Food Chain and Food Web (Ecosystem) EVS, B. Pharmacy 1st Year, Sem-II
Solar Energy Engineering
1. Fundamentals of
Solar Energy Engineering
Naveed ur Rehman
www.naveedurrehman.com
Note: Reference information is available at Google Drive/Solar Energy Engineering
2. Famous quotes about Solar energy
"I’d put my money on the Sun and Solar Energy, what a source of
Power! I hope we don’t have to wait until oil and coal run out,
before we tackle that.“
Thomas Edison (Inventor of light bulb)
"I have no doubt that we will be successful in harnessing the
sun's energy. If sunbeams were weapons of war, we would have
had solar energy centuries ago."
George Porter (Nobel Prize winner in Chemistry, 1967)
2
3. Famous quotes about Solar energy
"Because we are now running out of gas and oil, we must
prepare quickly for a third change, to strict conservation and to
the use of coal and permanent renewable energy sources, like
solar power."
Jimmy Carter (1977)
"We were delighted to have worked with Microsoft on its electric
solar system. Microsoft is effectively lowering operating costs,
reducing purchases of expensive peak electricity, and improving
the health and quality of life in California through its Silicon
Valley Campus solar power program.“
Dan Shuga (President of PowerLight)
3
4. Famous quotes about Solar energy
“Solar energy, radiant light and heat from the sun, has
been harnessed by humans since ancient times using a
range of ever-evolving technologies. Solar energy
technologies include solar heating, solar photovoltaics,
solar thermal electricity and solar architecture, which
can make considerable contributions to solving some of
the most urgent problems the world now faces.”
"Solar Energy Perspectives: Executive Summary"
International Energy Agency (2011)
4
5. Contents
• Chapter #1: The Light
• Chapter #2: Solar Geometry
• Chapter #3: Solar Radiations
• Chapter #4: Flat-Plate Collectors
• Chapter #5: Concentrated Systems
• Chapter #6: Photovoltaic Systems
5
6. Recommended books
1. Solar Engineering of Thermal Processes
John A. Duffie & William A. Beckman
2. Solar Energy Engineering: Processes and
Systems
Soteris A. Kalogirou
3. Solar-thermal energy systems: analysis and
design
John R. Howell, Richard B. Bannerot &
Gary C. Vliet
4. Fundamentals of Renewable Energy
Processes
Aldo. V. Da. Rosa 6
7. Recommended websites
1. Power from the Sun
http://www.powerfromthesun.net/
2. PV Education
http://www.pveducation.org/
3. SolarWiki
http://solarwiki.ucdavis.edu/
7
9. Photon
• Today, quantum-mechanics
explains both the
observations of the wave
nature and the particle
nature of light.
• Light is a type of quantum-
mechanical particle, called
a Photon, which may also
be pictured as “wave-
packet”.
Chapter #1: The Light
9
10. Photon
• A photon is characterized by either a
wavelength (λ) or energy (E), such that:
or
h = Plank’s constant = 6.626 × 10 -34 joule·s
c = Speed of light = 2.998 × 108 m/s
Therefore, a short wavelength photon will posses
high energy content and vice versa.
Chapter #1: The Light
10
13. Photon Flux
Chapter #1: The Light
13
• The photon flux is defined as the number of
photons per second per unit area:
• Note that the photon flux does not give
information about the characteristics of striking
photons i.e. energy or wavelength.
14. Power Density
Chapter #1: The Light
14
• The power density is calculated by multiplying
the photon flux by the energy of a single
photon:
Where, q = Electronic charge = 1.6 x 10-19 joules
15. Photon Flux and Power Density
Chapter #1: The Light
15
• The photon flux of high
energy (or short
wavelength) photons
needed to give a certain
power density will be
lower than the photon
flux of low energy (or long
wavelength) photons
required to give the same
power density.
Low
energy
photons
High
energy
photons
16. Spectral Irradiance
Chapter #1: The Light
16
• The spectral irradiance (F) is given as a
function of wavelength λ, and gives the power
(energy per unit time) received by the surface
for a particular wavelength of light.
• It gives an idea of how much power is being
contributed from each wavelength.
• It is the most common way of characterizing a
light source.
or
18. Radiant Power Density
Chapter #1: The Light
18
• The total power density emitted from a light
source can be calculated by integrating the
spectral irradiance over all wavelengths.
Where:
H = total power density emitted from the light
source = W/m2
F(λ) = spectral irradiance = W/m2μm
dλ = wavelength = μm
19. Blackbody Radiations
Chapter #1: The Light
19
• A blackbody absorbs all radiation incident on
its surface and emits radiation based on its
temperature.
• Many commonly encountered light sources,
including the sun and incandescent light bulbs,
are closely modeled as "blackbody" emitters.
• The spectral irradiance from a blackbody is
given by Planck's radiation law, shown in the
following equation
20. Blackbody Radiations
Chapter #1: The Light
20
• A blackbody absorbs all
radiation incident on its
surface and emits radiation
based on its temperature.
• Many commonly encountered
light sources, including the sun
and incandescent light bulbs,
are closely modeled as
"blackbody" emitters.
21. Blackbody Radiations
Chapter #1: The Light
21
• The spectral irradiance from a blackbody is
given by Planck's radiation law:
Where:
λ = wavelength of light (m)
T = temperature of the blackbody (K)
F = spectral irradiance (W/m2m)
k = Boltzmann’s constant(1.380 × 10-23 joule/K)
c = speed of light (m/s), h = Plank’s constant (j.s)
22. Blackbody Radiations
Chapter #1: The Light
22
• The total power density from a blackbody is
determined by integrating the spectral
irradiance over all wavelengths, which gives:
Where:
σ = Stefan-Boltzmann const. (5.67x10-8 W/m2K4)
T = temperature (K)
23. Blackbody Radiations
Chapter #1: The Light
23
• The peak wavelength is the wavelength at
which the spectral irradiance is highest.
