Renewable Energy 26 (2002) 587–598www.elsevier.com/locate/renene

Optimizing the tilt angle of solar collectors

Adnan Shariah, M-Ali Al-Akhras, I.A. Al-OmariDepartment of Applied Physics, Jordan University of Science and Technology, PO Box 3030, Irbid,

Jordan

Received 1 April 1997; accepted 19 April 2001

Abstract

Solar collectors need to be tilted at the correct angle to maximize the performance of thesystem. In this paper, the annual solar fraction of the system (the fraction of energy that issupplied by solar energy) is used as an indicator to find the optimum inclination angles for athermosyphon solar water heater installed in northern and southern parts of Jordan. Calcu-lations are carried out using the powerful computer program TRNSYS (Transient SystemSimulation). The system is assumed to operate with a daily hot water load of 150 l at 55°Cflowing during the day according to the widely used Rand consumption profile. The resultsshow that the optimum inclination angle for the maximum solar fraction is aboutf+(0→10°)for the northern region (represented by Amman) and aboutf+(0→20°) for the southern region(represented by the town of Aqaba). These values are greater than those for maximum solarradiation (which is commonly used as an indicator) at the top of the collector by about 5 to8°. 2002 Published by Elsevier Science Ltd.

1. Introduction

Solar systems, like any other system, need to be operated with the maximumpossible performance. This can be achieved by proper design, construction, instal-lation, and orientation. The orientation of the collector is described by its azimuthand tilt angles. Generally, systems installed in the northern hemisphere are orienteddue south and tilted at a certain angle. Many investigations have been carried outto determine, or at least estimate, the best tilt angle for such systems. Some of theseare, for example,f+20° [1], f+(10→30°) [2], f+10° [3] and f�10° [4], whereassome researchers suggest two values for the tilt angle, one for summer and the otherfor winter, such asf±20° [5], f±8° [6] and f±5° [7], wheref is the latitude, “+”for winter, and “�” for summer. In the past few years, computer programs havebeen used and the results have shown that the optimum tilt angle is almost equal tothe latitude [8–11]. The common approach used by researchers has been to calculate

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Nomenclature

Ac Collector area (m2)Dh Diameter of collector’s headers (m)Di, Do Diameter of collector’s inlet and outlet connecting pipes (m)Dr Diameter of collector’s risers (m)FRUL Slope of the collector efficiency curve [kJ/(h m2 °C)]FR(ta)n Intercept of the collector’s efficiency curvesGtest Collector’s test flow rate [kg/(h m2)]Haux Height of the auxiliary heating element above the bottom of the

tank (m)Hc Vertical distance between the outlet and inlet of the collector (m)Ho Vertical distance between outlet of the tank and inlet of the

collector (m)Hr Height of the collector’s return above the bottom of the tank (m)Ht Height of the tank (m)Hth Height of the auxiliary thermostat above the bottom of the tank (m)Lc Length of the collector (m)Lh Length of the collector’s headers (m)Li, Lo Length of inlet and outlet connecting piping (m)NB1, NB2 Number of bends in inlet and outlet connecting pipesNr Number of parallel collector risersPaux Power of the auxiliary heater (kJ/h)Qaux Energy input to tank from the auxiliary heater (J)Tmain Temperature of water from the mains (°C)Tset Temperature of water delivered to load (°C)Ui, Uo Heat loss coefficients for inlet and outlet connecting pipes [kJ/(h m2

°C)](UA)t Overall heat loss coefficient for storage tank [kJ/(h m2 °C)]Vl Volume of daily load (m3)Vt Volume of storage tank (m3)Wc Width of the collector (m)b Tilt angle of the collector (deg)h Annual efficiencyf Annual solar fractionf Latitude (deg)rg Ground reflectance

the tilt angle which maximizes the amount of solar radiation received by the collector.In the literature of solar heaters, there are very limited works that have studied theproblem using other approaches. For example, Prasad and Chandra [12] optimizedthe tilt angle of the collector to get maximum flow rate rather than maximum collec-

