2. Module 3
Performance analysis of Liquid flat plate collectors:
General description, collector geometry, selective surface,
(qualitative discussion), Basic energy balance equation, Stagnation
temperature, Transmissivity of the cover system, Transmissivity-
Absorptivity product, Numerical examples.
The overall loss coefficient, Correlation for the top loss coefficient,
bottom and side loss coefficient, problems (all correlations to be
provided).
Temperature distribution between the collector tubes, collector heat
removal factor, collector efficiency factor and collector flow factor,
mean plate temperature, instantaneous efficiency, (all expressions
to be provided), Effect of various parameters on the collector
performance, Collector orientation, selective surface, fluid inlet
temperature, number of covers, dust.
Photo voltaic conversion:
Description, principle of working and characteristics, Applications.2
3. Performance analysis of Liquid flat plate collectors:
General description, collector geometry, selective surface,
(qualitative discussion), Basic energy balance equation,
Stagnation temperature, Transmissivity of the cover
system, Transmissivity-Absorptivity product, Numerical
examples.
LIQUID FLAT-PLATE COLLECTORS
General Description of Flat Plate Collectors:
3
5. The basic elements making up a conventional
liquid flat plate collector are:
(i) the absorber plate
(ii) the tubes to the absorber plate through
which the liquid to heated flows,
(iii) the transparent covers and
(iv) the liquid container.
5
6. Flat - plate collectors can be designed for applications
requiring energy delivery at moderate temperatures,
up to perhaps 1000C above the ambient temperature.
They have advantages of using both beam and diffuse
solar radiation, not requiring orientation towards the
sun, and requiring little maintenance.
The principal disadvantage from which it suffers is that
because of the absence of optical concentration the
area from which heat is lost is large. As a result, the
collection efficiency is generally low.
The principal present applications of these units are in
solar water heating systems, while potential uses
include building heating and air conditioning. 6
7. SELECTIVE SURFACES:
Absorber plate surfaces which exhibit the characteristics of a high
value of absorptivity for incoming solar radiation and a low value of
emissivity for out - going re -radiation are called selective surfaces.
Such surfaces are desirable because they maximize the absorption
of solar energy and minimize the emission of the radioactive loss.
Obviously they would yield higher collector efficiencies than are
obtained when the absorptivity and emissivity are equal.
An ideal selective surface should have high absorptivity for
wavelengths less than 4μm and a low emissivity for wavelengths
greater than 4μm.
7
8. The various selective surfaces and their
absorptivity and emissivity are mentioned below.
Absorptivity (α) Emissivity (Є)
1. Copper oxide on Copper 0.89 0.17
2. Nickel black on GI 0.89 0.16
3. Black chrome on aluminum 0.868 0.088
8
9. Performance Analysis of Liquid flat plate collector:
Performance analysis of a liquid flat plate collector for steady
state situation.
An Energy balance on the absorber plate yields
qu = Ap S - ql, in which
qu= useful heat gain, i.e. rate of HT to the working fluid
S= Incident solar flux in the absorber plate, Ap= area of the
absorber plate, and ql = Rate at which heat is lost by convection
and re-radiation from the top, and by conduction and convection
from the bottom and sides.
9
10. Stagnation Temperature:
This “stagnation temperature” occurs at approximately
80°C for a simple flat-plate solar collector.
If water, for example, is passed through passages in the
plate collector, then it will stabilize at a lower
temperature and the water will extract some of the
energy in being usefully heated up.
10
11. Transmissivity of the Cover System
The transmissivity of the cover system of a collector can be
obtained with adequate accuracy by considering reflection –
refraction and absorption separately and is given by the product
form,
τ = τr τa
Where,
τr = Transmissivity obtained by considering only reflection and refraction, and
τa =Transmissivity obtained by considering only absorption.
11
14. Transmissivity based on reflection – refraction
When a beam of light of intensity Ibn travelling through a
transparent medium 1 strikes the interface separating it
from another transparent medium 2, It is reflected and
refracted as shown in Fig.4.19. The reflected beam has a
reduced intensity Ir and has a direction such that the
angle of reflection is equal to the angle of incidence. On
the other hand, the directions of the incident and
refracted beams are related to each other by Snell’s Law
which states that,
14
16. Transmissivity based on Absorption:
The Transmissivity based on absorption can be
obtained by assuming that the attenuation due to
absorption is proportional to the local intensity
(Bouger’s law).
