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   Concentrated Evacuated Tubes for Solar-Thermal
      Energy Generation using Stirling Engine
           Achintya Madduri Member, IEEE, Denise Loeder, Nic Beutler, Mike He Member, IEEE, Seth
                                           Sanders Fellow, IEEE



   Abstract—In this study a commercial evacuated tube solar hot-   the solar-thermal collection system, which is generated by
water system was modified to be used as a thermal-power source      the evacuated tube system. Tests were conducted on various
for a thermodynamic engine. Commercial hot-water systems           topologies using evacuated tubes for increasing the efficiency
are meant to operate at temperatures that are close to the
boiling point of water. Single-tube non-imaging concentrators      of solar-heat collection.
were built in order to increase the input solar-radiation per
tube and therefore supply thermal-power at temperatures of
180 − 220 ◦ C. Simulations and experiments show that it is
possible to use concentrators to increase the temperature range
of thermal power extracted from a commercial evacuated tube
system and use this modified system to increase the efficiency of
solar-thermal energy generation.
  Index Terms—Solar-Thermal Energy Generation, Non-imaging
Concentrators, Evacuated-tube Solar-Thermal Generators


                      I. I NTRODUCTION
       ENEWABLE energy technology will need to address             Figure 1. A system representation of a solar thermal electricity generation

R      important challenges in order to be adopted at high pen-
etrations in a modern electric grid. These challenges include
                                                                   scheme using a Stirling-cycle engine.


achieving low enough cost to be economically attractive and          The Carnot efficiency can be calculated using equation 1.
mitigating the variability inherent in renewable energy sources,
                                                                                                              Tamb
a problem most directly addressed by energy storage. There-                                 ηcarnot = 1 −                                 (1)
                                                                                                              Thot
fore, there exists a need for an electric generation technology
that easily incorporates low-cost energy storage. A Stirling         The heat engine is expected to operate at fraction of the
engine based system for distributed generation of electricity is   Carnot cycle (Equation 2) [1].
a renewable energy technology that addresses the challenges                                             2
described above [1]. The proposed system, as shown in Figure                               ηengine =      · ηcarnot                       (2)
                                                                                                        3
1, is comprised of a passive solar collector, a hot thermal
storage subsystem, a Stirling engine for energy conversion,           The total system efficiency of a heat engine is define as the
and a waste heat recovery system to implement combined             product of the thermal-conversion efficiency and the engine
heat and power. The hot-fluid storage tank can be implemented       thermodynamic efficiency (Equation 3).
with commercially available residential hot-water tanks or with
                                                                                        ηtotal = ηthermal · ηengine                       (3)
low cost thermal storage fluids, such as mineral or vegetable
oils. However, synthetic thermal storage fluids or phase-change
materials (PCMs) can also be deployed in order to achieve
higher energy storage density. The system as envisioned would      A. Evaluation Criteria
be appropriate for residential solar generation or on a small         The evaluation criteria for comparing the performance of
commercial building scale. The focus of this paper is on           unconcentrated evacuated tubes to concentrated evacuated
achieving high-efficiency performance from a commercially           tubes is the power output from an ideal Carnot engine per
available solar hot-water system at temperatures in the range      unit of installed solar-collector area. An insolation level of
of 180 − 220 ◦ C.                                                  Qin = 1000 W/m2 is often used as a way to standardize
   It is of particular interest to have a high-temperature input   performance metrics for solar-collectors. Since the input in-
to a thermodynamic engine, because the efficiency of a ther-        solation is normalized per unit area, it is also informative to
modynamic cycle is related to the temperature change, ∆T ,         normalize the thermal-power output by installed solar-collector
between the hot and cold sides of the engine. In this specific      area, i.e. report Qout in units of W/m2 as well. By multiplying
case the cold-side temperature of the engine is determined by      the thermal-power output, Qout , by the idea Carnot efficiency,
rejection to ambient Temperature, Tamb . The input temperature     ηcarnot (Equation 1), one achieves a measure of the theoretical
is determined by the temperature of the hot supply from            output mechanical power from a solar-powered heat engine per
                                                                                                                                                                      2


                                                                                            700
                                                                                                                                  Unconcentrated evacuated tube
                                                                                                                                  With concentration ratio A = 2.22
                                                                                            600

                                                                                                                               @ Qin = 1000 W/m2
                                                                                            500




