Investigations on heat losses from a solar cavity receiver

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Solar Energy 83 (2009) 157–170 www.elsevier.com/locate/solener

Investigations on heat losses from a solar cavity receiver M. Prakash, S.B. Kedare, J.K. Nayak * Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India Received 18 October 2007; received in revised form 9 April 2008; accepted 15 July 2008 Available online 12 August 2008 Communicated by: Associate Editor Robert Pitz-Paal

Abstract Thermal as well as optical losses affect the performance of a solar parabolic dish-cavity receiver system. Convective and radiative heat losses form the major constituents of the thermal losses. In this paper, an experimental and numerical study of the steady state convective losses occurring from a downward facing cylindrical cavity receiver of length 0.5 m, internal diameter of 0.3 m and a wind skirt diameter of 0.5 m is carried out. The experiments are conducted for fluid inlet temperatures between 50 °C and 75 °C and for receiver inclination angles of 0° (side ways facing cavity), 30°, 45°, 60° and 90° (vertically downward facing receiver). The numerical study is performed for fluid inlet temperatures between 50 °C and 300 °C and receiver inclinations of 0°, 45° and 90° using the Fluent CFD software. The experimental and the numerical convective loss estimations agree reasonably well with a maximum deviation of about 14%. It is found that the convective loss increases with mean receiver temperature and decreases with increase in receiver inclination. Nusselt number correlations are proposed for two receiver fluid inlet temperature ranges, 50–75 °C and 100–300 °C, based on the experimental and predicted data respectively. Besides no-wind tests, investigations are also carried out to study the effects of external wind at two different velocities in two directions (head-on and side-on). The wind induced convective losses are generally higher than the no-wind convective loss (varying between 22% and 75% for 1 m/s wind speed and between 30% and 140% for the 3 m/s wind speed) at all receiver inclination angles, the only exception being the loss due to side-on wind at 0° receiver inclination angle. This is because the wind acts as a barrier at the aperture preventing the hot air to flow out of the receiver. The head-on wind causes higher convective loss than the side-on wind. Nusselt number correlations proposed in this work are compared with the existing correlations in the literature. It is found that the correlations available in literature under-predict the convective losses at mean receiver temperatures between 100 °C and 300 °C. This is due to the fact that the correlations are developed for certain receiver geometries having the ratio of aperture diameter to receiver diameter equal to or lesser than one. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Parabolic dish-receiver systems; Cavity receiver; Convective loss; Nusselt number correlation

1. Introduction Among the various solar collectors, the parabolic dish concentrating collector is the most suitable system for meeting medium and high temperature process heat requirements. Generally, it consists of a reflector in the form of a dish and a receiver at the focus. The thermal and optical losses occurring from an open cavity solar *

Corresponding author. Tel.: +91 22 25767881; fax: +91 22 25764890. E-mail address: [email protected] (J.K. Nayak).

0038-092X/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2008.07.011

receiver are less when compared to other types of receivers and hence, such receivers are preferred (Harris and Lenz, 1985). The thermal losses of a solar cavity receiver include convective and radiative losses to the air in the cavity and conductive heat loss through the insulation used behind the helical tube surface. The radiative loss is dependent on the cavity wall temperature, the shape factors and emissivity/absorptivity of the receiver walls while conduction is dependent on the receiver temperature and the insulation material. The radiative and conductive losses are

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Nomenclature area of the receiver aperture (m2) concentration ratio specific heat of the working fluid (kJ/kg-K) specific heat of air (kJ/kg-K) receiver aperture diameter (m) constant used in Eq. (8) (W) constant used in Eq. (8) (W/K) Grashof number based on aperture diameter heat transfer coefficient based on aperture area (W/m2-K) k thermal conductivity of air (W/m-K) m_ mass flow rate of the working fluid (kg/s) Nusselt number based on aperture diameter NuD Nunw,D Nusselt number based on aperture diameter for no-wind condition Qconv/h convective loss at receiver angle h (W) Qconv/90°,numerical convective loss at receiver angle of 90° obtained numerically W) Qr+c/h radiative + conductive losses at receiver angle of h (W) Qr+c,nw/90° radiative + conductive losses at receiver angle of 90° for no-wind condition (W) Qrad=90 ;theoretical radiative loss at 90° inclination obtained theoretically (W) Aap CR Cp Cp,air D dh eh GrD hap

reported to be independent of the cavity inclination (Stine and McDonald, 1988; Leibfried and Ortjohann, 1995). The convective heat loss depends on the air temperature within the cavity, the inclination of the cavity and the external wind conditions (Clausing, 1983; Stine and McDonald, 1989), thus making the phenomenon complex. Convective losses from cubical and rectangular open cavities have been extensively studied (Le Quere et al., 1981a,b; Penot, 1982; Hess and Henze, 1984; Chen et al., 1985; Chan and Tien, 1985, 1986; Pavlovic and Penot, 1991; Skok et al., 1991; Chakroun et al., 1997). The general assumptions in these investigations are that the cavity walls are either uniformly heated or one wall is heated and others are maintained in adiabatic condition. Consequently the results cannot be directly used for solar cavity receivers used for process heat applications, which are mainly cylindrical in shape and have non-uniform wall temperatures. According to Clausing (1981, 1983), Stine and McDonald (1989), McDonald (1995) and Taumoefolau et al. (2004), the convective loss from the cavity receiver under no-wind condition decreases with increase in inclination. In other words, for a downward facing cavity receiver the convective loss is highest at 0° inclination (sideways facing cavity) and negligible at 90° inclination (vertically downward facing cavity) while for upward facing cavity the highest losses are observed between 30° and 60° inclination angles. Ma (1993) has reported the experimental investigations on the convective loss under wind

