Category Archives: Particle Image Velocimetry (PIV)

Experimental results

The study of the standard PV system and the hybrid PVT/AIR systems includes outdoor tests for the determination of the steady state electrical efficiency pel of the corresponding PV modules of all systems and the thermal efficiency pth of the PVT/AIR models. The electrical efficiency pel of PV modules depends on their temperature (TPV) and the incoming solar radiation and it is calculated by the measured data as: pel=ImVm/GAa, where Im and Vm are the current and the voltage of Pv module operating at maximum power and G the irradiance on the system aperture plane. Test results showed that the pel for PV, PVT/UNGL and PVT/TFMS type models was: r|el=0.1659-0.00094Tpv, while for PVT/GL type models was: pel=0.1457-0.00094TPV. The value of TPV for the standard module was calculated by the equation: TPV=30+0.0175(G-300)+1.14(Ta-25) (Lasnier and Ang, 1990) that correlates TPV with the parameters G and Ta. The TPV of the corresponding modules of PV+REF, PV-TILT and of all PVT/AIR systems was based on modified formulas of the above equation, which give approximately the PV module temperature and are presented in Table 1. These modified formulas were experimentally validated and correspond to the increase of PV operating temperature due to the reduced heat losses to the ambient.

The thermal efficiency nth of the PVT/AIR models depends on the incoming solar radiation (G), the input air temperature (Ti) and the ambient temperature (Ta). During tests for the determination of system thermal efficiency, the PV modules were connected with a load to simulate real system operation and to avoid PV module overheating by the solar radiation that is converted into heat instead of electricity. The steady state thermal efficiency i"|th of the tested hybrid PVT/AIR solar energy systems is calculated for the operating conditions with the lowest thermal losses (T=Ta) by the equation: i"|th = m Cp(T0-Ti)/GAa, where m is the fluid mass flow rate, Cp the fluid specific heat, Ti and To the input and output fluid temperatures and Aa the aperture area of the PV/T model. The results are presented in Table 1 for all studied systems. The experimental results for the thermal efficiency of the PV-TILT and PVT/AIR-TILT type systems were extracted from the tests where an additional thermal insulation sheet was mounted on the back of these systems, to simulate the tilted roof. In the calculation of the electrical and thermal output of the compound systems PV+REF and PVT/AIR+REF, we considered the net solar radiation on the aperture surface of PV modules and not the additional on the reflector, in order to have direct comparative results with the standard installation mode of the systems. The calculation of thermal efficiency i"|th (for T=Ta) of PVT+REF systems varies from a minimum value for December (CR=1.0) up to the maximum value for June (CR=1.3).

The effect of incident irradiance on the optical efficiency of the collector

An investigation into how incident power density affected the optical efficiency of the collector was conducted using the solar simulator to provide the irradiance source. Various irradiance power densities were achieved by modifying the spatial distribution of the source lamps and the displacement between the

simulator and collector planes. The collector was sloped at 45° with respect to the horizontal plane, the mass flow was maintained at 0.07 kgs-1 ± 1% and the collector temperature was held at ~3 K above the ambient temperature. Two typical irradiance

maps can be seen in Figure 2 for 590 and 1150 Wm"’

Figure 2 — 2-D Maps for the Solar Simulator Irradiance at average power densities of 590 ± 50 Wm-2 and 1150 ± 50 Wm-2 with the collector at a slope of 45° ± 2° with respect to the horizontal plane (Contour lines are in units of Wm-2)

The optical efficiency of the direct-flow evacuated tube collector was monitored for irradiances in the range 200 to 1400 Wm-2. Observations shown in Figure 3 revealed that the optical efficiency remained quasi-constant with increasing power density of the irradiance source; ^0 averaged at a value of 0.82 ± 0.02 over this range. The
corresponding global heat losses from the evacuated collector were determined for these experimental conditions. Values of UL ranged from 0.05 to 5.31 Wm-2K‘1 for increasing power density.

A fit to the data illustrated with the dashed black line in Figure 3 indicates that the global heat loss follows a simple power series. The calculation method

of ULand the corresponding heat loss mechanisms will be discussed later.

Background

The 354 MWe of parabolic trough plants (SEGS I — IX) installed in the Californian Mojave Desert have been one of the most successful showcase for solar projects worldwide in the last decades. Since nearly 20 years thousands of parabolic trough collectors — with a total reflecting surface of more than 2.000.000 m2 — are tracking on a day-to-day basis the sun and focus precisely the sunbeams onto the absorber tube. The extensive twenty-year operation records demonstrate impressively the reliability and maturity of the parabolic trough technology.