                                                                              Qout (W/m2)
                                                                                            400



                                                                                            300



                                                                                            200



                                                                                            100



                                                                                             0
Figure 2.   A representation of an Apricus evacuated tube system [2].
                                                                                                  0   50    100         150          200           250            300
                                                                                                            ∆T = Tabsorber−Tambient (°K)


unit installed solar-collector area. A reason to compare solar-               Figure 3. Theoretical output thermal-power per unit installed solar-collector
collection systems over the same installed collector area is                  area curves of an Apricus evacuated tube system. The red line represents the
that the available area is often the limiting factor. While cost              efficiency of the system with concentration. Equation 4 is used with input
                                                                              insolation of Qin = 1000 W/m2 to generate these curves.
of the components is also important, there is not much of a
difference in material cost between an unconcentrated and a
concentrated evacuated tube system.
                                                                              C. Non-Imaging Concentrators
B. Evacuated Tube System                                                         The foundations of non-imaging optics and concentrators
   The solar-collector system is comprised of evacuated tube                  are described in the classical work done by Winston et. al. [3],
absorbers with non-imaging concentrators to achieve the tem-                  [4]. The concentration ratio of a concentrator is described as
peratures required to maximize efficient operation at low                      the area of the input aperture to the area of the absorber. The 2-
cost. A commercially-available evacuated-tube solar-hot-water                 dimensional Compound Parabolic Concentrator (CPC) [4], has
collection system distributed by Apricus Inc., Figure 2 was                   been shown to have the maximum theoretical concentration-
used for the experiments described in this paper. The evacuated               ratio, wherein, all rays that fall within the entrance aperture
tube system is a simple technology where thermal-power is                     and acceptance angle are reflected out from the exit aperture.
collected by a vacuum insulated solar-radiation absorber and                  The 2-D CPC is also described as being an “ideal” concentra-
transferred to a working fluid by a heat-pipe. The evacuated                   tor due to a few other important characteristics:
tube absorber has a thermal-power output curve that is shown                         1) Since the CPC is a non-imaging concentrator there is
in Figure 3. The thermal-power output curve is normalized by                            no need for diurnal tracking. A CPC with an acceptance
the aperture area of the evacuated tubes. The industry standard                         angle of 56◦ (a concentration ratio of 1/sin 56◦ ≈ 1.21)
for modeling performance of evacuated tube absorbers is to                              can accept direct solar radiation for 6-8 hours a day
use a quadratic model shown in Equation 4.                                              without adjusting for seasonal variation.
              Qout = ao · Qin − a1 · ∆T − a2 · ∆T 2                     (4)          2) The performance of a non-imaging concentrator is much
                                                                                        better than that of an imaging one in the case of diffuse
   For the Apricus absorbers, the model parameters are: a0 =                            radiation. This also increases the ability of the solar-
0.687, a1 = 1.505 W/m2 ·◦ K , and a2 = 0.011 W/m2 ·◦ K 2 .                              collector to perform well over a wider range of weather
The coefficients are normalized such that Qout is in units of                            conditions.
thermal-power generated per unit of installed evacuated tube                         3) The high tolerance of non-imaging concentrators to
area (W/m2 ). It is necessary to minimize the losses per tube in                        aberrations is also very beneficial in allowing for ease
order to maximize ηthermal (Equation 3). It is easily possible                          in manufacturing.
to increase ηthermal by increasing the solar radiation input into
each tube while reducing the number of tubes used—the mag-
nitude of the tube loss coefficients (a1 , a2 ) is a function of the                                    II. T HEORETICAL D ESIGN
number of evacuated tubes used per unit of installation area.
A comparison of output thermal-power per unit installed-area                     In order to characterize the effectiveness of using concen-
of normal evacuated tubes to concentrated evacuated tubes is                  trated evacuated tubes as a thermal-power source for a heat
shown in Figure 3. One concentrated evacuated tube replaces                   engine, single-tube concentrators for the Apricus evacuated
three unconcentrated tubes, therefore, concentrating the solar                tube system were designed and built. A test setup was cre-
input to an individual tube while reducing the number of tubes                ated to compare the relative performance of concentrated to
used overall decreases the surface area, thereby increasing the               unconcentrated evacuated tubes. Both the concentrator design
system efficiency at ∆T = Thot − Tamb > 100 ◦ C.                               and the experimental setup are described in the sections below.
                                                                                                                                               3