Qtotal/h total loss at receiver angle h (W) Qtotal,nw/90° total loss at receiver angle of 90° for nowind condition (W) Qtotal;nw=90 ;aperture closed total loss at receiver angle of 90° for no-wind condition when aperture is closed (W) ambient temperature (°C) Ta average temperature of the exiting air at aperTc ture (°C) temperature of working fluid entering the receiTfi ver (°C) temperature of working fluid exiting the receiver Tfo (°C) mean receiver temperature, average of T fi and Tm Tfo (°C) overall heat transfer coefficient based on reflecU loss tor aperture area (W/m2-K) U loss;ap overall heat transfer coefficient based on receiver aperture area (W/m2-K) average air velocity into aperture (m/s) Va e emissivity of the receiver wall h receiver inclination angle (degrees) q density of air (kg/m3) r Stefan-Boltzmann constant (W/m2-K4)

conditions for a cylindrical receiver having an aperture diameter smaller than the receiver diameter. The tests have been carried out at wind speeds greater than 3 m/s. The trends obtained from these studies are similar to that of the no-wind case. Eyler (1981) and Sendhil Kumar and Reddy (2007) carried out a 2-dimensional numerical analysis of convective losses in rectangular and hemispherical solar cavity receiver respectively. Three-dimensional numerical analysis of cylindrical receivers is carried out by Paitoonsurikarn and Lovegrove (2002, 2003) and Paitoonsurikarn et al. (2004). The wall temperatures in these studies are assumed to be isothermal. The numerical studies are carried out on simplified geometries wherein the receiver tubes are modeled as plain walls. Analyses of convective heat losses with non-uniform wall temperatures are not reported. The literature survey shows that the types of receivers investigated both experimentally and numerically are cubical, rectangular, cylindrical and hemispherical in shape. The cylindrical receivers studied so far, do not have a wind skirt and the diameter of the receiver aperture is less than that of the cavity. The current investigation considers a cylindrical receiver having the ratio of aperture diameter to the cavity diameter greater than one. Experimental studies of such a receiver are extensively carried out at low temperatures (below 100 °C) and the convective losses under no-wind and wind conditions are estimated. The influence of the receiver inclination, the fluid inlet temperature and

M. Prakash et al. / Solar Energy 83 (2009) 157–170

the external wind on the convective losses is reported in this communication. Nusselt number correlations based on the receiver aperture diameter are proposed for the convective losses under no-wind conditions. A 3-dimensional (3-D) numerical analysis is carried out using Fluent CFD software (Fluent Inc., 2003) and the results are compared with the experimental data. The 3-D model is used to predict the convective losses at higher temperatures of up to 300 °C. The overall heat transfer coefficient obtained from the experimental analysis is compared with the value obtained from a field study of a similarly shaped receiver having dimensions twice that of the experimental receiver. 2. Description of the receiver The receiver used in the current investigation is shown in Fig. 1. It is a helical copper tube of diameter 0.33 m

159

and height 0.5 m. There is a wind skirt having an aperture diameter of 0.5 m. There are 39 turns along the height of the receiver and 9 turns each at the back wall and the wind skirt. The copper tube has a diameter of 0.009 m, the spacing between the coil turns is of the order of 0.003–0.004 m. The coils are coated with a polyurethane coating that can withstand temperatures up to 350 °C. A layer of mineral wool (0.075 m thick) is provided on the outer side of the tube coils. It is supported by an aluminium foil on the tube side and has a cladding of aluminium on the external side. This particular shape of the receiver is similar to the receiver used in a parabolic dish-receiver system installed at Mahananda dairy, Latur, Maharashtra, India for supplying process heat (Kedare et al., 2006). The receiver in the field has dimensions about twice that of the receiver analysed in this work.

Fig. 1. Front and side view of the solar cavity receiver.

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3. Experimental investigations The experimental studies of convective loss from a solar cavity receiver can be carried out under the on-flux or offflux mode. In the on-flux mode, the receiver is tested in actual solar conditions by placing it at the focus of a parabolic dish concentrator. Field tests and tests with solar simulators fall in this category. In the present study, the experiments are carried out under the off-flux mode in a controlled environment. The field conditions in the actual solar cavity receiver are simulated by passing hot water through the receiver tubes to get similar non-uniform temperature gradient within the helical coil. 3.1. Experimental set-up The schematic of the experimental set-up is shown in Fig. 2. It consists of a downward facing cylindrical cavity receiver supported on a stand. The receiver can be inclined to various angles with respect to the horizontal in steps of 15°. The hot water circulated in the receiver is supplied from a water tank of 125 l capacity having two heaters (total wattage of 3 kW). The working fluid is circulated through the receiver tubes using a 0.18 kW pump. A rotameter measures the mass flow rate of hot water entering the receiver. The hot water is circulated at constant inlet temperature through the receiver. The temperatures of the fluid in the tube at four locations (including the outlet) are

measured using K-type thermocouples, while the inlet temperature is measured by a Pt-100 RTD for better control of the inlet fluid temperature. ADVANTECHÒ Data Acquisition Modules (ADAMÒ) are used for data acquisition and the data are logged onto a computer using the ADAM View software. The flow is kept constant for the complete period of an experimental run. The system is operated under closed loop condition as the water exiting from the receiver flows back to the storage tank. The wind conditions are simulated using a blower assembly. A circular tunnel of 0.6 m diameter made of sheet metal is attached to the blower door. Within the tunnel there are two metal mesh sections and a honeycomb section which straighten the air flow and ensure that the air blowing into the cavity from the tunnel has uniform speed across the cavity aperture. The uniformity has been checked by making measurements of wind speed at different locations of the aperture plane. The open end of the tunnel is placed at a fixed distance of about 0.2 m from the receiver stand. Two types of wind conditions, viz. head-on and side-on have been investigated and Fig. 3 shows the head-on and side-on wind directions for receiver at 0° inclination. During the head-on tests, the wind blows in the direction normal to the receiver stand while during the side-on tests, the direction of the wind is parallel to the receiver stand. All the measuring instruments used in the experiments are calibrated. Thermocouples and RTDs were calibrated

Fig. 2. Schematic diagram of the experimental set-up.

M. Prakash et al. / Solar Energy 83 (2009) 157–170

161

4. Numerical investigations

Fig. 3. Head-on and side-on wind directions for the receiver at 0° inclination (top view); (a) head-on, (b) side-on.

with the help of standard which in turn was calibrated at ERTL (electronic regional test laboratory) West Zone, Mumbai, India. The rotameter is calibrated in the laboratory itself for different fluid temperature values. The thermocouples have an uncertainty of about ±0.5% for measurements between 50 °C and 75 °C, uncertainty in the RTD reading is about ±0.3% for 50 °C to 75 °C measurement. The rotameter had an uncertainty of about ±5% for 0.02 kg/s measurement.

