Master's thesis

Solar heating of a residential building in Kazakhstan
by
Ernar Aidargazaevich Makishev
A thesis submitted to the graduate faculty
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
Major: Mechanical Engineering
Program of Study Committee:
Michael B. Pate, Major Professor
Ron Nelson
Partha Sarkar
Iowa State University
Ames, Iowa
2007

- ii -
TABLE OF CONTENTS
1. INTRODUCTION.......................................................................................1
1.1. General Information........................................................................... 2
1.2. Climate............................................................................................... 3
1.3. Why there is a need for solar heating in a residential building ......... 4
1.4. Model description used in this study ................................................. 4
2. Radiation determination............................................................................11
2.1. Actual data ....................................................................................... 12
2.2. Solar radiation estimation using computer programming ............... 14
2.3. Extraterrestrial Radiation................................................................. 15
2.4. Clear-sky radiation........................................................................... 17
2.5. Radiation on a sloped surface .......................................................... 22
2.6. Optimal slope................................................................................... 26
2.7. Absorbed radiation........................................................................... 27
2.8. Utilizability ...................................................................................... 32
3. Solar Collectors.........................................................................................35
3.1. Energy balance in a flat-type solar collector ................................... 37
3.2. Overall loss coefficient .................................................................... 39
3.3 The heat transfer coefficient ............................................................. 44
4. Solar heating system simulation ..............................................................46
4.1. Heat exchangers ............................................................................... 47
4.2. Thermal energy storage.................................................................... 47
4.3. Radiant heating ................................................................................ 50
4.4. Programming.................................................................................... 53
4.5 Economy ........................................................................................... 53
5. Analysis and Results .................................................................................56

- iii -
6. Conclusion.................................................................................................62
REFERENCES..............................................................................................64
Appendix A. Computer program ..................................................................66
A.1. Final script....................................................................................... 66
A.2. Radiant floor program..................................................................... 75
A.3. Calculation of overall heat loss coefficient, useful gain, and outlet
water temperature.................................................................................... 76
A.4. Absorbed radiation program. .......................................................... 78
A.5. Calculation of an optimum slope for incident radiation Isotropic-sky
model....................................................................................................... 79
A.6. Calculation of transmittance of glass.............................................. 81
A.7. Heating load calculations................................................................ 82
A.8. Degree to radians conversion.......................................................... 85
A.9. Radians to degree conversion ......................................................... 85
A.10. Calculation of optimal degree for absorbed radiation. ................. 85
Appendix B. Solar radiation data..................................................................88
B.1. Diffuse radiation.............................................................................. 88
B.2. Number of hours of sunshine .......................................................... 89
B.3. Global Radiation 1964 to 1991 ....................................................... 89
B.4. Specifications for Form 4 and the File of Instantaneous Values of
Direct Solar Radiation............................................................................. 91
B.5. Specifications for Forms 1A & lB and Description File................. 93
B.6. 4.2. Specifications for Form 2 and Daily Sums File...................... 97
Appendix C. G series Solar Collectors .......................................................100
Appendix D. Building envelope surfaces areas..........................................113
Appendix E. Climate data ...........................................................................115

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LIST OF FIGURES
Figure 1: South elevation................................................................................ 5
Figure 2: East elevation ........................................................................................6
Figure 3: North elevation......................................................................................6
Figure 4: West elevation.......................................................................................6
Figure 5: Mean monthly sums of global and diffuse radiation on a horizontal
surface (Data for diffuse radiation covers 2 years from 1990 to 1992,
for global radiation covers 28 years from 1964 to 1992) ................. 13
Figure 6: Solar radiation program flow diagram............................................... 16
Figure 7: Extraterrestrial radiation on a horizontal surface.............................. 17
Figure 8: Mean monthly sums of extraterrestrial and actual global radiation on
a horizontal surface (Data covers 11 years from 1964 to 1991)....... 18
Figure 9: Clear-sky radiation on a horizontal surface ....................................... 21
Figure 10: Extraterrestrial and clear-sky radiation on a horizontal surface ..... 21
Figure 11: Mean monthly sums of global, global clear-sky and diffuse
radiations on a horizontal surface ..................................................... 22
Figure 12: Comparison of diffuse radiation calculated with the Collares-Pereira
and Rabal correlation and actual data (1992). .................................. 24
Figure 13: Comparison of actual radiation on a horizontal surface with
isotropic-sky and KT model radiation on a sloped surface (45
degrees) ............................................................................................. 26
Figure 14: Comparison of optimal slopes for maximum incident radiation and
maximum absorbed radiation (azimuth angle is zero)...................... 27
Figure 15: Average transmittance absorptance product fluctuation.................. 30
Figure 16: Comparison of daily radiation on a horizontal surface to absorbed
radiation on sloped surfaces with different angles............................ 32

