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Thermal advantages for solar heating systems with a glass cover with antireflection surfaces
Solar Energy 74 (2003) 513–523
Thermal advantages for solar heating systems with a glass cover with antireflection surfaces S. Furbo*, L. Jivan Shah Department of Civil Engineering, Technical University of Denmark, Building 118, DK-2800 Kgs. Lyngby, Denmark
Abstract Investigations elucidate how a glass cover with antireflection surfaces can improve the efficiency of a solar collector and the thermal performance of solar heating systems. The transmittances for two glass covers for a flat-plate solar collector were measured for different incidence angles. The two glasses are identical, except for the fact that one of them is equipped with antireflection surfaces by the company SunArc A / S. The transmittance was increased by 5–9%-points due to the antireflection surfaces. The increase depends on the incidence angle. The efficiency at incidence angles of 08 and the incidence angle modifier were measured for a flat-plate solar collector with the two cover plates. The collector efficiency was increased by 4–6%-points due to the antireflection surfaces, depending on the incidence angle. The thermal advantage with using a glass cover with antireflection surfaces was determined for different solar heating systems. Three systems were investigated: solar domestic hot water systems, solar heating systems for combined space heating demand and domestic hot water supply, and large solar heating plants. The yearly thermal performance of the systems was calculated by detailed simulation models with collectors with a normal glass cover and with a glass cover with antireflection surfaces. The calculations were carried out for different solar fractions and temperature levels of the solar heating systems. These parameters influence greatly the thermal performance associated with the antireflection surfaces. 2003 Elsevier Ltd. All rights reserved.
1. Introduction Investigations have shown that the transmittance of glass can be increased by 4% if the glass is equipped with antireflection surfaces and that the solar collector efficiency can be increased by 4% points if a glass with antireflection surfaces is used instead of a normal glass as the cover plate for the solar collector (Nostell et al., 1998; ¨ et al., 2000; Fischer and Helgesson et al., 2000; Hellstrom Hahne, 2000). Further, the investigations showed that the thermal performance of solar collectors can be increased by 6–13% depending on the operating temperature and that the yearly energy gain can be increased by 4% for a SDHW system if a glass with antireflection surfaces is used instead of a normal glass as cover plate for the solar collector. In this study the increase in the transmittance for glass
*Corresponding author. Tel.: 145-45-251-857; fax: 145-45931-755. E-mail address: [email protected] (S. Furbo).
with a commercial antireflection surfaces and the increase of the efficiency of a marketed solar collector by making use of a cover plate of the glass with the antireflection surfaces are measured. Further, calculations will be carried out, elucidating the thermal advantage by making use of the glass with the antireflection surfaces as cover plate for solar collectors for different solar heating systems. The calculations will be carried out for different solar fractions and operating temperatures of the solar heating systems, since these parameters greatly influence the thermal advantage.
2. Transmittance measurements Measurements have been carried out on two low iron 4 mm ‘Diamant’ glasses from Scan Glas A / S. One of the glasses is equipped with the commercial antireflection surfaces prepared by means of a liquid-phase etching by SunArcA / S. The measurements were carried out for different incidence angles in an outdoor solar tracker (Duer, 2000).
0038-092X / 03 / $ – see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016 / S0038-092X(03)00186-5
S. Furbo, L. Jivan Shah / Solar Energy 74 (2003) 513–523
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Nomenclature E Ed Et G ku Ta Tm u h t dif-h tu dh t hh u
total irradiance on the glass (W/ m 2 ) diffuse irradiance on the glass (W/ m 2 ) total transmitted irradiance through the glass (W/ m 2 ) solar irradiance on the solar collector (W/ m 2 ) incidence angle modifier of solar collector ambient temperature (8C) mean solar collector fluid temperature (8C) incidence angle (8) solar collector efficiency diffuse-hemispherical transmittance directional-hemispherical transmittance at the incidence angle u hemispherical–hemispherical transmittance at the incidence angle u
The diffuse-hemispherical transmittance t dif-h was measured under weather conditions without direct solar radiation. t dif-h is the ratio between the total radiation on the glass and the transmitted radiation under these conditions. Table 1 shows the measured results. The antireflection surfaces increase the diffuse–hemispherical transmittance by 5% points. The hemispherical–hemispherical transmittance t hh and the directional–hemispherical transmittance t dh were determined for 11 different incidence angles for both glasses by means of measurements of the total and diffuse irradiance on the glass, E and Ed , as well as of the total transmitted irradiance through the glass, Et . The measurements were carried out by means of three calibrated pyranometers, type CM 11, from Kipp and Zonen measuring the total irradiance on the glass, the diffuse irradiance on the glass, and the irradiance transmitted through the glass. The following equations are used to determine t hh and dh t :
t hh 5 Et /E
(1)
t dh 5 (Et 2 t dif-h ? Ed ) /(E 2 Ed )
(2)
The measured results are given in Tables 2 and 3 for the normal glass and the glass with the antireflection surfaces, respectively. Table 1 Measured diffuse-hemispherical transmittance for the two glasses Glass
Total radiation
Transmitted radiation
t dif-h
Normal glass Glass with antireflection surfaces
47 W/ m 2 34 W/ m 2
38 W/ m 2 30 W/ m 2
0.82 0.87
Table 2 Measured irradiances and t hh and t dh for different incidence angles for the normal glass Incidence angle (8)
E (W/ m 2 )
Ed (W/ m 2 )
Et (W/ m 2 )
t hh (2)
t dh (2)
0 20 27 35 40 43 55 59 66 71 74
954 917 868 773 757 678 541 484 388 321 278
52 55 68 70 49 64 64 61 58 71 68
863 827 788 699 678 601 455 394 288 215 173
0.90 0.90 0.91 0.90 0.89 0.89 0.84 0.81 0.74 0.67 0.62
0.91 0.91 0.91 0.91 0.90 0.89 0.84 0.81 0.73 0.63 0.56
Table 3 Measured irradiances and t hh and t dh for different incidence angles for glass with antireflection surfaces Incidence angle (8)