After the oil crisis in the 70’s, the Californian government established favourable legal and economic frameworks with tax incentives and long-term feed-in tariffs guaranteed by the government to support the market introduction of the concentrating solar power technologies. These investment-friendly environments together with a mature, economic and emission-free technology have been the main pillars for the success story of the SEGS plants.

After the withdrawal of the “solar” framework in the U. S. at the end of the 80’s, it needed nearly ten years that another industrialized country in the sunbelt of the world established similar favourable conditions for the erection and operation of solar thermal power plants. With the passing of the Royal Decree 2818/1998 — which encourages and outlines the conditions to meet Spanish objectives in the reduction of global greenhouse gas emissions — Spain provided the legal foundation for the development of the first parabolic trough power plant in Europe. The Solar Millennium Group with its Spanish subsidiaries started immediately after the publication of the new framework with the project development of
parabolic trough power plants in Spain. Extensive site studies in Southern Spain identified promising locations for the implementation of solar thermal power plants with parabolic trough technology in the region of Andalusia, Castilla-La Mancha, Extremadura and Murcia. After several modifications and revisions of the feed-in tariff, the Spanish government finally established with publication of Royal Decree 436 in March 2004 economic conditions and tariff stability which will attract equity and debt investors with risk- adjusted rate of returns on their investment. Royal Decree 436 might be the break-through for the commercial market introduction of this technology and the start in a new solar millennium.

EXPERIMENTAL INVESTIGATION AND NUMERICAL CODE VALIDATION

The numerical model has been validated with experimental data. An experimental vertical cylindrical latent thermal energy storage unit has been constructed and series of temperature measurements have been performed. Experimental test unit and thermocouples position inside the unit are shown in Fig. 2 and Fig. 3.

Fig. 3. Thermocuples position

An experimental test unit has been made of two concentric tubes, where the inside tube (0.033 m i. d., 0.035 m o. d. and 1 m length) has been made of copper, while the outside tube (0.128 m i. d., 0.133 m o. d. and 1 m length) has been made of brass. The outside tube has been well thermally insulated to reduce the heat losses. Sixteen K-type thermocouples have been placed inside the PCM at various locations. Two additional thermocouples have been placed at the inlet and outlet of the HTF into inside tube. All thermocouples have been connected to a data acquisition system. Labview commercial software has been used to record data in a database format on the personal computer. Temperature measurements have been recorded at a time intervals of 10 s. To maintain the axisymmetric melting around the inside tube, the test unit has been oriented in a vertical direction. Commercial paraffin Rubitherm RT 30, with thermophysical properties in Table 1, has been used in experimental studies as PCM, and water has been used as HTF.

Table 1. Thermophysical properties of the paraffin Rubitherm RT 30

Melting / solidification temperature

K

300.7

Latent heat capacity

kJ/kg

206

Thermal conductivity — solid / liquid

W/(mK)

0.18 / 0.19

Specific heat — solid / liquid

kJ/(kgK)

1.8 / 2.4

Density — solid / liquid

kg/m3

789 / 750

Series of melting and solidification experiments has been performed for different mass flow rates and inlet temperatures of HTF. Computational model has been set up to reproduce these experimental conditions. Numerical calculations have been carried out for a grid size of 250 (axial) and 73 (radial) nodes, and dimensionless time steps of 0.06. In Figs. 4 and 5 paraffin temperature histories at locations 5 (x = 0.35 m; r = 0.0265 m) and 9 (x = 0.65 m; r = 0.0265 m) during melting, as well as at locations 2 (x = 0.05 m; r = 0.0355 m) and 15 (x = 0.95 m; r = 0.0445 m) during solidification are shown for both experiment and simulation. Mass flow rates and inlet temperatures of the HTF as well as initial temperatures of the PCM are indicated in figures.

The comparison between numerical predictions of time-wise temperature variations and experimental data shows a good agreement, although the natural convection in the liquid phase of the PCM has been ignored in the numerical model. It can be seen from Fig. 4 that melting of the applied PCM occurred non-isothermally over a certain temperature range within the melting zone. The shape of the temperature curves indicates that the melting dominates at about 27.7 to 35 oC. During solidification, paraffin has an isothermal phase change temperature range and no subcooling property, as shown in Fig. 5.