Consider a beam of intensity ‘Ibn’ incident normally on
a transparent cover of thickness ‘δc’ and emerging
with an intensity ‘Il’ as shown in Fig.4.21.
16
17. Where, K is a constant of proportionality and is called
the extinction coefficient. It will be assumed to have a
value independent of wavelength. Integrating over the
length traversed by the beam, we have
17
18. In case the beam is incident at an angle q1, the path traversed through the cover
would be (δc/cosq2), where q2 is the angle of refraction. Then, Eqn. (4.69) gets
modified to the form,
The extinction coefficient K is a property of the cover material. Its
value varies from about 4 to 25cm-1 for different qualities of glass.
A low value is obviously desirable.
18
19. The extinction coefficient K is a property of the cover material. Its value varies
from about 4 to 25cm-1 for different qualities of glass. A low value is obviously
desirable.
Transmissivity for Diffuse Radiation
The preceding considerations apply only to beam radiation. Calculation of the
transmissivity of a cover system when diffuse radiation is incident on it
presents some difficulty; because the radiation comes from many directions.
The usual practice is to assume that the diffuse radiation is equivalent to beam
radiation coming at an angle of incidence of 60o.
This angle is arrived at by considering the variation of ‘t’ , and by assuming that
the amount of diffuse radiation coming from all directions is the same.
19
20. Problem:
Plot the variation of τr τa and τ with the angle
of incidence for the following cover system.
Material: Glass, No. of Covers =2,
Thickness of each cover = 4mm,
Refractive index of glass relative to air: 1.52,
Extinction coefficient of glass = 15m-1
20
21. Solution:
The calculation is given for one angle of incidence, viz. Ɵ1= 150.
Hence, Ɵ2 = sin-1[sin 150/1.521]= 9.800
ρI= Sin2(9.800-150)/sin2(9.800+150)=0.047
τrI= 1-0.047/1+(3x0.047) =0.835
ρII= tan2 (9.800-150)/tan2(9.800+150)=0.039
τrII = 1-0.039/1+(3x0.039) =0.860
τr =1/2 (0.835+0.860) = 0.848
τa= exp[-(2x15x4x10-3/cos 9.800)] =0.885
τ = 0.848x0.885 = 0.750
The transmissivities for other angles of incidence are obtained in a similar
manner. These are plotted as shown.
21
23. Overall Loss Coefficient and Heat Transfer Correlations.
It is convenient from the point of view of analysis to express the heat from the collector
in terms of an overall loss coefficient defined by the equation
Q=UA ∆T
23
24. The heat lost from the collector is the sum of the heat
lost from the top, the bottom and from the sides. Thus
24
The heat loss from collector
25. Each of these losses is also expressed in terms of
coefficients called the top loss coefficient, the
bottom loss coefficient and the side loss coefficient
and defined by the equations given by,
Where Tmp = average temperature of the absorber plate. 25
26. It will be noted that the definition of each of the
coefficients is based on the area Ap and the temperature
difference (Tmp-Ta). This is done for convenience and helps
in giving the simple additive equation,
26
27. Top Loss Coefficient
The top loss coefficient ‘Ut’ is evaluated by considering
convection and re-radiation losses from the absorber plate in the
upward direction. For purposes of calculation, it is further
assumed that the temperature drop across the thickness of the
covers is negligible and that the interaction between the
incoming solar radiation absorbed by the covers and the outgoing
loss may be neglected. The re-radiation is of large wave lengths.
For these wavelengths the transparent cover will be assumed to
be opaque. This is a very good assumption if the material is glass.
27
28. A schematic diagram for a two cover system is shown in Fig.4.25. In a steady state
the heat transferred by convection and radiation between (i) the absorption
plate and the first cover, (ii) the first cover and second cover, and (iii) the second
cover and the surrounding must be equal.
28
31. Side loss coefficient:
While considering the bottom loss coefficient, it will be assumed that the
conduction resistance dominates and that the loss of heat is one-dimensional and
steady. The one-dimensional approximation can be justified on the grounds that
the side loss coefficient is always much smaller than the top loss coefficient.
If the dimensions of the absorber plate are L1 x L2 and the height of the collector
casing is L3, then the area across which heat flows sideways is 2(L1+L2)xL3. The
temperature drop across which heat flow occurs varies from (Tpm-Ta) at the
absorber plate level to zero both at the top and bottom. Assuming, therefore, that
the average temperature drop across the side insulation is (Tpm-Ta)/2 and that
the thickness of this insulation is δs, we have
31
33. Empirical Equation for Top Loss Coefficient
Calculation of top loss coefficient by earlier methods
require a tedious iterative calculation. Based on
calculations for a large number of cases covering the
entire range of conditions normally expected for flat
plate collector, “Klein” has developed the following
convenient empirical equation for calculating the top loss
coefficient.
