Ch.2 Solar radiation and the greenhouse effect

ME – 414 (2, 0)
ENERGY RESOURCES &
UTILIZATION (ERU)
Teacher In-charge
PROF. DR. ASAD NAEEM SHAH
anaeems@uet.edu.pk
Arranged by Prof. Dr. Asad Naeem Shah

SOLAR RADIATION
“Sun is the primary source of all renewable energy
resources. The technology based on solar energy are eco-
friendly with environment.”

INTRODUCTION
 SOLAR RADIATION: The emission from the sun into every
corner of space appears in the form of electromagnetic (EM)
waves that carry energy at the speed of light.
 DIFFERENT SHAPES OF INCOMING IRRADIATION: Depending
on the geometry of the earth, its distance from the sun,
geographical location of any point on the earth, astronomical
coordinates, and the composition of the atmosphere,
radiations at any given point may take different shapes.
 THE SUN AS A SPHERE OF HOT GASES: It is a sphere of
intensely hot gaseous matter. The solar energy strikes our
planet after leaving the giant furnace, the sun which is 1.5 ×
1011 m away.

INTRODUCTION Cont.
 SOLAR SPECTRUM A AS BLACK BODY: It is roughly equivalent
to a perfect black body. The temperature in the central region
is estimated at 8 × 106 to 40 × 106 K.
 SUN AS A REACTOR: It is a continuous fusion reactor in which
hydrogen is turned into helium. The sun’s total energy output
is 3.8 × 1020 MW. This energy radiates outwards in all
directions. Only a tiny fraction of the total radiation is
intercepted by our earth. It reaches the Earth’s surface at a
maximum flux density of about 1 kWm-2.
 SUN AS AN ORIGIN OF ENERGY: Basically, all the forms of
energy in the world are solar in origin.

INTRODUCTION Cont.
 APPLICATIONS OF SOLAR ENERGY: It is used to heat and cool
buildings (both active and passive), to heat water for domestic
and industrial uses, to heat swimming pools, to power
refrigerators, to operate engines and pumps, to desalinate
water for drinking purposes, to generate electricity, even to
grow food or dry cloths, and many more.
 CATEGORIES OF THE SUN LIGHT: It may be split into three
categories:
a) Photovoltaic (PV): to produce electricity directly from the
sun’s light.
b) Photochemical (PC): to produce electricity or light & gaseous
fuels by means of non-living chemical processes, e.g.
degradation of plastics.
c) Photobiological (PB): to produce food & gaseous fuels by
means of living organism or plants. Arranged by Prof. Dr. Asad Naeem Shah

EXTRATERRESTRIAL SOLAR RADIATION &
ELECTROMAGNETIC (EM) SPECTRUM
 SUN’S ACTIVE CORE & PASSIVE LAYERS: The reactions in the
active core of the Sun produce very high temperatures
(~107 𝐾 ) and an inner radiation flux of uneven spectral
distribution. This internal radiation is absorbed in the outer
passive layers which are heated to about 5800K and so become
a source of radiation with a relatively continuous spectral
distribution.
 VARIATION OF RADIANT FLUX: The radiant flux (W/m2) from
the Sun at the Earth’s distance varies through the year by
±4%. Moreover, the radiance also varies by perhaps ±0.3 per
cent per year due to sunspots.

ELECTROMAGNETIC (EM) SPECTRUM Cont.
 EM AS WAVE & PARTICLE:
Wave and particle are two forms
of light or EM radiation.
 EM waves consist of electric and
magnetic fields, which are
perpendicular to each other and
perpendicular to the direction of
travel as shown in Fig. 1. The
wavelength and frequency are
related through the speed of
light, c, as: 𝜆𝑓 = 𝑐 →→→ (1)
Fig. 1: EM waves