                                                                                     factor of 1.21 × π ≈ 3.77 on a per-tube basis.
                                                                                  2) The evacuated tubes are housed in a copper header with
                                                                                     fixed inter-tube spacing as shown in Figure 2. The design
                                                                                     for concentration should be adaptable to the commercial
                                                                                     design without major redesign. A concentrator with
                                                                                     a 56 ◦ acceptance angle is the right size such that
                                                                                     every third tube position could be used to hold the
                                                                                     concentrated-tubes without unused spaces or overlaps.
                                                                                  3) The height of the concentrators is approximately equal to
                                                                                     the the diameter of the collecting aperture divided by the
                                                                                     tangent of collecting angle. This leads to a substantial
                                                                                     increase in height with decrease in acceptance angle.
                                                                                     While it is possible to truncate and still preserve higher
                                                                                     concentration ratios, the loss of acceptance angle and
                                                                                     hence time-of-day for direct radiation was considered
                                                                                     sub-optimal for this experiment.
                                                                                  4) As was discussed above in Section I, the important met-
Figure 4. Profile of a CPC with concentration ratio of 3 for a cylindrical
absorber [6]                                                                         ric in determining the value of adding concentrators to
                                                                                     the evacuated tubes is achieving a greater engine output
                                                                                     for the same installed roof-top area of solar-collectors
                                                                                     in the case where three unconcentrated evacuated tubes
                                                                                     are replaced with one concentrated evacuated tube. The
                                                                                     power output for a concentrated evacuated tube system
                                                                                     is:
                                                                                                 ao · A · Qin − a1 · ∆T − a2 · ∆T 2
                                                                                      Wout =                                           · ηcarnot
                                                                                                                   3
                                                                                                                                             (5)
                                                                                       where A is the solar radiation gain to the absorber—i.e.
                                                                                       increased solar flux due to a single tube concentrator
                                                                                       with acceptance angle of θmax .
                                                                                The comparison of the normalized power output of a Carnot
Figure 5. Representation of the concentrator used in this experiment. It has
an acceptance angle of 56 ◦ which translates to a concentration ratio of 1.21
                                                                                engine is shown in Figure 6. Based on the comparison, the
                                                                                case for using fewer concentrated tubes and operating at a
                                                                                higher temperature T = 150 + Tamb ≈ 180 ◦ C is clear for
A. Concentrator Design                                                          even a concentration ratio of 2.22. (Note: This concentration
                                                                                ratio corresponds to the simulated gain in incident radiation
   Concentrators for the evacuated tubes were designed based
                                                                                for a CPC with an acceptance angle of 56◦ as shown below
on the ideas from [3]. The main consideration was to design
                                                                                in Section III.)
a concentrator cross-section that was meant for the cylindrical
                                                                                   The concentrators were manufactured using a vacuum ther-
absorber architecture. The original CPC is designed for a
                                                                                moforming process. Vacuum thermoforming provides accurate
planar absorber. In order to be suitable for a non-planer
                                                                                plastic shapes that can be coated with a thin layer of reflective
absorber, the CPC design has to be adapted [5], [4]. The
                                                                                mylar sheeting. An example test concentrator is shown in
required modification is to have a section defined by the
                                                                                Figure 7.
involute of the absorber surface meet the profile of a CPC.
The meeting point of the two profiles is where the extreme
ray entering a CPC meets the surface of the CPC after one                                 III. S IMULATION S ETUP AND R ESULTS
reflection. The general profile of a CPC for a cylindrical                           The evacuated tubes were simulated in LightTools using
aperture is shown in Figure 4.                                                  materials that incorporated all the optical properties specified
   The concentrator profile that was used in this experi-                        by Apricus Inc. An overview of the optical properties imple-
ment is shown in Figure 5. An acceptance angle of 56 ◦ —                        mented in the simulations can be seen in Table I. A forward
concentration ratio of 1.21—was chosen for the concentrators.                   3-dimensional ray trace analysis was used in order to obtain
The motivations behind the relatively low concentration ratio                   simulated results of the absorbed radiation at the absorber
were the following:                                                             surface. Further, the sun was modeled not only to portray the
   1) In the normal operating case for the evacuated tubes,                     AM1.5G spectrum of the sun, but also to trace the arc that
      the acceptance aperture is equal to the diameter of the                   the sun traces in the sky over the course of a day due to local
      tube—the area that is exposed to incident solar radiation.                latitude and time of year. A characteristic day in Phoenix, AZ
      Hence the theoretical gain with a CPC with concentra-                     was chosen to model a day with peak incident radiation of
      tion ratio of 1.21 is an increase of solar radiation by a                 1000 W/m2 .
                                                                                                                                                                              4




