calculation program
using Matlab was developed after the discretization of
the linear equations, which allowed us to obtain a set of
numerical results, thus we will be able to know the
performance of the concentrator. Figure 7 shows the
evolution of optical performance versus time during the
day of the study, while Figure 8 shows the evolution of
thermal performance versus time for the same day.
8 9 10 11 12 13 14 15 16 17
0.4
0.45
0.5
0.55
0.6
0.65
time [hour]
O
p
ti
c
a
l
e
ff
ic
ie
n
c
y
time [hour]
Figure 7. Evolution of optical efficiency.
8 9 10 11 12 13 14 15 16 17
0.4
0.45
0.5
0.55
0.6
0.65
time [hour]
T
h
e
rm
a
l
e
ff
ic
ie
n
c
y
time [hour]
Figure 8. Thermal efficiency evolution versus the time.
It is noted that the thermal performance was equal to
60.61% at 12:00, after this time, the thermal efficiency
decreases with the decreasing of solar radiation
resources.
The receiver must absorb as much concentrated solar
flux as possible, and convert it into thermal energy; this
heat is transferred to water. The difference in temperature
between the two faces (internal and external) of the
absorber tube generates the creation of a heat flow.
Figure 9 represents the variations of the absorber tube
temperature, the fluid temperature and the glass
temperature, where the wind speed (Ww) during the day
was equal to 4.5 [m/s] and the water temperature inside
the absorbent tube was equal to 9°C.
At the beginning of the day (at 08:00am), the
temperature of the absorber tube was equal to the
ambient temperature (TA = Tamb = 292K), after one
hour of heating this temperature increases according to
the direct solar radiation concentrated to the absorber, it
reaches 302 k. It continues to increase where its value
becomes stationary. In this case, the absorber is in a state
M. Ghodbane et al.
IJECA-ISSN: 2543-3717. December 2017 Page 35
of equilibrium, that is to say that all the surfaces of the
absorber are at the same temperature, this state of
equilibrium was very difficult to establish because of the
influence of the wind. The maximum of the ambient
temperature was reached between 12:00 and 14:00 hours,
when the illumination is important.
The absorber tube is heated by concentrated direct
solar radiation; this radiant energy absorbed by the
absorber was converted into heat energy, which is
transferred by convection to the water inside the receiver,
which increases its temperature.
8 9 10 11 12 13 14 15 16 17
280
290
300
310
320
330
340
350
360
time [hour]
te
m
p
e
ra
tu
re
[
K
]
T
f
luide
T
a
bsorber tube
T
g
lass tube
- The temperature of the water
at the absorber tube inlet = 9 ° C.
-The wind speed during the day
is 4.5 m / s
Figure 9. Evolution of the temperatures (TA, TF and TV).
The heat transfer between the absorber tube and the
water comes from the macroscopic movement of the
water. According to figure 9, it is certain that the
absorber tube temperature (TA), the water temperature
(TF) and the glass temperature (TV) were directly related
to the experimental conditions of weather conditions.
The results in figure 9 show the rapid heating of water
by solar irradiation during the day. It is noted that the
temperature of the absorber (TA) is close to (TF) which it
has the maximum value at 14:55, we recorded an
absorber temperature equal to 353 (K), and this is a sign
of a good thermal insulation and low heat loss between
the absorber tube and the surrounding air. The selective
surfaces are taking advantage of different wavelengths of
incident solar radiation, so the selectivity of the surface
will result in a maximum absorption in the solar and
infrared spectrum minimum. Therefore, the absorber tube
has a high absorptivity for visible solar radiation and low
emissivity for the long‘s wavelength infrared radiation
due to the selective coating of the absorber. This coating
can retain the greater part of the incident solar energy on
the surface of the absorber and lose very little amount of
heat radiation in the wavelength when the absorbent
surface becomes hot.
The decrease of the absorber tube surface results in an
increase in the concentration, therefore the performances
are higher. For a test day with a constant volumetric
flow, the temperature depends mainly on the qabsorbed (t),
which is based on optical parameters, geometric of the
concentrator and direct radiation received by the
collector.
8 9 10 11 12 13 14 15 16 17
0
50
100
150
200
250
300
350
time [hour]
th
e
p
o
w
e
r
a
b
s
o
rb
e
d
[
W
]
Figure 10. Evolution of the power absorbed.
The inside of the absorber absorbs infrared radiation,
which undergoes a temperature increase (TA)
(greenhouse effect). Therefore, the temperature of the
outer side is lower and close to the ambient medium
subjected mainly to the wind speed, which creates
convection to the outer side of the absorber, that is why
the information about the meteorological data, including
wind speed and ambient temperature are important
parameters. The useful power absorbed by the receiver is
used to heat the water inside the receiver and increases its
temperature to a temperature of 353 k at 14:55.