- v -
Figure 17: Comparison of values of absorbed radiation on sloped surfaces with
different angles (W/m2).................................................................... 33
Figure 18: G series solar collector, Thermal systems LTD............................... 37
Figure 19: Heat transfer processes in a single glass solar collector. ................. 38
Figure 20: Flow chart of solar collector simulation. ......................................... 40
Figure 21: Solar space heating system............................................................... 46
Figure 22: Flow chart of the simulation ............................................................ 53
Figure 23: Cost comparison for an average year............................................... 56
Figure 24: Ratios of back up system load to solar heating system load (22 years
of simulation).................................................................................... 59
Figure 26: Present worth of a solar space heating system and an electric heating
system with different electricity costs. ............................................. 60

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LIST OF TABLES
Table 1: Design temperatures and wind speed for Astana, Kazakhstan [4]........3
Table 2: Material characteristics [5]....................................................................8
Table 3: Heat exchanger characteristics ............................................................ 47
Table 4: Propylene glycol thermodynamic properties [14]............................... 48
Table 5: Economic parameters [1]..................................................................... 54
Table 6: Present worth of heating systems ........................................................ 57
Table 7: Present worth of heating systems ........................................................ 58
Table 9: Present worth of solar space heating system and electric heating
systems................................................................................................. 60

- 1 -
1. INTRODUCTION
The goal of this Master's thesis is to design a residential house in Astana,
Kazakhstan, that does not consume energy for space heating from conventional power
plants or autonomous power generators. Space heating is the largest part of energy
consumption in cold climates. The primary source of energy chosen for this study is
solar energy. A solar energy building is a subclass of the more general term "zero energy
building."
The term "zero energy building" was coined by the Department of Energy of the
United States as part of its program to design more efficient buildings. There are various
names used across the literature pertaining to the same definition, including ‘green
buildings’ and ‘passive housing.’
Usually when we hear the term "zero energy building," we may immediately
visualize buildings equipped with alternative energy-harnessing devices. However, this
term represents an even bigger area of alternative energy technology. Human waste
utilization, for example, is in part zero energy technology.
Zero energy buildings must comply with stringent, specific criteria, such as:
• Exploiting alternative energy technology to supply energy needs;
• Reducing heat loss due to conduction through exterior materials;
• Diminishing water consumption and waste through more rational water use;
• Decreasing the amount of pollution produced by power plants for the heating
and cooling of residential houses.

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In addition, there are many other criteria that are related to the environmental
aspects of a building that are outside the scope of this thesis.
There is no part of the world that is not touched by rising energy costs. Even
though Kazakhstan has tremendous amounts of energy available to it, the exportation of
these sources is more profitable than fulfilling domestic market needs. Hence, the prices
charged by energy carriers are increasing. Eventually, these prices will reach the point
where alternative energy technologies, and solar energy technology in particular, will be
affordable for the middle class. The potential of solar energy use is not limited to space
heating. Solar cooling, water distillation, electric power generation, and many other
fields ensure a promising future for solar energy.
Solar energy is an attractive area of alternative energy technologies research, not
only because of its availability as an energy source and because of the high prices
charged by conventional energy carriers, but also due to the fact that most other
alternative energy technologies use energy sources that would not exist without solar
energy (i.e., wind as the result of the asymmetrical heating of the atmosphere or biomass
as the result of photosynthesis).
1.1. General Information
Kazakhstan, once a part of the USSR, is situated in the middle of Asia.
According to the recent July 2006 census, the population is 15,233,244 people [1].
Astana (formerly Celinograd) was designated the capital of Kazakhstan in 1997. The
following are the geographical coordinates of Astana: 51.18° N 71.45° E. Its elevation is

- 3 -
at 1148 feet or /350m, which is relatively average. Ames, Iowa, for example, is 1158 ft /
353 m above the mean sea level.
There are 3 coal power plants in Astana [2]. Each one produces 110 Mw of
electricity and provides residential space heating. The main type of heating is central
heating with hot water from power plants being delivered to the buildings. The
population of the city is 600,000 people, growing at a rate of 0.352 % (2007 est.) [2]. As
a consequence of this, an energy shortage is expected in the future.
1.2. Climate
According to the Köppen Climate Classification System, the best description of
Astana's type of climate is B s k, where B stands for arid climate, s stands for steppe and
k stands for cold arid climate [3]. Even though January has the lowest average minimum
temperature, Table 1 shows that February is the coldest month. From the engineering
point of view these conditions complicate the implementation of solar technologies since
the solar position in winter is low and the climate is harsh.
Table 1: Design temperatures and wind speed for Astana, Kazakhstan [4].
Data Value f,%
Coldest month/Design temperature 2/ -21.5 °C
Wind speed, mph
k/h
28.8
12.9
1
Hottest month/Design temperature 7/28.1 °C
Note: f is the annual cumulative frequency of occurrence.

