Evaluation of the Best Slope Angle for a Flat-Plate Solar Collector

The performance of flat plate solar collector is affected by the value of its slope angle with respect to horizontal plane, where the variation of slope angle changes the amount of incident solar radiation. So, using the solar tracking system for solar collector will get the maximum solar radiation, the application of the solar tracking system cost has high operation and maintenance. It is usually suitable to set the solar collector at a best fixed slope angle throughout the year with less reduction in solar radiation received on the collector surface. In this work, a best slope angles were calculated for solar collectors based on the monthly mean daily solar radiations on a horizontal surface over some Iraqi cities (Mosul, Rutba, and Basra). The total of rays flux incident upon a solar collector is mainly affected by the installation angle. The solar collector can be oriented at three different angle settings. The first angle setting is to adjust the collector monthly off to give highest incident solar radiation, while the second angle setting suggests the seasonally changes (Winter, Spring, Summer, Autumn) .The final adjustment for solar collector can be achieved using the mean value for the four seasons to get yearly averaged throughout the year.

kirkukjoursci@gmail.com which is considered the main variable affecting the collecting radiation of a set collector. In general, the best slope angle of a set collector is connected to the local climatic state, geographic latitude and the time of its use. Therefore, different places will have different best slope angles for a yearly-applied solar collector.
The maximum solar radiation is obtained by facing the southern hemisphere to the north with slope equal to its latitude and the maximum annual energy availability is obtained by (rules of thumb) in which the surface slope equal to latitude is the optimal [1]. The solar energy devices have to skewed to face south with a slope angle equals the latitude of the place in order to achieve the optimal performance all year round founded that at Jeddah by [2]. The horizontal radiation data registered in Hong Kong to find the best tilting angle found that a solar collector with the slope angle nearly equal to latitude of the place collects maximum yearly radiation [3]. An optimum tilt angle and insolation of BIPV panel are presented for different state capital of India by considering shadow effect of surrounding buildings [4]. The optimum slope angle for Izmir city in Turkey is calculated by searching for the values for which the total radiation on the collector surface is a maximum for a particular day or a specific period [5]. The best setting angle in Taiwan was calculated according to three different radiation types, the extraterrestrial radiation, global radiation which predicted by empirical model [6]. A relationship between the optimum slope angles and the geographic latitude of the place from 36° to 46° was studied [7]. Monthly, seasonal and annual optimum tilt angles were estimated for Aligarh and New Delhi cities. The annual optimum tilt angle for Aligarh and New Delhi was found as 27.62o and 27.95o respectively (close to the latitude of the respective location [8]. Determination of the optimum collector tilt angles for low latitudes in Nigeria was investigated for monthly, seasonal and yearly average daily values of insolation for tilt angles ranging from 0-40o [9]. A mathematical model was included to evaluate the best slope angle of the collector by differentiate the incidence angle with relative to the slope angle. The results was compared to the work of (Tang, Duffle and Beckman"s) equations, and this model gave good agreement to these equations [10]. are monthly mean daily beam, scatter, and ground reflected rays event on a slanted surface in MJ/m2-day respectively.
The monthly mean daily beam radiation received on an inclined surface can be expressed as follows [18]: Where H is the daily global radiation incident on a horizontal surface in MJ/m2-day, d H is the everyday circulate radiation event on a flat surface in MJ/m2day, and b R is the monthly average ratio of the daily beam rays on a skewed surface to that on a straight surface.
The ratio of the average daily beam radiation on a tilted surface to that on a horizontal surface for surfaces located at the northern hemisphere can be estimated as follows [1]: Where ϕ, β, and δ are the latitude of place, surface tilt, and sun declination angles in degrees respectively.
In the evening hour comer for the skewed flat for the middle day of the month can be rated from the following neutralization such that [1]: The angle s  is the sunrise hour angle for a sloped surface in degrees, and the ""min"" sign means the smaller of the two terms in the outside bracket.
The declination angle can be calculated from the following equation [1]: Where N is the Julian day ranging from 1 (at first of January) to 365 (at thirty one of December). The monthly mean daily ground reflected radiation can be written as follows [18]: Where  is the coefficient ground reflection (albedo), which is given to be equal to 0.2 as mentioned in the literature for no snow locations [17].
The sky common rays on sloped surface can be described as follows [ The angle s  is the sunrise or sunset hour angle in degrees, which is found equal to, [16]: The monthly mean daily clearness ratio T K can be estimated as the ratio of terrestrial global radiation on horizontal surface to the extraterrestrial radiation on the horizontal surface as follows [16]: As shown in these figures, in Winter, the ray and common motif are appearing close to each other due to inclination of earth rotation axis at northern hemisphere away from the sun, which make the sun rays incident on earth surface at very small acute angles. While, in Summer, the ray element is more than scatter part and thus the major help comes from the grin element.
The monthly value mean the total for every day radiation on a south opposite collector next to the slope angle from (0o-90o) for twelve months for the above three cities are shown in Figs.(2a,b), (3a,b) and (4a,b) respectively. The value of total radiation was increased and its reached to peak value at each month depending on a specified collector slope angle, and then it starts to decline for a value of (β) less than the optimum tilt angle.   Moreover, in Winter it needs to set the collector at high tilt angles approximately between (50o-60o) due to the low altitude of sun across the sky, while it needs to adjust at low angles for Summer between (10o-15o), due to the high elevation of sun in these months.
As mentioned above, the value of collector optimum slope angle depends on position of the sun across the sky (solar altitude angle) which depends on climate seasons and on latitude of the cities. So the optimal collector tilt angle becomes very small and approach to (10o) in Summer or especially in (June month), and its becomes very high and approach to (60o) in Winter especially in (January month) due to altitude of sun across these seasons. So the collector can be mounted in three settings, first: by make the collector tracks the sun at each month depending on the specified day number (N) for each month. Secondly: by make the collector tracks the sun seasonally or once at every season by taking the mathematical average for every three months which makes the tracking mechanism more simple and inexpensive.
Thirdly: by making the collector track the sun once in year by taking the mathematical average for the four seasons which makes the collector fixed in place and has one optimal tilt angle during the year as shown in Fig.(7). The geographical coordinates of Mosul, Rutba, and Basra cities are presented in Table (1). In Table (2) show the monthly, seasonally, and the yearly average slope angles for the above stations.

CONCLUSION:
A model for calculating the optimum collector tilt angles for some Iraqi cities has been examined. The representation is described as a relative between the collector installation angle and the values of total radiation that incident on flat-plate collector.

Volume 12, Issue 4, September 2017 ISSN 1992 -0849
Web Site: www.kujss.com Email: kirkukjoursci@yahoo.com, kirkukjoursci@gmail.com Monthly, seasonally and annually changes in best tip angles for the astral collectors in some Iraqi cities were resolute by using the meteorological datasets of the average monthly and daily universal solar rays on flat surface for three cities (Mosul, Rutba, and Basra).
The optimum tilt angle for the solar collector was appeared to be lower in the summer and higher in the winter seasons. Annual based optimum tilt angle is approximately equal to latitude of the location as mentioned in literatures, like [1], [2] and [15]. The results show that for maximum solar radiation, the collector may be installed at high tilt angles during the Winter, may be installed at moderate tilt angles, and may be installed at small slope angles through the Summer to enable the solar antenna face to soak up the maximum amount of solar rays.