2 CHAPTER TWO
THERMAL SOLAR TECHNOLOGY
2.1 Solar Geometry
As a result of the earth's axial rotation and its revolution around the sun, the sun is
constantly changing its position in the sky. This motion of the sun determines the amount
of solar energy incident upon a collector located on the earth's surface, since it depends
on the distance traveled by the sun's rays first to the earth and then through the earth's
atmosphere. Since the latter distance is determined by the angle at which the rays strike
the atmosphere, the terrestrial solar irradiation will change with the sun's position. The
area of a solar collector exposed to the direct solar radiation depends upon the angle
between the sun's rays and the collector. Similarly, the length of time for collecting solar
energy (day length) depends upon the sun's celestial motion. These and other factors
must be considered when deciding on the solar energy available to a collector, on the
way of focusing a concentrating collector, on the orientation of a permanent collector,
and on the mode of solar tracking when it is required.
This chapter examines the sun's motion in the sky due to the earth's motion about the
sun, as seen by an observer at a given location on the earth's surface.
2.2 Definitions and Terminology
2.2.1 Solar constant
The outer layer of the sun (called the photosphere) emits a continuous spectrum of radiation. Its
temperature is around 5000oC and for the purpose of solar calculations, the photosphere is
assumed to be a black body with a surface temperature of 5762 K.
The radiation emitted by the surface of the sun, E, is equal to the product of the Stefan-
Boltzmann constant, the fourth power of the absolute surface temperature T4 and the surface
area
Es = d 2T 4 W
Where:
Stefan Boltzmann constant, = 5.67 x 10-8 [W/m.k],
The surface temperature, T = 5762 K,
The diameter of the sun, D = 1.39 x 109 m
The radiation from the sun is in all direction and reaches the earth surface situated in a sphere
with the sun as its centre. The radius R is the mean distance between the sun and the earth and
equals to 1.5 x 1011 m. The surface area of the sphere equals 4R 2 . The radiation flux on a unit
area of the sphere surface, is called Irradiance
6
, d 2T 4
Irradiance, G = = 1353 W/m2
4R 2
The value of G is called the solar constant. Its unit is, G = 1353 W/m2
The practical maximum value of solar energy available on the earth's surface is 1000 W/m2
normally defined/termed as 1 sun.
2.2.2 Terrestrial and Extraterrestrial Radiation
The solar radiation available outside the earth's atmosphere as expressed by the solar constant of
1353 w/m2 is reduced in intensity by atmospheric absorption and reflection before reaching the
surface of the earth. Ozone in the atmosphere absorbs radiation of short wave lengths
(ultraviolet); carbon dioxide and water vapor absorb some of the radiation in the longer (infrared)
wave lengths. In addition to absorption, some radiation is scattered by gas molecules, dust and
water vapor in the atmosphere before reaching the earth. Consequently the radiation reaching the
earth’s surface is less than the maximum.
Extraterrestrial radiation, IEXT: This is the theoretical maximum of radiation, which can
fall on a surface when radiation losses are not considered.
Terrestrial radiation, IT: This is the actual radiation, which falls on the earth surface.
I EXT
The ratio c.i , is called clearness index
IT
2.3 Types of radiation
Ib – Direct beam
Id – Diffused radiation
Ir – Reflected radiation
Total radiation falling on an horizontal surface IT = Ib + Id + Ir
The sunlight that strikes a solar collecting surface can be direct, diffuse or reflected.
Direct sunlight: comes directly from the sun. Since the sun is far from the earth, rays of
direct sunlight are considered to be parallel.
Diffuse sunlight: does not come directly from the sun, but is first reflected from dust
particles, air, cloud and water vapor. Diffuse sunlight comes from all areas of the sky. Even
on a clear day, approximately 15 -20% of the sunlight is diffused. When the sky is totally
over cast, all of the sunlight is diffuse. The basic distraction between diffuse sunlight comes
in via scattering in the atmosphere while reflected sunlight comes from trees, snow,
landscapes, mirrors and other earthbound surfaces.
7
, Origin of direct beam and diffuse radiation
2.4 Measurements of Solar Radiation
Instruments for measuring solar radiation are called pyranometers or pyrheliometers.
Pyranometers measure total radiation, both direct and diffuse whereas pyrheliometers measures
only direct beam radiation.
2.4.1 Solar radiation calculations
2.4.2 Source of information
Many networks of meteorological stations in many countries measure total radiation received on
a horizontal surface for agricultural and other purposes that is the sum of direct and diffuse
components. Only a few stations have maintained separate records of the direct and diffuse
radiation-components. The direct and diffuse components are most useful for the calculation of
the total radiation on inclined surfaces. When integrated over 1-hour periods, the radiation is
termed insolation and the symbol of I is commonly used. These values are always recorded by
the meteorological departments and available for any part of our country.
Kenya lies between 4.7oS and 4.2oN (latitude) and between 34oE and 41.9oE (longitude). With
this geographical position, Kenya stands at a very good position where the sun is overhead in
most of the time of the year.
Eldoret town, lies at 0.5oE and receives the following averages of radiation distribution in W/m2.
Jan Feb March Apr May Jun Jul Aug Sep Oct Nov Dec
552 562 542 485 495 503 465 485 533 533 484 533
2.4.3 Total Radiation on an inclined plane
The following factors affect the quantity of radiation received in a solar collector or panels.
1. Angle of declination: The declination angle , is the angle the sun makes with the equatorial
plane. It is seasonal (provides a convenient measure of seasonal changes) and depends on
whether the sun's location is at the equator, tropic of cancer or tropic of Capricorn. The earth
tilts from +23.45o in June 21 to -23.45o in December 21.