Fig. 4. Experimental and numerical time-wise PCM temperature variations during melting

Fig. 5. Experimental and numerical time-wise PCM temperature variations during solidification

The results of analysis have signified that a developed numerical procedure could be efficiently used to simulate thermal behaviour of the latent thermal energy storage unit during charging and discharging.

Receiver System

The complete SOLGATE receiver system consists of three receiver modules that are connected in series (Fig. 2). There, the air coming from the compressor with 290°C is heated by solar energy up to max. 1000°C. The receiver modules have a hexagonal entrance aperture and are arranged like a honeycomb in the focal spot (Fig. 4). For higher power levels the complete focal spot can be covered by a number of low, medium and high temperature modules that are interconnected in serial and parallel way.

Two different receiver technologies for air heating in gas turbine cycles were developed:

• a volumetric receiver capable for temperatures up to 1000°C

• a low temperature receiver module at significantly reduced cost for the low flux

regions of the focal spot

To allow for outlet temperatures of 1000°C the absorber, the absorber mounting and the window cooling had to be modified [3]. A scheme of a pressurized volumetric receiver is shown in Fig. 5.

For the high temperatures a highly porous SiC ceramic foam absorber with a pore size of 20ppi is used. The pressure resistant, domed quartz window is actively cooled at the atmospheric side by air jets. For the low temperature receiver the aim was to achieve an overall cost reduction at the first, low temperature stage of the receiver cluster by utilizing simple, less expensive modules. The selected concept is a multi-tube coil attached to a hexagonal secondary concentrator, with the air being convectively heated while flowing through the tubes. The bent tubes are very flexible and thus reduce mechanical stresses from thermal expansion of the tube material. The final layout consists of 16 tubes connected in parallel, each with a length of 2.3 m and a diameter of 28 mm. According to

the design calculations the absorber should have a temperature increase of about 200 K and an associated pressure drop of 100 mbar.

Fig. 5: Scheme of a pressurized volumetric receiver

After pre-assembly of several components like secondary concentrators, receivers, or the gas turbine skid on the ground, the pieces were lifted onto the tower for final integration. A emergency shut down procedure was established to be able to shut down the solar power in less than two seconds with the help of a fast shutter, i. e. a white ceramic curtain in front of the receiver cluster.

The tests were divided into two parts. During Phase 1 (winter 2002/2003) the 3rd receiver stage was equipped with a metallic wire mesh absorber capable for 800°C. This phase was intended to demonstrate the general operational capability of the gas turbine together with the receiver cluster. In Phase 2 (summer 2003) the metallic absorber was replaced by a ceramic absorber for 1000°C. In addition an active external window cooling was installed, supported by a new high resolution infrared-scanner to measure the window temperature.

Test Phase 1

After commissioning the gas turbine generated for the first time electric power with a small solar fraction on December 15, 2002. In the following weeks, receiver temperature and electric output power were increased gradually. In March 2003 operation at 800°C receiver temperature and more than 230 kW electrical output was performed for several days. The system performed quite well and was able to handle all kinds of solar transients.

Test Phase 2

After installation of the new absorber, the window cooling and the IR scanner operation was resumed in June 2003. Measurements with the scanner indicated window temperatures that were about 100°C lower than predicted (eventually due to better optical quality of the quartz window). After increasing the receiver temperature above 800°C, the window cooling was activated. Temperature data from the window showed that the window cooling worked as expected.

After several weeks of successful operation, testing was interrupted by an emergency shut down, caused by a control error. Due to a too slow air evacuation through the emergency blow off pipe the second turbine shaft coupled to the generator reached overspeed. This resulted in some damage to the turbine. Anyway, the operation continued with reduced power but continuously increasing temperatures for some days. A problem with temperature peaks on the absorber could be solved by an improved heliostat aiming precision. Finally, a maximum temperature of 960°C was achieved, limited by the turbine damage.

Antireflective Coating

According to Fresnel’s law an antireflective (AR-) coating on glass is realized by a AM — layer with a refraction index of niayer = (ngias)1/2. To get such a low refraction index the density of the coating has to be lowered, e. g. by increasing the porosity. The thickness of the A /4-layer is matched with the wavelength of the most intensive part of the solar spectrum, i. e. 560 nm. Whereas reflectance in this part of the spectrum is nearly zero, it increases towards smaller or higher wavelengths in the solar spectrum. Therefore (including an extremely high transmittance of the 3 mm basic glass close to 92 %) an overall transmittance of the antireflective coated glass envelope of more than 96 % was achieved.