• It can be determined as:
• In other words, it is the wavelength where most
of the power is emitted.
28. The sun
• Effective blackbody
temperature of 5777 K
• Hot because of continuous
fusion reactions:
e.g. H + H → He + (Heat
Energy)
• Pores and sunspots on sun
surface
Chapter #2: Solar Geometry
28
29. The earth
• Very small as compared to sun
• Rotate about its own axis (day)
• Revolve around the sun in orbit (year)
Chapter #2: Solar Geometry
29
Rotation Revolution
30. Earth-sun distance
• Mean earth-sun distance is 1au (149.5Mkm)
• It varies by ± 1.7%
• This variation is not responsible for earth’s
seasons
Chapter #2: Solar Geometry
30
152 MKm 147 MKm
32. Earth’s geometry
Locating position on earth:
Chapter #2: Solar Geometry
Φ : Latitude
L : Longitude
Unit: Degrees
X
Prime-meridian
at Greenwich
(L=0°)
Equator
(ø=0°)
32
33. Earth’s geometry
Where is Karachi on earth?
Latitude (Φ) : 24.8508°N
Longitude (L) : 67.0181°E
Try: ”Latitude Karachi” at Google
Q1) In which hemisphere, Karachi is located?
Q2) To which direction from Greenwich, Karachi
is located?
Chapter #2: Solar Geometry
X
N
S
EW
33
34. Exercise-1:
Earth’s geometry
Where the following cities are located?
1) Sydney (Australia)
2) Nairobi (Kenya)
3) Balingen (Germany)
4) Jeddah (Saudi Arabia)
5) Oregon (USA)
6) Greenwich (UK)
Chapter #2: Solar Geometry
34
35. Magnetic compass directions
Chapter #2: Solar Geometry
• The magnetic poles are not
at the geographic poles.
• Directions shown by a
magnetic compass are not
the “Geographic” directions.
• All solar engineering
calculations are based on
geographic directions!
35
36. Magnetic declination
Chapter #2: Solar Geometry
• Magnetic declination is the
angle between geographic
north (Ng) and magnetic north
(Nm).
• Nm is M.D. away from Ng.
• Facts:
– M.D in Alberta (Canada) is
approx. 16°W
– For Karachi, M.D. is almost 0°!
To get M.D: http://magnetic-declination.com/
36
37. Magnetic declination
Chapter #2: Solar Geometry
(e.g. 16°W or -16°
i.e. Nm is 16°W of Ng) 37
(e.g. 16°E or 16°
i.e. Nm is 16°E of Ng)
38. Date and day
Chapter #2: Solar Geometry
• Date is represented by month and ‘i’
• Day is represented by ‘n’
38
Month nth day for ith date
January i
February 31 + i
March 59 + i
… …
December 334 + i
(See “Days in Year” in Reference Information)
39. Sun position from earth
Chapter #2: Solar Geometry
• Sun rise in the east and set in the west
• “A” sees sun in south
• “B” sees sun in north
N
S
EW
A
B
39
40. Solar noon
Chapter #2: Solar Geometry
40
Solar noon is the time when
sun is highest above the
horizon on that day
41. Solar altitude angle
Chapter #2: Solar Geometry
E
αs
W
• Solar altitude angle (αs) is the angle between
horizontal and the line passing through sun
• It changes every hour and every day
S N
In northern hemisphere
41
42. Solar altitude angle at noon
Chapter #2: Solar Geometry
E
αs,noon
W
Solar altitude angle is maximum at “Noon” for a
day, denoted by αs,noon
S N
In northern hemisphere
42
43. • Zenith angle (θz) is the angle between vertical
and the line passing through sun
• θz = 90 – αs
Zenith angle
Chapter #2: Solar Geometry
E
θz W
S N
In northern hemisphere
43
44. Zenith angle at noon
Chapter #2: Solar Geometry
• Zenith angle is minimum at “Noon” for a day,
denoted by θz,noon
• ϴz,noon = 90 – αs,noon
E
θz,noon W
S N
In northern hemisphere
44
45. Air mass
Chapter #2: Solar Geometry
• Another representation of solar altitude/zenith
angle.
• Air mass (A.M.) is the ratio of mass of
atmosphere through which beam passes, to the
mass it would pass through, if the sun were
directly overhead.
𝐴. 𝑀. = Τ1 cos 𝜃𝑧
If A.M.=1 => θz=0° (Sun is directly overhead)
If A.M.=2 => θz=60° (Sun is away, a lot of mass of air
is present between earth and sun)
45
47. Solar azimuth angle
Chapter #2: Solar Geometry
E
γs
W
• In any hemisphere, solar azimuth angle (γs) is
the angular displacement of sun from south
• It is 0° due south, -ve in east, +ve in west
Morning
(γs = -ve)
Evening
(γs = +ve)
Noon
(γs = 0°)
S
47
48. Solar declination
Chapter #2: Solar Geometry
December solstice
Northern
hemisphere is away
from sun
(Winter)
June solstice
Northern
hemisphere is
towards sun
(Summer)
March equinox
Equator faces sun directly
(Spring)
September equinox
Equator faces sun directly
(Autumn) 48
Important!
49. Solar declination (at solstice)
Chapter #2: Solar Geometry
A
A
A sees sun in north.
B sees sun overhead.
C sees sun in south.
C
B
A sees sun in south.
B sees sun in more south.
C sees sun in much more south.
N N
SS
June solstice December solstice
B
C
(Noon)
49
50. Solar declination (at equinox)
Chapter #2: Solar Geometry
A sees sun directly overhead
B sees sun in more south
C sees sun in much more south
Same situation happen during
September equinox.
March equinox
A
C
N
S
B
(Noon) 50
51. Solar declination
Chapter #2: Solar Geometry
N
S
ø
ø ø
Latitude from frame of reference of horizontal
ground beneath feet
51
52. Solar declination
Chapter #2: Solar Geometry
90 - φ
+23.45°
-23.45°
φ
W
NS
E
December
solstice
Equinox
June
solstice
Note: Altitude depends upon latitude but declination is independent.
