SOLAR ENERGY
Introduction and Scope
The sun exerts forces upon the earth and radiates solar energy produced
within the sun by nuclear fusion. A small fraction of that energy is
intercepted by the earth and is converted by nature to heat, winds, ocean
currents, waves, tides; makes plants grow, some of which over millions
of years produced fossil fuels (oil, coal, and gas); and creates biomass
which can be burned to generate heat and/or power. Solar energy is
implicit in many subject areas treated elsewhere in the Handbook; only
the more direct uses such as water heating, space heating and cooling,
swimming pool heating, solar distillation, solar drying and cooking,
solar furnaces, solar engines, solar electricity generation, and solar assisted
transportation will be treated here. The total field is widely
termed alternative or renewable sources of energy and their conversion.
Solar Energy Utilization Solar energy reaches the earth’s surface as
shortwave electromagnetic radiation in the wavelength band between
0.3 and 3.0 mm; its peak spectral sensitivity occurs at 0.48 mm (Fig.
9.1.10). Total solar radiation intensity on a horizontal surface at sea
level varies from zero at sunrise and sunset to a noon maximum which
can reach 340 Btu/(ft2 ? h) (1,070 W/m2) on clear summer days. This
inexhaustible source of energy, despite its variability in magnitude and
°
Fig. 9.1.10 Spectral distribution of solar radiation and radiation emitted by
blackbody at 95°F (35°C).
direction, can be used in three major processes (Daniels, ‘‘Direct Use of
the Sun’s Energy,’’ Yale; Zarem and Erway, ‘‘Introduction to the Utilization
of Solar Energy,’’ McGraw-Hill): (1) Heliothermal, in which the
sun’s radiation is absorbed and converted into heat which can then be
used for many purposes, such as evaporating seawater to produce salt or
distilling it into potable water; heating domestic hot water supplies;
house heating by warm air or hot water; cooling by absorption refrigeration;
cooking; generating electricity by vapor cycles and thermoelectric
processes; attaining temperatures as high as 6,500°F (3,600°C) in
solar furnaces. (2) Heliochemical, in which the shorter wavelengths can
cause chemical reactions, can sustain growth of plants and animals, can
convert carbon dioxide to oxygen by photosynthesis, can cause degradation
and fading of fabrics, plastics, and paint, can be used to detoxify
toxic waste, and can increase the rate of chemical reactions. (3) Helioelectrical,
in which part of the energy between 0.33 and 1.3 mm can be
converted directly to electricity by photovoltaic cells. Silicon solar batteries
have become the standard power sources for communication satellites,
orbiting laboratories, and space probes. Their use for terrestrial
power generation is currently under intensive study, with primary emphasis
upon cost reduction. Other methods include thermoelectric, thermionic,
and photoelectromagnetic processes and the use of very small
antennas in arrays for the conversion of solar energy to electricity (Antenna
Solar Energy to Electricity Converter/ASETEC, Air Force Report,
AF C FO 8635-83-C-0136, Task 85-6, Nov. 1988).
Solar Radiation Intensity In space at the average earth-sun distance,
92.957 million mi (150 million km), solar radiation intensity on a surface
normal to the sun’s rays is 434.6 6 1 Btu/(ft2 ? h) (1,370 6 3
W/m2). This quantity, called the solar constant ISC , undergoes small
(61 percent) periodic variations which affect primarily the shortwave
portion of the spectrum (Abbott, in Moon, Standard Polar Radiation
Curves, Jour. Franklin Inst., Nov. 1940). Recent measurements using
satellites give essentially the same results. Since the earth-sun distance
varies throughout the year, the intensity beyond the earth’s atmosphere
Io also varies by 63.3 percent (Table 9.1.3). The great seasonal variations
in terrestrial solar radiation intensity are due to the earth’s tilted
axis, which causes the solar declination d (the angle between the earth’s
equatorial plane and earth-sun line) to change from 0° on Mar. 21 and
Sept. 21 to 223.5° on Dec. 21 and 123.5° on June 21.
In passing through the earth’s atmosphere, the sun’s radiation is partially
and selectively absorbed, scattered, and reflected by water vapor and ozone, air molecules, natural dust, clouds, and artificial pollutants.
Some of the scattered and reflected energy reaches the earth as diffuse
or sky radiation Id .
The intensity of the direct normal radiation IDN depends upon the
clarity and the amount of precipitable moisture in the atmosphere and
the length of the atmospheric path, which is determined by the solar
altitude b and expressed in terms of the air mass m, which is the ratio of
the existing path length to the path length when the sun is at the zenith.
Except at very low solar altitudes, m 5 1.0/sin b.
Figure 9.1.10 shows relative values of the spectral intensity of solar
radiation in space for m 5 0 (Thekaekara, Solar Energy outside the
Earth’s Atmosphere, Solar Energy, 14, no. 2, 1973) and at sea level
(Moon, Standard Solar Radiation Curves, Jour. Franklin Inst., Nov.
1940) for a solar altitude of 30° (m 5 2.0). Table 9.1.4 shows the
variation at 40° north latitude throughout typical clear summer (June
21) and winter (Dec. 21) days of solar altitude and azimuth (measured
from the south), direct normal radiation, total solar irradiation of horizontal
and vertical south-facing surfaces.
