Problem (1)

Calculate the overall loss coefficient for a flat plate collector with two glass covers with the
following data:

Size of absorber plate (area) = 0.9 m x 1.9 m

Spacing between plate and first cover = 4 cm

Spacing between first and second cover = 4 cm

Plate emissivity, , Glass cover emissivity ,

Collector tilt , mean plate temperature,

Ambient air temperature,

Wind speed

Back insulation Thickness

Side insulation thickness

Thermal conductivity of insulation = 0.05

Solution:

𝑇𝐶

𝑇𝐶1

𝑇𝑃𝑀
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#1 #2 #3

325 305 174.8 167.6 127.9

326 307 165.7 160.7 153.4

326.4
307.4 162 161.1 158.4

326.5 307.5 161.1 160.4 161.1

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350.8236
Problem (2)
Use the top loss empirical equation to calculate the top loss coefficient for the data of
previous problem.
Take

Compare the answer with the value obtained by the exact procedure adopted in problem
(1).

Solution:

[ ]

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[ ]

( )( )

( )( ) ( )
[ ] [ ]

In Problem 1 we calculated

Heat transfer loss coefficient for 2 glass covers =

Heat transfer loss coefficient for 1 glass cover =

Conclusion : adding a second glass cover saves more heat energy to the collector
Problem (3)
Determine the collector top loss coefficient for a single glass cover ( M=1 ) with the following
specifications:

Plate to cover spacing = 25 mm

Plate emittence,

Ambient temperature , mean plate temperature =

Collector tilt = , wind heat transfer coefficient

Solution:

[ ]

( )( )

1
( )( )
[ ]
( )( )
[ ( ) ]
Problem (4)
For the collector of Problem (3) with a top loss coefficient of 6.6 .

Calculate the overall loss coefficient with the following additional specifications:

Back insulation thickness = 50mm, Insulation conductivity = 0.045

Collector bank length = 10m , Collector bank width = 3m , Collector thickness =75 mm

Edge (side) insulation thickness = 25 mm

Solution:

, 1 , , ,

( 1 )
1
 Solar Collector Efficiency

Defining Collector Efficiency

Solar hot water collectors are tested by third party laboratories in order to obtain product
certifications such as Australia Standards (AS/NZS 2712), SRCC OG100 and Solarkeymark. The
testing provides a set of performance variables for each solar collector that can be used to
determine the heat output under a set of given environmental and operating conditions.
These values can be used in a formula to calculate an instantaneous heat output value. That,
however, isn't particularly useful to the average end user, as it is only a snapshot of performance,
and not total annual output. To obtain a more accurate estimate of energy over a full year,
complex modeling software is required. For large scale commercial projects, Apricus uses
modeling software to complete forecasts of expected energy output and savings.
For a simple residential applications, such complex modeling is simply not required, with basic
rule of thumb sizing sufficient, as provided here.
The link  http://www.apricus.com/html/solar_collector_size.htm#.VmTvnFQdAjU

Collector Surface Area

Solar collector performance variables can be used to promote the "performance" of a solar
collector; in particular the peak efficiency value is used. A value of 60-80% is common for most
thermal solar collectors, but this value needs to be taken with a grain of salt, with the surface area
it is based on considered.
There are three different surface areas that may be used to define the size of a thermal solar
collector: Gross, Aperture & Absorber.
Gross Area
Calculated as the total width x height.
This measure therefore can include the frame, manifold casing, and in the case of evacuated tube
collectors even the spaces between the tubes. It is a good value to look at when considering if a
solar collector will fit on a roof, but not really useful for comparing efficiency.
Aperture Area
 Flat Plate Collectors: Calculated as the area of the glazing (glass) exposed to sunlight.
 Evacuated Tube Collectors: Calculated as the inner diameter of the clear glass tube.
Aperture has been adopted by most countries and industry associations as the standard surface
area to use when quoting efficiency values
Absorber Area
 Flat Plate Collectors: Calculated as the exposed area of the solar absorber.
 Evacuated Tube Collector: Calculated as the diameter of the round absorber, or flat area
of the absorber for evacuated tubes with absorber fins inside.

Note that Aperture, Absorber and Gross measurements may differ between test labs and
countries based on their definitions. Eg. Solarkeymark and SRCC are different.

Efficiency Comparisons
As stated above, Aperture is the most widely accepted surface area to use when looking at
performance variables. This is very important, as using the wrong type of surface area greatly
effects the values.
Example:
The "peak efficiency" value for an AP solar collector is 68.7% based on Aperture area of
2.83m2. If based on gross area of 4.4m2, this value is only 43.7%.
A flat plate collector may have a performance value of 75% based on aperture area, but because
the gross area is almost the same as aperture, the gross value will only be slightly lower. So
comparing a flat plate collector's gross area to the gross area of an evacuated tube collector
provides very misleading results.
Sun Angle (IAM)
Depending on the design of the collector, the output may change as the angle between the
collector and the sun changes. This is referred to as Incidence Angle Modifier (IAM). A more
layman friendly term to use is the Sun Angle Factor. Flat plate collectors generally all have the
same curves, but evacuated tube collectors and those with reflectors can have very different
curves throughout the day. For this reason it is important to understand and consider the Sun
Angle Factor for collectors when doing a comparison.
The two types of IAMs are as follows:
 Transversal IAM measures the change in performance as the angle of the sun in relation
to the collector changes through the DAY.
 Longitudinal IAM measures the change in performance as the angle of the sun in relation
to the collector changes through the YEAR.

Below are examples of IAM curves for the average flat plate collector, and then the Apricus AP
evacuated tube collector.
For flat plate collectors, both the longitudinal and transversal curves follow the same path, which
is close to a cosine curve. As the angle of the sun passes the 45o point the amount of light the
collector receives rapidly drop, reaching zero at 90o.
The graph shown above is for the Apricus AP evacuated tube solar collector
(Link for More info & Reference : http://www.apricus.com/html/solar_collector.htm#.VmTwRlQdAjU )
. For such evacuated tubes collectors that have the tubes installed in the vertical orientation (up-
down, not left-right) the longitudinal curve is virtually the same as a flat plate. The transversal
curve, however, differs greatly, with the actual shape of the curve depending greatly on the
spacing of the evacuated tubes and if a reflective panel is present or not. The IAM angle factors
can be multiplied by an energy output calculation (outlined earlier) to obtain the actual output from
the collector at a certain time of the day. Below are the raw values for each angle which are
required if doing solar collector output calculations.

0o 10o 20o 30o 40o 50o 60o 70o 80o 90o

Longitudinal 1.00 1.00 1.00 0.99 0.97 0.92 0.84 0.70 0.45 0.00

Transversal 1.00 1.02 1.08 1.18 1.35 1.47 1.39 1.57 0.95 1.00
The shape of the transversal IAM curve is linked to the round shape of the evacuated tubes and
the space between the tubes that allow light through at midday.

Due to the 360o absorber surface, Apricus evacuated tubes Passively Track the sun throughout
the day, as the round absorber is facing the sun from 7am to 5pm. This is a key advantage over
flat plate collectors than only have maximum sun exposure (angle factor = 1) at midday.
Passive tracking of Apricus AP evacuated tube solar collectors and the resultant Sun Angle
Factor adjustment is required to get true output values. Ignoring this and just comparing to
another collector based on the performance variables would not provide accurate real life output
values. Modeling software packages such as Polysun (used by Apricus) take into full
consideration both the longitudinal and transversal IAM factors to provide a very accurate output
model for a system over a typical full year of operation.

REFERENCE: Apricus Tech Centre catalogue

Link : http://www.apricus.com