A 3-D numerical investigation of the cavity receiver is carried out and the simulations are limited to convective heat transfer analysis. The fluid inlet temperature and the fluid mass flow rate are the only inputs for the simulation. A helical coil as shown in Fig. 4a representing the cavity receiver is generated by using the Gambit tool of the Fluent 6.1.22 software. For the model, the region outside the cavity is surrounded by a cylindrical enclosure having diameter and length about 15 times the receiver aperture diameter. This is to ensure that the air flow within the cavity is unaffected. The fluid inlet and the outlet tubes of the receiver are extended to the enclosure walls and are assumed to be adiabatic so that they do not affect the temperature and flow profile in the region external to the cavity. A fine mesh is used within the cavity including the tubes and the region between the receiver tubes and the receiver walls. A coarse mesh is used for the region outside the cavity. The mesh progressively coarsens as the enclosure walls are approached from the cavity centre. An enlarged portion of the mesh is shown in Fig. 4b so as to differentiate between the meshes of the tube, cavity interior and the enclosure. There are 326,837 mesh elements in the tube, 707,601 elements in the cavity interior and 503,485 elements in the enclosure volume. The interval size of the fine mesh varies between 4 and 20 while the coarse mesh has an interval size of 250. The material properties of air, working fluid and the helical coil used for the simulation are taken from Holman (2002). The Boussinesq approximation is used in the low temperature cases for the air properties. At higher temperatures, the ideal gas characteristics are used due to the temperature limitations of the Boussinesq approximation (Gray and Giorgini, 1976). The boundary conditions used for the numerical analysis are as follows:

3.2. Experimental procedure The working fluid is hot water and experiments with different inlet temperatures between 50 °C and 75 °C have been carried out. For each test, the inlet fluid temperature is maintained constant. The working fluid enters and exits the receiver as shown in Fig. 2. The working fluid inlet is at the topmost portion of the receiver and the outlet is at the wind skirt. This is to ensure that the highest temperatures are at the top of the cavity receiver and lower temperatures near the aperture similar to the situation in the field operations. The flow rate of water is kept constant at 0.02 kg/s. The tube temperatures and the fluid temperatures are measured at intervals of one minute and the experiment is continued till the outlet temperature remains steady for about half an hour. This signifies that the system has reached steady state which generally is attained in 3 h time. The thermal losses are estimated at steady state.

(1) The fluid inlet temperature (at the receiver outlet) and the fluid velocity as specified. (2) Enclosure walls are maintained at ambient temperature. (3) Adiabatic condition is assumed for the cavity external wall. The solutions are obtained by solving the continuity equation, the momentum equation and the energy equation simultaneously. The semi-implicit pressure linked equation (SIMPLE) scheme of the Fluent software is used. The SIMPLE algorithm allows the flow governing equations to be solved in terms of primitive variables consisting of velocity components and pressure which is computationally less intensive when compared to the stream function-vorticity approach. It involves a pressure–velocity coupling and is used with a segregated solver, for steady state problems. The SIMPLE scheme is suited for complicated 3-D

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M. Prakash et al. / Solar Energy 83 (2009) 157–170

Fig. 4. The cavity model and the grid used for numerical analysis; (a) cavity model, (b) computational grid.

problems involving transitional and turbulent flow and is more stable than other pressure–velocity coupling schemes. The momentum and energy solution controls are of the first order upwind type. The convergence criteria for the residuals of continuity and the velocity equations are of the order of 103 while for the energy equation it is 106. The solutions are obtained once the convergence criteria are satisfied. The behaviour of the residuals is also monitored and it is ensured that the residuals remain low for 50 iterations or more before concluding that the solution has converged (Fluent Inc., 2003).

5. Results and discussion The total heat loss and the convective loss for the nowind and wind conditions obtained from the experiments are discussed. The no-wind convective loss obtained from the experimental and numerical studies are compared. Nusselt number correlations are proposed for the no-wind convective losses and compared with those reported in the

literature. The Uloss values obtained from the experiments are compared with those obtained from the field tests. An extensive experimental investigation was carried out to determine the stagnation and convective zones in such a receiver (Prakash et al., 2008). The air temperatures within the receiver were measured at 20 different locations and were compared with the numerical model. The air velocity profiles were obtained from the numerical studies. The air velocity and temperature profiles are analysed. Based on the analysis the boundary between the two zones is determined. The zone boundary is found to be nearly a horizontal plane passing through the topmost point of the cavity aperture and validates the results reported in the literature (Clausing, 1981, 1983). A term called ‘‘critical air temperature gradient” is defined for this purpose. The locations within the cavity having the temperature gradient less than the critical temperature gradient represent the stagnation zone. The locations having air temperature gradient more than the critical temperature gradient represent the convective zone. The critical temperature gradient from the experiments is found to be between 16 °C/m and 20 °C/m for

M. Prakash et al. / Solar Energy 83 (2009) 157–170

inlet fluid temperatures lying between 50 °C and 75 °C for the shape and size of the cavity studied. The near stagnant air and almost uniform temperature within the stagnation zone suggests that it does not take part in the convective heat transfer and the convective heat loss takes place from the convective zone. It is observed from the study (Prakash et al., 2008) that the stagnation zone area decreases with decrease in inclination (maximum stagnation area at 90° inclination and minimum at 0° inclination) while the convective zone area increases with decrease in receiver inclination. The stagnation zone is absent for all inclinations except 90° for the wind cases.

163

1150

90º

60º

1050

45º

30º

950

0º

Total loss (W)

850 750 650 550 450 350 250 15

5.1. Heat loss estimation

20

25

30

35

40

45

Tm-Ta (ºC)

5.1.1. Total heat loss The overall thermal loss from a receiver inclined at an angle (h) for no-wind as well as for wind condition is calculated using the following equation: _ p ðT fi  T fo Þ Qtotal=h ¼ mC

Fig. 5. Variation of total loss with temperature difference for no-wind condition.

