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SIMULATION OF PARABOLIC-TROUGH COLLECTOR (MODEL TE38) USING SOLAR POSITIONS COORDINATES OF BAUCHI
I. S. Sintali, G. Egbo and H. Dandakouta
ibrahimsaidu98@gmail.com; gegbo2000@yahoo.co.uk; dandakuta@yahoo.co.uk
Department of Mechanical Engineering Faculty of Engineering and Engineering Technology Abubakar Tafawa Balewa University, Bauchi
The model equations included the universal time (UT), day (n), month (M), year (Y), delta T (∆T), longitude (γ) and latitude (ϕ) in radian.
The heliocentric longitude (H), geocentric global coordinates and local topocentric sun coordinates were considered in the modeling
equations. The thermal efficiency ηth of the PTC considered both the direct �Egd� and reflected �Egr� solar energy incident on the glass- cover as well as the thermal properties of the collector and the total energy losses (Qlosses) in the system. The model equations were used
to simulate the PTC (Model TE38) using meteorological and radiative data of Bauchi. The results show that the temperature of the glass-
cover (Tg), absorber-tube (Tt), and the working fluid (Tf) increases with increase in time from 35oC, 61oC and 39oC to 43oC, 125oC and
117oC respectively. The efficiency of the PTC increases with increase in time to a maximum value of 95% at 11:00hrs and reduces gradually to a minimum value of 62% at 19:00hrs.
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Parabolic-trough Collector (PTC) consists of a reflecting
Receiver
Glass envelope
Drive motor/gear box assembly
surface made by bending highly polished stainless steel reflector and fixed on a parabolic contour. The reflecting surface may also be made of polished mirror. The parabolic contour is supported by steel framework and
mounted on a reflector support structure. A hand-wheel
Flex hose
Pylon
Foundation Reflector
Fig 1. Parabolic-trough Concentrator
operated tilting mechanism permits adjustment of declination, in order to track the sun, thus, maintains the focusing of the solar radiation on the receiver. The receiver assembly comprises of the absorber-tube covered with a glass-cover tube to reduce heat losses, is placed along the focal line of the receiver as shown in figure 1.
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The definition of a parabola provides that all paraxial rays striking the parabolic reflector are reflected toward the line-focus. Concentration is achieved by using the reflector to channel natural concentration of energy on the reflector’s aperture area into a significantly smaller area, the receiver assembly that is mounted on the focal line of the parabola. Typically, concentrator systems will not work efficiently without tracking, so at least single-
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axis tracking is required. This is as a result of the
continuous changing sun’s position in the sky with respect to time of the day as the sun moves across the sky. Thus, the location of the sun may be predicted for any latitude, time of day, and any day of the year, using simple trigonometric formulae.
The accuracy of the solar tracking depends to a great extent on the solar coordinates at a particular location and at a given instant. This would greatly influence the solar radiation collection and thus the efficiency of the system. This necessitates the need to simulate the PTC using solar position coordinates in order to enhance the performance of the collector.
When the sun is observed from a position on the earth, the point of interest is to know the position of the sun relative to a coordinate system that is located at the point of observation not at the center of the earth. The position of the sun relative to these coordinates can be fixed by two
angles; solar altitude angle (α) and the solar azimuth
angle (A). These are as shown in figure 2 [1].
Williams and Raymond, [1] stated that solar altitude angle
passing through the point and the sun and the line passing
through the point tangent to the earth and passing below the sun.
Fig. 2. Composite View of Parallel Sun Rays Relative to the Earth
Surface and the Earth Center Coordinates
The solar azimuth angle (A) is the angle between the line under the sun and the local meridian pointing to the
equator, or due south in the northern hemisphere. It is positive when measured to the east and negative when
measured to the west. The solar zenith angle ( 𝜃𝑧 ) is the
angle between a solar ray and local vertical direction and
it is the complement of (α).