In northern hemisphere
Declination
angles
52
53. Exercise-2:
Solar declination and altitude angle
What is the altitude of sun at noon in Karachi
(Latitude=24.8508) on:
1) Equinox
2) June solstice
3) December solstice
Chapter #2: Solar Geometry
53
54. Solar declination
• For any day in year, solar declination (δ) can be
calculated as:
𝛿 = 23.45 sin 360
284 + 𝑛
365
Where, n = numberth day of year
(See “Days in Year” in Reference Information)
• Maximum: 23.45 °, Minimum: -23.45°
• Solar declination angle represents “day”
• It is independent of time and location!
Chapter #2: Solar Geometry
54
55. Solar declination
Chapter #2: Solar Geometry
Days to
Remember δ
March, 21 0°
June, 21 +23.45°
September, 21 0°
December, 21 -23.45°
Can you prove this?
55
δ
n
56. Solar altitude and zenith at noon
• As solar declination (δ) is the function of day
(n) in year, therefore, solar altitude at noon
can be calculated as:
αs,noon = 90 – ø + δ
• Similarly zenith angle at noon can be
calculated as:
ϴz,noon = 90 – αs,noon= 90 – (90 – ø + δ)= ø - δ
Chapter #2: Solar Geometry
56
57. Exercise-3:
Solar declination and altitude angle
What is the altitude of sun at noon in Karachi
(Latitude=24.8508) on:
1) January, 12
2) July, 23
3) November, 8
Chapter #2: Solar Geometry
57
58. Solar time
• The time in your clock (local time) is not same
as “solar time”
• It is always “Noon” at 12:00pm solar time
Chapter #2: Solar Geometry
Solar time “Noon” Local time (in your clock) 58
59. Solar time
The difference between solar time (ST) and local
time (LT) can be calculated as:
𝑆𝑇 − 𝐿𝑇 = 𝐸 −
4 × 𝑆𝐿 − 𝐿𝐿
60
Where,
ST: Solar time (in 24 hours format)
LT: Local time (in 24 hours format)
SL: Standard longitude (depends upon GMT)
LL: Local longitude (+ve for east, -ve for west)
E: Equation of time (in hours)
Chapter #2: Solar Geometry
Try: http://www.powerfromthesun.net/soltimecalc.html59
60. Solar time
• Standard longitude (SL) can be calculated as:
SL = (𝐺𝑀𝑇 × 15)
• Where GMT is Greenwich Mean Time, roughly:
If LL > 0 (Eastward):
𝐺𝑀𝑇 = 𝑐𝑒𝑖𝑙 Τ𝐿𝐿 15
If LL < 0 (Westward):
𝐺𝑀𝑇 = −𝑓𝑙𝑜𝑜𝑟 Τ𝐿𝐿 15
• GMT for Karachi is 5, GMT for Tehran is 3.5.
• It is recommended to find GMT from standard
database e.g. http://wwp.greenwichmeantime.com/
Chapter #2: Solar Geometry
60
61. Solar time
• The term Equation of time (E) is because of
earth’s tilt and orbit eccentricity.
• It can be calculated as:
Chapter #2: Solar Geometry
𝐸 =
229.2
60
×
0.000075
+0.001868 cos 𝐵
−0.032077 sin 𝐵
−0.014615 cos 2𝐵
−0.04089 sin 2𝐵
61
Where,
𝐵 = Τ𝑛 − 1 360 365
62. Hour angle
• Hour angle (ω) is another representation of
solar time
• It can be calculated as:
𝜔 = (𝑆𝑇 − 12) × 15
(-ve before solar noon, +ve after solar noon)
Chapter #2: Solar Geometry
11:00am
ω = -15°
12:00pm
ω = 0°
01:00pm
ω = +15°
62
63. Exercise-4:
Solar time from local time
What is the solar time and hour angle in
Karachi (Longitude=67.0181°E) on 8 November
2:35pm local time?
Hint:
Find in sequence LT, LL, GMT, SL, n, B, E, ST and finally ω
Remember! You can always find solar time from local
time if you are given with longitude and day
Chapter #2: Solar Geometry
63
64. Exercise-5:
Local time from solar time
At what local time, sun will be at noon in
Karachi on 8 November?
Hint:
Solar time is given in terms of “noon”. Find in sequence
ST, LL, GMT, SL, n, B, E and finally ST
Chapter #2: Solar Geometry
64
65. A plane at earth’s surface
• Tilt, pitch or slope angle: β (in degrees)
• Surface azimuth or orientation: γ (in degrees,
0° due south, -ve in east, +ve in west)
Chapter #2: Solar Geometry
E
W
γ
S
β
(γ = -ve)
(γ = +ve)
(γ = 0) N
65
66. Summary of solar angles
Chapter #2: Solar Geometry
66Can you write symbols of different solar angles shown in this diagram?
67. Interpretation of solar angles
Chapter #2: Solar Geometry
Angle Interpretation
Latitude φ Site location
Declination δ Day (Sun position)
Hour angle ω Time (Sun position)
Solar altitude αs Sun direction (Sun position)
Zenith angle θz Sun direction (Sun position)
Solar azimuth γs Sun direction (Sun position)
Tilt angle β Plane direction
Surface azimuth γ Plane direction
1
2
3
4
67
Set#
68. Angle of incidence
Angle of incidence (θ) is the angle between
normal of plane and line which is meeting plane
and passing through the sun
Chapter #2: Solar Geometry
E
W
S N
θ
68
69. Angle of incidence
• Angle of incidence (θ) depends upon:
– Site location (1): θ changes place to place
– Sun position (2/3): θ changes in every instant
of time and day
– Plane direction (4): θ changes if plane is
moved
• It is 0° for a plane directly facing sun and at
this angle, maximum solar radiations are
collected by plane.