These observations are as expected. Additional experimental data is reported in Table 1 for 0° inclination as the total losses are highest at that inclination. The data from all 45° experiments are also reported as a representative data for all other inclinations. The variation of total heat loss with temperature difference (Tm–Ta) for different head-on wind conditions is shown in Figs. 6 and 7. It can be seen that the trend is similar to the no-wind case except that the magnitudes of the heat loss is greater. The total heat loss values increase with an increase in head-on wind speed. The maximum

ð1Þ

The experimental observations and the total loss values of the receiver are shown in Table 1. The variation of total heat loss with temperature difference (Tm–Ta) for the nowind condition is shown in Fig. 5, where Tm is the average value of T fi and Tfo. The total heat loss increases with increase in temperature difference while the loss value decreases with increase in inclination. The highest heat loss for the no-wind condition occurs at 0° inclination. Table 1 Total heat loss from the receiver Test description

Inclination 90°

60°

45°

30°

0°

Tfi (°C)

Tfo (°C)

Total loss (W)

Tfi (°C)

Tfo (°C)

Total loss (W)

Tfi (°C)

Tfo (°C)

Total loss (W)

Tfi (°C)

Tfo (°C)

Total loss (W)

Tfi (°C)

Tfo (°C)

Total loss (W)

51.17

47.38

316

51.38

46.9

375

512

470

61.01

54.4

555

61.26

53

693

75.5

67.6

665

75.25

65.8

790

470 441 462 613 623 625 890 890 877

44.43

55.71

46.8 44.98 45.01 53 53.56 53.68 65.9 64.56 64.73

50.57

61.41

52.46 50.27 50.56 60.36 61 61.14 76.5 75.15 75.18

76

64.7

957

50.67 50.33 50.24 60.78 60.27 60.7 76.2 75.25 75.21

43.85 43.83 43.11 52 51.86 52.28 63.7 63.1 63.1

568 542 594 740 703 704 1044 1020 1016

Head-on wind tests (1 m/s)

50.5 59.75 75.9

45.7 52.51 65.09

400 603 908

50.5 60.01 75.17

44.7 52.45 64.08

478 632 931

50.3 60.4 75.8

43.7 51.5 63.9

550 744 999

50.84 60.17 76.02

44.15 51.04 63.73

557 763 1032

51.09 59.74 75.87

43.3 49.9 63.27

648 822 1058

Head-on wind tests (3 m/s)

50.31 59.63 75.28

44.69 51.83 63.9

468 650 955

49.9 60.3 75.42

43.23 51.68 62.82

556 720 1058

50.5 59.7 75.73

43.06 50.2 63.19

620 794 1054

51 60.23 75.36

43.38 50.25 62.32

635 834 1095

50.84 59.75 75.84

42.06 49.16 61.9

730 885 1170

Side-on wind tests (1 m/s)

50.5 59.75 75.9

45.7 52.51 65.09

400 603 908

50.85 60.01 74.93

46 52.5 63.85

404 627 930

50.81 60.23 75.26

45.8 52.5 63.51

416 646 987

51 59.9 75.26

45.72 51.68 63.06

440 687 1019

51.1 59.9 75.2

47.05 52.25 64.25

338 639 925

Side-on wind tests (3 m/s)

50.31 59.63 75.28

44.69 51.83 63.9

468 650 955

51.02 59.74 75.35

45.27 51.33 64.13

479 703 942

51.1 60.01 74.42

44.4 50.69 62.44

558 779 1006

51.3 60.06 75.07

44.23 50.2 61.6

590 824 1131

51.33 60.01 75.27

45.57 50.94 62.27

480 758 1117

No-wind tests

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M. Prakash et al. / Solar Energy 83 (2009) 157–170 1200 1150

1100

1050 950

900 90º

800

60º

700

45º

30º

600

0º

850 Total loss (W)

Total loss (W)

1000

90º

750

60º 45º

650

30º

550

0º

500 450

400 350

300 15

20

25

30

35

40

250

45

15

20

25

Tm-Ta (ºC)

30

35

40

45

Tm -Ta (ºC)

Fig. 6. Variation of total loss with temperature difference for 1 m/s headon wind condition.

Fig. 8. Variation of total loss with temperature difference for 1 m/s sideon wind condition.

1400 1300 1300 1200

1200

1100

1000

90º 60º

900

45º

800

30º

700

0º

600

1000 90º 60º

900

45º

800

30º 0º

700

500 400 300 15

Total loss (W)

Total loss (W)

1100

600 20

25

30

35

40

45

Tm-Ta (ºC)

Fig. 7. Variation of total loss with temperature difference for 3 m/s headon wind condition.

500 400 15

20

25

30

35

40

45

Tm -Ta (ºC)

Fig. 9. Variation of total loss with temperature difference for 3 m/s sideon wind condition.

value is observed at a wind speed of 3 m/s and receiver inclination of 0°. The effect of inclination on the total heat loss is negligible for the inclination angles between 30° and 45°. The results under side-on wind conditions are shown in Fig. 8 and 9. It is observed that the total heat loss increases with decrease in inclination, reaches a maximum value at 30° inclination and then decreases at 0° angle. At 0°, the total heat loss for 1 m/s and 3 m/s side-on wind is lower than the no-wind total loss value. This is due to the fact that the wind acts as a barrier at the cavity aperture preventing the hot air movement from the receiver. This trend is noticed for all fluid inlet temperature values tested. Higher wind speeds produce higher heat loss but loss values are lower than the loss due to head-on wind, the reason being that the side-on wind would not be able to induce convective currents within the receiver as effectively as the head-on wind due to the wind direction and receiver geometry which includes the wind skirt. The heat losses at 90° inclination for the head-on as well as side-on wind condition are higher than that of the nowind case. This is because only a small part of the receiver

is covered by the stagnation zone and the convective zone covers the remaining lower portions of the receiver. The higher the convective currents the greater will be the heat losses. The uncertainty in the total loss measurement is about 8%. 5.1.2. Convective heat loss The convective losses at different inclinations are estimated by subtracting Qr+c/h (the radiative loss and the loss due to conduction) from the total heat loss, Qtotal/h. In order to calculate Qr+c/h, the following procedure is adopted: The receiver is inclined at 90° (downward facing receiver) and the aperture of the receiver is closed by an acrylic sheet insulated on all sides by mineral wool insulation. This prevents the convective and radiative heat loss through the receiver aperture. The tests are then performed for inlet fluid temperatures between 50 °C and 75 °C. The loss obtained from these tests is the conductive loss occurring from the support structure and the sides of the

M. Prakash et al. / Solar Energy 83 (2009) 157–170

receiver. The radiative loss through the aperture is theoretically calculated using the following equation:

500

Qrad=90 ;theoretical ¼ r e Aap ðT 4m  T 4a Þ

400

45º

Convective loss (W)