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tion. Saraf and Hamad [13] found the optimum tilt angle by searching for the valuefor which the useful energy gained by the collector was at its maximum for a parti-cular day or a specified period of time for a typical collector in Basra, Iraq. Theyfound that the optimum tilt angle was higher than the latitude by about 8°. Iqbal[14] investigated the optimum collector tilt for a liquid active solar heating systememploying flat-plate collectors. He has studied the collector tilt as a function ofcollector area, annual heating load, and the ratio of space heating load to service hotwater load for the values of 5 and 15. He found that the optimum collector tilt variedfrom f�10° to f+15°, depending on the solar fraction.

Generally, domestic solar water heaters are installed to supply 70–80% of therequired energy and may reach a value of 90–95% in warm and hot climates. Ourhypothesis is that the optimum tilt angle for a solar water heater is one which maxim-izes the annual solar fraction of the system. This angle is not necessarily equal tothe one which maximizes the solar radiation at the top of the collector. Usually solarwater heaters installed in warm climates, like that in Jordan, are operated with asolar fraction of unity during summer. In fact, the useful energy from the collectorcan be higher than that required for the load. Therefore, there is no advantage intilting the collector at an angle that increases the solar intensity at the top of thecollector during this period. It is feasible to increase the solar fraction of the systemby increasing the useful energy in winter and decreasing the energy collected duringsummer, taking into account that this should not be lower than the load energy. Thiscan be done by searching for a tilt angle that maximizes the annual solar fractionof the system throughout the year.

For this purpose, the powerful computer program TRNSYS (Transient SystemSimulation) [15] was used to calculate the annual optimum tilt angle for a thermosy-phon solar water heater installed in both northern and southern Jordan, representedby two places (Amman and the town of Aqaba respectively).

2. System description and mathematical model

The schematic diagram of the system studied in the present work is shown in Fig.1. It consists of a flat-plate collector, with a length of 1.8 m, connected to a verticalstorage tank, with a height of 1 m, leveled up with the top of the collector. A checkvalve is added to the pipes connecting the collector and the storage tank to preventreverse circulation at times of low or no solar radiation. An auxiliary heater and athermostat are placed in the storage tank, 10 cm below the surface of water, to meetthe required load energy when the useful energy gained by the collector is not suf-ficient to meet the load. A daily load of 150 l at a temperature of 55°C was deliveredto the user and distributed over a 24-hour period according to the well-known Randhot-water distribution profile (Fig. 2) [16]. To ensure that hot water is delivered atthe desired temperature, a flow mixer is mounted between the system and the faucetto mix the water coming from the storage tank, when its temperature is higher thanthe load temperature, with water from the mains. The area of the collector was variedbetween 2 and 5 m2 in order to organize various solar fractions. During this variation,

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Fig. 1. Schematic diagram of the considered system.

Fig. 2. Rand hot water consumption profile.

the ratio of the storage tank volume to the collector area was kept at 50 l/m2 asrecommended by [17]. The values of the parameters FRUL and FR(ta)n, whichcharacterize the optical and thermal properties of the collector, were 21.6 kJ/(h m2

°C) and 0.6 respectively. These values are the average for most solar collectorsmanufactured in Jordan as indicated by [18]. A full description of the system under

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consideration is shown in Table 1. The values appearing in the table are taken fromthe results of [14–16]. The storage tank is modeled as a fully stratified tank with avariable number of nodes or segments. A detailed description of the model of thestorage tank is given in [19,20].

The required hourly solar radiation and dry bulb temperature for the simulationprogram TRNSYS were calculated from the monthly average daily values suppliedby the Jordanian Meteorological Department [21] using a component supplied withTRNSYS. The method of calculation used by this component was based on theresults of [22–24] and the method used to calculate solar radiation on the tiltedsurfaces is given in detail in [25].