The SCHOTT AR-coating is the result of a dipping process using the sol-gel technique to produce the required porosity. The thickness of the AR-layer in the range of > 100 nm will be controlled by the viscosity of the sol and the velocity of withdrawing from the solution.

The weak point of competing AR-coatings is their low adhesion to the borosilicate glass substrate. They are normally removable with a handkerchief. To overcome this weakness SCHOTT has developed a new composition of the AR-layer on silicate basis which guarantees long-term stability against abrasion.

The abrasion resistance of the AR-layer has been measured using a standard method developed by SCHOTT. A cylindrical standard eraser (MIL-E-12397) with a cross-section of 5 mm is moved under pressure (0,5N/mm2 = 72 PSI) and the number of strokes needed to remove the layer are counted. According to this the SCHOTT AR-coating tolerates at least 50 strokes whereas competing AR-coatings are already removed after 5 strokes.

Conclusions and considerations

The paper presents an algorithm for the structural synthesis of mechanisms for tracking systems as Multibody Systems and applications to planar linkages are discussed. The method can be extended also for spatial linkages, cams or gear mechanisms.

Their conception as Multibody Systems provides all the general fundamental structures for a defined complexity (number of bodies) and degree of freedom (mobility) of a mechanism. Based on the fundamental particularities of the sun-tracking, applicable mechanical concepts are obtained.

The application presented has as result possible versions (existing and new ones) for the imposed input data. For example, Fig.6.2 represents an existent configuration for this kind of devices while Fig.6.1, 6.3, 6.12 represent new systems based on the same graph where the driving motion is introduced in different ways.

The figures from 6.5 to 6.11 show different configurations with 3 bodies that allow many possibilities to introduce the driving motion. Solutions as described in Fig. 6.4, 6.6, 6.8, may be reliable because of their compact structure, but also spherical mechanisms as in Fig.6.12 can offer an accurate orientation in order to follow the sun path.

Considering the design principles of the sun trackers and also the technological implications in manufacturing these types of systems, the mechanism configurations have to be developed in order to provide a good accuracy. An exergy calculation is necessary for an efficient energy balance between their own feed consumption and the energy provided by the renewable energy system.

Part Load Performance of the Solar Thermal Power Plant

Since the solar thermal power plant will operate in part load most times of the year the knowledge of the part load behaviour is crucial. In a first step the system performance is calculated as a function of the load. This gives an impression of the part-load behaviour of each option. To assess the performance of both options at the site specified a yearly calculation using the according meteorological data is performed.

The system performance strongly depends on the operation mode of the solar thermal power plant. For the following comparison three different operation modes are considered: fixed pressure, gliding pressure and modified gliding pressure mode.

In case of the fixed pressure mode the operation pressure is 65 bar for all mass fluxes lower than the design mass flux. For mass fluxes higher than the design mass flux the operation pressure is increased appropriately. In gliding pressure mode the operation
pressure is a direct function of the load and thus of the mass flux. A third option is the modified gliding pressure mode. Here the operation pressure is also a function of the load but it is always higher than 30 bar. This pressure limit of 30 bar is chosen since so far the DISS test facility has only been operated at an operation pressure higher than 30 bar. No reliable operation experience is available for an operation pressure lower than 30 bar.

It is assumed that the inlet temperature difference at the air cooled condenser is 28 K and the inlet temperature difference 14 K[14]. For the first part-load calculation the ambient temperature is set to 25°C.

Part-Load Calculation

Figure 8 displays the efficiency of the collector field as a function of the corrected DNI. The solar field efficiency for the saturated steam option (solid lines) is always higher than that of the superheated steam option. As described above this is caused by the lower fluid temperature in the solar field and the according lower thermal losses.

Comparing the efficiency characteristic of the different operation modes for a given process option, the gliding pressure mode has the superior part-load performance followed by the modified gliding pressure and the fixed pressure mode. In case of the fixed pressure mode the operation pressure and thus the operation temperature of the evaporation section is fixed whereas the pressure and thus the temperature and the according thermal losses decreases in the other cases. The efficiency of the gliding pressure and the modified gliding pressure mode are identical as long as the operation pressure of the modified gliding pressure mode is higher than 30 bar. For a lower irradiation the pressure and thus the operation temperature will remain at this level and accordingly the efficiency will fall below that of the gliding pressure mode.