The time of the year is specified by the topocentric solar declination (𝛿𝑡). The time of the day is specified by the
hour angle (ℎ𝑡 ). The hour angle is defined as zero at local
solar noon and increases by 15o for each hour. Solar time
is location dependent and is generally different from local time, which is defined by time zones and other approximation. Some situations such as performance correlations, determination of true south, and tracking algorithms require an accurate knowledge of the difference between solar time and the local time [2].
Other critical factors to be considered in the analysis of the solar concentrating collector are its material properties. When radiation strikes a body, part of it is reflected, a part is absorbed and if the material is transparent, a part is transmitted. The fraction of the incident radiation reflected is the reflectance (ρ), the fraction of the incident radiation transmitted is the transmittance (τ) and the fraction absorbed is the absorptance (α) as shown schematically in figure 3.
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Body
In-coming radiation
Transmittance
Reflectance
Absorptance
The Universal Time (UT), or Greenwich civil time, is
used to calculate the solar position based on the earth’s rotation and is measured in hours from 0-hour at midnight. The minutes and seconds must be converted into fraction of an hour.
Fig. 3. Reflection, Absorption and Transmission of incident solar radiation by a solid body.
Absorption of solar radiation is what solar heat collector is
The time scale, ( tG
and t ) are the Julian day and the
all about; therefore, a blackbody surface is ideal surface for making any solar collector’s absorbing surface. For this reason, the latter is usually made as black as possible so that it will have a high absorption capacity.
In developing the model equations for computing the
Ephemeris Julian day respectively. These are used to
overcome the drawbacks of irregularly fluctuating mean solar time due to elliptical shape of the earth’s orbit i.e. the interval between two successive passages of the sun through the meridian, is not constant. They are defined as follows [4].
𝑡𝐺 = 𝐼𝑁𝑇�365.25(𝑌 − 2000)� + 𝐼𝑁𝑇�30.6001(𝑀 +
1)� + 𝑛 + 𝑈𝑇 − 1158.5 Eqn. 1
24
efficiency of PTC using solar coordinates, the input
parameters are determined by the time scales because of
𝑡 = 𝑡𝐺
+ ∆𝑇
86400
Eqn. 2
the importance of using the correct time in the calculation of solar position for solar radiation application.
2.1 Determination of Delta T (∆Τ)
Delta T (∆Τ) is a measure of the difference between a time scale based on the rotation of the Earth (Universal
time UT) and an idealized uniform time scale at the
where INT is the integer of the calculated terms, Y is the
year, M is the month of the year, n is the day of the month with decimal time and UT is the Universal Time.
Sun position is also very location-dependent, so it is
critical that the longitude and latitude of the site are known before calculations are carried out. In this case the
surface of the Earth (Terrestrial time TT). The values of
∆Τ can be obtained from the (TT – UT) smoothed data provided in Bulletin B of the International Earth Rotation
longitude and latitude of Bauchi are 9.81o
respectively [5].
E and 10.33o N
and Reference Systems, (IERRS) [3]. The value of ∆𝑇
was obtained for the year 2014 to be approximately 67.7
seconds.
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center of the sun. This is the most critical point, and the
main source of errors. The heliocentric longitude (H) is the sum of four terms defined as follows;
𝐻 = 𝐿𝑦 + 𝐿𝑚 + 𝐿ℎ + 𝐿𝑝 Eqn. 3
where: Ly = 1.74094 + 1.7202768683e−2t +
3.34118e−2sinσ + 3.488e−4 × sin2Ao Eqn. 4
𝐴𝑜 = 1.72019𝑒−2𝑡 − 0.0563 Eqn. 5
than completely smooth motion, thus the need to compute
the correction to geocentric longitude defined by the following relation [6].
∆𝛾 = 8.33𝑒−5 × sin(9.252𝑒−4t − 1.173) Eqn. 10
This is the inclination of the center of the earth axis to the
sun and is correlated as follows [6].