The performance of the system is characterized by the annual solar fraction (thefraction of load supplied by the solar energy) and the annual efficiency of the collec-tor, which are defined as

f�Q1−Qaux

Q1

(1)

h�Qu

Ac−�IT

(2)

where Qu, Ql, Qaux, and �AcIT, respectively, are useful energy, energy delivered to

the load, energy supplied by the auxiliary heater, and the sum of the hourly radiationon the surface of the collector over a specified period of time.

3. Results and discussion

The variation of the annual solar fraction of the thermosyphon solar water heaterwith the inclination angle of the collector is shown in Figs. 3 and 4 for various

Table 1System design parameters

Ac Varied from 2 to 5 m2 NB1,NB2 5Dh 20 mm Li, Lo 4 m, 3 mDi, Do 15 mm Nr varied from 5 to 19Dr 5 mm Paux 100 MJ/hFRUL 21.6 kJ/(h m2 °C) Tmain 22°CFR(ta)n 0.6 Tset 55°CGtest 72 kg/(h m2) Ui, Uo 10 kJ/(h m2 °C)Haux 0.9 cm (UA)t 5.4 kJ/(h m2 °C)Hc 0.95 m Vl 150 l/dayHo 0.95 m Vt varied from 100 to 250 lHr 0.9 m Wc varied from 1.12 to 2.78 mHt 1.0 m b variable (deg)Hth 0.9 m f variable (deg)Lh 5 m rg 0.2

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Fig. 3. Variation of the yearly solar fraction with the inclination angle for different collector areas forAmman region.

Fig. 4. Variation of the yearly solar fraction with the inclination angle for different collector areas forAqaba region.

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collector areas and for Amman and Aqaba regions respectively. When the area ofthe collector is small (Ac=2 m2), the system operates with a relatively low solarfraction: below 70% for Amman and around 80% for Aqaba. The optimum tilt anglefor the system is about f�3° (where f is the latitude) for Amman and about f forAqaba. If the area of the collector is 3 m2, the solar fraction will increase accordinglyand reach a value of 82% for Amman and 92% for Aqaba. The maximum valuesare observed at a tilt angle range of about f+(0→5°) for both Amman and Aqaba.If the area of the collector is increased by 1 m2 (or Ac=4 m2), the solar fraction willincrease to reach a value of 87% and 96% for Amman and Aqaba respectively. Thesemaximum values correspond to a tilt angle range of about f+(0→10°) for Ammanand about f+(0→20°) for Aqaba. The results for Ac=5 m2 are found to be the sameas for Ac=4 m2. On the other hand, the solar radiation at the top of the collector isshown in Fig. 5 for various collector areas and for both places. It is clear that themaximum solar radiation received by the collector occurs at tilt angles of about f�8°for Amman and f�5° for Aqaba. The above-mentioned optimum values for boththe maximum solar fraction and the maximum solar radiation at the top of the collec-tor are shown in Table 2. Comparing the results in this table, one can see that forAc=2 m2 the optimum tilt angle for maximum solar fraction is greater than the anglethat maximizes solar radiation by about 5° for both regions. If the area of the collectoris 3 m2, the optimum angle for the maximum solar fraction will have a range ofvalues (5° for Amman and 10° for Aqaba) rather than a single value, and is largerthan the angle that maximizes the solar radiation by about 8° for Amman and about5° for Aqaba. For large collector areas (Ac=4 or 5 m2) the optimum angle formaximum solar fraction is greater than those for maximum solar radiation by about

Fig. 5. Variation of the yearly solar radiation at the top of the collector with the inclination angle forboth regions.

