Page 521 - Bird R.B. Transport phenomena

§16.4 Direct Radiation Between Black Bodies in Vacuo at Different Temperatures 501

Sun Earth Fig. 16.4-5. Estimation of the solar
,, constant.
dA 2

reader wishing further information on radiative heat exchange in enclosures in referred
to the literature. 4

EXAMPLE 16.4-1 The radiant heat flux entering the earth's atmosphere from the sun has been termed the "solar
constant" and is important in solar energy utilization as well as in meteorology. Designate the
Estimation of the sun as body 1 and the earth as body 2, and use the following data to calculate the solar con-
Solar Constant stant: D^ = 8.60 X 10 miles; r = 9.29 X 10 miles; q$ = 2.0 X 10 Btu/hr • ft 2 (from Example
5
7
7
12
16.3-1).
SOLUTION In the terminology of Eq. 16.4-5 and Fig. 16.4-5,
solar constant = = ^?f cos
cos

4 ) 4

7
2.0 X 10 ^8.60 x
4 \9.29 X 10 7
430 Btu/hr • ft 2 (16.4-16)
This is in satisfactory agreement with other estimates that have been made. The treatment of
r 2 2 as a constant in the integrand is permissible here because the distance r varies by less
12
than 0.5% over the visible surface of the sun. The remaining integral, / cos в^А , is the pro-
}
2
jected area of the sun as seen from the earth, or very nearly TTD /4.
EXAMPLE 16.4-2 Two black disks of diameter 2 ft are placed directly opposite one another at a distance of 4 ft.
Disk 1 is maintained at 2000°R, and disk 2 at 1000°R. Calculate the heat flow between the two
Radiant Heat Transfer disks (a) when no other surfaces are present, and (b) when the two disks are connected by an
Between Disks adiabatic right-cylindrical black surface.

SOLUTION (a) From Eq. 16.4-9 and curve 1 of Fig. 16.4-4,

Q = A,F cKrt - T )
12 12 2
4
8
= TT(0.06)(0.1712 X 10" )[(2000) 4 - (1000) ]
= 4.83 X 10 Btu/hr (16.4-17)
3
(b) From Eq. 16.4-15 and curve 5 of Fig. 16.4-4,
Qn = Af.MT* - T\)
4
8
= 7K0.34X0.1712 X 10" )[(2000) 4 - (1000) ]
3
= 27.4 X 10 Btu/hr (16.4-18)