8
THERMAL SOLAR TECHNOLOGY
2.1 Solar Geometry
As a result of the earth's axial rotation and its revolution around the sun, the sun is
constantly changing its position in the sky. This motion of the sun determines the amount
of solar energy incident upon a collector located on the earth's surface, since it depends
on the distance traveled by the sun's rays first to the earth and then through the earth's
atmosphere. Since the latter distance is determined by the angle at which the rays strike
the atmosphere, the terrestrial solar irradiation will change with the sun's position. The
area of a solar collector exposed to the direct solar radiation depends upon the angle
between the sun's rays and the collector. Similarly, the length of time for collecting solar
energy (day length) depends upon the sun's celestial motion. These and other factors
must be considered when deciding on the solar energy available to a collector, on the
way of focusing a concentrating collector, on the orientation of a permanent collector,
and on the mode of solar tracking when it is required.
This chapter examines the sun's motion in the sky due to the earth's motion about the
sun, as seen by an observer at a given location on the earth's surface.
2.2 Definitions and Terminology
2.2.1 Solar constant
The outer layer of the sun (called the photosphere) emits a continuous spectrum of radiation. Its
temperature is around 5000oC and for the purpose of solar calculations, the photosphere is
assumed to be a black body with a surface temperature of 5762 K.
The radiation emitted by the surface of the sun, E, is equal to the product of the Stefan-
Boltzmann constant, the fourth power of the absolute surface temperature T4 and the surface
area
Es = d 2T 4 W
Where:
Stefan Boltzmann constant, = 5.67 x 10-8 [W/m.k],
The surface temperature, T = 5762 K,
The diameter of the sun, D = 1.39 x 109 m
The radiation from the sun is in all direction and reaches the earth surface situated in a sphere
with the sun as its centre. The radius R is the mean distance between the sun and the earth and
equals to 1.5 x 1011 m. The surface area of the sphere equals 4R 2 . The radiation flux on a unit
area of the sphere surface, is called Irradiance
6
, d 2T 4
Irradiance, G = = 1353 W/m2
4R 2
The value of G is called the solar constant. Its unit is, G = 1353 W/m2
The practical maximum value of solar energy available on the earth's surface is 1000 W/m2
normally defined/termed as 1 sun.
2.2.2 Terrestrial and Extraterrestrial Radiation
The solar radiation available outside the earth's atmosphere as expressed by the solar constant of
1353 w/m2 is reduced in intensity by atmospheric absorption and reflection before reaching the
surface of the earth. Ozone in the atmosphere absorbs radiation of short wave lengths
(ultraviolet); carbon dioxide and water vapor absorb some of the radiation in the longer (infrared)
wave lengths. In addition to absorption, some radiation is scattered by gas molecules, dust and
water vapor in the atmosphere before reaching the earth. Consequently the radiation reaching the
earth’s surface is less than the maximum.
Extraterrestrial radiation, IEXT: This is the theoretical maximum of radiation, which can
fall on a surface when radiation losses are not considered.
Terrestrial radiation, IT: This is the actual radiation, which falls on the earth surface.
I EXT
The ratio c.i , is called clearness index
IT
2.3 Types of radiation
Ib – Direct beam
Id – Diffused radiation
Ir – Reflected radiation
Total radiation falling on an horizontal surface IT = Ib + Id + Ir
The sunlight that strikes a solar collecting surface can be direct, diffuse or reflected.
Direct sunlight: comes directly from the sun. Since the sun is far from the earth, rays of
direct sunlight are considered to be parallel.
Diffuse sunlight: does not come directly from the sun, but is first reflected from dust
particles, air, cloud and water vapor. Diffuse sunlight comes from all areas of the sky. Even
on a clear day, approximately 15 -20% of the sunlight is diffused. When the sky is totally
over cast, all of the sunlight is diffuse. The basic distraction between diffuse sunlight comes
in via scattering in the atmosphere while reflected sunlight comes from trees, snow,
landscapes, mirrors and other earthbound surfaces.
7
, Origin of direct beam and diffuse radiation
2.4 Measurements of Solar Radiation
Instruments for measuring solar radiation are called pyranometers or pyrheliometers.
Pyranometers measure total radiation, both direct and diffuse whereas pyrheliometers measures
only direct beam radiation.
2.4.1 Solar radiation calculations
2.4.2 Source of information
Many networks of meteorological stations in many countries measure total radiation received on
a horizontal surface for agricultural and other purposes that is the sum of direct and diffuse
components. Only a few stations have maintained separate records of the direct and diffuse
radiation-components. The direct and diffuse components are most useful for the calculation of
the total radiation on inclined surfaces. When integrated over 1-hour periods, the radiation is
termed insolation and the symbol of I is commonly used. These values are always recorded by
the meteorological departments and available for any part of our country.
Kenya lies between 4.7oS and 4.2oN (latitude) and between 34oE and 41.9oE (longitude). With
this geographical position, Kenya stands at a very good position where the sun is overhead in
most of the time of the year.
Eldoret town, lies at 0.5oE and receives the following averages of radiation distribution in W/m2.
Jan Feb March Apr May Jun Jul Aug Sep Oct Nov Dec
552 562 542 485 495 503 465 485 533 533 484 533
2.4.3 Total Radiation on an inclined plane
The following factors affect the quantity of radiation received in a solar collector or panels.
1. Angle of declination: The declination angle , is the angle the sun makes with the equatorial
plane. It is seasonal (provides a convenient measure of seasonal changes) and depends on
whether the sun's location is at the equator, tropic of cancer or tropic of Capricorn. The earth
tilts from +23.45o in June 21 to -23.45o in December 21.
8