              150
                                                                Unconcentrated evacuated tube
                            @ Qin = 1000 W/m2                   With concentration ratio A = 2.22

              125




              100
Qout (W/m2)




              75




              50




              25

                                                                                                      Figure 8. Picture of 30-tube Apricus hot-water system integrated with a
                                                                                                      storage tank. The system is setup as a thermosyphon to operate without the
               0                                                                                      need of a pump. The heat transfer fluid is Soybean oil.
                    0           50        100         150          200           250            300
                                          ∆T = Tabsorber−Tambient (°K)


Figure 6. Theoretical comparison of power output from an ideal Carnot heat                               In order to analyze the effect of the highly reflective roof
engine per unit area of installed solar-collectors given an insolation level of                       of our test site simulations of an evacuated tube without
Qin = 1000 W/m2 . Equations 1 and 4 were used to generate these curves.                               a reflective roof-surface were compared to simulations of
                                                                                                      an evacuated with a representative roof-surface with optical
                                                                                                      reflection properties corresponding to a “bitumen” roof . For
                                                                                                      simulating the performance of the CPC, a SolidWorks model
                                                                                                      with an acceptance angle of 56 ◦ (Figure 5) was imported into
                                                                                                      the LightTools simulation environment.
                                                                                                         There is a gain-factor of 1.41 in incident solar-radiation
                                                                                                      due to the radiation reflected onto the back of an evacuated
                                                                                                      tube installed on a highly reflective roof. (Note: gain-factor in
                                                                                                      simulations is a measure of the increase in net solar flux on
                                                                                                      an absorber over a period of 6 hours centered at midday.)
                                                                                                         The measured gain-factor of a concentrated evacuated tube
                                                                                                      in comparison to an unconcentrated evacuated tube with a
                                                                                                      highly reflective roof is 1.57. In comparison, without a reflec-
                                                                                                      tive roof, the measured gain-factor of a concentrated tube in
                                                                                                      comparison to an unconcentrated evacuated tube is 2.22. The
                                                                                                      deviation of this gain-factor from the theoretical concentration
                                                                                                      ratio of 1.2 × π ≈ 3.77 can be explained by the variation in
                                                                                                      the incident angle of solar radiation due to the arc of the sun
                                                                                                      in the sky. Further deviance from the ideal can be explained
                                                                                                      by the realistic modeling of the glass cover, the absorber and
                                                                                                      the CPC wall coating.
Figure 7. Picture of finished single-tube concentrator formed using a plastic
thermoforming process and coated with reflective mylar.                                                        IV. E XPERIMENTAL R ESULTS AND A NALYSIS
                                                                                                         A full test system with integrated storage, as shown in
                                                                                                      Figure 8, was built to measure the performance of a stock
                                                                                                      30-tube Apricus solar hot-water system. The heat storage
                        Component         Material          Ref      Trans        Abs                 fluid was chosen based on a cost and performance basis. The
                         Absorber         Al/Al-N           0.02     0.02         0.96                important characteristics desired were low vapor pressure and
                          Cover        Borosilicate 3.3     0.04     0.92         0.04                low viscosity at temperatures in the range of 200 − 300 ◦ C.
                        CPC coating      Al Mylar           0.98     N/A          0.02                Due to these considerations, soybean oil was used [7].
                             Table I                                                                     Temperature measurements of the fluid were made at var-
O PTICAL PROPERTIES IMPLEMENTED FOR THE SIMULATIONS OF THE CPC                                        ious points in the system loop. While collecting data for
          AND EVACUATED TUBES WHERE R EF =R EFLECTANCE ,
          T RANS =T RANSMITTANCE , AND A BS =A BSORPTION .                                            the entire system, it was determined that the thermosyphon
                                                                                                      dynamics were too complicated to extract an effective compar-
                                                                                                      ison of the performance of unconcentrated evacuated tubes to
                                                                                                      concentrated evacuated tubes. Therefore, for the experimental
                                                                                                                                             5



data used in this paper, the individual tubes were disconnected
from the fluid loop. The heat-pipes (Figure 2) of the tubes
were connected to thermocouples and were insulated using
two inches of fiberglass sheeting and Al foil, which corre-
sponds to an R-value of 11. The temperature measurements
were made with thermocouples placed directly on the heat-
pipe bulb and underneath the fiberglass insulation—time-series
measurements were collected every 30 seconds for two hours.