Lm = 3.13e−5 × sin (0.2127730t − 0.585) Eqn. 6
ε = −6.21e−9t
+ 0.409086 + 4.46e−5
× sin(9.262e−4t +
Lh = 1.26e−5 × sin(4.243e−3t + 1.46) + 2.35e−5 ×
sin(1.0727e−2t + 0.72) + 2.76e−5 × sin(1.5799e−2t +
2.35) + 2.75e−5 × sin(2.1551e−2t − 1.98) +
1.26e−5 × sin(3.1490e−2t − 0.80) Eqn. 7
𝐿𝑝 = (�(−2.30796𝑒−7𝑡2 + 3.7976𝑒−6 )𝑡2 − 2.0458𝑒−5�𝑡2
2
0.397) Eqn. 11
This is the coordinates of the sun with respect to the earth’s center.
The geocentric solar longitude may be estimated using the
+ 3.976𝑒−5)𝑡2
Eqn. 8
following relation [6].
with 𝑡2 = 0.001𝑡 Eqn. 9
where Ly , Lm , Lh , and Lp are linear increase with annual
oscillation, moon perturbation, harmonic correction and
polynomial correction respectively. The time scale t2 is introduced in order to have more homogenous quantities
in the products within the polynomial, avoiding too rough rounding approximation [6].
“Geocentric” means that the sun position is calculated
with respect to the earth center [4]. One problem is that the sun's apparent diurnal and annual motions are not
𝛾𝑔 = 𝐻 + 𝜋 + ∆𝛾 − 9.932𝑒−5 Eqn. 12
The ascension angle (𝛼𝑎 ) is defined by [6].
𝛼𝑎 = 𝑎𝑟𝑐tan(𝑠𝑖𝑛𝛾𝑔 𝑐𝑜𝑠𝜀 𝑐𝑜𝑠𝛾𝑔 )
where arctan is an arctangent function that is applied to maintain the correct quadrant of the 𝛼 where 𝛼 is in the
range from – 𝜋 to 𝜋.
2.6.3 Computation of geocentric declination (δ )
The geocentric solar declination is the declination of the sun with respect to the earth’s center. The angle between the earth’s equatorial plane and the earth-sun line varies
𝑜
completely regular, due to the ellipticity of the Earth's
between ±23.45
throughout the year. This angle is called
orbit and its continuous disturbance by the moon and planets. Consequently, the complex interactions between
the bodies produce a wobbly motion of the earth rather
the declination(𝛿). At the time of the year when the
northern part of the earth’s rotational axis is inclined
toward the sun, the earth’s equatorial plane is inclined
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23.45o to the earth-sun line. At this time, the solar noon is
at its highest point in the sky and the declination angle(𝛿) = ±23.45𝑜 as illustrated in figure 4. This
condition is called the summer solstice [7]. Thus, the declination can be computed at any given instant by equation 14.
𝛿 = 𝑎𝑟𝑐sin(𝑠𝑖𝑛𝜀 𝑠𝑖𝑛𝛾𝑔 ) Eqn. 14
Fig. 4. Solar Declination Angle
The hour angle is the angle through which the earth must turn to bring the meridian of a point directly in line with the sun’s rays. At solar noon the hour angle is 0 and it expresses the time of a day with respect to solar noon. It is measured positively west ward from the observer. One
𝑜
According to Reda and Andreas, [4] topocentric sun coordinates means that the sun position is calculated with respect to the observer local position at the earth surface. The topocentric coordinates differ from the geocentric because they have their origin on the earth surface, and not on the earth center; the difference must be considered. Grena [6] stated that topocentric sun coordinates affects the sun positions by many seconds of arc.
2.9.1 Topocentric right ascension (𝛼𝑡 )
The topocentric ascension angle is correlated as [6].
𝛼𝑡 = 𝛼𝑎 + ∆𝛼 Eqn. 17
2.9.2 Topocentric solar declination (𝛿𝑡)
This is the declination as expressed in section 2.6.3 with
respect to the local observer position. This angle is given as [6].
𝛿𝑡 = 𝛿 − 4.26𝑒−5 × (𝑠𝑖𝑛𝜙 − 𝛿𝑐𝑜𝑠𝜙) Eqn. 18
where 𝛿 geocentric declination and 𝜙 observer local
latitude.