Chapter #2: Solar Geometry
69
70. Angle of incidence
If the sun position is known in terms of
declination (day) and hour angle, angle of
incidence (θ) can be calculated as:
cos 𝜃
= sin 𝛿 sin ∅ cos 𝛽 − sin 𝛿 cos ∅ sin 𝛽 cos 𝛾
+ cos 𝛿 cos ∅ cos 𝛽 cos 𝜔
+ cos 𝛿 sin ∅ sin 𝛽 cos 𝛾 cos 𝜔
+ cos 𝛿 sin 𝛽 sin 𝛾 sin 𝜔
Chapter #2: Solar Geometry
70(Set 1+2+4)
71. Angle of incidence
If the sun position is known in terms of sun
direction (i.e. solar altitude/zenith and solar
azimuth angles), angle of incidence (θ) can be
calculated as:
cos 𝜃 = cos 𝜃𝑧 cos 𝛽 + sin 𝜃𝑧 sin 𝛽 cos 𝛾𝑠 − 𝛾
Remember, θz = 90 – αs
Note: Solar altitude/zenith angle and solar azimuth
angle depends upon location.
Chapter #2: Solar Geometry
71(Set 1+3+4)
72. Exercise-6:
Angle of incidence
Calculate angle of incidence on a plane located
in Karachi (Latitude=24.8508°N,
Longitude=67.018°E) at 10:30am (solar time)
on February 13, if the plane is tilted 45° from
horizontal and pointed 15° west of south.
Hint:
Convert given data into solar angles and then check
which equation for calculating θ suits best.
For geeks!
Solve the same problem if 10:30am is local time.
Chapter #2: Solar Geometry
72
73. Special cases for angle of incidence
• If the plane is laid horizontal (β=0°)
–Equation is independent of γ (rotate!)
–θ becomes θz because normal to the plane
becomes vertical, hence:
Chapter #2: Solar Geometry
cos 𝜃𝑧 = cos ∅ cos 𝛿 cos 𝜔 + sin ∅ sin 𝛿
Remember, θz = 90 – αs
73
Note: Solar altitude/zenith angle depends
upon location, day and hour.
74. Exercise-7:
Special cases for angle of incidence
Reduce equation for calculating angle of
incidence for the following special cases:
1. Plane is facing south
2. Plane is vertical
3. Vertical plane is facing south
4. A plane facing south and is tilted at angle
equals to latitude
Chapter #2: Solar Geometry
74
75. Solar altitude and azimuth angle
Solar altitude angle (αs) can be calculated as:
sin𝛼 𝑠 = cos ∅ cos 𝛿 cos 𝜔 + sin ∅ sin 𝛿
Solar azimuth angle (γs) can be calculated as:
𝛾𝑠 = sign 𝜔 cos−1
cos 𝜃𝑧 sin ∅ − sin 𝛿
sin 𝜃𝑧 cos ∅
Chapter #2: Solar Geometry
75
76. Sun path diagram or sun charts
Chapter #2: Solar Geometry
Note: These diagrams are different for different latitudes.
αs
γs 76
-150° -120° -90° - 60° -30° 0° 30° 60° 90° 120° 150°
77. Exercise-8:
Sun path diagram or sun charts
Draw a sun path diagram for Karachi with lines
of June, 21 and December, 21.
Hint:
You need to calculate αs and γs for all hour angles of the
days mentioned in question.
Chapter #2: Solar Geometry
77
78. Shadow analysis (objects at distance)
Chapter #2: Solar Geometry
• Shadow analysis for objects at distance (e.g. trees,
buildings, poles etc.) is done to find:
– Those moments (hours and days) in year when
plane will not see sun.
– Loss in total energy collection due to above.
• Mainly, following things are required:
– Sun charts for site location
– Inclinometer
– Compass and information of M.D.
78
79. Inclinometer
Chapter #2: Solar Geometry
A simple tool for finding azimuths and altitudes of objects
http://rimstar.org/renewnrg/solar_site_survey_shading_location.htm 79
80. Shadow analysis using sun charts
Chapter #2: Solar Geometry
αs
γs 80
-150° -120° -90° - 60° -30° 0° 30° 60° 90° 120° 150°
81. Sunset hour angle and daylight hours
• Sunset occurs when θ z = 90° (or αs = 0°). Sunset hour
angle (ωs) can be calculated as:
• Number of daylight hours (N) can be calculated as:
For half-day (sunrise to noon or noon to sunrise),
number of daylight hours will be half of above.
Chapter #2: Solar Geometry
cos 𝜔𝑠 = − tan ∅ tan 𝛿
𝑁 =
2
15
𝜔𝑠
81
82. Exercise-9:
Sunset hour angle and daylight hours
What is the sunset time (solar) on August, 14 in
Karachi (Latitude=24.8508°N) and Balingen
(Latitude=48.2753°N)? Also calculate number
of daylight hours for each city.
For geeks!
Also convert solar time (sunset hour angle) to local
time. You will need longitudes of these places.
Chapter #2: Solar Geometry
82
83. Profile angle
It is the angle through which a plane that is initially
horizontal must be rotated about an axis in the plane of
the given surface in order to include the sun.
Chapter #2: Solar Geometry
83
84. Profile angle
• It is denoted by αp and can be calculated as follow:
Chapter #2: Solar Geometry
84
tan 𝛼 𝑝 =
tan 𝛼 𝑠
cos 𝛾𝑠 − 𝛾
• It is used in calculating shade of one collector (row) on
to the next collector (row).
• In this way, profile angle can also be used in calculating
the minimum distance between collector (rows).
85. Profile angle
• Collector-B will be in shade of collector-A, only when:
Chapter #2: Solar Geometry
85
𝛼 𝑝 < ҧ𝛽
86. Exercise-10:
Profile angle and shading
According to figure, for a 25° profile angle, will
the collector-B be in the shade of collector-A?