 Particle nature of EM radiation exhibits properties as photons
(having mass) made up of packets of energy E, which is related to
frequency f as:
𝐸 = ℎ𝑓 → (2)
where h is the Plank constant, h = 6.626×10−34 J.s.
𝐸 =
ℎ𝑐
𝜆
→ (3)
 THE SOLAR ENERGY SPECTRUM: It contains wavelengths that are
too long to be seen by the naked eye, and also wavelengths that are
too short to be visible. Thus the solar spectrum can be divided into
three main regions:
a) Ultraviolet region (λ < 0.4 µm); about 5% of the irradiance
b) Visible region (0.4 µm < λ < 0.7 µm); about 43% of the irradiance
c) Infrared region (λ ˃ 0.7 µm); about 52% of the irradiance

 SPECTRAL DISTRIBUTION: Figure 2
shows the spectral distribution of the
solar irradiance at the Earth’s mean
distance, uninfluenced by the
atmosphere.
 SOLAR CONSTANT: The area beneath
this curve is the solar constant G0 =
1367Wm−2. This is the RFD (Radiant
flux density) incident on a plane
directly facing the Sun and outside
the atmosphere at a distance of 1.5
× 1011 m from the Sun (i.e. at the
Earth’s mean distance from the Sun).
Fig. 2: Spectral distribution of
extraterrestrial solar irradiance.

 MAXIMUM SOLAR IRRADIANCE: As it can be seen from Fig. 2
that the maximum solar irradiance occurs at λ= 0.5 μm. The
proportions given in figure are received at the Earth’s surface
with the Sun incident at about 45°. The contribution to the
solar radiation flux from wavelengths greater than 2.5 µm is
negligible, and all three regions contributing to the irradiance
are classed as solar short wave radiation.
 WIEN'S DISPLACEMENT LAW: According to the law, the
wavelength corresponding to the maximum of solar irradiance
from the sun can be obtained from:
λmaxT = 2897.6 µm K→→→ (4)

 INTENSITY OF EXTRATERRESTRIAL RADIATION (𝑮 𝒆𝒙𝒕.):
 The orientation of the earth’s orbit around the sun-earth distance
varies slightly and since the solar radiation outside the earth’s
atmosphere at the mean sun-earth distance is nearly of fixed
intensities, so the RFD is considered constant throughout the year.
 However, this extraterrestrial radiation suffers variation due to the
fact that the earth revolves around the sun not in a circular orbit but
follows an elliptic path (Fig.3), with sun at one of the foci.
 The intensity of extraterrestrial radiation measured on a plane
normal to the radiation on the nth day of the year is given as :
𝐺 𝑒𝑥𝑡 = 𝐺0 1 + 0.033 𝑐𝑜𝑠
360𝑛
365
→ (5)

Fig. 3

PROBLEM
 Obtain Wien's displacement law by using Plank’s law of
radiation i.e.
𝑬 𝝀𝒃 =
𝑪 𝟏
𝝀 𝟓. 𝒆
𝑪 𝟐
𝝀𝑻 − 𝟏
where 𝐶1 = 3.743 × 108 𝑊. 𝜇𝑚4. 𝑚−2 &
𝐶2 = 14387.9 𝜇𝑚. 𝐾
HINTS: Differentiate the above equation w.r.t. 𝜆 and set it equal
to zero to get 𝝀 𝒎𝒂𝒙

RADIATION COMPONENTS
 DIRECT & DIFFUSE RADIATION:
Solar radiation incident on the
atmosphere from the direction of
the sun is the solar extraterrestrial
beam or direct radiation. Beneath
the atmosphere, at the Earth’s
surface, the radiation will be
observable from the direction of
the Sun’s disc as beam as well as
diffuse radiation as shown in Fig. 1.
 GENERATION OF DIFFUSE RADIATION:
Diffuse radiation is first intercepted
by the constituents of the air and
then released as scattered
radiation in many directions.
Fig. 1: Origin of direct beam
and diffuse radiation.