This is as explained in section 2.7 and is determined with respect to the local observer position [6].
hour is equivalent to 2𝜋 = 0.262𝑟𝑎𝑑 𝑜𝑟 360
= 15𝑜[4].
ℎ = ℎ − Δ𝛼 Eqn. 19
24 24 𝑡
ℎ = 6.3003880990𝑡𝐺 + 4.8824623 + 0.9174∆𝛾 + 𝛾 −
𝛼𝑎 Eqn. 15
The parallax correction may be computed using the
following correlation [6].
∆𝛼 = −4.26𝑒−5 × 𝑐𝑜𝑠𝜙𝑠𝑖𝑛ℎ Eqn. 16
𝑐ℎ𝑡 = cosh + Δ𝛼𝑠𝑖𝑛ℎ (Appro.cosine of ht ) Eqn. 20
𝑠ℎ𝑡 = 𝑠𝑖𝑛ℎ + Δ𝛼𝑐𝑜𝑠ℎ (Appro. sine of h t ) Eqn. 21
Refraction Correction (𝑒𝑜 )
Atmospheric refraction is the deviation of light or
other electromagnetic wave from a straight line as it passes through the atmosphere due to the variation in air density as a function of altitude and is given by [8].
𝑒𝑜 = 𝑎sin(𝑠𝑖𝑛𝜙𝑠𝑖𝑛𝛿𝑡 + 𝑐𝑜𝑠𝜙𝑐𝑜𝑠𝛿𝑡 𝑐ℎ𝑡 ) Eqn. 22
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maximum amount of solar radiation reaching the surface
(or geometric aperture) is reduced by cosine of this angle.
This correction factor is correlated as [9].
Δe = 0.08421P
�(273+T)tan eo+ 0.0031376 �
eo+ 0.089186
Eqn. 23
The other angle of importance is the tracking angle𝜌𝑡.
Most type of medium and high-temperature collectors
where T is Temperature at a particular time of the day and
P is the pressure at that same time.
The solar zenith angle 𝜃𝑧 is the angle between a solar ray
and local vertical direction and it is the complement of the altitude 𝐴 as illustrated in figure 2.
require a tracking drive system to align at least one and
often both axes of the collector aperture perpendicular to the sun’s central ray. This is illustrated in figure 5.
θz =
− e − Δe Eqn. 24
2
The solar azimuth is the angle between the line under the sun and the local meridian pointing to the equator, or due south in the northern hemisphere. It is positive when measured to the east and negative when measured to the west as illustrated in figure 2.
A = 𝑎tan2(sht cht sinϕ − tanδt cosϕ) Eqn. 25
Fig. 5. Solar Parabolic-trough Tracking Aperture where tracking rotation is about the axis.
For practical application when the tracking axis is oriented
in the north-south direction the incidence angle,𝜃𝑖 , and the tracking angle, 𝜌𝑡, and are given by equation 27 and 28
respectively [10].
𝑐𝑜𝑠𝜃𝑖 = �1 − 𝑐𝑜𝑠2 𝛼𝑎 𝑐𝑜𝑠2 𝐴 Eqn. 27
The solar altitude at a point on the earth is the angle
𝑡𝑎𝑛𝜌𝑡 =
sin 𝐴
tan 𝛼𝑡
Eqn. 28
between the line passing through the point and the sun and the line passing through the point tangent to the earth and passing below the sun as shown in figure 2.
α = sinϕsinδt + cosϕcosδt cosht Eqn. 26
where; 𝜙 is the local latitude.
In the design of solar energy systems, it is most important to be able to predict the angle between the sun’s rays and a vector normal to the aperture or surface of the collector.