For all fluid inlet conditions corresponding to 90° tilt of the receiver, the conductive and radiative losses are obtained from the following equation: ð3Þ

30º

0º

350 300 250 200 150 100

These values are plotted against (Tm–Ta) and a linear relation is obtained. The radiative and conductive losses are dependent on Tm and the linear relation is used to estimate the values of Qr+c,nw/h for all other inclinations using the corresponding (Tm–Ta) values as obtained from the experiments. These are presented in Table 2 and are assumed to be the same for the corresponding wind cases also. The convective loss for any inclination is obtained by subtracting the conductive and radiative losses from the total loss Qconv=h ¼ Qtotal=h  Qrþc=h

90º

60º

450

ð2Þ

Qrþc;nw=90 ¼ Qtotal;nw=90 ;aperture closed þ Qrad=90 ;theoretical

165

50 0 15

20

25

30

35

40

45

Tm-T a (ºC)

Fig. 10. Variation of no-wind convective loss with (Tm–Ta).

convective loss is very less. This is mainly due to the fact that the whole of the receiver at 90° inclination is within the stagnation zone and the convective zone is limited to regions very close to the receiver aperture. The stagnation zone area decreases with decrease in receiver inclination and at 0° inclination the convective zone covers the entire receiver leading to very high convective and total losses. The convective loss occurring from the cavity receiver is obtained from the 3-dimensional (3-D) numerical analysis using two methods. In the first method, the numerical convective loss is calculated as a product of fluid mass flow rate, temperature difference between the fluid inlet and

ð4Þ

Fig. 10 shows the variation of no-wind convective loss with (Tm–Ta). It can be seen that as the temperature difference increases, the convective loss increases showing a linear trend. The convective loss increases with decrease in inclination (Fig. 11), a trend similar to the total heat loss variation for no-wind condition. It can also be observed that at 90° inclination angle for the no-wind case, the radiative and conductive losses are dominant while the Table 2 Heat losses due to radiation and conduction Test description

Inclination 90°

60°

45°

30°

0°

Tfi (°C)

Tfo (°C)

Qr+c/h (W)

Tfi (°C)

Tfo (°C)

Qr+c/h (W)

Tfi (°C)

Tfo (°C)

Qr+c/h (W)

Tfi (°C)

Tfo (°C)

Qr+c/h (W)

Tfi (°C)

Tfo (°C)

Qr+c/h (W)

51.17

47.38

301

51.38

46.9

299

277

427

61.01

54.4

415

61.26

53

407

75.5

67.6

601

75.25

65.8

588

305 290 312 402 416 418 598 608 595

44.43

55.71

46.8 44.98 45.01 53 53.56 53.68 65.9 64.56 64.73

50.57

61.41

52.46 50.27 50.56 60.36 61 61.14 76.5 75.15 75.18

76

64.7

588

50.67 50.33 50.24 60.78 60.27 60.7 76.2 75.25 75.21

43.85 43.83 43.11 52 51.86 52.28 63.7 63.1 63.1

276 271 306 397 380 385 580 578 578

Head-on wind tests (1 m/s)

50.5 59.75 75.9

45.7 52.51 65.09

285 394 589

50.5 60.01 75.17

44.7 52.45 64.08

278 395 577

50.3 60.4 75.8

43.7 51.5 63.9

270 392 581

50.84 60.17 76.02

44.15 51.04 63.73

277 387 581

51.09 59.74 75.87

43.3 49.9 63.27

272 376 580

Head-on wind tests (3 m/s)

50.31 59.63 75.28

44.69 51.83 63.9

277 389 577

49.9 60.3 75.42

43.23 51.68 62.82

264 392 571

50.5 59.7 75.73

43.06 50.2 63.19

267 378 575

51 60.23 75.36

43.38 50.25 62.32

272 382 567

50.84 59.75 75.84

42.06 49.16 61.9

262 371 567

Side-on wind tests (1 m/s)

50.5 59.75 75.9

45.7 52.51 65.09

285 394 589

50.85 60.01 74.93

46 52.5 63.85

289 396 574

50.81 60.23 75.26

45.8 52.5 63.51

288 397 574

51 59.9 75.26

45.72 51.68 63.06

288 389 571

51.1 59.9 75.2

47.05 52.25 64.25

298 393 579

Side-on wind tests (3 m/s)

50.31 59.63 75.28

44.69 51.83 63.9

277 388 577

51.02 59.74 75.35

45.27 51.33 64.13

285 386 579

51.1 60.01 74.42

44.4 50.69 62.44

280 383 561

51.3 60.06 75.07

44.23 50.2 61.6

280 380 560

51.33 60.01 75.27

45.57 50.94 62.27

289 385 568

No-wind tests

M. Prakash et al. / Solar Energy 83 (2009) 157–170 500

500

450

450

400

400

350 300 50ºC

250

60ºC

75ºC

200

Convective loss (W)

Convective loss (W)

166

350 90º

300

60º

250

45º

30º

200

0º

150

150 100 100

50

50

0 15

0 0

15

30

45

60

75

20

25

90

Receiver inclination (degrees)

Fig. 11. Variation of no-wind convective loss with receiver inclination.

1 q Aap V a C p;air ðT c  T a Þ 2

40

45

650

Convective loss (W)

550

90º

450

60º 45º 30º

350

0º

250

ð5Þ

where Ta is the ambient air temperature, q is the density of air, Aap is the area of the aperture and Cp,air is the specific heat of air. A good agreement is observed between the experimental convective loss and the convective loss values calculated using the Clausing (1983) approach with maximum variation of 13%. The comparison of experimental and numerical values for different inclinations and fluid inlet temperatures are shown in Table 3. A good agreement is observed between the experimental convective loss and the numerical convective loss values calculated using the two approaches. The numerical study is also carried out for fluid inlet temperatures of between 100 °C and 300 °C at receiver inclinations of 0°, 45° and 90° inclination. The trends in

35

Fig. 12. Variation of convective loss with (Tm–Ta) for 1 m/s head-on wind.

outlet and specific heat of the working fluid. The convective heat losses thus estimated is compared with the experimental results. It is found that the values agree reasonably well; the maximum deviation is about 14%. In the second method, the convective losses from the 3D numerical study of the cavity receiver are evaluated by analysing the temperature and velocity profiles at the aperture of the receiver. The temperature and velocity of air at different points in the convective zone of the receiver are calculated. Tc is the average value of all these temperatures while Va represents the corresponding quantity for velocity. The convective loss is then calculated as (Clausing, 1983) Qconv=h ¼