E (W/ m 2 )
Ed (W/ m 2 )
Et (W/ m 2 )
t hh (2)
t dh (2)
0 20 27 35 40 46 54 60 65 70 75
944 911 865 789 756 658 547 475 397 337 264
51 55 68 67 49 70 64 61 57 71 68
895 863 825 752 717 617 500 415 328 256 180
0.95 0.95 0.95 0.95 0.95 0.94 0.91 0.87 0.83 0.76 0.68
0.95 0.95 0.96 0.96 0.95 0.94 0.92 0.87 0.82 0.73 0.62
S. Furbo, L. Jivan Shah / Solar Energy 74 (2003) 513–523
Approximated equations for t hh and t dh determined by regression analyses based on the measurements are:
SD S]u2 D
u 4.04 ] t hh u / 0.907 5 1 2 tan 2
for the normal glass
(3)
4.55 t hh u / 0.954 5 1 2 tan
for the glass with antireflection surfaces
SD S]u2 D
u 3.45 ] t dh u / 0.915 5 1 2 tan 2
for the normal glass
(4) (5)
4.05 t dh u / 0.961 5 1 2 tan
for the glass with antireflection surfaces hh u
(6)
where u is the incidence angle (8); t is the hemispherical–hemispherical transmittance at the incidence angle u ; t dh is the directional-hemispherical transmittance at the u incidence angle u. Fig. 1 shows, for different incidence angles, the measured hemispherical–hemispherical transmittances as well as the regression curves, while Fig. 2, for different incidence angles, shows the measured directional–hemispherical transmittances as well as the regression curves. The measuring inaccuracy of the pyranometers is within 2%. This results in inaccuracies of all transmittances determined by the measurements within the interval 0.02– 0.03. As the measured points are within the range of the measuring inaccuracy from the regression curves in Figs. 1 and 2, the regression curves are justified. For all incidence angles, the glass with the antireflection surfaces has higher t hh and t dh than the normal glass. For
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incidence angles between 08 and 708 the increases in the transmittances due to the antireflection surfaces are between 5 and 9% points, and for incidence angles between 708 and 908, between 9 and 0%-points. The maximum transmittance increases are found at an incidence angle of about 708. The transmittance increase due to the antireflection surfaces increases with increasing the incidence angle from 08 to 708 and decreases by increasing the incidence angle from 708 to 908. 3. Solar collector efficiency measurements The efficiency of the solar collector type LB 2.5 from Wagner & Co. Solartechnik GmbH. was measured in the solar tracker for different incidence angles with the two tested glasses as cover plates. The collector is a normal flat plate collector based on a selective strip absorber and a single cover plate. The transparent area of the collector is 2.56 m 2 . The efficiency measurements were carried out according to ISO standards. However, the wind speed along the collector surface was close to zero since all measurements were carried out in days without wind of any significance. Water was used as the solar collector fluid. The measured efficiencies for the collector with the two glass covers for an incidence angle of 08 are given in Table 4. Based on the measurements the following equations for the efficiencies at an incidence angle of 08 were determined by means of regression analyses: h 5 0.794–2.49 ? (T m 2 T a ) /G 2 0.018 ? (T m 2 T a )2 /G for the collector with the normal glass
Fig. 1. Measured hemispherical–hemispherical transmittance for the two glasses.
(7)
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Fig. 2. Measured directional–hemispherical transmittance for the two glasses.
h 5 0.832–2.43 ? (T m 2 T a ) /G 2 0.018 ? (T m 2 T a )2 /G for the collector with the glass with antireflection surfaces (8) where h is the solar collector efficiency; T m is the mean solar collector fluid temperature (8C); T a is the ambient temperature (8C); G is the solar irradiance on the solar collector (W/ m 2 ). Fig. 3 shows the efficiencies for the collector with the two glasses at an incidence angle of 08 and a solar 2 irradiance of 800 W/ m . The efficiency is increased by 4–5%-points due to the antireflection surfaces. The solar collector efficiencies were measured at incidence angles of 08, 308, 458, 608 and 708 for the collector with the two glasses, see Table 5.
The efficiencies of the collector for (T m 2 T a ) /G 5 0 are determined by means of the measured efficiencies corrected by means of the heat loss coefficient of the collector determined at incidence angles of 08. Based on the measurements the incidence angle modifiers based on the total solar irradiance on the collector, ku , determined by regression analyses were: ku 5 1 2 tan
3.06
(u / 2)
for the collector with the normal glass ku 5 1 2 tan
3.37
(9)
(u / 2)
for the collector with the glass with antireflection surfaces (10) Fig. 4 shows the incidence angle modifiers for the collector with the two glasses.
Table 4 Measured collector efficiencies for an incidence angle equal to 08 Cover plate
Inlet temp. (8C)
Outlet temp. (8C)
Volume flow rate (m 3 / s)
Total solar irradiance on collector (W/ m 2 )
Ambient temp. (8C)
(T m 2T a ) /G ((K?m 2 ) / W)
Collector efficiency
Normal glass
21.3 41.7 56.8 69.5
28.7 48.2 62.7 74.5
0.0000590 0.0000625 0.0000625 0.0000648
930 939 937 908
15.1 15.2 14.9 14.1
0.0106 0.0317 0.0479 0.0638
0.77 0.70 0.63 0.57
Glass with antireflection surfaces
23.5 40.9 55.0 70.0
31.7 48.0 61.8 76.0
0.0000590 0.0000618 0.0000632 0.0000650
990 959 998 995
14.5 14.8 15.3 13.9
0.0132 0.0309 0.0432 0.0594
0.78 0.74 0.69 0.62
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Fig. 3. Solar collector efficiency at an incidence angle of 08 and a solar irradiance of 800 W/ m 2 .
The collector efficiency for T m 2T a 50 is for all incidence angles higher if the glass with the antireflection surfaces is used instead of the normal glass. For incidence angles between 08 and 658 the collector efficiency increase for T m 2T a 50 due to the antireflection surfaces is from 4 to 6%-points, and for incidence angles between 658 and 908, from 6 to 0%-points. The maximum efficiency increase is found at an incidence angle of about 658. The increase in collector efficiency for T m 2T a 50 due
to the antireflection surfaces increases for increasing incidence angles in the interval from 08 to 658, while the collector increase decreases for increasing incidence angles in the interval from 658 to 908. As expected, due to the fact that the absorber absorptance and the collector efficiency factor are lower than 1, the %-point increase in the solar collector efficiency is lower than the glass transmittance %-point increase due to the antireflection surfaces.