The efficiency characteristic of the power block is displayed in figure 9 for both options. As explained above the efficiency of the superheated steam option is higher than that of the saturated steam option. And again the gliding pressure mode is superior to the other operation modes. The lower efficiency of the fixed pressure and the modified gliding pressure mode is caused by the throttling losses in the first turbine stage of these options.

Yearly Calculation

For the final assessment of the system performance a yearly calculation of the power plant is performed using the satellite data for the DNI and the ambient temperature described in a previous section. As described above it is assumed that the plant is only operated for a DNI multiplied by the cosine of the incident angle higher than 250 W/m2, lower values are neglected. This threshold is reached for 2770 hours per year. The performance calculation is performed using IPSEpro. As an example figure 11 displays the results for the gross and net efficiency for each hour of the year for the saturated steam option operated in fixed pressure mode.

This calculation has been performed for both process options for the three different operation modes. From the results presented in figure 11 the peak and mean net efficiencies, the net electricity production and the equivalent full load hours have been derived. The according results are presented in table 3.

Saturated Steam

Superheated Steam

GP

MGP

FP

GP

MGP

FP

Max Net Efficiency [%]

17,5

17,5

17,5

17,6

17, 6

17,6

Mean Net Efficiency [%]

13,7

13,5

13,1

13,4

13,2

12,9

Net Electricity Prod. [MWh/a]

10467

10434

10174

10033

9995

9738

Full Load Hours [h]

1930

1923

1876

1 849

1 842

1795

Table 3: Results of the yearly calculation (GP = gliding pressure, MGP = modified gliding pressure, FP = fixed pressure)

According to table 3 the net electricity production of the saturated steam option for the specified site is approx. 4% higher for all operation modes. Although the absolute values given in table 3 have to regarded as preliminary it comes out that the saturated steam option is an interesting option for small size DSG solar thermal power plants.

Annual performance of PV and PV/T systems

The electrical efficiency from the tests of standard PV modules and also the electrical and thermal efficiencies of all PV/T models were used to calculate the monthly energy output and from them the annual values for the weather conditions of Patras. In the calculations we considered PV and PV/T system slope equal to the latitude of Patras for both horizontal and tilted building roof installation. The complete systems include the necessary additional components (Balance Of System, BOS, for the electricity and the BOS for the heated air circulation) and therefore the final energy output is reduced due to the electrical and thermal losses from these systems. Estimating a minimum energy reduction of about 15% for the PV electrical energy that is converted in electricity (inverter), we take a value for BOS equal to 85% to calculate the final electrical energy output of the PV and PV/T systems. Regarding system thermal part, we consider also efficiency 85% for the final heat output (tubes, fan, etc) and we take these new values as the final use energies. The annual energy output per m2 of the considered PV modules and of the PV/T systems are
included in Table 2. The calculated values for PV and PV/T systems with BOS of 85% for both electrical and thermal system parts are calculated considering the annual solar input (1644.72 kWhm"2yr"1) on the plane of the PV module for Patras. The main scenarios for the practical use of the heated air are the following:

1. The heated air is used for twelve months. This consideration is for reference purposes and corresponds to application of annual needs in heated air, as for example in some industries.

2. The heated air is used for six months (November to April), while the rest six months (May to October) the heated air is ejected to the ambient, cooling the PV modules only. This consideration corresponds to typical PVT/AIR applications, as the space heating of buildings.

3. The heated air is used twelve months, six months (November to April) for the effective use of air (e. g. for space heating of buildings) and six months (May to October) for water preheating through heat exchanger. The thermal output in water preheating is lower than that of the air heating only, as there are additional thermal losses in the air — water heat exchanger.

From the given results we observe that the total energy output (electrical plus thermal) of PVT/AIR systems is higher than that of the standard PV modules, while regarding only the electrical output, it is higher only of PVT/UNGL-TILT and PVT/TFMS-TILT systems. The suggested TFMS modification in the air channel results to higher total energy output compared to the PVT/UNGL type systems and to higher electrical output compared to PVT/GL type systems. The practical use of the heated air only for six months is not efficient enough (almost 40% of that from the reference mode of the 12 months). In the case of water preheating for the rest six months, the total thermal energy output can be considered satisfactory (about 75% to that of the reference mode of the 12 months).