The total solar irradiation reaching a terrestrial surface is the sum of
the direct, diffuse, and reflected components: It 5 IDN cos u 1 Id 1 Ir ,
where u is the incident angle between the sun’s rays and a line perpendicular
to the receiving surface and, Ir is the shortwave radiation reflected
from adjacent surfaces.
Direct beam solar radiation intensity is measured by pyroheliometers
with collimating tubes to exclude all but the direct rays from their
sensors, which may use calorimetric, thermoelectric, or photovoltaic
means to produce a response proportional to the irradiation rate. Similar
but uncollimated instruments called pyranometers are used to measure
the total radiation from sun and sky; when their sensors are shaded from
the sun’s direct rays, they also can measure the diffuse component.
Incident Angle Determination The incident angle u affects both the
direct solar intensity and the solar optical properties of the irradiated
surface. For a flat surface tilted at an angle o from the horizontal,
cos u 5 cos b cos g sin o 1 sin b cos o. For vertical surfaces, o 5
90°; so cos u 5 cos b cos g; for horizontal surfaces, o 5 0° and u 5
90° 2 b. (See ASHRAE, ‘‘Handbook of Fundamentals,’’ for values of
solar altitude, azimuth, and direct normal radiation throughout the year
for 0 to 56° north latitude.)
Solar Optical Properties of Transparent Materials When solar radiation
with total intensity It falls on a transparent material, part of the
energy is reflected, part is absorbed, and the remainder is transmitted.
At any instant,
It 5 qt 1 qA 1 qR 5 It(t 1 a 1 r)
The sum of the solar optical properties t, a, and r must equal unity,
but the individual values depend upon the incident angle and wavelength
of the radiation, the composition of the material, and the nature of
any coatings which may be applied to the surfaces.
For uncoated single-strength (3⁄32-in or 2.4-mm) clear window glass
(Fig. 9.1.11), solar transmittance at normal incidence (u 5 0°) is approximately
0.90, but the transmittance for longwave thermal radiation
(5 mm) is virtually zero. Thus glass acts as a ‘‘heat trap’’ by admitting
solar radiation readily but retaining most of the heat produced by the
absorbed sunshine. This ‘‘greenhouse effect,’’ which is also exhibited
but to a lesser degree by some plastic films (see Whillier, Plastic Covers
for Solar Collectors, Solar Energy, 7, no. 3, 1964), is the basis for most
heliothermal processes. Heat absorbing glass [1⁄4 in (6.3 mm) thick (Fig.
9.1.11)], which absorbs more than 50 percent of the incident solar radiation,
is widely used by architects to reduce the heat and glare admitted
through unshaded windows. Reflective coatings (Yellott, Selective Reflectance,
Trans. ASHRAE, 69, 1963) have been developed to serve
similar purposes.
For all types of glass, transmittance falls and reflectance rises as u
exceeds about 30°. Absorptance increases somewhat owing to the
increased path length and then drops off sharply toward zero as u exceeds
60°.
Absorptance and Emittance of Opaque Surfaces Opaque materials
absorb or reflect all the incident sunshine. The absorptance a for
solar radiation and the emittance « for longwave radiation at the temperature
of the receiving surface are particularly important in heliotechnology.
For a true blackbody, the absorptance and emittance are equal
and do not change with wavelength. Most real surfaces have reflectances
and absorptances which vary with wavelength (Fig. 9.1.12).
Aluminum foil has a consistently low absorptance and high reflectance
over the entire spectrum from 0.25 to 25 mm, while black paint has a
high absorptance and low reflectance. White paint, however, has low shortwave (solar) absorptance, but beyond 3 mm its absorptance and
reflectance are virtually the same as for black paint.
Solar collectors require a high a/« ratio, while surfaces which should
remain cool, such as rooftops or space vehicles, should have low ratios since their objective usually is to absorb as little solar radiation and emit
as much longwave radiation as possible. Special surface treatments
have been developed (see ASHRAE, ‘‘Solar Energy Use for Heating
and Cooling of Buildings,’’ 1977) for which the ratio a/« is above 7.0,
making them suitable for solar collectors; others with ratios as low as
0.15 are useful as heat rejectors for space applications (see Table 9.1.5).
In addition, the absorptance can be changed and controlled by paint composition (grain material and size, binder, thickness etc.) and surface
configuration, both large and small.
Equilibrium Temperatures for Concentrating Collectors When a
surface is irradiated, its temperature rises until the rate of solar radiation
absorption equals the rate at which heat is removed from the surface. If
no heat is intentionally removed, the maximum temperature which
can be attained by a blackbody (a 5 «) is found from IDNCa 5
0.1713«(Tp/100)4, where C is the concentration ratio. Figure 9.1.13
shows the variation of blackbody equilibrium temperatures for earth and
near space where IDN 5 320 and Io 5 435 Btu/ft2 ?h (1,000 and
1,370 W/m2).
For flat plate collectors, C 5 1.0; so their maximum attainable temperatures
are below 212°F (100°C) unless a selective surface is used
with a/« . 1.0, or both radiation and convection loss are suppressed by
the use of multiple glass cover plates. Only the direct component of the
total solar radiation can be concentrated, and concentrating collectors
must follow the sun’s apparent motion across the sky or use heliostats

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