Table 5 Measured collector efficiencies at different incidence angles Cover plate
Incidence angle (8)
Inlet temp. (8C)
Outlet temp. (8C)
Volume flow rate (l / min)
Total solar irradiance on collector (W/ m 2 )
Ambient temp. (8C)
(T m 2T a ) /G ((K?m 2 ) / W)
Collector efficiency
Collector efficiency for (T m 2T a ) /G50
Normal glass
0 30 45 60 70
24.6 23.7 23.6 21.2 20.1
31.5 30.2 28.5 24.4 21.7
3.50 3.53 3.51 3.44 3.44
877 859 685 498 319
15.1 15.6 15.5 15.6 15.4
0.0149 0.0132 0.0154 0.0146 0.0174
0.74 0.73 0.69 0.61 0.49
0.78 0.76 0.73 0.64 0.52
Glass with antireflection surfaces
0 30 45 60 70
24.8 22.2 21.3 21.4 20.1
31.7 28.6 26.4 25.0 21.9
3.58 3.52 3.50 3.49 3.42
877 801 651 524 312
15.0 16.0 16.7 15.1 15.1
0.0151 0.0118 0.0110 0.0155 0.0187
0.78 0.78 0.75 0.67 0.54
0.82 0.80 0.77 0.71 0.58
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Fig. 4. Incidence angle modifier for the collector with the two glasses.
4. Simulations of solar heating systems In order to investigate how antireflection surfaces on the glass cover of solar collectors influence the yearly thermal performance of solar heating systems, simulations were carried out for small and large solar domestic hot water (SDHW) systems, solar combi heating systems for combined space heating demand and domestic hot water supply and solar heating plants using Danish TRY (Test Reference Year) weather data (Statens Byggeforskningsinstitut (1982)). Calculations with the collector model of (prEN 12975-2) were carried out with the tested solar collector with the normal glass and with the glass with the antireflection surfaces.
4.1. Small SDHW systems Low flow SDHW systems with one, two and three solar collector panels facing south and tilted 458 and with a 183 l mantle tank were taken into calculation with the simulation program MANTLSIM which was originally developed and validated by Furbo and Berg (1990) and later modified by Shah and Furbo (1996), Shah (1999) and Shah (2000).
The upper 87 l of the tank are heated to 50.5 8C by an auxiliary energy source. Daily average hot water (50 8C) consumptions of 50, 100 and 160 l / day were used in the calculations. The cold-water temperature varies throughout the year between 2.5 and 15.5 8C and a realistic hot-water consumption pattern was used (Jordan, 2000; Jordan and Vajen, 2000). Fig. 5 shows the yearly net utilised solar energy as a function of the solar collector area. The net utilised solar energy is defined as the tapped energy from the heat storage of the system minus the auxiliary energy supplied to the heat storage of the system. The net utilised solar energy increases for increasing collector area and for increasing hot-water consumption. The systems with the collector with the glass with the antireflection surfaces perform better than the systems with the collector with the normal glass. Figs. 6 and 7 show the net utilised solar energy for a 2.56 m 2 SDHW system as a function of the collector tilt angle and as a function of the collector orientation. The optimum collector tilt angle is from 45 to 608 and the net utilised solar energy decreases with increasing collector orientation angle. The percentage decrease of the net
S. Furbo, L. Jivan Shah / Solar Energy 74 (2003) 513–523
Fig. 5. Yearly net utilised solar energy for SDHW systems as a function of the collector area and hot-water consumption.
utilised solar energy for a non-optimum placement of the collector is smaller for a system with the collectors with the glass with the antireflection surfaces than for a system with the collectors with the normal glass. Fig. 8 shows yearly performance ratios of the system with the collectors with the glass with antireflection surfaces as a function of the yearly solar fraction of the system with the collectors with the normal glass. The
Fig. 6. Yearly net utilised solar energy of a 2.56 m 2 SDHW system as a function of the collector tilt angle.
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Fig. 7. Yearly net utilised solar energy of a 2.56 m 2 SDHW system as a function of the collector orientation.
performance ratio is defined as the ratio between the yearly net utilised solar energy of the system with the collector with the glass with the antireflection surfaces and the yearly net utilised solar energy of the system with the
Fig. 8. Yearly performance ratios for small SDHW systems based on solar collectors with the glass with antireflection surfaces as a function of the yearly solar fraction for small SDHW systems based on solar collectors with the normal glass.
520
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collector with the normal glass. The solar fraction is defined as the ratio between the net utilised solar energy and the hot-water demand. The performance ratio of the system with the collectors with the glass with antireflection surfaces decreases for increasing solar fraction of the system with the collectors with the normal glass. The extra yearly thermal performance by using glass with antireflection surfaces instead of normal glass is 4% if the yearly solar fraction of the SDHW system is 60% and 10% if the yearly solar fraction is 25%.
4.2. Large SDHW systems Large SDHW systems with different solar collector areas and a 5000 l hot-water tank were analysed with the simulation program SPIRALSOL which was developed and validated by Furbo (1984). The collectors are facing south and the collector tilt angle is 458. The upper 1500 l of the tank are heated to 50.5 8C by the auxiliary energy source. The daily hot-water consumption is 5000 l / day. Fig. 9 shows the yearly net utilised solar energy as a function of the collector area and Fig. 10 shows the yearly performance ratio for the system with the collectors with the antireflection surfaces. The definitions used in Section 4.1 are also used here. The thermal advantage of using collectors with glass with the antireflection surfaces also here increases for decreasing solar fractions. The extra thermal performance by using the glass with the antireflec-
Fig. 10. Yearly performance ratio for large SDHW systems based on solar collectors with the glass with antireflection surfaces as a function of the yearly solar fraction for large SDHW systems based on solar collectors with the normal glass.
tion surfaces is almost the same for the small SDHW systems as long as the solar fraction is the same.
4.3. Combi systems
Fig. 9. Yearly net utilised solar energy for SDHW systems as a function of the collector area.