This angle is called the angle of incidence θi ; the
The solar radiation incident on the concentrator is reflected on to the receiver (absorber tube) located at the focal line through which working fluid flows and which is covered by concentric-transparent glass cover. As the temperature of the receiver increases, heat transfer processes take place. Energy in transition under the motive force of a temperature difference between components of the collector forms the basis for the determination of heat gained and heat losses to and from one component to
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another. The PTC (Model TE38) used for the simulation
(𝑊 − 𝐷)𝐿
𝐴𝑡 𝜎�𝑇𝑡 𝑔
𝜌𝑐 𝛼𝑔 �
𝜋 � (𝐼𝑏𝑒𝑎𝑚 ∗ 𝑅𝑏 ) + 1
𝐴𝑡
4 − 𝑇 4 �
1
shown in figure 6 has the following data:
𝜀𝑡 + 𝐴𝑔 �𝜀𝑔 − 1�
4 − 𝑇 4 � − 𝐴 ℎ �𝑇 − 𝑇 � =
Inclination and azimuth - Adjustable
Parabolic reflector - Stainless Steel
−𝜎𝜀𝑔 𝐴𝑔 �𝑇𝑔
𝑚𝑔 𝑐𝑝𝑔 𝑑𝑇𝑔 ⁄𝑑𝑡
𝑠𝑘𝑦
𝑔 𝑐 𝑔
𝑠𝑢𝑟
Eqn. 29
Aperture width ( W ) - Collector length ( L ) - Focal length ( f ) - Aperture area ( Aa ) -
Rim angle ( ψrim ) -
800mm (0.8m)
300mm (0.3m)
487mm (0.487m)
0.24m2
450
Where: absorptance of the glass-cover material ( α g ), outer radius of the enveloping glass-cover ( R ),outer diameter of the enveloping glass-cover ( D ), length of the concentrator ( L ), tilt factor ( Rb ), beam radiation on a horizontal surface ( I beam ), diffuse radiation ( I diff
), reflectance of the concentrator ( ρ c ), aperture width of the concentrator ( W ), surface area of the enveloping glass-cover ( Ag ), mass of the enveloping-glass-cover
material ( mg ), specific heat capacity of the enveloping-
Fig. 6. Basic Components of the Parabolic-Trough
Collector
Energy balance equations for a PTC by by Egbo et al, [11], considered the heat-energy-gain, the heat-energy- loss and the heat-energy-transfer between the components, i.e. the reflecting surface, the glass-cover and the absorber-tube, the thermal properties of the materials of the components and geometric dimensions of the SPTC. The equation for the enveloping glass-cover temperature developed by by Egbo et al, [11] is given as follows;
The energy balance equation for the enveloping glass- cover can be written as follows;
2𝛼𝑔 𝑅𝐿�(𝐼𝑏𝑒𝑎𝑚 ∗ 𝑅𝑏 ) + 𝐼𝑑𝑖𝑓𝑓 � +
glass-cover material ( Cp g ), surface area of the absorber-tube ( At ), Stefan-Boltzmann’s constant of radiation ( σ ), temperature of the absorber-tube ( Tt ),
temperature of the enveloping glass-cover ( Tg ),
emittance of the enveloping glass-cover material ( ε g ), emittance of the coating material on the absorber-tube (
ε t ), sky temperature ( Tsky ), ambient temperature ( Tsurr ) and convective heat transfer coefficient (h), temperature gradient of the enveloping-glass-cover (
dTg ) as shown in figure 7. Where D is the outer
dt
diameter of the enveloping glass cover, D 1 is the inner
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diameter of the enveloping glass cover, Xg thickness of
the enveloping glass cover.
d
Where: absorptance of the absorber-tube material ( α t ), transmittance of the enveloping glass-cover material (
τ g ), surface area of the tube based on internal diameter
r
2
qc
Xg
of absorber-tube ( Atin ) and temperature of the fluid (
T f ), convective heat transfer coefficient of the fluid (
Fig. 7: The enveloping glass-cover showing heat Gain and heat Loss
For purpose of solar concentrator design, it is often necessary to convert the beam radiation data on a horizontal surface to radiation on a tilt surface by using
a conversion ratio Rb . This depends solely on the solar topocentric angles [11]. Consequently, the beam
radiation incident on the aperture of the concentrating
h f ), inner radius of the absorber-tube ( r1 ) and outer radius of the absorber-tube ( r ), mass of the absorber- tube material ( mt ), specific heat capacity of the enveloping-glass-cover material ( Cpt ) and temperature
gradient of the absorber-tube ( dTt ).
