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Mini Project # 1: Solar Radiation
MECH 473
Group #8
Procedure
Dry Bulb Temperature
To determine the design day dry bulb temperatures, the formula is used:
DBoa,h=DBoa,design-zhDRThe input outdoor air design dry bulb temperature (DBoa, design) is found in the ASHRAE design conditions table in the Mean Coincident Dry Bulb Temperature section for 1% in July. The values for zh are found in table 4 of Handout 2 in the generating design day data section. The daily range (DR) is found in the ASHRAE design condition sheet in the Monthly Mean Daily Temperature Range section for July. The output of this formula is the hourly outdoor air dry bulb temperature (DBoa.h).
Solar Angles
To determine the solar altitude (β), the following formula is used: sinβ=cosLcosδcosH+sinLsinδ. The latitude (L) is given in the mini project handout. The solar declination angle (δ) is determined based on the time of year (n):
δ=23.45sin⁡{360284+n365},
which is given in the project handout on July 21st. The hour angle (H) varies hourly based on the local solar time (LST):
H=15(LST-12).
Once the solar altitude is known the solar azimuth angle (ϕ) can be determined from:
cosφ=sinβsinL-sinδcosβcosLIt must be noted here that when determining ϕ, the arccosine of cosϕ is taken. The result of this will give ±ϕ. The angle is measured from South and is given as 90° at West, and -90° at East. Since the sun rises in the East, ϕ will be negative in the morning, zero at noon and positive in the afternoon.

The surface-solar azimuth (γ) is found from the formula:
γ=φ-ψThe azimuth angle (ψ) is the angle from south normal to the calculated surface in the horizontal plane. For the west side of the building, ψ = 90° and for the East side of the building, ψ = -90°.
Finally, the solar incident angle (θ) is found from either of the following two formulas:
cosθ=sinβ (surface tilt angle (Σ) = 0°)
cosθ=cosβcosγ (Σ = 90°)
The first equation is used to determine the solar incident angle when considering the roof, and the latter equation is used to determine the solar incident angle when considering the building walls.
Solar Radiation
The total solar radiation (Gt) is given by:
Gt=GD+Gd+Gr.
The direct incident solar radiation (GD) is determined by:
GD=CNGNDcosθ.
The sky clearness number (CN) is given as 1.0 for our design day. The normal direct irradiation GND is given by:
GND=Ae(Bsinβ).
Next, the diffuse incident solar radiation is given by:
Gd=CGND(1+cosΣ2)The coefficients A, B, and C for GND and Gd are given in table 7 in Handout 3 for July 21st. Furthermore, the reflected solar irradiation (GR) is given by:
GR=Gthρg(1-cosΣ2)The total (direct and diffuse) solar radiation (Gth) is given by:
Gth=GND(sinβ+C)The solar reflectance of the ground or horizontal surface (ρg) is given in the mini project handout, one value for the ground and another value assigned to the roof. Finally, the equations and values to determine the Sol-air temperature are given in the mini project 1 handout.
Observation
The direct solar radiation starts to increase from zero when the solar altitude becomes positive. Once the direct solar radiation reaches the maximum at 7:00 am (East), 5:00 pm (West), 12:00 pm (South), 12:00 pm (south), and 6:00 am and 6:00 pm (North), it decreases to zero until the solar altitude becomes zero. Two local maximum points can be observed in the North wall graph because the direct solar rays are blocked by the South wall from 8:00 am to 4:00 pm due to the large incident angle. Since the axis of the earth is tilted by solar declination angle and Winnipeg is located at the latitude of 49.4-degrees North, the sun rises in the North East, moves to South, and sets in the North West. The direct solar radiation depends on the solar incident angle and direct normal irradiance. The building walls receive the maximum radiation when the sun rays are more nearly perpendicular to the wall surface, and the direct normal irradiance is large. The direct solar radiation can be thought of as the solar rays strike the building surface at an angle of incident, so there would be no direct solar radiation when the solar incident angle is over 90 degrees, and the solar altitude is less than zero.
The diffuse and reflected solar radiations also draw the downward parabolas in the graphs. The maximum of diffuse solar radiation occurs from 11:00 am to 1:00 pm and the maximum of reflected solar radiation occurs at 12:00 pm for all sides. The diffuse and reflected solar radiations have the same values for all sides because they only vary based on the normal direct irradiance and they are not influenced by the incident angles. The values of diffuse and reflected radiation, including the maximum point, are much lower compared to the direct solar radiation because the diffuse and reflected radiations come indirectly from many directions at different angles, unlike the direct solar radiation. As long as the solar altitude remains positive, the diffuse and reflected radiations are not zero.
The sol-air temperatures follow the trend of the direct solar radiations. If the direct solar radiation becomes zeros, it only follows the trend of Dry Bulb temperatures. It shows that direct solar radiation is a dominant variable. The roof has the maximum sol-air temperature at noon because it has larger maximum direct radiation compared to other walls. When the color of the walls and roof are changed from light to dark, the sol-air temperatures are significantly decreased. Roof and walls colors play a vital role in determining the value of sol-air temperature. The right selection of the color of the walls and roof is essential in minimizing the thermal impact on walls and roof.
Conclusion
The walls and roof receive the maximum direct radiation when the sun’s rays are more nearly perpendicular to the surfaces, and the value of direct normal irradiance is nearly the maximum. The minimum direct solar radiation occurs when the solar incident angle is over 90 degrees, or the solar altitude is less than zero. The diffuse and reflected solar radiations have the same values for all sides because they only depend on normal direct irradiances which are the same. The values of diffuse and reflected radiation including the maximum point are much lower compared to the direct solar radiation because they come indirectly from many directions at different angles, unlike direct solar radiation. As long as the solar altitude remains positive, the diffuse and reflected radiations are not zero. When the direct solar radiation becomes zeros, it only follows the trend of Dry Bulb temperatures. When the color of walls and roof are changed from light to dark, the sol-air temperatures are significantly decreased. The light color of walls and roof is essential to minimize the thermal impact on walls and roof.

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