Solar heating systems with different solar collector areas and a 460 l tank in tank heat storage consisting of a 136 l hot-water tank and a 324 l pressureless tank surrounding the hot-water tank were taken into calculations with the program TRNSYS (Klein et al., 1996). The collectors are facing south and the collector tilt angle is 458. The upper 262 l of the heat storage are heated to 50.5 8C by the auxiliary energy system. The system is shown in Fig. 11. The daily hot water (50 8C) consumption is 100 l. The cold-water temperature varies throughout the year from 2.5 to 15.5 8C. The space heating demand is 16 530 and 3770 kWh / year corresponding to a normal house and a low-energy house. The heating system is based on traditional radiators. Fig. 12 shows the yearly net utilised solar energy as a function of the solar collector area, and Fig. 13 shows the yearly performance ratio of the system with the collectors with the glass with the antireflection surfaces as a function of the yearly solar fraction of the system with the collectors with the normal glass. The net utilised solar energy is defined as the hot-water consumption plus the space heating demand minus the auxiliary energy supply. The solar fraction is the ratio between the net utilised solar energy and the energy demand for space heating and domestic hot water supply. The performance ratio of the system with the collectors with the glass with the antirefl-
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Fig. 11. Schematic illustration of the solar combi system taken in calculation.
ection surfaces is the ratio between the net utilised solar energy of the system with the collectors with the glass with the antireflection surfaces and the net utilised solar energy of the system with the collectors with the normal glass. The thermal performance of the systems increases for increasing collector area, and the extra thermal performance by using the collectors with the glass with the antireflection surfaces increases for decreasing solar fraction. For a solar fraction of 25% the thermal performance is increased by 6% by using collectors with the antireflection surfaces instead of normal collectors and for a solar
fraction of 12% the increase is 10% for the low energy house. For the normal house the extra yearly net utilised solar energy by using the glass with the antireflection surfaces is 7% for a solar fraction of 12% and 10% for a solar fraction of 6%.
4.4. Solar collectors for solar heating plants The yearly thermal performance of collectors working at different constant temperatures was calculated with the simulation program Solvarmecentral, which was developed
Fig. 12. Yearly net utilised solar energy for combisystems as a function of the collector area and the house in which the system is installed.
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Fig. 13. Yearly performance ratios for combi systems with antireflection glass as a function of the yearly solar fraction for combi systems with normal glass.
by Jensen et al. (2001). The collectors are facing south and the collector tilt angle is 458. Fig. 14 shows the calculated yearly energy output from the two collectors and the ratio between the yearly energy output of the collector with the glass with the antireflection surfaces and the energy output of the collector with the normal glass as a function of the mean temperature of the solar collector fluid. For increas-
ing collector fluid temperature the energy output from the collector decreases. The extra percentage of energy output by using the collector with the glass with the antireflection surfaces instead of the collector with the normal glass increases with increasing temperature. Consequently, the higher the collector working temperature, the more benefit will be achieved by using glass with the antireflection surfaces. With a mean working temperature of 60 and 100 8C, respectively, the energy output by using glass with the antireflection surfaces is increased by 12 and 20%, respectively.
5. Conclusion
Fig. 14. The yearly thermal performance of solar heating plant solar collectors and yearly extra thermal performance of the solar collectors due to the antireflection surfaces as a function of the mean solar collector fluid temperature in the solar heating plant.
For incidence angles between 08 and 708 the solar transmittance of glass is increased by 5–9%-points and the efficiency of a flat plate solar collector is increased by 4–6%-points by using antireflection glass. Calculations showed that the yearly thermal performance of SDHW systems with yearly solar fractions of 25% and 60%, respectively, is increased by 10% and 4%, respectively, if a collector with a glass with antireflection surfaces is used instead of a collector with a normal glass. Calculations showed that the yearly thermal performance of solar combi systems in a low energy house with yearly solar fractions of 12% and 25%, respectively, is increased by about 10% and 6%, respectively, if a collector with a glass with antireflection surfaces is used instead of a collector with a normal glass.
S. Furbo, L. Jivan Shah / Solar Energy 74 (2003) 513–523
The percentage increase of the net utilised solar energy by using glass with antireflection surfaces is increasing for decreasing solar fractions. The main reason is that a high solar fraction indicates that the system is oversized, that is: in sunny summer periods the solar fraction is already high when a low efficient collector is used. Consequently, only a limited thermal advantage is gained by using a high efficient collector. Finally, calculations showed that the yearly energy produced of a solar collector in a solar heating plant can be increased by about 12% and 20%, respectively, by using a glass cover with antireflection surfaces instead of a normal glass as cover plate if the mean solar collector fluid is 608C and 100 8C, respectively. The extra costs for collectors using glass with the antireflection surfaces instead of normal glass is about 50 DKK or 6 USD per m 2 collector. With such a relatively small increase of the system costs it can be concluded that solar collectors with antireflection surfaces are attractive for all solar heating systems.
References Duer, K., 2000. Characterisation of advanced windows. Determination of thermal properties by measurements. Department of Buildings and Energy, Technical University of Denmark, Report R-045. Fischer, S., Hahne, E., 2000. The effect of different glass covers on the yearly energy gain of a solar collector. In: EuroSun 2000 Proceedings. Furbo, S., 1984. Varmelagring til solvarmeanlæg. Ph.D. thesis. Technical University of Denmark, Thermal Insulation Laboratory, Report 162.