33
35. Temperature distribution between the collector tubes,
collector heat removal factor, collector efficiency
factor and collector flow factor, mean plate
temperature, instantaneous efficiency, (all expressions
to be provided),
Effect of various parameters on the collector
performance, Collector orientation, selective surface,
fluid inlet temperature, number of covers, dust.
35
36. Collector Efficiency Factor:
The heat lost from the collector can thus be calculated, if the average plate
temperature is known. However, this temperature is generally not known. It
will, therefore be necessary to consider the flow of heat in the absorber plate
and across the fluid tubes to the fluid so that the values of Tpm can be related
to the value of the inlet fluid temperature which is a known quantity.
In order to simplify the problem, the approach adopted will be to conduct a
number of one- dimensional analysis. First, the one – dimensional flow of heat
in the absorber plate in a direction at right angles to the direction of fluid flow
will be considered. This will be followed by a consideration of the heat flow
from the plate to the fluid across the tube wall. Finally, the one – dimensional
flow of fluid inside the tube will be analyzed.
36
37. Consider a collector having an absorber plate of length L1 and width L2. Assume
that there are N fluid tubes and that the pitch of the tube is W = (L2/N). Let Di and
Do be the inside and outside diameter of the tubes.
Consider a section of the absorber plate with two adjacent fluid tubes. The
temperature in the plate (Tp) will vary in the x-direction in the manner as
shown in Fig 4.27. It will be assumed that the same distribution exists
between any two tubes. Above the fluid tubes, the temperature will be
constant, while in between the tubes, temperature will pass through the
maximum. Taking a slice ‘dy’ along the flow direction and neglecting heat
conduction in the plate in that direction, we can write energy balance for an
element dx x dy of the plate.
37
39. Expression for Collector Efficiency factor:
Where, F1 represents the ratio of the actual useful gain rate
per tube per unit length to the gain which would occur, if the
collector absorber plate were at the temperature Tf.
39
41. Instantaneous efficiency:
Instantaneous Efficiency (of a Solar Collector) is the
amount of energy absorbed by a solar collector area
during the measuring period.
ηi = Useful Heat gain = qu /AcIT
Radiation incident on the collector
41
43. 43
PHOTOVOLTAIC CONVERSION
The word Photovoltaic (PV) comes from the Greek word "photo" meaning light and
the modern word "Volt" or "Voltage”, a unit of electrical potential energy (named in
honour of the Italian physicist Alessandro Volta (1745–1827),
The devices used in photovoltaic conversion are called solar cells. When solar
radiations fall on these devices it is converted directly into electricity.
Solar cell, also called photovoltaic cell is a device that directly converts the energy
of light into electrical energy through the photovoltaic effect. The overwhelming
majority of solar cells are fabricated from silicon—with increasing efficiency and
lowering cost as the materials range from amorphous (non crystalline) to poly
crystalline to crystalline (single crystal) silicon forms.
Unlike batteries or fuel cells, solar cells do not utilize chemical reactions or require
fuel to produce electric power, and, unlike electric generators, they do not have any
moving parts.
44. 44
How does a PV Cell work?
Sunlight is composed of photons, or particles of radiant solar energy. These
photons contain various amounts of energy depending on the wavelength
of the solar spectrum.
When the photons strike a solar cell, some are absorbed while others are
reflected. When the material absorbs sufficient photon energy, electrons
within the solar cell material dislodge from their atoms.
The electrons migrate to the front surface of the solar cell, which is
manufactured to be more receptive to the free electrons. When many
electrons, each carrying a negative charge, travel toward the front surface
of the cell, the resulting imbalance of charge between the cell's front and
back surfaces creates a voltage potential like the negative and positive
terminals of a battery. When the two surfaces are connected through an
external load, electricity flows.
45. 45
Individual solar cells vary in size from about 1 cm to about 10
cm across. A cell of this size can only produce 1 or 2 watts,
which isn't enough power for most applications. To increase
power output, cells are electrically connected into a module.
Modules are connected to form an array. The term "array"
refers to the entire generating plant, whether it is made up of
one or several thousand modules.