Chapter #2: Solar Geometry
86
87. Angles for tracking surfaces
• Some solar collectors "track" the sun
by moving in prescribed ways to
minimize the angle of incidence of
beam radiation on their surfaces and
thus maximize the incident beam
radiation.
• Tracking the sun is much more
essential in concentrating systems
e.g. parabolic troughs and dishes.
(See “Tracking surfaces” in Reference
Information)
Chapter #2: Solar Geometry
87
89. Types of solar radiations
1. Types by components:
Total = Beam + Diffuse
or Direct or Sky
Chapter #3: Solar Radiations
89
90. Types of solar radiations
2. Types by terrestre:
Extraterrestrial Terrestrial
Chapter #3: Solar Radiations
• Solar radiations
received on earth
without the presence
of atmosphere OR solar
radiations received
outside earth
atmosphere.
• We always calculate
these radiations.
• Solar radiations
received on earth in
the presence of
atmosphere.
• We can measure or
estimate these
radiations. Ready
databases are also
available e.g. TMY. 90
91. Measurement of solar radiations
1. Magnitude of solar radiations:
Irradiance Irradiation/Insolation
Chapter #3: Solar Radiations
• Rate of
energy
(power)
received
per unit
area
• Symbol: G
• Unit: W/m2
Energy received per unit area in a
given time
Hourly: I
Unit: J/m2
Monthly avg. daily: H
Unit: J/m2
Daily: H
Unit: J/m2
91
92. Measurement of solar radiations
2. Tilt (β) and orientation (γ) of measuring
instrument:
– Horizontal (β=0°, irrespective of γ)
– Normal to sun (β=θz, γ= γs)
– Tilt (any β, γ is usually 0°)
– Latitude (β=ø, γ is usually 0°)
Chapter #3: Solar Radiations
92
93. Representation of solar radiations
• Symbols:
–Irradiance: G
–Irradiations:
I (hourly), H (daily), H (monthly average daily)
• Subscripts:
–Ex.terr.: o Terrestrial: -
–Beam: b Diffuse: d Total -
–Normal: n Tilt: T Horizontal -
Chapter #3: Solar Radiations
93
94. Exercise-1
Representation of solar radiations
What are these symbols representing?
Chapter #3: Solar Radiations
1. Go
2. Gn
3. Gon
4. GT
5. GoT
6. G
7. Gb
1. Io
2. In
3. Ion
4. IT
5. IoT
6. I
7. Ib
1. Ho
2. Hn
3. Hon
4. HT
5. HoT
6. H
7. Hb
1. Ho
2. Hn
3. Hon
4. HT
5. HoT
6. H
7. Hb
A B C D
94
95. Extraterrestrial solar radiations
Chapter #3: Solar Radiations
Solar
constant
(Gsc)
Irradiance
at normal
(Gon)
Irradiance at
horizontal
(Go)
Mathematical integration…
Hourly
irradiations on
horizontal
(Io)
Daily
irradiations on
horizontal
(Ho)
Monthly avg.
daily irrad. on
horizontal
(Ho)
95
96. Solar constant (Gsc)
Extraterrestrial solar radiations received at
normal, when earth is at an average distance
(1 au) away from sun.
𝐺𝑠𝑐 = 1367 Τ𝑊 𝑚2
Adopted by World Radiation Center (WRC)
Chapter #3: Solar Radiations
Gsc96
97. Spectral dist. of ext. terr. sol. rad.
Chapter #3: Solar Radiations
97
98. Spectral dist. of ext. terr. sol. rad.
Chapter #3: Solar Radiations
98(See “Fraction of Solar Irradiance” in Reference Information)
To calculate solar irradiance in
particular wavelength range:
1. Take the difference of f0-λ
given against the
wavelengths.
2. Multiply the difference by
solar constant (=1367W/m2)
3. This can also be done by
taking difference of Gsc, λ
99. Ex.terr. irradiance at normal
Extraterrestrial solar radiations received at
normal. It deviates from GSC as the earth
move near or away from the sun.
𝐺 𝑜𝑛 = 𝐺𝑠𝑐 1 + 0.033 cos
360𝑛
365
Chapter #3: Solar Radiations
Gon99
100. Example-2
Ex.terr. irradiance at normal
What is the extraterrestrial solar irradiance
at normal on the following days of year:
1. April, 1
2. October, 1
3. June, 10
4. December, 10
Chapter #3: Solar Radiations
100
101. Ex.terr. irradiance on horizontal
Chapter #3: Solar Radiations
Go101
Extraterrestrial solar radiations received at
horizontal. It is derived from Gon and
therefore, it deviates from GSC as the earth
move near or away from the sun.