dt
The equation for the fluid temperature developed by Egbo et al, [11] is given as follows;
𝐴𝑖𝑛�𝑇𝑡−𝑇𝑓 �
2𝐴𝑐�𝑇𝑓 −𝑇𝑠𝑢𝑟𝑟�
𝑑𝑇 ⁄𝑑𝑡
Eqn. 32
collector becomes𝐼𝑏𝑒𝑎𝑚 ∗ 𝑅𝑏 .
𝑟
𝐴𝑖𝑛𝑙𝑛� �
1 + 1
𝑓 𝑝𝑓 𝑓
𝑅𝑏 =
𝑐𝑜𝑠(𝜙−𝜌)𝑐𝑜𝑠𝛿𝑡 𝑐𝑜𝑠ℎ𝑡+ 𝑠𝑖𝑛(𝜙−𝜌)𝑠𝑖𝑛 𝛿𝑡
𝑐𝑜𝑠𝜙 𝑐𝑜𝑠𝛿𝑡𝑐𝑜𝑠ℎ𝑡+ 𝑠𝑖𝑛𝜙 𝑠𝑖𝑛𝛿𝑡
Eqn. 30
� 1 +
ℎ𝑓
𝑟𝑖 �
2𝜋𝐾𝐿
ℎ𝑐
ℎ𝑓
The energy balance for the absorber-tube is as shown in figure 8 and can be written as in equation 31 follows;
Where: mass of the working fluid ( m f ), specific heat
capacity of the working fluid ( Cp f ) and temperature
dTf
gradient of the working fluid, ( )
dt
E
d
Receiver Tube
q
f
Xt
d1 d
Collector (𝜼𝒕𝒉 )
The thermal efficiency of the Parabolic-trough
Collector is given by;
Et r q 1
𝜂𝑡ℎ = 1 −
𝑄𝑙𝑜𝑠𝑠𝑒𝑠
𝑄𝑖𝑛𝑝𝑢𝑡
Eqn. 33
Fig. 8: Representation of heat gain and heat loss by absorber- tube.
where Q losses is the total heat losses and Qinput is the
𝛼𝑡 𝜏𝑔 �
2𝑅𝐿
𝜋
� �(𝐼𝑏𝑒𝑎𝑚 ∗ 𝑅𝑏 ) + 𝐼𝑑𝑖𝑓𝑓 � +
4 4
total heat supplied to the receiver.
The hourly heat supplied to the receiver (Q input ) can be
𝛼𝑡 𝜏𝑔 𝜌𝑐 �
(𝑊−𝐷)𝐿
� [𝐼𝑏𝑒𝑎𝑚 ∗ 𝑅𝑏 ] −
𝐴𝑡𝜎�𝑇𝑡 − 𝑇𝑔 � −
𝜋2
1 𝐴𝑡 1
𝐴𝑖𝑛�𝑇𝑡−𝑇𝑓�
𝑟
= 𝑚𝑡 𝑐𝑝𝑡 𝑑𝑇𝑡 ⁄𝑑𝑡
𝜀𝑡+𝐴𝑔�
−1�
Eqn. 31
computed as follows:
𝑄𝑖𝑛𝑝𝑢𝑡 = �(𝐼𝑏𝑒𝑎𝑚 ∗ 𝑅𝑏 ) + 𝐼𝑑𝑖𝑓𝑓
𝐴𝑖𝑛𝑙𝑛� �
�[𝑊𝐿] Eqn. 34
� 1 +
ℎ𝑓
𝑟𝑖 �
2𝜋𝐾𝐿
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The total heat losses in the system ( Qlosses ) is considered as the sum of the radiative heat-loss from
the surface of the enveloping glass-cover to the
surroundings ( q ), the convective heat loss from the
2
surface of the enveloping glass-cover to the surroundings ( qc ) and the conductive/convective heat
loss from the fluid to the surroundings ( q1 ). This can
be expressed as follows;
𝑄𝑙𝑜𝑠𝑠𝑒𝑠 = 𝑞𝑟2 + 𝑞𝑐 + 𝑞1 Eqn. 35
Mat lab program was employed for the simulation. The prediction of temperature change of the glass-cover, the absorber-tube and the fluid with change in time, using simulation model are carried out aimed at ascertaining the performance of a solar parabolic-trough concentrating collector (Model TE 38). The results are presented in Tables 1 and Figures 9-12.