A. Evacuated Tube Thermal Analysis
   The dynamics of the individual evacuated tubes are based on
the heat balance (Equation 6). The temperature was measured
at the heat-pipe bulb since it is the dominant thermal mass
of the system. Equation 6 expresses the rate of temperature
change of the heat-pipe.
           ˙                                         4
  mtube · T = Qin − C · (T − Tamb ) − R · (T 4 − Tsky ) (6)
   This model is a simplified version from [8]. The terms in
the equation are as follows:
   1) C is the conductive loss term (W/◦ K ), which is mainly
      from the bulb, where it is not vacuum sealed.
   2) R is the radiative loss term (W/◦ K 4 ), which is primarily
      from the absorber surface. This is a small term, but
      becomes important at higher-temperatures.
   3) Tsky is the sky temperature that can be derived from
      the dry bulb temperature and the dew point ambient
      temperature as follows [8]:
                      Tsky = (ǫsky )0.25 · Tamb              (7)

                                 tdp              tdp 2
          ǫsky = 0.711 + 0.56 · (    ) + 0.73 · (     )   (8)
                                 100              100
  4) mtube is the thermal mass of an evacuated tube, which is       Figure 9. Temperature vs. Time and Temperature vs. ∆T for an experiment
     effectively the thermal mass of the heat-pipe (inclusive       comparing the performance of an unconcentrated vs. a concentrated evacuated
                                                                    tube.
     of bulb and working fluid). The thermal mass was
     estimated to be mtube = 330 J/◦ K using a differential                           Date            Measured Concentration Ratio
     mass measurement described in the appendix.                                July 15th , 2011                   1.3
  5) Qin is the solar radiation flux (W/m2 ) measure                           July 19th , 2011 (1)                 1.2
                                                                              July 19th , 2011 (2)                 1.4
B. Single-Tube Concentrator Performance                                         July 27th , 2011                   1.44
                                                                                    Average                        1.33
   Multiple experiments were conducted to measure the in-
crease in performance due to the concentrators. The data                                        Table II
                                                                      O BSERVED CONCENTRATION RATIO MEASURED AS THE RATIO OF THE
analysis procedure was to first use time-series temperature data          ESTIMATED INPUT SOLAR RADIATION FOR CONCENTRATED VS .
and extract a plot of ∆T (rate of change of bulb temperature)           UNCONCENTRATED EVACUATED TUBES WITH HIGHLY REFLECTIVE
                                                                                           BACKGROUND .
vs. Tamb . Once ∆T is available, a constrained linear-least-
squares algorithm was used to estimate the model parameters
of Equation 6. As can be seen in Figure 9, the extracted model
parameters fit the time-series data very accurately.
                                                                    C. Analysis
   Concentration ratio is determined as the ratio of measured
increase in solar flux, Qin , extracted from the experimental           The theoretical concentration ratio for the single-tube con-
data. The concentration ratios comparing a concentrated evac-       centrators is 1.21 × π ≈ 3.77. In experiments, the measured
uated tube to an unconcentrated evacuated tube on a reflective       gain-factor in solar radiation input from concentrated evacu-
roof (Table II) corresponded very closely to the simulations—       ated tubes in comparison to unconcentrated evacuated tubes on
a gain-factor of 1.57 from simulation results. The average          a highly reflective roof was 1.33. As is explained in Section
concentration ratio was measured from experimental data to be       III, where this increase was measured from simulations to be
1.33, this is based on four experiments conducted in Berkeley,      1.57, the deviation from theory is due to the non-ideal arc that
California around the time of maximum solar altitude for each       the Sun follows during a day based on local latitude and time
of those days.                                                      of year. Also, there are losses from the non-ideal reflective
                                                                                                                                                           6



surfaces of the concentrators used for the above experiments.                  Achintya Madduri is a Ph. D. student at the Department of Electrical
                                                                               Engineering and Computer Science at the University of California, Berkeley.
                                                                               He is working under Professor Seth Sanders on designing thermal collectors
                                                                               for use in solar-thermal generation and also on developing architecture for
                          V. C ONCLUSIONS                                      “smart” DC micro-grids.