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Furbo, S., Berg, P., 1990. Calculation of the thermal performance of small hot water solar heating systems using low flow operation. In: North Sun 90, Reading, UK. Helgesson, A., Karlsson, B., Nostell, P., 2000. Angular dependent optical properties from outdoor measurements of solar glazings. In: EuroSun 2000 Proceedings. ¨ ¨ ˚ Hellstrom, B., Adsten, M., Nostell, P., Wackelgard, E., Karlsson, B., 2000. The impact of optical and thermal properties on the performance of flat plate solar collectors. In: EuroSun 2000 Proceedings. Jensen, K.L., Nielsen, T., Andersen, K.R., 2001. Solfangerydelser i solvarmecentraler ved forskellige temperaturniveauer. Technical University of Denmark, Department of Civil Engineering. Jordan, U., 2000. Statistically generated DHW-load profiles on a one-minute time scale. IEA SHACP Task 26. Jordan, U., Vajen, K., 2000. Influence of the DHW-load profile on the fractional energy savings: A case study of a solar combisystem with Trnsys simulations. In: Proceedings of EuroSun 2000 Congress, Copenhagen, Denmark. Klein, S.A. et al., 1996. TRNSYS 14.1, User Manual. University of Wisconsin Solar Energy Laboratory. Nostell, P., Roos, A., Karlsson, B., 1998. Antireflection of glazings for solar energy applications. Sol. Energy Mater. Sol. Cells 54, 223–233. prEN 12975-2: Thermal solar systems and components, Solar collectors, Test Methods. 1999. Shah, L.J., 1999. Investigation and modelling of low flow SDHW solar heating systems. Ph.D. thesis. Department of Buildings and Energy, Technical University of Denmark. Report R-034. Shah, L.J., 2000. Heat transfer corrections for vertical mantle heat exchangers. Solar Energy 69 (Suppl.), 157–171. Shah, L.J., Furbo, S., 1996. Optimisation of mantle tanks for low flow solar heating systems. Proceedings EuroSun ’96, Freiburg, Vol. I, pp. 369–375. Statens Byggeforskningsinstitut (1982), Vejrdata for VVS og ˚ TRY. Statens Byggeforskningsinstitut energi. Dansk referencear (1982)
Thermal advantages for solar heating systems with a glass cover with antireflection surfaces S. Furbo*, L. Jivan Shah Department of Civil Engineering, Technical University of Denmark, Building 118, DK-2800 Kgs. Lyngby, Denmark
Abstract Investigations elucidate how a glass cover with antireflection surfaces can improve the efficiency of a solar collector and the thermal performance of solar heating systems. The transmittances for two glass covers for a flat-plate solar collector were measured for different incidence angles. The two glasses are identical, except for the fact that one of them is equipped with antireflection surfaces by the company SunArc A / S. The transmittance was increased by 5–9%-points due to the antireflection surfaces. The increase depends on the incidence angle. The efficiency at incidence angles of 08 and the incidence angle modifier were measured for a flat-plate solar collector with the two cover plates. The collector efficiency was increased by 4–6%-points due to the antireflection surfaces, depending on the incidence angle. The thermal advantage with using a glass cover with antireflection surfaces was determined for different solar heating systems. Three systems were investigated: solar domestic hot water systems, solar heating systems for combined space heating demand and domestic hot water supply, and large solar heating plants. The yearly thermal performance of the systems was calculated by detailed simulation models with collectors with a normal glass cover and with a glass cover with antireflection surfaces. The calculations were carried out for different solar fractions and temperature levels of the solar heating systems. These parameters influence greatly the thermal performance associated with the antireflection surfaces. 2003 Elsevier Ltd. All rights reserved.
1. Introduction Investigations have shown that the transmittance of glass can be increased by 4% if the glass is equipped with antireflection surfaces and that the solar collector efficiency can be increased by 4% points if a glass with antireflection surfaces is used instead of a normal glass as the cover plate for the solar collector (Nostell et al., 1998; ¨ et al., 2000; Fischer and Helgesson et al., 2000; Hellstrom Hahne, 2000). Further, the investigations showed that the thermal performance of solar collectors can be increased by 6–13% depending on the operating temperature and that the yearly energy gain can be increased by 4% for a SDHW system if a glass with antireflection surfaces is used instead of a normal glass as cover plate for the solar collector. In this study the increase in the transmittance for glass
*Corresponding author. Tel.: 145-45-251-857; fax: 145-45931-755. E-mail address: [email protected] (S. Furbo).
with a commercial antireflection surfaces and the increase of the efficiency of a marketed solar collector by making use of a cover plate of the glass with the antireflection surfaces are measured. Further, calculations will be carried out, elucidating the thermal advantage by making use of the glass with the antireflection surfaces as cover plate for solar collectors for different solar heating systems. The calculations will be carried out for different solar fractions and operating temperatures of the solar heating systems, since these parameters greatly influence the thermal advantage.
2. Transmittance measurements Measurements have been carried out on two low iron 4 mm ‘Diamant’ glasses from Scan Glas A / S. One of the glasses is equipped with the commercial antireflection surfaces prepared by means of a liquid-phase etching by SunArcA / S. The measurements were carried out for different incidence angles in an outdoor solar tracker (Duer, 2000).
0038-092X / 03 / $ – see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016 / S0038-092X(03)00186-5
S. Furbo, L. Jivan Shah / Solar Energy 74 (2003) 513–523
514
Nomenclature E Ed Et G ku Ta Tm u h t dif-h tu dh t hh u
total irradiance on the glass (W/ m 2 ) diffuse irradiance on the glass (W/ m 2 ) total transmitted irradiance through the glass (W/ m 2 ) solar irradiance on the solar collector (W/ m 2 ) incidence angle modifier of solar collector ambient temperature (8C) mean solar collector fluid temperature (8C) incidence angle (8) solar collector efficiency diffuse-hemispherical transmittance directional-hemispherical transmittance at the incidence angle u hemispherical–hemispherical transmittance at the incidence angle u
The diffuse-hemispherical transmittance t dif-h was measured under weather conditions without direct solar radiation. t dif-h is the ratio between the total radiation on the glass and the transmitted radiation under these conditions. Table 1 shows the measured results. The antireflection surfaces increase the diffuse–hemispherical transmittance by 5% points. The hemispherical–hemispherical transmittance t hh and the directional–hemispherical transmittance t dh were determined for 11 different incidence angles for both glasses by means of measurements of the total and diffuse irradiance on the glass, E and Ed , as well as of the total transmitted irradiance through the glass, Et . The measurements were carried out by means of three calibrated pyranometers, type CM 11, from Kipp and Zonen measuring the total irradiance on the glass, the diffuse irradiance on the glass, and the irradiance transmitted through the glass. The following equations are used to determine t hh and dh t :
t hh 5 Et /E
(1)