𝐺 𝑜 = 𝐺 𝑜𝑛 × cos ∅ cos 𝛿 cos 𝜔 + sin ∅ sin 𝛿
102. Example-3
Ex.terr. irradiance on horizontal
What is the extraterrestrial solar irradiance
on horizontal at 10:00am on February 19, in
1. Karachi (Latitude=24.8508°N)
2. Balingen (Latitude=48.2753°N)
3. Nairobi (Latitude=1.2833°S)
Chapter #3: Solar Radiations
102
103. Ex.terr. hourly irradiation on
horizontal
𝐼 𝑜
=
12 × 3600
𝜋
𝐺𝑠𝑐 × 1 + 0.033 cos
360𝑛
365
× ቈcos ∅ cos 𝛿 sin 𝜔2 − sin 𝜔1
Chapter #3: Solar Radiations
Io103
104. Example-4
Ex.terr. hourly irradiation on horizontal
What is the extraterrestrial hourly solar
irradiations on horizontal between 10:00am
and 11:00am on February 19, in Karachi
(Latitude=24.8508°N)
Chapter #3: Solar Radiations
104
105. Ex.terr. daily irradiation on
horizontal
𝐻 𝑜
=
24 × 3600
𝜋
𝐺𝑠𝑐 × 1 + 0.033 cos
360𝑛
365
× cos ∅ cos 𝛿 sin 𝜔𝑠 +
𝜋𝜔𝑠
180
sin ∅ sin 𝛿
Chapter #3: Solar Radiations
Ho105
106. Example-5
Ex.terr. daily irradiation on horizontal
What is the extraterrestrial daily solar
irradiations on horizontal on February 19, in
Karachi (Latitude=24.8508°N)
Chapter #3: Solar Radiations
106
107. Ex.terr. monthly average daily
irradiation on horizontal
ഥ𝐻 𝑜
=
24 × 3600
𝜋
𝐺𝑠𝑐 × 1 + 0.033 cos
360𝑛
365
× cos ∅ cos 𝛿 sin 𝜔𝑠 +
𝜋𝜔𝑠
180
sin ∅ sin 𝛿
Where day and time dependent parameters
are calculated on average day of a particular
month i.e. 𝑛 = ത𝑛
Chapter #3: Solar Radiations
Ho107
108. Example-6
Ex.terr. mon. avg. daily irrad. on horiz.
What is the extraterrestrial monthly average
daily solar irradiations on horizontal in the
month of February, in Karachi
(Latitude=24.8508°N)
Chapter #3: Solar Radiations
108
109. Terrestrial radiations
Can be…
• measured by instruments
• obtained from databases e.g. TMY, NASA
SSE etc.
• estimated by different correlations
Chapter #3: Solar Radiations
109
110. Terrestrial radiations measurement
• Total irradiance can
be measured using
Pyranometer
Chapter #3: Solar Radiations
• Diffuse irradiance can
be measured using
Pyranometer with
shading ring
110
111. Terrestrial radiations measurement
• Beam irradiance can
be measured using
Pyrheliometer
Chapter #3: Solar Radiations
• Beam irradiance can
also be measured
by taking difference
in readings of
pyranometer with
and without
shadow band:
beam = total - diffuse
111
112. Terrestrial radiations databases
Chapter #3: Solar Radiations
1. NASA SSE:
Monthly average daily total irradiation on
horizontal surface ( ഥ𝐻) can be obtained from
NASA Surface meteorology and Solar Energy
(SSE) Database, accessible from:
http://eosweb.larc.nasa.gov/sse/RETScreen/
(See “NASA SSE” in Reference Information)
112
113. Terrestrial radiations databases
Chapter #3: Solar Radiations
2. TMY files:
Information about hourly solar radiations can be
obtained from Typical Meteorological Year files.
(See “TMY” section in Reference Information)
113
114. Terrestrial irradiation estimation
Chapter #3: Solar Radiations
• Angstrom-type regression equations are
generally used:
ഥ𝐻
ഥ𝐻 𝑜
= 𝑎 + 𝑏
ത𝑛
ഥ𝑁
(See “Terrestrial Radiations Estimations” section in Reference
Information)
114
115. Terrestrial irradiation estimation
Chapter #3: Solar Radiations
For Karachi:
ഥ𝐻
ഥ𝐻 𝑜
= 0.324 + 0.405
ത𝑛
ഥ𝑁
Where,
ത𝑛 is the representation of cloud
cover and ഥ𝑁 is the day length of
average day of month.
115
116. Example-7
Terrestrial irradiation estimation
What is the terrestrial monthly average
daily irradiations on horizontal in the month
of February, in Karachi (Latitude=24.8508°N)
Chapter #3: Solar Radiations
116
117. Clearness index
Chapter #3: Solar Radiations
• A ratio which mathematically represents sky
clearness.
=1 (clear day)
<1 (not clear day)
• Used for finding:
–frequency distribution of various radiation
levels
–diffuse components from total irradiations
117
119. Frequency distribution of various
radiation levels
Chapter #3: Solar Radiations
Example:
For a month
having average
clearness index
0.4, 50% and
less days will
have clearness
index of ≈0.4
119
120. Example-8
Freq. dist. of various rad. levels
What is the fraction of time, the days in
month of February in Karachi will have
clearness index less than or equals to 0.4?
Chapter #3: Solar Radiations
120
121. Diffuse component of hourly
irradiation (on horizontal)
Chapter #3: Solar Radiations
Orgill and Holland correlation:
𝐼 𝑑
𝐼
= ቐ
1 − 0.249𝑘 𝑇, 𝑘 𝑇 ≤ 0.35
1.557 − 1.84𝑘 𝑇, 0.35 < 𝑘 𝑇 < 0.75
0.177, 𝑘 𝑇 ≥ 0.75
Erbs et al. (1982)
121
122. Example-9
Diff. comp. of hourly irrad. (on horiz.)
How much is the hourly beam irradiations
when total hourly extraterrestrial and total
hourly terrestrial irradiations are 12 MJ/m2
and 6 MJ/m2?
Chapter #3: Solar Radiations
122
124. Diffuse component of monthly average
daily irradiation (on horizontal)
Chapter #3: Solar Radiations
Collares-Pereira and Rabl correlation:
ഥ𝐻 𝑑
ഥ𝐻
= 0.775 + 0.00606 𝜔𝑠 − 90
− ሾ0.505
124
125. Hourly total irradiation from daily
irradiation (on horizontal)
Chapter #3: Solar Radiations
For any mid-point (ω) of an hour,
𝐼 = 𝑟𝑡 𝐻
According to Collares-Pereira and Rabl:
𝑟𝑡 =
𝜋
24
𝑎 + 𝑏 cos 𝜔
cos 𝜔 − cos 𝜔𝑠
sin 𝜔𝑠 −
𝜋𝜔𝑠
180
cos 𝜔𝑠
Where,
𝑎 = 0.409 + 0.5016 sin 𝜔𝑠 − 60
𝑏 = 0.6609 − 0.4767 sin 𝜔𝑠 − 60
125
126. Hourly diffuse irradiations from daily
diffuse irradiation (on horizontal)
Chapter #3: Solar Radiations
For any mid-point (ω) of an hour,
𝐼 𝑑 = 𝑟𝑑 𝐻 𝑑
From Liu and Jordan:
𝑟𝑑 =
𝜋
24
cos 𝜔 − cos 𝜔𝑠
sin 𝜔𝑠 −
𝜋𝜔𝑠
180
cos 𝜔𝑠
126
127. Air mass and radiations
Chapter #3: Solar Radiations
• Terrestrial radiations depends upon the path
length travelled through atmosphere. Hence,
these radiations can be characterized by air
mass (AM).