In nature, there are three modes of heat transfer,
thermal transfer by conduction, by convection (natural
and / or forced) and by radiation. From these three modes
of transfer results three types of thermal losses: thermal
losses by conduction, by convection and finally by
radiation. For the PTC solar concentrator, the heat losses
are important because the temperature of the absorber
tube is high. Moreover, these concentrators require
regular maintenance to maintain the optical quality of the
mirrors subjected to dust and corrosion of the
environment. Figure 11 shows the variation in the
coefficient of thermal losses as a function of the
difference in temperature between the absorber tube and
the ambient temperature (TA-Tamb). In general, the heat
loss coefficients depend on the insulation quality of PTC
collector.
0 10 20 30 40 50 60 70
3.250
3.375
3.500
3.625
3.750
3.875
4.000
4.125
4.250
4.375
4.500
4.625
4.750
4.875
5.000
th
e
rm
o
l
lo
s
s
e
s
c
o
ff
e
c
ie
n
t
[W
/m
².
K
]
(T
A
-T
amb
) [°C]
Equation
y = Intercept + B1*x^1 + B2*x^2
Weight No Weighting
Residual Sum
of Squares
3.23177E-28
Adj. R-Square 1
Value Standard Error
Intercept 3.4719 1.28987E-15
B1 0.0281 4.41468E-17
B2 -1E-4 3.02289E-19
Figure 11. Evaluation of thermal losses coefficient.
M. Ghodbane et al.
IJECA-ISSN: 2543-3717. December 2017 Page 36
It can be seen from figure 11 that the coefficients of
global heat losses (UL) increase slightly with increasing
temperature. Thus, the coefficient of overall losses varies
proportionally with the difference in temperature
between the receiver tube and the ambient temperature
(TA-Tamb), and this is due to the amount of heat absorbed
by the absorber. UL increases with the increase of (TA-
Tamb), it varies from 3.4 to 5 W / m².K where 0° C < (TA-
Tamb) <70 ° C. Therefore, we see that the coefficient of
losses varies in a slightly slow way; this is due to the
range of operating temperature that is not high, and also
to the good thermal insulation of the receiver.
Generally, the climatic conditions vary from season to
another (intensity of solar radiation and the ambient
temperature) affect the productivity of hot water.
Through our study on linear concentrator [3-6, 10, 11],
we can conclude that the results are very encouraging to
exploit and build fields of linear concentrators in all
regions of the country (north, south, east and west).
V. Conclusion
This work is a numerical study of a parabolic trough
concentrator (PTC) in a volatile day in the winter (Low
air temperature with some wind). Tap water was used as
heat transfer fluid. The study was based on the numerical
analysis of the energy balance equations of the absorbent
tube, the water and the glass envelope surrounding the
absorbent tube. According to this numerical solution, we
can control the absorber temperature, the fluid outlet
temperature and the glass temperature. The thermal
efficiency of device exceeds 61%, where the fluid
temperature at outlet of the absorber tube is equal to 344
[K]. The results are very encouraging for the
development of this type of solar concentrator in the
country.
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Nomenclatures
.
V
Volume flow rate (m
3
/s)
Intercept factor
AA Absorber area (m²)
Ac Collector aperture area (m²).
CA Specific heat of the absorber (J/kg k).
CF Specific heat of the fluid (J/kg k).
Cp Thermal capacity (J/kg k).
DA,ext External diameter of the absorber (m).
DA,int Internal diameter of the absorber (m).
DV,ext External diameter of the glass tube (m).
DV,int
Internal diameter of the glass (the
transparent envelope) (m).
hv
Coefficient of transfer by convection of
the wind (W/m².K).
Kcam
Angle of incidence correction factor
modified
qabsorbed
Heat absorbed in the absorber tube
(W/m²).
qexte
Heat quantity lost to the outside
(convection + conduction) between the
glass and ambient (W/m²).
qint
Internal heat (convection + conduction)
between the glass and ambient (W/m²).
qu
Heat exchanged by convection between
the absorber and the fluid (W/m²).
Se
The effective area of a sensor reflector
(m²).
Ww Wind velocity (m/s).
TA Temperature of the absorber (K).
Tamb Ambient temperature (K).
TF Fluid temperature (K).
TV Temperature of the glass (K).
UL
Overall coefficient of heat loss
(W/m².K).
εA Emissivity of the absorber tube
εV
Emissivity of the casing transparent
glass
ρA Density of the absorber (kg/m
3
).
ρF Fluid density (kg/m
3
).
σ Stefan-Boltzmann constant (W/m
2
.K
4
).