Solar radiation with a clear sky
Solar radiation with a clear sky consists of three parts:
• Direct radiation, Gd
• Diffuse radiation, Gd
• Reflected radiation, Gr
Total solar radiation on a horizontal surface, GtH GtH = Gdh + GdH, Gr=0 Total radiation on a tilted surface Gte = G ne + Gde + Gr All the three parts are the functions of normal direct radiation, Gnd
G A
110 exp(B / sin Я)
Where A = apparent solar radiation (TTable 6-1, ATable 8)
B = atmospheric extinction coefficient (T Table 6-1, A Table 8)
Я = solar altitude
Direct solar radiation on a surface of arbitrary orientation
Gd6 = Gnd Cn cos 0
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Where |
Cn = clearness number (T Figure 6-7)
0 = incident angle
On a horizontal surface, cos 0 = sin (3
Gdh = Gnd Cn sin (3
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W-Winter Figure 6-7 Estimated atmospheric clearness numbers CN in the United States for nonindustrial localities, percent. (Reprinted by permission from ASHRAE Handbook, Fundamentals Volume, 1989) |
Diffuse radiation On a horizontal surface:
GdH = CGND/CN2
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Where |
C = ratio of diffuse on a horizontal surface to direct nonnal radiation (T Table 6-1, A Table 8)
On a tilted surface
Gde = (C Gnd / Cn2) Fws
Fws = view factor between the surface and the sky Fws= (1 + cos Z)/2
For a horizontal surface Fws = 1 and for a vertical surface Fws = 0.5.
• Reflected Radiation
Gr = (Gdh + GdH) pg Fwg
Where pg = reflectance of ground
Fwg — view factor between the surface and the ground
FWg = (1 — cos Z)/2
For a horizontal surface Fwg = 0 and for a vertical surface Fwg = 0.5.
Continue from Example 7-3. If the ground reflectivity is 0.3, find the total solar radiation on the vertical window surface.
Solution
From T Table 6-1 or A Table 8, A = 1187 W/m2, B = 0.142, and C = 0.104.
From T Figure 6-7, Cn = 1.0
G A
ND exp (B / sin Я)
________ H87_______
~~ exp(0.142/sin37.85°)
= 942 W/m2
Gdg = Gnd Cn cos 0
= 0 No direct solar radiation
GdH = C Gnd / Cn2 = 0.104×942/ 1.02 =98 W/m2
Gde = GdH F = Gd (1 + cos X)/2 = 98 (1 + cos 90°)/2 = 49 W/m2
Gr = (Gdh + GdH) pg Fwg = (Gnd Cn sin Я + Gd) pg (1 — cos X)/2 = (942 x 1.0 x sin 37.85 ° + 49) x 0.3 x (1 — cos 90°)/2 = 94 W/m2
Gte — Gdg + Gde + Gr
= 0 + 49 + 94 = 143 W/m2
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