RADIATION COMPONENTS Cont.
 CONTRIBUTION OF DIFFUSE RADIATION: Even on a cloudless,
clear day, there is always at least 10% diffuse irradiance from the
molecules in the atmosphere.
 DISTINCTION: The practical distinction between the two
components is that only the beam radiation can be focused. The
ratio between the beam irradiance and the total irradiance thus
varies from about 0.9 (on a clear day) to zero (on a completely
overcast day).
 TOTAL IRRADIANCE: The total irradiance on any plane is the sum
of the beam and diffuse components, so:
Gt = Gb + Gd

GEOMETRY OF THE EARTH AND SUN

GEOMETRY OF THE EARTH AND SUN
 Latitude(𝝓): The angular distance (north
or south of the earth's equator),
measured in degrees along a meridian
from the equator to a point on the earth’s
surface. Latitude is positive for points
north of the equator, negative south of
the equator. If C is the center of the Earth,
a point P on the Earth’s surface is
determined by its latitude.
 Longitude (𝝍): The angular distance
measured (in degrees) from the prime
(solar noon) meridian through Greenwich
(UK), west or east to a point on the earth’s
surface. By international agreement it is
measured positive eastwards from
Greenwich.
Fig. 1: Sketch for latitude
and longitude

GEOMETRY OF THE EARTH AND SUN Cont.
 NOON SOLAR TIME: It is the
time when a local meridional plane
includes the sun (i.e. CEP includes
the sun) so that all points having
that longitude. It occurs once every
24 h.
 It represents the solar altitude at
noon above the horizon and
changes by 47° from 21 June to 21
December owing to change in
declination angle.

 CIVIL TIME: It is the time that a larger part of a country (15° of
longitude) observe in order to share the same official zone.
 THE HOUR ANGLE 𝝎 : It is the angle through which the
Earth has rotated since solar noon. It is positive in the evening
and negative in the morning.
𝝎 = 𝟏𝟓°𝒉−𝟏 𝒕 𝒔𝒐𝒍𝒂𝒓 − 𝟏𝟐𝒉
where 𝑡 𝑠𝑜𝑙𝑎𝑟 = 𝑡𝑖𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑎𝑦.
 DECLINATION ANGLE 𝜹 : The angle between the line joining
the center of the sun and the earth & its projection on the
equatorial plane.
Fig. 1: View of declination angle.

 It is due to the rotation of the earth, and varies from +23.5˚ (on
June, 21) to -23.5˚ (on December, 21). Analytically, it may be
calculated as:
𝛿 = 23.5 𝑠𝑖𝑛
360° 284 + 𝑛
365
where n is the day in the year (For example, n = 1 on 1 January).
Fig. 2: Variation of δ. Arranged by Prof. Dr. Asad Naeem Shah

GEOMETRY OF COLLECTOR & THE
SOLAR BEAM
 SLOPE (𝜷): It is the angle between the plane surface under consideration
and the horizontal. It is positive for the surface sloping or pitching towards
south and negative for the surface sloping towards north.
 ZENITH ANGLE 𝜽 𝒛 : The angle b/w normal to H.P & beam radiation.
 SURFACE AZIMUTH ANGLE (𝜸): It is the angle between the line due
south and the projection of the normal to inclined plane in an H.P. For east of
south i.e. eastward orientation of the surface, it varies 0˚ to -180˚. For a
horizontal surface, it is 0˚ always.
Fig. 3: View of various angles.

GEOMETRY OF COLLECTOR & THE
SOLAR BEAM Cont.
 SOLAR AZIMUTH ANGLE 𝜸 𝒔 :
It is the angle in a horizontal
plane (H.P) between the line due
south and the projection of beam
radiation on the H.P.
 ANGLE OF INCIDENCE 𝜽𝒊 : It
is the angle between beam
radiation on a surface & normal
to that surface.
 SOLAR ALTITUDE ANGLE 𝜶 𝒔 :
It is the angle between the sun
ray and its projection in a
horizontal plane. It is
complement to the zenith angle
(i.e. 𝛼 𝑠 + 𝜃𝑧 = 90°).