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Table 2Comparison between optimum inclination angles for different collector areas

Region Ac (m2) fopt for maximum solar fopt for maximum solarradiation fraction

Amman 2 f�8° f�3°3 f�8° f+(0→5°)4 f�8° f+(0→10°)5 f�8° f+(0→10°)

Aqaba 2 f�5° f3 f�5° f+(0→10°)4 f�5° f+(0→20°)5 f�5° f+(0→20°)

the same amount as for Ac=3 m2. However, the range of values for the optimum tiltangles for maximum solar fraction is about 10° for Amman and about 20° for Aqaba.It is clear that for all Ac values, the optimum tilt angles for the maximum solarfraction are higher than those for maximum solar radiation by about 8° for Ammanand by about 5° for Aqaba. The optimum angle for the maximum solar fraction,being higher than that for the maximum solar radiation, can be explained with thehelp of Figs. 6–9 where the monthly average daily useful energy from the collector

Fig. 6. Monthly average daily useful energy and daily load energy for different inclination angles andfor Ac=2 m2.

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Fig. 7. Monthly average daily useful energy and daily load energy for different inclination angles andfor Ac=3 m2.

is given as a function of the months of the year for various collector areas andinclination angles. Only data for Amman are shown in these figures to avoid rep-etition. The thick solid line in these figures represents the required energy for theload, whereas the other curves represent tilt angles ranging from f�10° to f+10°as indicated in the figures. It is clear that the maximum useful energy values obtainedfrom the collector during summer correspond to a small tilt angle, f�10°, and theamount of collected energy decreases as the tilt angle reaches a value of f+10° withan increment of 5°. In winter when the maximum useful energy occurs at large tiltangles, the situation is reversed. The reason for this trend is that for small tilt anglesthe solar radiation has minimum incident angles at noon during the summer period,when the solar intensity is maximum. In winter this occurs for tilt angles greaterthan the latitude. Therefore, tilting the collector at angles smaller than the inclinationangle will maximize the collected energy in summer and minimize it in winter. Fromthe viewpoint of this discussion, and keeping in mind that the portion of energy thatis greater than the load energy is useless, (this occurs in the North Pole in summer),one can find the optimum inclination angle for the solar collectors by searching forthe value that maximizes the solar fraction of the system, which, in this case, is themeasure of the usefulness of the energy gained by the collector. For Ac=2 m2 (Fig.6), the useful energy for the tilt angles ranging from f�10° to f+5° is higher thanthe load energy throughout summer. This suggests that tilting the collector at an

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Fig. 8. Monthly average daily useful energy and daily load energy for different inclination angles andfor Ac=4 m2.

angle of f+5° rather than f�10° will result in an increase in the collected energyin winter but will keep the system operating with a solar fraction of unity in summer.This is true for mid-summer and winter. However, the loss in spring (March to June)is not negligible. Therefore, the optimum tilt angle is between these two values(Table 2 shows that this angle is about f�3°). For Ac=3 m2 (Fig. 7), the usefulenergy is higher than the load energy for about seven months of the year for all tiltangles. During the remainder of the year, however, higher values for the usefulenergy are observed at larger tilt angles. Therefore, tilting the collector at an angleof f+10° rather than f�10° will increase the solar fraction of the system. It is clearthat the preferred tilt angle will decrease the amount of useful energy during summer,but this reduction will affect only the amount of energy that is beyond the need forthe load. This result is more pronounced for collector areas of 4 and 5 m2 (Figs. 8and 9).

4. Conclusion

The present work has studied the optimum tilt angles for a thermosyphon solarwater heater by using the annual solar fraction as an indicator, and has reached thefollowing conclusions:

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Fig. 9. Monthly average daily useful energy and daily load energy for different inclination angles andfor Ac=5 m2.

1. The optimum tilt angle for the maximum solar fraction is larger than any of thosefor the maximum solar radiation at the top of the collector by about 5 to 8°.

2. The optimum tilt angle of the collector depends on the operation strategy.3. Systems operating with sufficiently high solar fraction have a range of optimum

angles from f to f+20°.4. The useful energy collected by the system is noticeably higher than the load

energy during summer especially for a collector with an area of 3 m2 or larger.

The author recommends that further work should be conducted to analyze the effectof the latitude and different climates on the optimum tilt angle.

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