• Extraterrestrial solar radiations are
symbolized as AM0.
• For different air masses, spectral distribution
of solar radiations is different.
127
128. Air mass and radiations
Chapter #3: Solar Radiations
128
129. Air mass and radiations
Chapter #3: Solar Radiations
• The standard spectrum at the Earth's surface
generally used are:
– AM1.5G, (G = global)
– AM1.5D (D = direct radiation only)
• AM1.5D = 28% of AM0
18% (absorption) + 10% (scattering).
• AM1.5G = 110% AM1.5D = 970 W/m2.
129
130. Air mass and radiations
Chapter #3: Solar Radiations
130
131. Radiations on a tilted plane
Chapter #3: Solar Radiations
To calculate radiations on a tilted plane,
following information are required:
• tilt angle
• total, beam and diffused components of
radiations on horizontal (at least two of
these)
• diffuse sky assumptions (isotropic or
anisotropic)
• calculation model
131
133. Diffuse sky assumptions
Chapter #3: Solar Radiations
Diffuse radiations consist of three parts:
1. Isotropic (represented by: iso)
2. Circumsolar brightening (represented by : cs)
3. Horizon brightening (represented by : hz)
There are two types of diffuse sky assumptions:
1. Isotropic sky (iso)
2. Anisotropic sky (iso + cs, iso + cs + hz)
133
134. General calculation model
Chapter #3: Solar Radiations
𝑋 𝑇 = 𝑋 𝑏 𝑅 𝑏 + 𝑋 𝑑,𝑖𝑠𝑜 𝐹𝑐−𝑠 + 𝑋 𝑑,𝑐𝑠 𝑅 𝑏 + 𝑋 𝑑,ℎ𝑧 𝐹𝑐−ℎ𝑧 + 𝑋𝜌 𝑔 𝐹𝑐−𝑔
Where,
• X, Xb, Xd: total, beam and diffuse radiations
(irradiance or irradiation) on horizontal
• iso, cs and hz: isotropic, circumsolar and horizon
brightening parts of diffuse radiations
• Rb: beam radiations on tilt to horizontal ratio
• Fc-s, Fc-hz and Fc-g: shape factors from collector to sky,
horizon and ground respectively
• ρg: albedo
134
135. Calculation models
Chapter #3: Solar Radiations
1. Liu and Jordan (LJ) model (iso, 𝛾=0°, 𝐼)
2. Liu and Jordan (LJ) model (iso, 𝛾=0°, ഥ𝐻)
3. Hay and Davies (HD) model (iso+cs, 𝛾=0°, 𝐼)
4. Hay, Davies, Klucher and Reindl (HDKR) model
(iso+cs+hz, 𝛾=0°, 𝐼)
5. Perez model (iso+cs+hz, 𝛾=0°,𝐼)
6. Klein and Theilacker (K-T) model (iso+cs, 𝛾=0°, ഥ𝐻)
7. Klein and Theilacker (K-T) model (iso+cs, ഥ𝐻)
(See “Sky models” in Reference Information) 135
138. Introduction
1. Flat-plate collectors are special type of
heat-exchangers
2. Energy is transferred to fluid from a
distant source of radiant energy
3. Incident solar radiations is not more
than 1100 W/m2 and is also variable
4. Designed for applications requiring
energy delivery up to 100°C above
ambient temperature.
138
Chapter #4:Flat-Plate Collectors
139. Introduction
1. Use both beam and diffuse solar
radiation
2. Do not require sun tracking and thus
require low maintenance
3. Major applications: solar water heating,
building heating, air conditioning and
industrial process heat.
139
Chapter #4:Flat-Plate Collectors
145. Heat transfer: Fundamental
Heat transfer, in general:
145
𝑞 = 𝑄/𝐴 = Τ𝑇1 − 𝑇2 𝑅 = Τ∆𝑇 𝑅 = 𝑈∆𝑇[W/m2]
Where,
𝑇1 > 𝑇2: Heat is transferred from higher to lower
temperature
∆𝑇 is the temperature difference [K]
R is the thermal resistance [m2K/W]
A is the heat transfer area [m2]
U is overall H.T. coeff. U=1/R [W/m2K]
Chapter #4:Flat-Plate Collectors
147. Example-1
Heat transfer: Circuits
Determine the heat transfer per unit area(q)
and overall heat transfer coefficient (U) for the
following circuit:
147
R1 R2T1 T2
R4
R3
q
Chapter #4:Flat-Plate Collectors
148. Heat transfer: Radiation
Radiation heat transfer between
two infinite parallel plates:
Chapter #4:Flat-Plate Collectors
148
𝑹 𝒓 = Τ𝟏 𝒉 𝒓
and,
𝒉 𝒓 =
𝝈 𝑻 𝟏
𝟐
+ 𝑻 𝟐
𝟐
𝑻 𝟏 + 𝑻 𝟐
𝟏
𝜺 𝟏
+
𝟏
𝜺 𝟐
− 𝟏
Where,
𝜎 = 5.67 × 10−8
W/m2K4
𝜖 is the emissivity of a plate
149. Heat transfer: Radiation
Radiation heat transfer between a
small object surrounded by a large
enclosure:
Chapter #4:Flat-Plate Collectors
149
𝑹 𝒓 = Τ𝟏 𝒉 𝒓
and,
𝒉 𝒓 =
𝝈 𝑻 𝟏
𝟐
+ 𝑻 𝟐
𝟐
𝑻 𝟏 + 𝑻 𝟐
Τ𝟏 𝜺
= 𝜺𝝈 𝑻 𝟏
𝟐
+ 𝑻 𝟐
𝟐
𝑻 𝟏 + 𝑻 𝟐 [W/m2K]
150. Heat transfer: Sky Temperature
1. Sky temperature is denoted by Ts
2. Generally, Ts = Ta may be assumed
because sky temperature does not make
much difference in evaluating collector
performance.
