Radiation: Processes and Properties- Environmental Radiation -

Chapter 12

Section 12.8

Solar Radiation

Solar Radiation

• The sun is a nearly spherical source of radiation whose outer diameter is 1.39 x 109 m and whose emissive power approximates that of a blackbody at 5800K.

• The distance from the center of the sun to the center of the earth varies with time of year from a minimum of 1.471 x 1011 m to a maximum of 1.521 x 1011 m, with an annual average of 1.496 x 1011 m.

• 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

xS cq f S

2 the or heat flux 1353 W/mwhen the earth is at its mean distan

solar constace from the .

nun

ts

cS

correction factor accounting for eccentricityof the earth's orbit 0.97 < <1.03

ff

Solar Radiation (cont).

• Extraterrestrial irradiation of a surface whose normal is at a zenith angle relative to the sun’s rays is

, x x cosS o cG f S

• Interaction of solar radiation with earth’s atmosphere:

Absorption by aerosols over the entire spectrum.

Absorption by gases (CO2, H2O ( ), O3) in discrete wavelength bands.v

Scattering by gas molecules and aerosols.

Solar Radiation (cont).

• Effect of Atmosphere on Spectral Distribution of Solar Radiation:

Attenuation over the entire spectrum but more pronounced in spectral bands associated with polar molecules.

Note concentration of all radiation in the spectral region and peak at

0 3 3 m .0 5 m. .

Why is the assumption of graybody behavior often inappropriate for surfaces experiencing solar irradiation?

Solar Radiation (cont).

• Effect of Atmosphere on Directional Distribution of Solar Radiation:

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).

Directional distribution of radiation at the earth’s surface has two components.

– Direct radiation: Unscattered and in the direction of the sun’s rays.– Diffuse radiation: Scattered radiation strongly peaked in the forward direction.

Calculation of solar irradiation for a horizontal surface often presumes the scattered component to be isotropic.

S S dir S dif dir dirG G G q I , , cos

0 1 1 0S dir SG G ,. / .Clear skies Completely overcast

Terrestrial Radiation

Terrestrial Radiation• Emission by Earth’s Surface:

4E T

Emissivities are typically large. For example, from Table A.11:

Sand/Soil: 0 90Water/Ice: 0 95Vegetation: 0 92Snow: 0 82Concrete/Asphalt: 0 85

.

.

.

.

.

Emission is typically from surfaces with temperatures in the range of 250 < T < 320K and hence concentrated in the spectral region with peak emission at 4 40 m, 10 m .

• Atmospheric Emission: Largely due to emission from CO2 and H2O (v) and concentrated in the spectral regions 5 8 m and 13 m .

Terrestrial Radiation (cont).

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

4atm skyG T

effective sky te mperatu et rhe skyT

230K< 285KskyT Cold, clear sky Warm, overcast sky

• Can water in the natural environment freeze if the ambient air temperature exceeds 273K? If so, what environmental conditions (wind and sky)

favor ice formation?

Surface Properties

Surface Radiative Properties• Concentration of solar and terrestrial in different spectral regions often precludes use of the gray surface approximation .

0 3 3 m. 4 40 m

S

Note significant differences in for the two spectral regions: snow, human skin, white paint.

and

In terms of net radiation transfer to a surface with solar irradiation, the parameter has special significance. Why?/S

Surface Properties (cont).

Surface

Snow 0.29

Human skin 0.64

White paint 0.22

Black paint 1.0

Evaporated Al film 3.0

/S

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)

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): 6 215 10 m 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 S = 0.16 and0.93.

(b) Performing an energy balance on the outer surface of the roof, S S conv condG q E q 0 ,

it follows that

4S S s,o s,o s,o s,iG h(T T ) T (k t)(T T )

SCHEMATIC:

Problem: Heat Load on Food Delivery Truck (cont)

where it is assumed that convection is from the air to the roof. With

7L 6 2

VL 30 m s(5 m)Re 10

15 10 m s

4 / 5 1/ 3 7 4 / 5 1/ 3L LNu 0.037 Re Pr 0.037(10 ) (0.71) 13,141

2Lh Nu (k L) 13,141(0.026 W m K/5 m 68.3W m K .

Substituting numerical values in the energy balance and solving by trial-and-error, we obtain Ts,o = 295.2 K.

(d) From parametric calculations based on the foregoing model, the following results are obtained.

(c) The heat load through the roof is

2s s,o s,iq (kA t)(T T ) (0.05 W m K 10 m 0.025m)35.2 K 704 W .

Problem: Heat Load on Food Delivery Truck (cont)

5 10 15 20 25 30

Velocity, V(m/s)

280

285

290

295

300Te

mpe

ratu

re, T

so(K

)

5 10 15 20 25 30

Velocity, V(m/s)

500

550

600

650

700

Hea

t loa

d, q

(W)

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 S/.