Table 2. Annual electrical and thermal output of all studied PV and PVT/AIR systems

ENERGY OUTPUT OF SYSTEMS

ANNUAL ELECTR OUTPUT KWh yr-1 (per m2)

12 MO THERM OUTPUT

kWh yr-1 (per m2)

12 MO ELECTRIC OUTPUT

kWh yr-1

(BOS 85%) (30 m2)

12 MO THERMAL OUTPUT

kWh yr-1

(BOS 85%) (30 m2)

6 MO THERMAL OUTPUT

kWh yr-1

(BOS 85%) (30 m2)

6 MO AIR+

6 MO WATER THERMAL OUTPUT kWh yr-1 (BOS 85%) (30 m2)

PV

203.15

5180.33

PV+REF

241.70

6163.35

PV-TILT

184.05

4693.30

PVT/UNGL

200.77

521.64

5119.64

13301.78

5207.24

10510.52

PVT/UNGL+REF

223.28

705.57

5693.60

17991.99

6386.22

13966.79

PVT/UNGL-TILT

193.00

536.13

4921.50

13671.27

5351.88

10802.48

PVT/GL

168.39

839.38

4293.84

21404.22

8379.09

16912.74

PVT/GL+REF

189.14

948.78

4823.14

24193.79

9082.82

18970.25

PVT/GL-TILT

160.76

855.07

4099.38

21804.29

8558.39

17236.67

PVT/TFMS

201.96

594.09

5150.03

15149.25

5930.46

11970.31

PVT/TFMS+REF

224.50

738.71

5724.85

18837.16

6857.39

14687.48

PVT/TFMS-TILT

194.20

608.58

4952.10

15518.74

6075.11

12262.27

The effect of mass flow-rate on collector optical efficiency

The mass flow-rate is an important parameter for thermal solar collectors. In most cases flow-rate will be the only system parameter that a domestic/industrial end user will be able to influence. Therefore the relationship linking mass flow and optical efficiency needs to be

Figure 4 — [a] and [b] The variation of optical efficiency with mass flow and the corresponding global heat losses, [c] the variation of 1/AT with mass flow and the deviation from the linear fit for intercept zero and [d] the plot of AT against mass flow and the applied correction to calculate the global heat losses for the collector

well understood in order to ascertain the effects for evacuated tubes collectors. The optical efficiency on the collector was monitored for mass flows ranging 0.02 to 1.50 kgs-1 at 590 and 1150 Wm-2 respectively.

The optical efficiency of the collector was found to be significantly affected by mass flow in the system. Figures 4a, b show two distinct regimes; for mass flow-rates <0.07 kgs-1 the efficiency was found to reduce by up to ~25 % with decreasing flow. However, at rates >0.07 kgs-1 the optical efficiency slowly increases with increasing flow. Ismail et al5 also observed these phenomena for flat-plate collectors with heat-pipes, in that case the efficiency stabilised to a constant value at higher flow-rates.

Morrison1 explains this as the ‘low flow penalty’; this was caused due to the fact that experimentally measured values of ATexp across the collector were less than the predicted values at low flow-rates, for UL independent of temperature. This was demonstrated in Figure 4c, the experimental data of 1/AT against flow-rate; at low mass flow, the experimental data deviates away from the linear fit (intercept zero) shown by the dashed black lines. This indicates that observed AT was less than would be expected for a system with no losses. As a result of the low mass flow the useful gain Qu (that directly depends on AT) decreases and therefore the corresponding efficiency of the collector also decreases; this is a fundamental property of low flow systems.

A simple empirical method was used to calculate the global heat losses from the collector at normal incidence under the described conditions. From eq.1 (the equation of useful heat gain) it was possible to determine an expression for AT assuming no heat losses given by eq.2

QU = mCpAT = AcFr[Gt{t+)-Ul T — Ta)]

where UL = 0, as seen in Figure 4d (green dashed line). A correction was applied to AT in order to match the experimentally measured values ATexp (red dashed line Figure 4d). This modification took the form shown in eq.3

where x = 0.98. Substituting this expression for ATx into eq.4 an approximation of the global heat losses from the collector could be calculated for the collector, where Ti > Ta.

The global heat losses from the collector were found to decrease with increasing mass flow-rate as shown in Figures 4a, b. The heat losses range from 6.0 to 0.2 Wm-2K-1 depending on the mass flow-rate and incident irradiance power density.