Fundamental Concepts of
Radiation
- Environmental Radiation Chapter 12
Section 12.8
12.8 Environmental (Solar) Radiation
• The sun’s emissive power approximates that of a blackbody at 5800 K.
• Due to the large sun-to-earth distance, the sun’s rays are nearly parallel at the
outer edge of the earth’s atmosphere, and the corresponding radiation flux is
q′′S = f x Sc
f → correction factor accounting for
eccentricity of the earth's orbit
( 0.97 < f < 1.03)
Sc → the solar constant or heat flux
(1353 W/m ) when the earth is
2
at its mean distance from the sun.
The sun (太陽):
– is a nearly spherical body.
– diameter of D ≈ 1.39 x 109 (m),
– mass of m ≈ 2 x 1030 (kg),
– mean distance of L = 1.496 x 1011 (m) from the earth,
– emits radiation energy continuously at a rate of
Esun ≈ 3.8 x 1026 (W),
– about 1.7 x 1017 (W) of this energy strikes the earth,
– the temperature of the outer region of the sun is about 5800 K.
• The value of the total solar irradiance (Sc) can be used to estimate
the effective surface temperature of the sun from the requirement
that
(
)
4π L2 Sc =
(
)
4
4π r 2 σ Tsun
此公式可決定太陽光熱輻射之
有效溫度 (~ 5800 K)
Sc
Assume blackbody!
• Extraterrestrial irradiation of a surface whose normal is at a zenith angle θ
relative to the sun’s rays is
GS ,o = (f x Sc ) x cosθ
• Interaction of solar radiation with earth’s atmosphere:
¾ Absorption by aerosols over the entire spectrum.
¾ Absorption by gases (CO2, H2O (v), O3) in discrete wavelength bands.
¾ Scattering by gas molecules and aerosols.
• Effect of Atmosphere on Spectral Distribution
of Solar Radiation:
¾ Attenuation over the entire spectrum but more pronounced in spectral
bands associated with polar molecules.
¾ Note concentration of all radiation in the spectral region 0.3 < λ < 3µ m and
peak at λ ≈ 0.5µ m.
¾ Why is the assumption of graybody behavior often inappropriate for
surfaces experiencing solar irradiation?
• Effect of Atmosphere on Directional Distribution of Solar Radiation:
¾ Rayleigh scattering is approximately uniform in all directions (isotropic
scattering), while Mie scattering is primarily in the direction of the sun’s
rays (forward peaked).
¾ Directional distribution of radiation at the earth’s surface has two components.
– Direct radiation: Unscattered and in
the direction θ of the sun’s rays.
– Diffuse radiation: Scattered radiation
strongly peaked in the forward direction.
¾ Calculation of solar irradiation for a horizontal surface often presumes
the scattered component to be isotropic.
′′ cosθ + π I dif
GS = GS ,dir + GS ,dif = qdir
0.1 < ( GS ,dif / GS ) < 1.0
Clear skies
Completely overcast
Terrestrial (地球) Radiation
• Emission by Earth’s Surface:
E = εσ T 4
¾ Emissivities are typically large. For example, from Table A.11:
Sand/Soil:
Water/Ice:
Vegetation:
Snow:
Concrete/Asphalt:
ε
ε
ε
ε
ε
> 0.90
> 0.95
> 0.92
> 0.82
> 0.85
¾ Emission is typically from surfaces with temperatures in the range of
250 < T < 320 K and hence concentrated in the spectral region
4 < λ < 40 µ m, with peak emission at λ ≈ 10 µ m.
• Atmospheric Emission:
¾ Largely due to emission from CO2 and H2O (v) and concentrated
in the spectral regions 5 < λ < 8 µ m and λ > 13µ m.
¾ Although far from exhibiting the spectral characteristics of blackbody emission,
earth irradiation due to atmospheric emission is often approximated by a
blackbody emissive power of the form
4
G atm = σ Tsky
Tsky → the effective sky temperature
230 K < Tsky < 285 K
Cold, clear sky
Warm, overcast sky
• Can water in the natural environment freeze if the ambient air temperature
exceeds 273 K? If so, what environmental conditions (wind and
sky) favor ice formation?
Cold, clear sky and no wind!
Surface Radiative Properties
• Concentration of solar ( 0.3 < λ < 3µ m ) and terrestrial ( 4 < λ < 40µ m ) in
different spectral regions often precludes use of the gray surface approximation
(ε ≠ α S ) .
¾ Note significant differences in ρλ and α λ for the two spectral regions:
snow, human skin, white paint.
¾ In terms of net radiation transfer to a surface with solar irradiation, the
parameter α S / ε has special significance. Why?
Surface
α S /ε
Snow
0.29
Human skin
0.64
White paint
0.22
Black paint
1.0
Evaporated Al film
3.0
Rejection
Collection
Problem: Heat Load on Food Delivery Truck
Problem 12.119: Determination of preferred roof coating (Parsons Black,
Acrylic White, or Zinc Oxide White) and corresponding
heat load for prescribed operating conditions.
KNOWN: Dimensions and construction of truck roof. Roof interior surface temperature. Truck
speed, ambient air temperature, and solar irradiation.
FIND: (a) Preferred roof coating, (b) Roof surface temperature, (c) Heat load through roof,
(d) Effect of velocity on surface temperature and heat load.
Problem: Heat Load on Food Delivery Truck (cont)
SCHEMATIC:
ASSUMPTIONS: (1) Turbulent boundary layer development over entire roof, (2) Constant
properties, (3) Negligible atmospheric (sky) irradiation, (4) Negligible contact resistance.
PROPERTIES: Table A.4, Air (Ts,o ≈ 300 K, 1 atm): ν = 15 × 10−6 m 2 s , k = 0.026 W m⋅ K ,
Pr = 0.71.
ANALYSIS: (a) To minimize heat transfer through the roof, minimize solar absorption relative
to surface emission. Hence, from Table A.12, use zinc oxide white for which αS = 0.16
and ε = 0.93.
′′
′′
− E − q cond
= 0,
(b) Performing an energy balance on the outer surface of the roof, αS GS + q conv
it follows that
4
αS GS + h(T∞ − Ts,o ) = εσ Ts,o
+ (k t)(Ts,o − Ts,i )
Problem: Heat Load on Food Delivery Truck (cont)
where it is assumed that convection is from the air to the roof. With
Re L =
VL
ν
=
30 m s(5 m)
15 × 10
−6
m
2
= 107
s
Nu L = 0.037 Re4L / 5 Pr1/ 3 = 0.037(107 ) 4 / 5 (0.71)1/ 3 = 13,141
h = Nu L (k L) = 13,141(0.026 W m⋅ K/5 m) = 68.3 W m 2⋅ K .
Substituting numerical values in the energy balance and solving by trial-and-error, we obtain
Ts,o = 295.2 K.
(c) The heat load through the roof is
q = (kA s t)(Ts,o − Ts,i ) = (0.05 W m ⋅ K × 10 m 2 0.025 m)35.2 K = 704 W .
(d) From parametric calculations based on the foregoing model, the following results are
obtained.
300
700
295
650
Heat load, q(W)
Temperature, Tso(K)
Problem: Heat Load on Food Delivery Truck (cont)
290
600
550
285
500
280
5
10
15
20
25
30
5
10
Velocity, V(m/s)
15
20
25
30
Velocity, V(m/s)
The surface temperature and heat load decrease with decreasing V due to a reduction in the
convection heat transfer coefficient and hence convection heat transfer from the air.
COMMENTS: The heat load would increase with increasing αS/ε.