Extreme subtle rewording!!!

The literature states that a solar collector facing south has an azimuth angle of 180 degrees, while 0 degrees when facing north. In the northern hemisphere, where we are currently located, between the latitudes of 23 and 90, the sun is always in the south. For this reason, panels are often directed to the south to get the most out of the sun’s energy. 

The azimuth angle of a collector has an important effect in the efficiency of a solar collector. Different values of the Azimuth angle for a panel will play a role in increasing or decreasing its efficiency. There are a series of equations that relate the efficiency of the solar collector to the azimuth angle. This relation will help us understand how the efficiency changes with the azimuth angle. 

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First, the efficiency ƞ of a solar collector is given by Eq 1.
Where Eq 1represents the useful heat gain, Ac the area of the collector and Ic the irradiance measured on the tilted plane of the collector.

The irradiance (Ic) measured on the tilted plane of the collector is calculated by adding the direct beam radiation (IBc) striking a collector’s face, the diffuse radiation(IDc) on the collector and the radiation (IRc) reflected by surfaces in front of the panel as seen in Equation 2 below. 

The direct beam radiation (IBc) is the portion of IC that accounts for the solar azimuth angle of the collector. The translation of direct-beam radiation (IB) into direct beam insolation striking a solar collector (IBc) is a function of the angle of incidence ϴ, which is located between a line drawn normal to the collector face and the incoming solar beam radiation (Figure 7).

Figure 7. The incidence angle θ between a normal to the collector face and the incoming solar beam radiation.

The angle of incidence θ will be a function of the collector orientation and the altitude and azimuth angles of the sun at any time. Similarly, the solar collector is tipped up at an angle Ʃ and faces in a direction described by its azimuth angle φC, as shown in Figure 8 below. 

Figure 8. Illustrating the collector azimuth angle φC and tilt angle Ʃ, along with the solar azimuth angle φS and altitude angle β.
The incidence angle is given by Eq 3.

Equation 3 describes the cosine of the incidence angle (ϴ) where β represents the altitude angle, φc the collector azimuth angle, φs is the solar azimuth angle and Ʃ the tilt angle. 

Similarly, the cosine of the incidence angle is used to calculate the direct-beam radiation striking the collector as shown in Equation 4.
Where IB represents the direct beam radiation. 

As we can see from the relations given, if we manipulate the value of the collector’s azimuth angle the angle of incidence will change and so the value for IBc. Consequently, IC will also change, and so the efficiency will vary. 
Now, if this angle is increased it will go through a cycle of positive and negative values. Since cosine is periodic between 0 and 2п, it cannot increase. Therefore, if we go through the calculations, we will find out that increasing the azimuth angle can increase or decrease the value of Ic. Since Ic is in the denominator of the formula to calculate efficiency, when IC is decreased, the efficiency of the collector will increase and if IC is increased, the efficiency of the collector will decrease.
Using different values in the calculation of the Azimuth angle shows that the optimal azimuth angle is with the collector facing south. 
Also, the array facing east would generate slightly more energy than the one facing west. Finally, if the panel is installed facing north, the energy production could be reduced up to 35%.


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