30

Tm-T a (ºC)

150 15

20

25

30

35

40

45

Tm-Ta (ºC)

Fig. 13. Variation of convective loss with (Tm–Ta) for 3 m/s head-on wind.

the variation of convective losses with receiver inclination and fluid inlet temperature are similar in this case as well. The variation of convective loss with temperature difference (Tm–Ta) for different wind speeds and wind directions are shown in Figs. 12–15. The loss values increase with an increase in temperature difference. Among the wind speeds and directions tested in the current work, the convective loss is maximum for head-on wind of 3 m/s. The loss patterns for the head-on wind have a trend that is

Table 3 Comparison of experimental and numerical convective loss Fluid inlet temperature (°C)

Inclination (deg)

75–77

0 45 0 45 0 45

60–62 50–52

Experimental values (W) Exp. 1

Exp. 2

Exp. 3

Average

464 291 343 211 291 164

442 281 323 207 271 151

438 282 319 206 288 150

448 285 328 208 283 155

Numerical values (W)

Numerical values based on Eq. (5) (W)

386 252 312 184 264 147

405 248 311 182 248 150

M. Prakash et al. / Solar Energy 83 (2009) 157–170

167

500

50ºC, 1m/s

700

60ºC,1m/s 75ºC,1m/s

600

50ºC,3m/s 60ºC,3m/s 75ºC, 3m/s

500

300

90º 60º 45º

200

30º 0º

100

Convective loss (W)

Convective loss (W)

400

400

300

200 0 15

20

25

30

35

40

100

45

Tm-Ta (ºC) 0

Fig. 14. Variation of convective loss with (Tm–Ta) for 1 m/s side-on wind.

0

15

30

45

60

75

90

Receiver inclination (degrees)

Fig. 16. Variation of convective loss with inclination for head-on wind. 650 700 50ºC, 1m/s 60ºC,1m/s

600

75ºC,1m/s

50ºC,3m/s

90º

450

60º

45º 30º

350

0º

250

60ºC,3m/s

500

Convective loss (W)

Convective loss (W)

550

75ºC, 3m/s

400

300

200

150 15

20

25

30

35

40

45

Tm-Ta (ºC)

100

Fig. 15. Variation of convective loss with (Tm–Ta) for 3 m/s side-on wind. 0 0

approximately linear while for side-on wind conditions no such trends are noticed. The convective loss trends for head-on and side-on wind condition for different receiver inclinations are shown in Figs. 16 and 17, respectively. The head-on convective loss increases with decrease in inclination angle as expected. In case of side-on wind condition, the convective loss value increases with decrease in inclination attains a maximum value at 30° inclination and then decreases at 0° inclination, a trend similar to the side-on total heat loss variation. It may be mentioned that the effect of inclination angle on the side-on convective loss is less in case of the side-on case compared to the no-wind and head-on condition. This result agrees with those reported by Leibfried and Ortjohann (1995).

15

30

45

60

75

90

Receiver inclination (degrees)

Fig. 17. Variation of convective loss with inclination for side-on wind. h

D

number, NuD ¼ apk where D is the aperture diameter and k is the thermal conductivity of air. The heat transfer coefficient based on the aperture area is calculated from hap ¼

Qconv=h ðT m  T a Þ Aap

ð6Þ

where Qconv/h is the convective loss at a particular inclination h, and Aap is the receiver aperture area. It is seen that the Nusselt number decreases with increase in inclination, being lowest at 90° inclination and highest at 0° inclination. The Nusselt number correlation with Grashof number for the convective heat loss is found to be

5.2. Correlations developed

Nunw;D ¼ 0:21 GrD

The values of the convective losses under no-wind condition for fluid inlet temperatures of 60 °C and 75 °C for all inclinations have been used to calculate the Nusselt

where h is the receiver inclination angle in degrees. Tm and Ta are in Kelvin. The Grashof number (GrD) is calculated taking the aperture diameter as the characteristic diameter.

ð1=3Þ

ð1 þ cos hÞ3:02 ðT m =T a Þ1:5

ð7Þ

168

M. Prakash et al. / Solar Energy 83 (2009) 157–170 1200

Table 4 Values of d and e used in Eq. (8)

1000

Inclination

d (W)

e (W/K)

90° 60° 45° 30° 0°

19 15 59 144 157

1.41 3.76 3.8 3.82 5.04

NuD corre lated

800

600

400

200

0 0

200

400

600

800

1000

1200

NuD experimental

Fig. 18. Experimental and correlated Nusselt number (no-wind tests).

The value of ðT m =T a Þ varies between 1.08 and 1.14. Grashof number is between 3.3  108 and 4.9  108. In conformity with the literature, the Grashof number is raised to the power of (1/3) in order to avoid the shape and size effects. It is noticed that there is a decrease in the Nusselt number for an increase in Grashof number for the fluid inlet temperature ranges between 60 °C and 75 °C. This is observed for all receiver inclinations tested here and is due to property variations. The ratio (Tm/Ta) is introduced in the Nusselt number correlations to take care of the property variations. Fig. 18 shows the parity plot between the experimental and the correlated Nusselt number. The coefficient of correlation is about 0.98. The maximum variation between the experimental and correlated Nusselt number is found to be about 12%. The correlation is suitable for medium temperature industrial process heat applications where the fluid outlet temperature is about 125 °C when the fluid inlet temperatures are about 25 °C.

where Tm and Ta are in Kelvin and ðT m =T a Þ vary between 1.2 and 1.9. The correlation coefficient is about 0.97. The convective loss values at high receiver mean temperatures are compared with the numerical calculations and are presented in Fig. 19. There is a good agreement between these results. Fig. 19 also shows the Qconv/h obtained experimentally at low temperature ranges for reference. For temperature ranges of 100–300 °C, a number of correlations have been proposed in the literature (Le Quere et al., 1981b; Clausing, 1983; Stine and McDonald, 1989). The present correlation is compared with these correlations. It is seen from Figs. 20 and 21 that all the existing correlations under-predict the convective loss values for all inclinations. This is as expected since the correlations reported in literature are developed for different geometrical shapes of cavity receivers. Besides, the ratios of receiver aperture diameter to receiver diameter are lesser or equal to one. It may be noted that the order of magnitude of the current correlation matches with those of the others. The correlation proposed by Paitoonsurikarn and Lovegrove (2006) for a cylindrical receiver has been obtained from numerical and experimental data at high receiver temperatures between (450 °C and 650 °C). This has not been compared with the present correlation. 5.4. Overall heat transfer coefficient (Uloss) The overall heat transfer coefficient of the receiver is calculated using the following equation:

5.3. Convective loss at high fluid inlet temperatures As discussed in Section 5.1.2, Fig. 10 shows that the values of convective heat loss follow a linear trend with (Tm–Ta). A linear relation has been fitted to the data and is of the form 1:1

ð8Þ

where d and e are constants and the subscript h denotes a particular receiver inclination. Each receiver inclination has a value of d and e as shown in Table 4. Such a relationship has also been reported in the literature (Stine and McDonald, 1988; Leibfried and Ortjohann, 1995). In order to develop an appropriate correlation for Nusselt number based on the cavity mouth diameter (D) in the higher temperature range, Qconv/h has been calculated from Eq. (8) using d and e values obtained from low temperature data for Tm lying between 100 °C and 300 °C. The correlation is found to be ð1=3Þ

Nunw;D ¼ 0:246 GrD

ð1 þ cos hÞ

2:03

ðT m =T a Þ

0:58

ð9Þ

0 º predicted 30 º predicted 45 º predicted 60 º predicted 90 º predicted 0 º numerical 45 º numerical 90 º numerical 0 º experimental 30 º experimental 45 º experimental 60º experimental 90º experimental

2400 2200 2000 Convective loss (W)

Qconv=h ¼ d h þ eh ðT m  T a Þ

2600

1800 1600 1400 1200 1000 800 600 400 200 0

0

50

100

150

200

250

300

Tm-Ta (ºC)

Fig. 19. Experimental, predicted and numerical no-wind convective loss variation with (Tm–Ta).

M. Prakash et al. / Solar Energy 83 (2009) 157–170

Present value

Tm=200ºC

1800

Stine and McDonald

1600

based on the reflector aperture area is calculated using the following equation:

Le Quere et al.

1400

U loss ¼

Convective loss (W)

Clausing

1200

Qtotal=h Aap CR ðT m  T a Þ

ð11Þ

The U loss obtained from the experiments range between 0.76 and 1.0 W/m2-K. The values from the field tests are expected to be higher as the U loss value is obtained from tests carried out at higher mean receiver temperatures (between 60 °C and 100 °C) and for external wind speeds between 2 m/s and 4 m/s. The U loss value from the field system is about 1.195 W/m2-K (Rakesh Sharma et al., 2006).

1000 800 600 400 200 0 0

15

30

45

60

75

90

Receiver inclination (degrees)

6. Conclusions

Fig. 20. Comparison of present correlation with existing correlations (Tm =200 °C).

Present value

Tm=300ºC 3000

Stine and McDonald Le Quere et al.

2500 Clausing

Convective loss (W)

169

In this communication, the effects of fluid inlet temperature, receiver inclination angle and external wind on the total thermal loss and the convective losses are studied experimentally as well as numerically for a downward facing cavity receiver made up of helical coil tube having cavity diameter less than the depth as well as the aperture diameter. The following conclusions can be drawn from this study.

2000

1500

1000

500

0

0

15

30

45

60

75

90

Receiver inclination (degrees)

Fig. 21. Comparison of present correlation with existing correlations (Tm =300 °C).

U loss;ap ¼

Qtotal=h Aap ðT m  T a Þ

ð10Þ

where Qtotal=h is the total loss at inclination h (including 90° inclination), Aap is the area of the receiver aperture, (TmTa) is the temperature difference. The value of U loss;ap varies between 80 W/m2-K and 220 W/m2-K. To compare the overall heat transfer coefficient with the values from the field tests (Rakesh Sharma et al., 2006), the Uloss has to be based on the reflector aperture area by dividing it by geometric concentration ratio (CR). The concentration ratio (CR) is about 160 for the field system at Latur, Maharashtra (Rakesh Sharma et al., 2006) and the same CR is used here to calculate the Uloss based on reflector aperture area. The 3 m/s wind speed experimental data is compared with the field values. The comparison is carried out for the mean fluid temperature of about 70 °C as the U loss value proposed for the field tests are derived at mean receiver temperatures higher than 60 °C. The U loss

(1) The highest total and convective losses are obtained for the head-on wind condition at 0° inclination of the receiver. The losses are higher than the side-on wind convective loss. The no-wind convective loss at 0° inclination is greater than that due to 1 m/s and 3 m/s side-on wind as the side-on wind presumably prevents the hot air from flowing out of the cavity. At 3 m/s wind speed, the total and convective losses are independent of wind direction for all inclination except 0° receiver inclination. The effect of inclination on losses due to the side-on wind condition is very small when compared to the no-wind and head-on wind conditions. (2) The experimental results are compared with the numerical values. They agree reasonably well, the maximum deviation being about 14%. (3) The correlations for Nusselt number have been developed for no-wind convective losses with a correlation coefficient of 0.98. (4) The relationship of convective heat loss with (Tm–Ta), established for low temperature range under no-wind condition, has been extrapolated to high temperature values up to 300 °C. These compare reasonably well with the corresponding numerical values. This shows that the no-wind convective loss analysis at low mean receiver temperatures (up to 75 °C) can be extended to receiver mean temperatures up to 300 °C satisfactorily. The extension of the low temperature analysis to high temperatures for the wind induced convective loss is not feasible as the loss values are not linear.

170

M. Prakash et al. / Solar Energy 83 (2009) 157–170

(5) The present correlation proposed for temperature range between 100 °C and 300 °C is compared with correlations existing in literature. All existing correlations under-predict the convective loss values. The agreement between the existing and present correlation improves as the receiver mean temperature increases. (6) The overall heat loss coefficient (Uloss) obtained from the study carried out is comparable with that obtained from a field receiver of twice the dimension, tested at Latur, Maharashtra, India.