t dh 5 (Et 2 t dif-h ? Ed ) /(E 2 Ed )
(2)
The measured results are given in Tables 2 and 3 for the normal glass and the glass with the antireflection surfaces, respectively. Table 1 Measured diffuse-hemispherical transmittance for the two glasses Glass
Total radiation
Transmitted radiation
t dif-h
Normal glass Glass with antireflection surfaces
47 W/ m 2 34 W/ m 2
38 W/ m 2 30 W/ m 2
0.82 0.87
Table 2 Measured irradiances and t hh and t dh for different incidence angles for the normal glass Incidence angle (8)
E (W/ m 2 )
Ed (W/ m 2 )
Et (W/ m 2 )
t hh (2)
t dh (2)
0 20 27 35 40 43 55 59 66 71 74
954 917 868 773 757 678 541 484 388 321 278
52 55 68 70 49 64 64 61 58 71 68
863 827 788 699 678 601 455 394 288 215 173
0.90 0.90 0.91 0.90 0.89 0.89 0.84 0.81 0.74 0.67 0.62
0.91 0.91 0.91 0.91 0.90 0.89 0.84 0.81 0.73 0.63 0.56
Table 3 Measured irradiances and t hh and t dh for different incidence angles for glass with antireflection surfaces Incidence angle (8)
E (W/ m 2 )
Ed (W/ m 2 )
Et (W/ m 2 )
t hh (2)
t dh (2)
0 20 27 35 40 46 54 60 65 70 75
944 911 865 789 756 658 547 475 397 337 264
51 55 68 67 49 70 64 61 57 71 68
895 863 825 752 717 617 500 415 328 256 180
0.95 0.95 0.95 0.95 0.95 0.94 0.91 0.87 0.83 0.76 0.68
0.95 0.95 0.96 0.96 0.95 0.94 0.92 0.87 0.82 0.73 0.62
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Approximated equations for t hh and t dh determined by regression analyses based on the measurements are:
SD S]u2 D
u 4.04 ] t hh u / 0.907 5 1 2 tan 2
for the normal glass
(3)
4.55 t hh u / 0.954 5 1 2 tan
for the glass with antireflection surfaces
SD S]u2 D
u 3.45 ] t dh u / 0.915 5 1 2 tan 2
for the normal glass
(4) (5)
4.05 t dh u / 0.961 5 1 2 tan
for the glass with antireflection surfaces hh u
(6)
where u is the incidence angle (8); t is the hemispherical–hemispherical transmittance at the incidence angle u ; t dh is the directional-hemispherical transmittance at the u incidence angle u. Fig. 1 shows, for different incidence angles, the measured hemispherical–hemispherical transmittances as well as the regression curves, while Fig. 2, for different incidence angles, shows the measured directional–hemispherical transmittances as well as the regression curves. The measuring inaccuracy of the pyranometers is within 2%. This results in inaccuracies of all transmittances determined by the measurements within the interval 0.02– 0.03. As the measured points are within the range of the measuring inaccuracy from the regression curves in Figs. 1 and 2, the regression curves are justified. For all incidence angles, the glass with the antireflection surfaces has higher t hh and t dh than the normal glass. For
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incidence angles between 08 and 708 the increases in the transmittances due to the antireflection surfaces are between 5 and 9% points, and for incidence angles between 708 and 908, between 9 and 0%-points. The maximum transmittance increases are found at an incidence angle of about 708. The transmittance increase due to the antireflection surfaces increases with increasing the incidence angle from 08 to 708 and decreases by increasing the incidence angle from 708 to 908. 3. Solar collector efficiency measurements The efficiency of the solar collector type LB 2.5 from Wagner & Co. Solartechnik GmbH. was measured in the solar tracker for different incidence angles with the two tested glasses as cover plates. The collector is a normal flat plate collector based on a selective strip absorber and a single cover plate. The transparent area of the collector is 2.56 m 2 . The efficiency measurements were carried out according to ISO standards. However, the wind speed along the collector surface was close to zero since all measurements were carried out in days without wind of any significance. Water was used as the solar collector fluid. The measured efficiencies for the collector with the two glass covers for an incidence angle of 08 are given in Table 4. Based on the measurements the following equations for the efficiencies at an incidence angle of 08 were determined by means of regression analyses: h 5 0.794–2.49 ? (T m 2 T a ) /G 2 0.018 ? (T m 2 T a )2 /G for the collector with the normal glass
Fig. 1. Measured hemispherical–hemispherical transmittance for the two glasses.
(7)
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Fig. 2. Measured directional–hemispherical transmittance for the two glasses.
h 5 0.832–2.43 ? (T m 2 T a ) /G 2 0.018 ? (T m 2 T a )2 /G for the collector with the glass with antireflection surfaces (8) where h is the solar collector efficiency; T m is the mean solar collector fluid temperature (8C); T a is the ambient temperature (8C); G is the solar irradiance on the solar collector (W/ m 2 ). Fig. 3 shows the efficiencies for the collector with the two glasses at an incidence angle of 08 and a solar 2 irradiance of 800 W/ m . The efficiency is increased by 4–5%-points due to the antireflection surfaces. The solar collector efficiencies were measured at incidence angles of 08, 308, 458, 608 and 708 for the collector with the two glasses, see Table 5.
The efficiencies of the collector for (T m 2 T a ) /G 5 0 are determined by means of the measured efficiencies corrected by means of the heat loss coefficient of the collector determined at incidence angles of 08. Based on the measurements the incidence angle modifiers based on the total solar irradiance on the collector, ku , determined by regression analyses were: ku 5 1 2 tan
3.06
(u / 2)
for the collector with the normal glass ku 5 1 2 tan
3.37
(9)
(u / 2)
for the collector with the glass with antireflection surfaces (10) Fig. 4 shows the incidence angle modifiers for the collector with the two glasses.
Table 4 Measured collector efficiencies for an incidence angle equal to 08 Cover plate
Inlet temp. (8C)
Outlet temp. (8C)
Volume flow rate (m 3 / s)
Total solar irradiance on collector (W/ m 2 )
Ambient temp. (8C)
(T m 2T a ) /G ((K?m 2 ) / W)
Collector efficiency
Normal glass
21.3 41.7 56.8 69.5
28.7 48.2 62.7 74.5
0.0000590 0.0000625 0.0000625 0.0000648
930 939 937 908
15.1 15.2 14.9 14.1
0.0106 0.0317 0.0479 0.0638
0.77 0.70 0.63 0.57
Glass with antireflection surfaces
23.5 40.9 55.0 70.0
31.7 48.0 61.8 76.0
0.0000590 0.0000618 0.0000632 0.0000650
990 959 998 995
14.5 14.8 15.3 13.9
0.0132 0.0309 0.0432 0.0594
0.78 0.74 0.69 0.62
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Fig. 3. Solar collector efficiency at an incidence angle of 08 and a solar irradiance of 800 W/ m 2 .
The collector efficiency for T m 2T a 50 is for all incidence angles higher if the glass with the antireflection surfaces is used instead of the normal glass. For incidence angles between 08 and 658 the collector efficiency increase for T m 2T a 50 due to the antireflection surfaces is from 4 to 6%-points, and for incidence angles between 658 and 908, from 6 to 0%-points. The maximum efficiency increase is found at an incidence angle of about 658. The increase in collector efficiency for T m 2T a 50 due
to the antireflection surfaces increases for increasing incidence angles in the interval from 08 to 658, while the collector increase decreases for increasing incidence angles in the interval from 658 to 908. As expected, due to the fact that the absorber absorptance and the collector efficiency factor are lower than 1, the %-point increase in the solar collector efficiency is lower than the glass transmittance %-point increase due to the antireflection surfaces.