From the result shown in figure 9, the temperature of the glass-cover increases with increase in time to a maximum value of 51oC at 16:00hrs and subsequently
reduces gradually to a value of 43oC at 19:00hrs. This is
as a result of decrease in the intensity of the solar radiation falling on the collector which reduces as the sun set is approached. The transmissivity of the glass- cover and energy losses from the glass-cover to surroundings may result in making the temperature of the glass-cover to be low; the higher the transmissivity of the material the more the solar radiation being transmitted to the absorber-tube, thus less temperature would be experienced on the glass cover [12]. This may
increase the efficiency of the PTC as more temperature
is being received by the absorber-tube. The decrease in temperature that occurred between 9:00hr-10:00hr is due to cloudy condition and increase in velocity experienced in morning hours thus, reduces the temperature momentarily.
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Table 1: Simulated Hourly Temperatures of the Glass-Cover�𝑇𝑔 �, Absorber-Tube(𝑇𝑡 ), Working Fluid
(% 90 95 95 95 94 93 91 89 83 72 62
�𝑇𝑓 �and Thermal Efficiency(𝜂𝑡ℎ )
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ISSN 2229-5518
631
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52
50
48
46
44
42
40
38
36
34
9 10 11 12 13 14 15 16 17 18 19
Time(Hours)
Fig. 9: Relationship between the Temperatures
the convective heat loss and reduces the heat losses due to radiation, because the produced heat from the absorber-tube is trapped as stated by Egbo, [13]. These factors greatly influence the temperature of the absorber-tube to increase.
Figure 11 shows the relationship between the temperatures of the fluid with time. The fluid
o o
130
120
110
100
90
of the Glass-Cover and time of the day
temperature increases from 39 C at 9:00hrs to 117 C
at 19:00hrs with increase in time. This is as a result of conductive and convective heat transfer from the absorber-tube to the fluid inside the tube which increases with time.
80
120
70 110
60
9 10 11 12 13 14 15 16 17 18 19
Time(Hours)
100
90
Fig. 10: Relationship between the Temperatures
of the Absorber-tube and time of the day
Figure 10 shows the relationship of the temperature of the absorber-tube with time of the day. The temperature increases gradually with time from 61oC at 9:00hrs to a maximum temperature of 125oC at
80
70
60
50
40
30
9 10 11 12 13 14 15 16 17 18 19
Time(Hours)
Fig. 11: Relationship between Temperatures of the fluid and time of the day
19:00hrs. This trend is as a result of increase in the amount of solar radiation from the collector through the glass-cover to the absorber-tube which increases with time as the sun rises. The high transmissivity of the glass-cover, high absorptivity of the absorber-tube (copper tube) and coating of the absorber-tube with emulsion black paint that has low emittance has
100
95
90
85
80
75
70
65
60
9 10 11 12 13 14 15 16 17 18 19
Time(Hours)
Fig. 12: Relationship between thermal efficiency and time of the day
contributed to the rate of incident solar radiation absorbed by the absorber-tube. Also, the space between the glass-cover tube and the absorber-tube was hermetically closed and evacuated; it eliminates
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When the temperature difference between the fluid and the contact surface causes density variation in the fluid, convective heat transfer takes place and thus heat is
International Journal of Scientific & Engineering Research, Volume 5, Issue 9, September-2014 633
ISSN 2229-5518
being transfer from the absorber-tube to the fluid [12].