Acknowledgements The authors wish to thank the Ministry of New and Renewable Energy (MNRE), Government of India for the financial assistance provided for carrying out the research work. We are also grateful to our laboratory staff for the help provided in setting up the experiment. References Chakroun, W., Elsayed, M.M., Al-Fahed, S.F., 1997. Experimental measurements of heat transfer coefficient in a partially/fully opened tilted cavity. Journal of Solar Energy Engineering 119, 298–303. Chan, Y.L., Tien, C.L., 1985. A numerical study of two-dimensional laminar natural convection in shallow open cavities. International Journal of Heat and Mass Transfer 28, 603–612. Chan, Y.L., Tien, C.L., 1986. Laminar natural convection in shallow open cavities. Journal of Heat Transfer 108, 305–309. Chen, K.S., Humphrey, J.A.C., Sherman, F.S., 1985. Convective flow in a heated cavity – free and mixed convective flow of air in a heated cavity of variable rectangular cross-section and orientation. Philosophical Transactions of the Royal Society of London A 316, 57–84. Clausing, A.M., 1981. An analysis of convective losses from cavity solar central receivers. Solar Energy 27 (4), 295–300. Clausing, A.M., 1983. Convective losses from cavity solar receiverscomparisons between analytical predictions and experimental results. Journal of Solar Energy Engineering 105, 29–33. Eyler, L.L., 1981. Predictions of convective losses from a solar cavity receiver. In: Proceedings DOE/SERI/SNLL Workshop on Convective Losses from Solar Receivers, Sandia Laboratory Report SAND81– 8014, Livermore, California, pp. 93–104. Fluent Inc., copyright 2003, CFD software package. Gray, D.D., Giorgini, A., 1976. The validity of the Boussinesq approximation for liquids and gases. International Journal of Heat and Mass Transfer 19, 545–551. Harris, J.A., Lenz, T.G., 1985. Thermal performance of solar concentrator/cavity receiver systems. Solar Energy 34 (2), 135–142. Hess, C.F., Henze, R.H., 1984. Experimental investigations of natural convection losses from open cavities. Journal of Heat Transfer 106, 333–338. Holman, J.P., 2002. Heat Transfer, 8 ed. Tata McGraw-Hill Publishing Company Limited, New Delhi. Kedare, S.B., Nayak, J.K., Paranjape, A.D., 2006. Development, Installation and Evaluation of Large Scale Concentrating Solar Collector for Medium Temperature Industrial Thermal Applications. Final Report of R&D project no. 15/9/2002-ST, Ministry of New and Renewable Energy, Govt. of India.

Leibfried, U., Ortjohann, J., 1995. Convective heat loss from upward and downward-facing cavity solar receivers: measurements and calculations. Journal of Solar Energy Engineering 117, 75–84. Le Quere, P., Humphrey, J.A.C., Sherman, F.S., 1981a. Numerical calculation of thermally driven two-dimensional unsteady laminar flow in cavities of rectangular cross section. Numerical Heat Transfer 4, 249–283. Le Quere, P., Penot, F., Mirenayat, M., 1981b. Experimental study of heat loss through natural convection from an isothermal cubic open cavity. In: Proceedings DOE/SERI/SNLL Workshop on Convective Losses from Solar Receivers, Sandia Laboratory Report SAND81-8014, Livermore, California, pp. 165–174. Ma, R.Y., 1993. Wind Effects on Convective Heat Loss from a Cavity Receiver for a Parabolic Concentrating Solar Collector. Sandia National Laboratories Report, SAND92-7293. McDonald, C.G., 1995. Heat Loss from an Open Cavity, Sandia National Laboratories Report, SAND95-2939. Paitoonsurikarn, S., Lovegrove, K., 2002. Numerical investigation of natural convection loss in cavity-type solar receivers. In: Proceedings of Solar 2002, ANZSES Annual Conference, Newcastle, Australia. Paitoonsurikarn, S., Lovegrove, K., 2003. On the study of convection loss from open cavity receivers in solar paraboloidal dish application. In: Proceedings of Solar 2003, ANZSES Annual Conference, Melbourne, Australia. Paitoonsurikarn, S., Taumoefolau, T., Lovegrove, K., 2004. Estimation of convection loss from paraboloidal dish cavity receivers. In: Proceedings of Solar 2004: Life, the Universe and Renewables, 42nd Annual Conference of the Australian and New Zealand Solar Energy Society, Perth, Australia. Paitoonsurikarn, S., Lovegrove, K., 2006. A new correlation for predicting the free convection loss from solar dish concentrating receivers. In: Proceedings of Solar 2006: Clean Energy?-Can Do!, ANZSES 2006, Canberra, Australia Pavlovic, M.D., Penot, F., 1991. Experiments in the mixed convection regime in an isothermal open cubic cavity. Experimental Thermal and Fluid Science 4, 648–655. Penot, F., 1982. Numerical calculation of two-dimensional natural convection in isothermal open cavities. Numerical Heat Transfer 5, 421–437. Prakash, M., Kedare, S.B., Nayak, J.K., 2008. Determination of Stagnation and Convective Zones in a Solar Cavity Receiver, communicated to International Journal of Thermal Sciences. Rakesh Sharma, V., Bhosale, S.J., Kedare, S.B., Nayak, J.K., 2006. Field tests of the performance of paraboloid solar concentrator ARUN160 at Latur. In: Proceedings of First National Conference on Advances in Energy Research (AER 2006), Mumbai, India, Macmillan India Ltd., pp. 182–187. Sendhil Kumar, N., Reddy, K.S., 2007. Numerical investigation of natural convection heat loss in modified cavity receiver for fuzzy focal solar dish concentrator. Solar Energy 81 (7), 846–855. Skok, H., Ramadhyani, S., Schoenhals, R.J., 1991. Natural convection in side-facing open cavity. International Journal of Heat and Fluid Flow 12 (1), 36–45. Stine, W.B., McDonald, C.G., 1988. Cavity receiver heat loss measurements. In: Proceedings of ASME Solar Energy Division Conference, Denver, Colorado. Stine, W.B., McDonald, C.G., 1989. Cavity receiver convective heat loss. In: Horigome, T., Kimura, K., Takakura, T., Nishino, T., Fujii, I. (Eds.), . In: Proceedings of International Solar Energy Society Solar World Congress, Kobe, Japan, vol. 2. Pergamon Press, pp. 1318–1322. Taumoefolau, T., Paitoonsurikarn, S., Hughes, G., Lovegrove, K., 2004. Experimental investigation of natural convection heat loss from a model solar concentrator cavity receiver. Journal of Solar Energy Engineering 126, 801–807.