3. For a bit more accuracy:
In hot climates: Ts = Ta+ 5°C
In cold climates: Ts = Ta+ 10°C
Chapter #4:Flat-Plate Collectors
150
151. Heat transfer: Convection
Convection heat transfer between parallel plates:
Chapter #4:Flat-Plate Collectors
151
𝑹 𝒄 = Τ𝟏 𝒉 𝒄 and 𝒉 𝒄 = Τ𝑵 𝒖 𝒌 𝑳
Where,
𝑵 𝒖 = 𝟏 +
𝟏. 𝟒𝟒 𝟏 −
𝟏𝟕𝟎𝟖 𝐬𝐢𝐧 𝟏. 𝟖𝜷 𝟏.𝟔
𝑹 𝒂 𝒄𝒐𝒔 𝜷
𝟏 −
𝟏𝟕𝟎𝟖
𝑹 𝒂 𝒄𝒐𝒔 𝜷
+
+
𝑹 𝒂 𝐜𝐨𝐬 𝜷
𝟓𝟖𝟑𝟎
Τ𝟏 𝟑
− 𝟏
+
Note: Above is valid for tilt angles between 0° to 75°.
‘+’ indicates that only positive values are to be
considered. Negative values should be discarded.
152. Heat transfer: Convection
Chapter #4:Flat-Plate Collectors
152
𝑅 𝑎 =
𝑔𝛽′∆𝑇𝐿3
𝜗𝛼
also 𝑃𝑟 = Τ𝜗 𝛼
Where,
Fluid properties are evaluated at mean temperature
Ra Rayleigh number
Pr Prandtl number
L plate spacing
k thermal conductivity
g gravitational constant
β‘ volumetric coefficient of expansion
for ideal gas, β‘ = 1/T [K-1]
𝜗, α kinematic viscosity and thermal diffusivity
153. Example-2
Heat transfer: Convection
Find the convection heat transfer coefficient
between two parallel plates separated by 25 mm
with a 45° tilt. The lower plate is at 70°C and the
upper plate is 50°C.
Hint:
Calculate k, T, β’, 𝜗, α at mean temperature using air
thermal properties table. Then calculate Ra, Nu and
finally h.
153
Chapter #4:Flat-Plate Collectors
154. Heat transfer: Conduction
Conduction heat transfer through a
material:
Chapter #4:Flat-Plate Collectors
154
𝑹 𝒌 = Τ𝑳 𝒌
Where,
L material thickness [m]
k thermal conductivity [W/mK]
155. General energy balance equation
155
In steady-state:
Useful Energy = Incoming Energy – Energy Loss [W]
𝑸 𝒖 = 𝑨 𝒄 𝑺 − 𝑼 𝑳 𝑻 𝒑𝒎 − 𝑻 𝒂
Ac = Collector area [m2]
Tpm = Absorber plate temp. [K]
Ta = Ambient temp. [K]
UL = Overall heat loss coeff. [W/m2K]
Qu = Useful Energy [W]
SAc = Incoming (Solar) Energy [W]
AcUL(Tpm-Ta) = Energy Loss [W]
Chapter #4:Flat-Plate Collectors
Incoming Energy
Useful Energy
Energy
Loss
156. Thermal network diagram
156
Chapter #4:Flat-Plate Collectors
Ta
Ta
Ambient (a)
Cover (c)
Structure (b)
QuS
Rr(c-a) Rc(c-a)
Rr(p-c) Rc(p-c)
Rr(b-a) Rc(b-a)
Rk(p-b)
a
c
p
b
a
Plate (p)
Top losses
Bottom losses
qloss (top)
qloss (bottom)
157. Thermal network diagram
157
Chapter #4:Flat-Plate Collectors
Ta
Ta
QuS
Rr(c-a) Rc(c-a)
Rr(p-c) Rc(p-c)
Rr(b-a) Rc(b-a)
Rk(p-b)
a
c
p
b
a
R(c-a) =1/(1/Rr(c-a) + 1/Rc(c-a))
R(p-c) =1/(1/Rr(p-c) + 1/Rc(p-c))
Ta
Tc
Tp
R(b-a) =1/(1/Rr(b-a) + 1/Rc(b-a))
Rk(p-b)
Tb
Ta
QuS
158. Cover temperature
158
Chapter #4:Flat-Plate Collectors
R(c-a)
R(p-c)
Ta
Tc
Tp
R(b-a)
Rk(p-b)
Tb
Ta
QuS
1. Ambient and plate temperatures are
generally known.
2. Utop can be calculated as:
Utop= 1/(R(c-a) +R(p-c))
3. From energy balance:
qp-c = qp-a
(Tp-Tc)/R(p-c) = Utop(Tp-Ta)
=>Tc = Tp- Utop (Tp-Ta)x R(p-c)
160. Numerical problem
160
Chapter #4:Flat-Plate Collectors
Calculate the top loss coefficient for an absorber with a
single glass cover having the following specifications:
Plate-to-cover spacing: 25mm
Plate emittance: 0.95
Ambient air and sky temperature: 10°C
Wind heat transfer coefficient: 10 W/m2°C
Mean plate temperature: 100°C
Collector tilt: 45°
Glass emittance: 0.88