The rate at which heat is actively removed from the absorber-tube to the fluid determines the operating temperature of the collector. The copper tube which was used as the absorber-tube is coated with emulsion black paint that has low emittance thermal property, increases the absorptance of the incident solar irradiance and reduces simultaneously the reflectance, thus increases the amount of heat transferred to the fluid [12].
A maximum efficiency of 95% was attained at the
11:00hrs, subsequently the efficiency reduces to a minimum value of 62% at 19:00hrs as shown in Figure
22. The thermal efficiency of the PTC reduces as a result of decrease in the intensity of the solar radiation falling on the collector which reduces as the sun set and the rate of energy losses within the collector system. Thus a model equation for simulation of a Parabolic- trough Collector System using solar coordinates of Bauchi is successfully developed and tested.
The input data considered for the model equations are the Universal Time (𝑈𝑇), Delta T(∆𝑇), Date (day n,
months M, and years Y), longitude 𝛾 and latitude 𝜙 (in
radians) of Bauchi. The data also include the geometric
global coordinates and local topocentric sun coordinates. The thermal efficiency (𝜂𝑡ℎ ) of the
Parabolic-trough collector, considered both the total energy supplied to the receiver 𝑄𝑖𝑛𝑝𝑢𝑡 and the total
energy losses 𝑄𝑙𝑜𝑠𝑠𝑒𝑠in the system. The results show
that the temperatures of the glass-cover, absorber-tube,
and the working fluid increases with increase in time.
The thermal efficiency of the collector increases with
increase in time to a maximum value of 95% at
11:00hrs. However, it reduces to a minimum value of
62% at 19:00hrs.
[1] William, B. S. and Raymond, W. H. “Solar Energy Fundamentals and Design with Computer Applications”. John Wiley and Sons Inc. New York, pp. 38-62, 1985
[2] John, R. H., Richard, B. B. and Gary, C. V. “Solar
Thermal Energy Systems; Analysis and Design”. McGraw-Hill Book Company, New York pp. 54-78, 1982.
[3] International Earth Rotation and Reference Centre.
Current values and longer term predictions of Delta T (2000 to 2050). Retrieved February 21, 2012; from: http//asa.usno.navy.mil/seck/DeltaT.html
[4] Reda, I. and Andreas, A. “Solar Position Algorithm for
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[5] Nigerian Meteorological Agency (NIMET). Bauchi
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[6] Grena, R. “An Algorithm for the Computation of the Solar
Position”. Elsevier, Solar Energy Vol. 82, pp. 462-470,
2008.
[7] Blanco-Muriel, M., Alarcon-Padilla, D. C., Loea- Moratalla, T. and Lara-Coira, M. ”Computing the Solar Vector”. Elsevier, Solar Energy, 70(5), pp. 431-441,
2001.
[8] Wilkinson, B. J. “The effect of atmospheric refraction on the solar Azimuth”. Elsevier Solar Energy. Vol. 30, pp.
295, 1983.
[9] Muir, L. R. “Comments on The effect of atmospheric refraction on the solar azimuth”. Elsevier, Solar Energy, Vol. 30, pp. 295, 1983.
[10] Williams, B. and Geyer, M. “Power form the Sun.
Retrieved March 03, 2004; from: http:/www.powerfrom the sun.net/book, 2003.
[11] Egbo, G. I., Sambo A. S. and Asere, A. A. “Development
of Energy Equations for Parabolic-trough Solar Collector” Nigerian Journal of Engineering Research and Development. 4(1), pp. 28-36, 2005.
[12] Tiwari, G. N. “Solar Energy: Fundamentals, Design,
Modeling and Applications”. Narosa Publishing House, India, 2006.
[13] Egbo, G “Experimental Performance Evaluation of a Solar Parabolic-Trough Collector (Model Te. 38) in Bauchi” International Journal of Pure and Applied Sciences Vol. (2)1, pp.55-64, 2008
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