Non - Conventional Energy Sources
Liquid Flat-Plate Collectors
Liquid Flat-Plate Collectors
The basic parts that make up a conventional liquid flat-plate collector are (i) the absorber
plate, (ii) the tubes fixed to the absorber plate through which the liquid to be heated flows,
(iii) the transparent cover and (iv0 the collector box. The main advantage of a flat plate
collector is that it utilises both the beam and diffuse components of the solar radiation. In
addition, because of its simple stationary design, it requires little maintenance. Its principal
advantage 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 liquid heated is generally water. However, sometimes mixtures of water and
ethylene glycol are used if ambient temperatures below 0C are likely to be encountered. The
absorber plate is usually made from a thin metal sheet ranging in thickness from 0.2 to 0.7
mm, while the tubes, which are also of metal, range in diameter from 1 to 15cm. They are
soldered, brazed or pressure bonded to the bottom of the absorber plate with the pitch ranging
from 5 to 12cm. In some designs, the tubes are bonded to the top or in-line and integral with
the absorber plate. The metal most commonly used, both for the absorber plate and the tubes,
is copper. The header pipes, which lead the liquid in and out of the collector and distribute it
to the tube, are made of the same metal as the tubes and have slightly larger diameters (2 to
2.5cm).
The cover should be made of a material which is highly transparent to incoming solar
radiation and at the same time, opaque to long wavelength re-radiation emitted by the
absorber plate. Glass with low ferric oxide content satisfies these requirements. Toughened
glas of 4 to 5mm thickness is the most favoured material. This type of glass is able to
withstand thermal shock as well as the impact of objects which may fall on the collector face.
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The usual practice is to have one cover with a spacing ranging from 1.5 to 3cm between the
cover and absorber plate.
The bottom and sides are usually insulated by mineral wool, rock wool or glass wool
with a covering of aluminium foil and has a thickness ranging from 2.5 to 8 cm. The whole
assembly is contained within a box which is tilted at a suitable angle. The collector box is
usually made of aluminium with an epoxy coating on the outside for protection.
The face areas of most commercially available collectors are around 2m2, with the
length (along the sloping direction) being usually larger than the width.
Performance Analysis
An energy balance on the absorber plate yields the following equation for a steady state.
In which,
qu =useful heat gain, i.e. the rate of heat transfer to the working fluid
Ap = area of the absorber plate
S = incident solar flux absorbed in the absorber plate
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.
The flux incident on the top cover of the collector is given by
Each of the terms in the above equation is multiplied by a term called the transmissivity-
absorbtivity product () in order to determine the flux S absorbed in the absorber plate.
Thus,
In which,
= transmissivity of the glass cover system, the ratio of the solar radiation coming through
after reflection at the glass-air interfaces and absorption in the glass to the radiation incident
on the glass cover system.
= absorptivity of the absorber plate
()b = transmissivity- absorptivity product for beam radiation falling o the collector
()d = transmissivity- absorptivity product for diffuse radiation falling o the collector
The instantaneous collection efficiency is given by
Where Ac is the collector gross are (the area of the topmost cover including the frame).
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If the liquid flow rate through the collector is stopped, there is no useful heat gain and the
efficiency is zero. In this case, the absorber plate attains a temperature such that Ap S = ql.
This temperature is the highest that the absorber plate can attain and is called the stagnation
temperature. Knowledge of the stagnation temperature is useful as an indicator for comparing
different collector designs. It also helps in choosing proper materials for the construction of
the collector.
The above expression is used for the calculation od hourly collection efficiency, if q u is the
useful heat gain in one hour (kJ/h) and IT is the energy incident on the collector face in one
hour (kJ/m2-h).
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
Where r = transmissivity obtained by considering only reflection and refraction
a= transmissivity obtained by considering only absorption
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. 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
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The reflectivity = Ir/Ibn is related to the angles of incidence and refraction by the equations
I and II being the reflectivity of the two components of polarization.
For the special case of normal incidence (1=0), it can be shown that
The transmissivity r is given by an expression similar to that for.
I and II being the transmissivity of the two components of polarization.
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Consider one of the components of polarisation of a beam incident on a single cover. Because
of the fact that there are two interfaces, multiple reflections and refractions will occur.
These results can be readily extended to a system of M covers for which it can be shown
that
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 the beam of
intensity Ibn incident normally on a transparent cover of thickness c and emerging with an
intensity Il.
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Where K is the 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
In case the beam is incident at an angle 1, the path traversed trough the cover would be
(c/cos2), where 2 is the angle of refraction. Then
The extinction coefficient k is a property of the cover material. Its value varies from about 4
to 25 m-1 for different qualities of glass. A low value is desirable. If there are multiple (M)
covers then the exponent in these equations would be multiplied by M.
Example
Plot the variation of r, a and with the angle of incidence for the following cover system.
Material: Glass
Number of covers: 2
Thickness of each cover: 4mm
Refractive Index of glass relative to air: 1.52
Extinction coefficient of glass: 15/m
The transmissivities for other angles of incidence are obtained in a similar manner. Their
variation with the angle of incidence is shown below. It will be seen that the values are
essentially constant up to angles of incidence of 45. Thereafter, the values drop rather
sharply to zero as the angle of incidence increases to 90.
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Transmissivity- Absorptivity Product
The transmissivity- absorptivity product is defined as the ratio of the flux absorbed in the
absorber plate to the flux incident on the cover system, and is denoted by the symbol (), an
appropriate subscript (b or d0 being added to indicate the type of incident radiation.
Out of the fraction transmitted through the cover system, a part is absorbed and a part
reflected diffusely. Out of the reflected part, a portion is transmitted through the cover system
and a portion reflected back to the absorber plate. The process of absorption and reflection at
the absorber plate surface goes on indefinitely, the quantities being successively smaller.