   The focus of this paper was to characterize the importance                  Denise Loeder is a visiting student researcher from Technische Universtät
of using concentrators for achieving high-efficiency solar-                     München at the Department of Electrical Engineering and Computer Science
                                                                               at the University of California, Berkeley. She is working under Professor Seth
thermal conversion from a commercial evacuated tube system                     Sanders on thermal collectors for use in solar-thermal generation.
supplying input thermal-power at temperatures of 180−220 ◦ C
to a heat-engine. As is shown in Figures 3 and 6, the thermal
                                                                               Nic Beutler is a visiting student researcher from Technische Universtät
and mechanical efficiency of using concentrated evacuated                       München at the Department of Electrical Engineering and Computer Science
tubes at this temperature range are 35% and 12% respectively.                  at the University of California, Berkeley. He is working under Professor Seth
This is based on simulation results of a concentrator with an                  Sanders on thermal storage for use in solar-thermal generation.
acceptance angle of 56◦ over the course of 6 hours in a day
with peak insolation of 1000 W/m2 . Experiments with custom                    Seth Sanders is a Professor in the Department of Electrical Engineering and
manufactured concentrators and a commercial evacuated tube                     Computer Science at the University of California - Berkeley. He joined the
                                                                               UC Berkeley faculty in 1989. His research interests are in high-frequency
system prove that simulations are accurate and useful in pre-                  power conversion circuits and components, in design and control of electric
dicting thermal performance of a concentrated evacuated tube                   machine systems, and in nonlinear circuit and system theory as related to the
system. Both simulations and experiments show that using                       power electronics field.
a concentrated evacuated tube system will convert incident
solar radiation to thermal-power more efficiently at higher                     Mike He is a Ph.D. student in the Department of Electrical Engineering and
temperatures and therefore increase the mechanical power                       Computer Science at the University of California - Berkeley. He is working
                                                                               under Professor Seth Sanders on Stirling engines for distributed solar thermal
output from a heat-engine per unit of installed solar-collector                electric generation. He is an NSF Graduate Fellow.
area.


                               A PPENDIX

   In order to get a measure of the thermal mass of the evacu-
ated tube heat-pipe, a known mass of (600 g) or (231 J/◦ K ) of
copper was added to a tube in the form of multiple layers of
.005 ” thick copper foil. This copper mass was tightly wrapped
around the heat-pipe bulb. Time-series measurements of the
temperatures of an evacuated tube with an additional thermal
mass and one without were collected with the same input
solar irradiance. The temperature data was analyzed to extract
the thermal mass of the Apricus evacuated tubes, which was
estimated as mtube = 330 J/◦ K .


                             R EFERENCES

[1] A. Der Minassians and S. Sanders, “Multiphase Stirling Engines,” Journal
    of Solar Energy Engineering, vol. 131, p. 021013, 2009.
[2] Apricus Solar Co Ltd., Apricus 30 tube collector: product specifications
    sheet, Jan. 2009.
[3] W. T. Welford and R. Winston, High collection nonimaging optics.
    Academic Press, 1989.
[4] R. Winston, “PRINCIPLES OF SOLAR CONCENTRATORS OF A
    NOVEL DESIGN,” Solar Energy, vol. 16, no. 2, pp. 89–95, 1974.
[5] A. Rabl, J. O’Gallagher, and R. Winston, “Design and test of non-
    evacuated solar collectors with compound parabolic concentrators,” Solar
    Energy, vol. 25, no. 4, pp. 335–351, 1980.
[6] R. Winston and H. Hinterberger, “Principles of cylindrical concentrators
    for solar energy,” Solar Energy, vol. 17, no. 4, pp. 255–258, 1975.
[7] H. Noureddini, B. Teoh, and L. Davis Clements, “Densities of vegetable
    oils and fatty acids,” Journal of the American Oil Chemists’ Society,
    vol. 69, no. 12, pp. 1184–1188, 1992.
[8] S. Odeh, G. Morrison, and M. Behnia, “Thermal analysis of parabolic
    trough solar collectors for electric power generation,” Proceedings of
    ANZSES 34th annual conference, Darwin, Australia, pp. 460–7, 1996.

				
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