Table 5 Measured collector efficiencies at different incidence angles Cover plate
Incidence angle (8)
Inlet temp. (8C)
Outlet temp. (8C)
Volume flow rate (l / min)
Total solar irradiance on collector (W/ m 2 )
Ambient temp. (8C)
(T m 2T a ) /G ((K?m 2 ) / W)
Collector efficiency
Collector efficiency for (T m 2T a ) /G50
Normal glass
0 30 45 60 70
24.6 23.7 23.6 21.2 20.1
31.5 30.2 28.5 24.4 21.7
3.50 3.53 3.51 3.44 3.44
877 859 685 498 319
15.1 15.6 15.5 15.6 15.4
0.0149 0.0132 0.0154 0.0146 0.0174
0.74 0.73 0.69 0.61 0.49
0.78 0.76 0.73 0.64 0.52
Glass with antireflection surfaces
0 30 45 60 70
24.8 22.2 21.3 21.4 20.1
31.7 28.6 26.4 25.0 21.9
3.58 3.52 3.50 3.49 3.42
877 801 651 524 312
15.0 16.0 16.7 15.1 15.1
0.0151 0.0118 0.0110 0.0155 0.0187
0.78 0.78 0.75 0.67 0.54
0.82 0.80 0.77 0.71 0.58
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Fig. 4. Incidence angle modifier for the collector with the two glasses.
4. Simulations of solar heating systems In order to investigate how antireflection surfaces on the glass cover of solar collectors influence the yearly thermal performance of solar heating systems, simulations were carried out for small and large solar domestic hot water (SDHW) systems, solar combi heating systems for combined space heating demand and domestic hot water supply and solar heating plants using Danish TRY (Test Reference Year) weather data (Statens Byggeforskningsinstitut (1982)). Calculations with the collector model of (prEN 12975-2) were carried out with the tested solar collector with the normal glass and with the glass with the antireflection surfaces.
4.1. Small SDHW systems Low flow SDHW systems with one, two and three solar collector panels facing south and tilted 458 and with a 183 l mantle tank were taken into calculation with the simulation program MANTLSIM which was originally developed and validated by Furbo and Berg (1990) and later modified by Shah and Furbo (1996), Shah (1999) and Shah (2000).
The upper 87 l of the tank are heated to 50.5 8C by an auxiliary energy source. Daily average hot water (50 8C) consumptions of 50, 100 and 160 l / day were used in the calculations. The cold-water temperature varies throughout the year between 2.5 and 15.5 8C and a realistic hot-water consumption pattern was used (Jordan, 2000; Jordan and Vajen, 2000). Fig. 5 shows the yearly net utilised solar energy as a function of the solar collector area. The net utilised solar energy is defined as the tapped energy from the heat storage of the system minus the auxiliary energy supplied to the heat storage of the system. The net utilised solar energy increases for increasing collector area and for increasing hot-water consumption. The systems with the collector with the glass with the antireflection surfaces perform better than the systems with the collector with the normal glass. Figs. 6 and 7 show the net utilised solar energy for a 2.56 m 2 SDHW system as a function of the collector tilt angle and as a function of the collector orientation. The optimum collector tilt angle is from 45 to 608 and the net utilised solar energy decreases with increasing collector orientation angle. The percentage decrease of the net
S. Furbo, L. Jivan Shah / Solar Energy 74 (2003) 513–523
Fig. 5. Yearly net utilised solar energy for SDHW systems as a function of the collector area and hot-water consumption.
utilised solar energy for a non-optimum placement of the collector is smaller for a system with the collectors with the glass with the antireflection surfaces than for a system with the collectors with the normal glass. Fig. 8 shows yearly performance ratios of the system with the collectors with the glass with antireflection surfaces as a function of the yearly solar fraction of the system with the collectors with the normal glass. The
Fig. 6. Yearly net utilised solar energy of a 2.56 m 2 SDHW system as a function of the collector tilt angle.
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Fig. 7. Yearly net utilised solar energy of a 2.56 m 2 SDHW system as a function of the collector orientation.
performance ratio is defined as the ratio between the yearly net utilised solar energy of the system with the collector with the glass with the antireflection surfaces and the yearly net utilised solar energy of the system with the
Fig. 8. Yearly performance ratios for small SDHW systems based on solar collectors with the glass with antireflection surfaces as a function of the yearly solar fraction for small SDHW systems based on solar collectors with the normal glass.
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collector with the normal glass. The solar fraction is defined as the ratio between the net utilised solar energy and the hot-water demand. The performance ratio of the system with the collectors with the glass with antireflection surfaces decreases for increasing solar fraction of the system with the collectors with the normal glass. The extra yearly thermal performance by using glass with antireflection surfaces instead of normal glass is 4% if the yearly solar fraction of the SDHW system is 60% and 10% if the yearly solar fraction is 25%.
4.2. Large SDHW systems Large SDHW systems with different solar collector areas and a 5000 l hot-water tank were analysed with the simulation program SPIRALSOL which was developed and validated by Furbo (1984). The collectors are facing south and the collector tilt angle is 458. The upper 1500 l of the tank are heated to 50.5 8C by the auxiliary energy source. The daily hot-water consumption is 5000 l / day. Fig. 9 shows the yearly net utilised solar energy as a function of the collector area and Fig. 10 shows the yearly performance ratio for the system with the collectors with the antireflection surfaces. The definitions used in Section 4.1 are also used here. The thermal advantage of using collectors with glass with the antireflection surfaces also here increases for decreasing solar fractions. The extra thermal performance by using the glass with the antireflec-
Fig. 10. Yearly performance ratio for large SDHW systems based on solar collectors with the glass with antireflection surfaces as a function of the yearly solar fraction for large SDHW systems based on solar collectors with the normal glass.
tion surfaces is almost the same for the small SDHW systems as long as the solar fraction is the same.
4.3. Combi systems
Fig. 9. Yearly net utilised solar energy for SDHW systems as a function of the collector area.