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The symbol d represents the diffuse reflectivity of the cover system. It can be found by
determining the value a(1-r) for the cover system for an incidence angle of 60.
d = 0.21 for a two glass cover system
d = 0.15 for one-glass cover system
Overall loss coefficient and Heat lost from the collector in terms of an
overall loss coefficient
Heat lost from the collector, ql = UlAp (Tpm-Ta)
Ul = overall loss coefficient
Ap = area of the absorber plate
Tpm = average temperature of the absorber plate
Ta= temperature of the surrounding air (assumed to be the same on all sides of the collector)
The heat lost from the collector is the sum of the heat lost frm te top, the bttom and the sides.
Thus
ql = qt + qb + qs
qt =rate at which heat is lost from the top
qb= rate at which heat is lost from the bottom
qs= rate at which heat is lost from the sides
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
Also
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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 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 analyses. 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-dimentional flow of fluid inside the tubes be analysed.
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 tubes is W (=L2/N). Let Di and Do be the inside and
outside diameters of the tubes.
Consider a section of the absorber plate with two adjacent fluid tubes. The temperature in the
plane (Tp) will vary in the x-direction in the manner as shown below. 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 a maximum.
Taking a slice dy along the flow direction and neglecting heat conduction in the plane in that
direction, we can write an energy balance for an element dx dy of the plate.
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Plate effectiveness (): is defined as the ratio of the heat conducted through the plate to the
fluid tube, to the heat which would have been conducted if the thermal conductivity of the
plate material was infinite. A higher value of means higher rate of heat transfer to the
flowing fluid from the absorber plate
Collector efficiency factor F’ : is the ratio of heat transfer resistance from fluid to ambient
air to the heat transfer resistance from plate to ambient air and is a constant for any collector
design and fluid flow rate
Collector heat removal factor FR : it represents the ratio of actual useful heat gain rate to
the gain which would occur if the collector was at the temperature of fluid at inlet
everywhere. It is a measure of thermal resistance encountered by absorbed radiation in
reaching collector fluid.
Numerical
A solar flat plate collector has an absorber plate of area 1.5m2 and has the following data:
• Inner diameter of the water tube= 14mm
• Water tube wall thickness = 2mm.
• The tube centre-to-centre distance = 12cm.
• Water flow rate=70kg/h.
• Inlet water temperature to collector = 30oC above ambient temperature.
• Ambient Temperature = 25oC
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• Heat transfer coefficient on inside surface of water tube = 205 W/m2K
• Overall loss coefficient = 4.605W/m2K
• Solar flux absorbed by the absorber plate = 600W/m2
• Absorber plate effectiveness is = 0.9207
Adhesive used to connect tubes to absorber plate has negligible thermal resistance. Find the
heat removal factor, collector efficiency factor, the useful heat gain rate for the collector and
the instantaneous thermal efficiency of the solar collector if the solar flux incident on the
glass cover at the location is 1000W/m2.
Effect of Various Parameters on Performance
1. Selective surfaces
Absorber plate surfaces which exhibit the characteristic of a high
value of absorptivity for incoming solar radiation and a low value
of emissivity for outgoing re- radiation are called selective
surfaces. Such surfaces are desirable because they maximize the
absorption of solar energy and minimize the emission of the
radiative loss. They yield higher collector efficiencies.
2. Number of covers
It is observed that the highest efficiency is obtained with one cover
if the absorber plate is selective. With the addition of more covers,
the efficiency goes on decreasing. On the other hand, when the
absorber surface is non-selective, the efficiency increases as the
number of cover is increased from one to two. Thereafter, the
efficiency goes on deceasing with the addition of more covers.
Thus it is optimum to use only one cover if the absorber plate is
selective and two covers if the surface is non-selective.
3. Spacing
The proper spacing to be kept between the absorber plate and the
first cover, or two covers is very important from the point of view
that the heat loss from the top, the values of the convective heat
transfer coefficients are minimized. The variation of convective
heat transfer coefficient is a function of temperature difference, tilt
and service conditions. Optimum spacing is difficult to achieve.
Spacing of 4 to 8cm is suggested.
4. Effect of shading
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The main problem associated with the use of large spacings is that
shading of the absorber plate by the side walls of the collector
casing increases. Some shading always occurs in every collector
and needs to be corrected for. The shading is particularly important
in the early morning and late evening hours.
5. Collector tilt
The flat plate collectors are stationary in nature. They do not track
the sun. Thus the tilt given at installation is critical based on
maximum insolation. The parameters are latitude of the location,
application (space heating or refrigeration which depends upon
season), etc.
6. Fluid inlet temperature
It is an operational parameter which strongly influences the
performance of a flat-plate collector.
It is seen that the efficiency of the collector deceases more or less
linearly with increasing value of fluid inlet temperature from 30C to
90C. this decrease is because of the higher temperature level at which
the collector as a whole operates when the fluid inlet temperature
increases. Because of this, the top loss coefficient as well as the
temperature difference with the surroundings increase and the useful heat
gain decreases.
7. Cover transmissivity
The transmissivity of the cover affects the performance of a
collector significantly. The higher the transmissivity( i.e. lower the
extinction coefficient of the cover material), the better is the
performance of the collector
8. Dust on the top cover
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The calculations are done on the basis of the assumption that the
top covers are clean. But in reality dust starts accumulating over a
period of time. Suitable correction factors needs to be introduced
time to time. The amount of dust accumulated is a function of
locality, season, etc. A cleaning frequency of 20 days is suggested
for consistent performance.
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