ANGLE BETWEEN BEAM AND
COLLECTOR
 SOLAR MODELING: It is performed through the following equation
involving the various attributes:
𝐜𝐨𝐬 𝜽𝒊 = 𝑨 − 𝑩 𝐬𝐢𝐧 𝜹 + 𝑪 𝐬𝐢𝐧 𝝎 + 𝑫 + 𝑬 𝐜𝐨𝐬 𝝎 𝐜𝐨𝐬 𝜹 → (𝟏)
where
𝐴 = sin 𝜙 cos 𝛽
𝐵 = cos 𝜙 sin 𝛽 cos 𝛾
𝐶 = sin 𝛽 sin 𝛾
𝐷 = cos 𝜙 cos 𝛽
𝐸 = sin 𝜙 sin 𝛽 cos 𝛾

EXAMPLE
Calculate the angle of incidence of beam radiation on a surface located
at Glasgow (56˚N, 4˚W) at 10 a.m. on 1 February, if the surface is
oriented 20˚ east of south and tilted at 40˚ to the horizontal.
SOLUTION:
Hints: n = 32 (1 February), Thus
𝛿 = 23.5 𝑠𝑖𝑛
360° 284 + 𝑛
365
= −17.5℃
 Also 𝜔 can be calculated at 10 AM, which is −30°
 Thus from the Eqn. given below, 𝜃𝑖 may be calculated:
cos 𝜃𝑖 = 𝐴 − 𝐵 sin 𝛿 + 𝐶 sin 𝜔 + 𝐷 + 𝐸 cos 𝜔 cos 𝛿
𝜽𝒊 = 𝟑𝟖. 𝟓° Arranged by Prof. Dr. Asad Naeem Shah

LATITUDE, SEASON AND DAILY
INSOLATION Cont.
Arranged by Prof. Dr. Asad Naeem ShahFig. 1 : Variation with 𝝓.

INSOLATION Cont.
 ROLE OF ORIENTATION OF RECEIVING SURFACE: The horizontal
plane at a certain location (positioning in the northern hemisphere) is
oriented much more towards the solar beam in summer than in
winter as shown in Fig. below.

INSOLATION Cont.
 EFFECT OF ZENITH ANGLE 𝜽 𝒛
ON RADIATION: The zenith
angle 𝜃𝑧 is given as:
cos 𝜃𝑧 = cos(𝜙 − 𝛿) → (3)
 The location of the place,
hence, plays an important role
in the variation of 𝜃𝑧.
 The solar radiation is, actually,
attenuated in the atmosphere
depending upon the value of 𝜃𝑧.
The larger 𝜃𝑧 means larger
distance (𝐴𝐵 > 𝐴𝐶) covered by
the solar radiation in the
atmosphere, and thus intensity
of attenuation increases with
increase in θz and vice versa. Arranged by Prof. Dr. Asad Naeem Shah
𝜽 𝒛

OPTIMUM ORIENTATION OF A
COLLECTOR
 A concentrating collector should always point towards the
direction of the solar beam (i.e. 𝜃𝑖 = 0 ). However, the
optimum direction of a fixed flat plate collector may not be
obvious, because the collector insolation (𝐻𝑐) is the sum of
both the beam and the diffuse components:
𝑯 𝒄 = 𝑮 𝒃
∗
𝒄𝒐𝒔 𝜽𝒊 + 𝑮 𝒅 𝒅𝒕
where * denotes the plane perpendicular to the beam.
 A suitable fixed collector orientation for most purposes is
facing the equator with a slope equal to the latitude. As the
angle of solar noon varies considerably over the year, it is
sensible to adjust the ‘fixed’ collector slope month by month.

HOURLY VARIATION OF IRRADIANCE
 The variation of solar radiation on a horizontal plane (𝐺ℎ) for clear and cloudy
days is given in Fig. 1(a) & Fig. 1(b), respectively.
Fig. 1: variation of solar radiation.

HOURLY VARIATION OF IRRADIANCE
Cont.
 On clear days the form of Fig. 1(a) follows the relation given as:
𝑮 𝒉 ≈ 𝑮 𝒉
𝒎𝒂𝒙
𝒔𝒊𝒏
𝝅𝒕
𝑵
→ 𝟏
where 𝑡 = time after sunrise & N = the duration of
daylight for a particular clear day.
 Integrating Eqn.(1) over the daylight period (N) for a clear day
yields:
𝑯 𝒉 ≈ 𝟐𝑵
𝝅 𝑮 𝒉
𝒎𝒂𝒙
→ (𝟐)
 The horizontal insolation 𝑯 𝒉 depends on N, and may be
calculated using Eqn. (2).

Ch.2 Solar radiation and the greenhouse effect

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