Solar heating systems with different solar collector areas and a 460 l tank in tank heat storage consisting of a 136 l hot-water tank and a 324 l pressureless tank surrounding the hot-water tank were taken into calculations with the program TRNSYS (Klein et al., 1996). The collectors are facing south and the collector tilt angle is 458. The upper 262 l of the heat storage are heated to 50.5 8C by the auxiliary energy system. The system is shown in Fig. 11. The daily hot water (50 8C) consumption is 100 l. The cold-water temperature varies throughout the year from 2.5 to 15.5 8C. The space heating demand is 16 530 and 3770 kWh / year corresponding to a normal house and a low-energy house. The heating system is based on traditional radiators. Fig. 12 shows the yearly net utilised solar energy as a function of the solar collector area, and Fig. 13 shows the yearly performance ratio of the system with the collectors with the glass with the antireflection surfaces as a function of the yearly solar fraction of the system with the collectors with the normal glass. The net utilised solar energy is defined as the hot-water consumption plus the space heating demand minus the auxiliary energy supply. The solar fraction is the ratio between the net utilised solar energy and the energy demand for space heating and domestic hot water supply. The performance ratio of the system with the collectors with the glass with the antirefl-
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Fig. 11. Schematic illustration of the solar combi system taken in calculation.
ection surfaces is the ratio between the net utilised solar energy of the system with the collectors with the glass with the antireflection surfaces and the net utilised solar energy of the system with the collectors with the normal glass. The thermal performance of the systems increases for increasing collector area, and the extra thermal performance by using the collectors with the glass with the antireflection surfaces increases for decreasing solar fraction. For a solar fraction of 25% the thermal performance is increased by 6% by using collectors with the antireflection surfaces instead of normal collectors and for a solar
fraction of 12% the increase is 10% for the low energy house. For the normal house the extra yearly net utilised solar energy by using the glass with the antireflection surfaces is 7% for a solar fraction of 12% and 10% for a solar fraction of 6%.
4.4. Solar collectors for solar heating plants The yearly thermal performance of collectors working at different constant temperatures was calculated with the simulation program Solvarmecentral, which was developed
Fig. 12. Yearly net utilised solar energy for combisystems as a function of the collector area and the house in which the system is installed.
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Fig. 13. Yearly performance ratios for combi systems with antireflection glass as a function of the yearly solar fraction for combi systems with normal glass.
by Jensen et al. (2001). The collectors are facing south and the collector tilt angle is 458. Fig. 14 shows the calculated yearly energy output from the two collectors and the ratio between the yearly energy output of the collector with the glass with the antireflection surfaces and the energy output of the collector with the normal glass as a function of the mean temperature of the solar collector fluid. For increas-
ing collector fluid temperature the energy output from the collector decreases. The extra percentage of energy output by using the collector with the glass with the antireflection surfaces instead of the collector with the normal glass increases with increasing temperature. Consequently, the higher the collector working temperature, the more benefit will be achieved by using glass with the antireflection surfaces. With a mean working temperature of 60 and 100 8C, respectively, the energy output by using glass with the antireflection surfaces is increased by 12 and 20%, respectively.
5. Conclusion
Fig. 14. The yearly thermal performance of solar heating plant solar collectors and yearly extra thermal performance of the solar collectors due to the antireflection surfaces as a function of the mean solar collector fluid temperature in the solar heating plant.
For incidence angles between 08 and 708 the solar transmittance of glass is increased by 5–9%-points and the efficiency of a flat plate solar collector is increased by 4–6%-points by using antireflection glass. Calculations showed that the yearly thermal performance of SDHW systems with yearly solar fractions of 25% and 60%, respectively, is increased by 10% and 4%, respectively, if a collector with a glass with antireflection surfaces is used instead of a collector with a normal glass. Calculations showed that the yearly thermal performance of solar combi systems in a low energy house with yearly solar fractions of 12% and 25%, respectively, is increased by about 10% and 6%, respectively, if a collector with a glass with antireflection surfaces is used instead of a collector with a normal glass.
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The percentage increase of the net utilised solar energy by using glass with antireflection surfaces is increasing for decreasing solar fractions. The main reason is that a high solar fraction indicates that the system is oversized, that is: in sunny summer periods the solar fraction is already high when a low efficient collector is used. Consequently, only a limited thermal advantage is gained by using a high efficient collector. Finally, calculations showed that the yearly energy produced of a solar collector in a solar heating plant can be increased by about 12% and 20%, respectively, by using a glass cover with antireflection surfaces instead of a normal glass as cover plate if the mean solar collector fluid is 608C and 100 8C, respectively. The extra costs for collectors using glass with the antireflection surfaces instead of normal glass is about 50 DKK or 6 USD per m 2 collector. With such a relatively small increase of the system costs it can be concluded that solar collectors with antireflection surfaces are attractive for all solar heating systems.
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Furbo, S., Berg, P., 1990. Calculation of the thermal performance of small hot water solar heating systems using low flow operation. In: North Sun 90, Reading, UK. Helgesson, A., Karlsson, B., Nostell, P., 2000. Angular dependent optical properties from outdoor measurements of solar glazings. In: EuroSun 2000 Proceedings. ¨ ¨ ˚ Hellstrom, B., Adsten, M., Nostell, P., Wackelgard, E., Karlsson, B., 2000. The impact of optical and thermal properties on the performance of flat plate solar collectors. In: EuroSun 2000 Proceedings. Jensen, K.L., Nielsen, T., Andersen, K.R., 2001. Solfangerydelser i solvarmecentraler ved forskellige temperaturniveauer. Technical University of Denmark, Department of Civil Engineering. Jordan, U., 2000. Statistically generated DHW-load profiles on a one-minute time scale. IEA SHACP Task 26. Jordan, U., Vajen, K., 2000. Influence of the DHW-load profile on the fractional energy savings: A case study of a solar combisystem with Trnsys simulations. In: Proceedings of EuroSun 2000 Congress, Copenhagen, Denmark. Klein, S.A. et al., 1996. TRNSYS 14.1, User Manual. University of Wisconsin Solar Energy Laboratory. Nostell, P., Roos, A., Karlsson, B., 1998. Antireflection of glazings for solar energy applications. Sol. Energy Mater. Sol. Cells 54, 223–233. prEN 12975-2: Thermal solar systems and components, Solar collectors, Test Methods. 1999. Shah, L.J., 1999. Investigation and modelling of low flow SDHW solar heating systems. Ph.D. thesis. Department of Buildings and Energy, Technical University of Denmark. Report R-034. Shah, L.J., 2000. Heat transfer corrections for vertical mantle heat exchangers. Solar Energy 69 (Suppl.), 157–171. Shah, L.J., Furbo, S., 1996. Optimisation of mantle tanks for low flow solar heating systems. Proceedings EuroSun ’96, Freiburg, Vol. I, pp. 369–375. Statens Byggeforskningsinstitut (1982), Vejrdata for VVS og ˚ TRY. Statens Byggeforskningsinstitut energi. Dansk referencear (1982)