46. 46
The performance of a photovoltaic array is dependent upon
sunlight. Climate (e.g. clouds, fog) has a significant effect on
the amount of solar energy received by a PV array and, in
turn, its performance.
The advantages associated with the solar cells are:
•They are simple compact and have a very high power to
weight ratio.
•They have no moving parts and probably yield the highest
overall conversion of solar energy into electricity.
•Theoretically the solar cell has unlimited life although in
practice they suffer from radiation damage.
47. 47
The disadvantages with the solar cells are the high cost associated with
the system fabrication. The raw material is in-expense but the production
techniques are quite expensive.
50. 50
Silicon is material generally used for making the solar cells.
Single crystal silicon cells are thin wafers about 180-220 µm in thickness,
sliced from a single crystal of p-type doped silicon. A shallow junction
(about 0.3 µm) is formed at one end by diffusion of the n-type impurity. An
anti reflection coating of silicon nitride, having a thickness of about 0.075
µm is applied on the top surface. Metal electrodes made from a Ti-Ag
solder are attached to the front and back side of the cell. On the front side
of the electrode is in the form of the metal with fingers which permit the
sunlight to go through on the back side of the electrode, completely covers
the surface. Each cell develops a voltage of 0.5-1V and a current density
of 20-40 mA/cm2.To obtain higher voltage and current, individual cells are
fixed side by side on a back up board to form an module, which in turn
are arrayed.
51. 51
Working:
The 2 steps involved in working of solar cell
•Creation of the pairs of positive and negative charges (electron–hole
pairs) in the solar cell by absorbed solar radiation.
•Separation of positive and negative charges by a potential gradient within
the cell.
The cell must be made of a material which can absorb energy associated
with photons of sunlight. Energy (E) is related to the wavelength (λ) by the
equation
E= hc/λ
h = Planck’s constant =6.62 x 10-27 ergs
c = velocity of light =3 x 108m/s, λ is in μm
Substituting these values, E=1.24/ λ
Where E is in electron-volts (eV) and λ is in μm.
52. 52
Semiconductor material like silicon, cadmium sulphide,
gallium arsenide etc are suitable for absorbing energy of
photons. In a semiconductor, the electrons occupy one of two
energy bands, the valence band and the conduction band.
The valence band has electrons at a lower energy level and
is fully occupied, while the conduction band has electrons at a
higher energy level and is not fully occupied. The difference
between energy levels of the electrons in two bonds is called
band gap energy Eg.
53. 53
Eg: Photons of sunlight having energy E greater
than band gap energy Eg are absorbed in the cell
material and excite some of the electrons .These
electrons jump across the band gap from the
valence band to the conductor band leaving behind
holes in the valence band .Thus electron –hole
pairs are created. The electrons in conductor band
and holes in the valence band can be separated
and made to flow through an external circuit, if a
potential exists within the cell.
54. 54
In silicon, the potential gradient is obtained by making cell
as a sandwich of two types of silicon p-type and n-type.
Silicon of p-type in silicon doped with some atoms of
phosphorus.
The energy levels of the conductor and valence bands in p-
type silicon are slightly higher than corresponding levels in the
n-type silicon. Thus when junction is formed a jump in the
energy levels occurs. Potential gradient is adequate to
separate electrons and poles to cause a direct electric current
to flow in the external circuit.
57. 57
Conversion Efficiency:
The behavior of solar cell is displayed by plotting its current –
voltage characteristics
Where I sc short circuit current
Voc open circuit voltage
58. 58
The max useful power corresponds to the
point on the curve which yields a rectangle
with the largest area. Values of current and
voltage at which the maximum power occurs
are Im and Vm. The ratio (ImVm/IscVoc)is
called the fill factor (ff) of the cell. Its value
obviously ranges between 0 and 1. Good
silicon solar cells have FF values greater than
0.75.
59. 59
Max conversion efficiency of a solar cell is given by the
ratio of max useful power to the incident solar radiation.
ηmax = ImVm = FFIscVoc
ITAC ITAC
Where IT =incident solar flux and AC = area of the
cell
60. 60
Applications of Photovoltaic Cells:
•Pumping water for irrigation and drinking
•Electrification for remote villages for providing street lighting and
community services.
•Telecommunication for other post and telegraph and railway
communication network.
•Space applications.
•Satellites
•Portable power supplies
•Water treatment
•Electric fences
•Toys, Watches, Calculators
•Remote lighting systems