- 4 -
This climotological definition is geographically similar to most other interior
locations of large land masses as Kazakhstan is situated in the middle of Eurasia and does
not have marine access (except for the Caspian Sea, which does not flow directly into any
international waters).
As we can see from Tables E.2 and E.3, the cooling load in the summer is not a
significant part of the annual energy consumption; therefore, cooling loads are assumed
to be negligible during the summer period.
1.3. Why there is a need for solar heating in a residential building
Kazakhstan has experienced a relatively high demographic increase since the fall
of the Soviet Union. Economic improvement and a relatively stable political situation
have encouraged people to obtain mortgages for new apartments. Therefore, there is a
need for affordable housing for the growing population. Currently, most of the urban
population lives in condominiums within the city limits.
Astana itself is a rapidly growing city (with an increase in population from 1997
to 2007 of 500 % [2]), and suburbs are only just starting to be developed. Future
shortages in energy supplies and the above-mentioned boom in suburban development
indicate a large potential market for alternative energy technologies such as solar space
heating.
1.4. Model description used in this study
The model building is a typical American-style three-bedroom residential house
[5]. The reason for choosing an American-style building is the efficiency of its

- 5 -
construction. Most residential houses in Kazakhstan are built in the same way as they
were 70 years ago: brick enveloped with poor inner insulation and low quality windows.
They do not have ventilation or cooling systems. Uncontrolled infiltration and poor
insulation design lead to uncomfortable conditions inside of these buildings. Conversely,
American-style buildings (2x6 frames) show good results in reducing heating and cooling
loads and providing comfortable conditions for their inhabitants. In addition, the absence
of ventilation in Kazakhstan buildings increases the risk of radon contamination within
the building [6]. A full description of the building is in Appendix D. Figures 1 to 4 show
exterior of the building that is used in the simulation of solar space heating.
The heating area is:
1st = floor1534
2
ft
Unheated area (garage) = 791
2
ft
Figure 1: South elevation

- 6 -
Figure 2: East elevation
Figure 3: North elevation
Figure 4: West elevation

- 7 -
1.4.1. Heating loads
Heating loads are calculated using standard ASHRAE methods [6] for the calculation
of heating loads for residential houses. The total exposed area of the house is listed in
Appendix D.
ASHRAE methods use the following approximations [6]:
• The average wind speed is 15 mph;
• The temperature in uninsulated area is at the outdoor temperature;
• Disregard of the effects of rooms on heating load calculations;
• The unit leakage area (average construction type) [6];
2
2
0.04ul
in
A
ft
= (1.2)
The exposed surface area (gross wall area);
2
2905esA ft= (1.2)
The average unit leakage area:
L es ulA A A= (1.3)
Where:
- esA is the building’s exposed surface area, 2
ft ;
- ulA is the unit leakage area, 2 2
/in ft .
Infiltration driving force can be calculated using following formula:
,
1 2( ( ))
1000
L flue
o
L
A
I H T I I
A
IDF
+ × × + ×
= (1.4)
Where:

- 8 -
- H is the building’s average stack height, ft;
- 1 2, ,oI I I are coefficients;
- T is the difference between inside and outside air, K;
- ,L flueA is the flue effective leakage area, ft;
- LA , is the average unit leakage area, ft.
Table 2: Material characteristics [5]
Envelope Insulation type
Basement walls 2” rigid R10 Dow insulation on exterior;
2x6 walls R19 batts;
Attic R46 blown fiberglass;
Windows Low-e windows 'Pella';
Note: Window and door properties are specified on a floor plan.
Infiltration rate can be calculated by:
L60 (A )
ACH=
IDF
V
× ×
(1.5)
Where:
- ACH is air change per hour;
- V is the building volume, 3
ft
- LA is the average unit leakage area, ft;

- 9 -
- Infiltration driving force.
Required ventilation flow rate can be found as:
0.01 7.5 ( 1)v cf brQ A N= × + × + (1.6)
Where:
- cfA is the building conditioned floor area, 2
ft ;
- brN is the number of bedrooms.
Heat losses through the building envelope are calculated by:
Q U A T= (1.7)
Where:
- U is material conductivity, 2
BTU
h ft F
;
- A is gross area, 2
m ;
- T is the temperature difference between inside and outside air, F.
1.4.2 Radiation influence
The sun adds great amounts of energy to the heating loads; however, considering
the severe climate conditions, this amount of energy can be disregarded to add reliability
to the system.
1.5.3. Programming
A computer program that calculates heating loads has been developed to work
with the main program of solar heating system simulation. This computer program is a

- 10 -
'black-box' type of program. The only input parameter is the number of a month. The
output is the heating load in BTU/h. A full listing of the program is a part of the main
program in Appendix A. Heating loads are calculated for the heating season, which starts
in October and ends in March. Since we do not have reliable daily temperature data,
average temperatures have been used in the simulation.

- 11 -
2. Radiation determination
In order to use solar energy, an estimation of the amount of solar energy that is
incident on a particular location is essential. Solar energy that is incident on the Earth
depends on several factors, such as solar trajectory, the change of seasons, atmospheric
characteristics, and so on.
Solar trajectory has been studied since ancient times and precise methods have
been developed to measure it. On the other hand, the atmospheric influence on solar
radiation had not been researched until meteorology was established as a science in the
nineteenth century.
The atmosphere acts as a protective shield against solar radiation. There are two
major obstacles that determine the amount of energy that passes through the atmosphere:
a) scattering and b) absorption. Scattering mostly occurs due to the interaction of
radiation with air, water, and dust particles. The major effect of scattering is the result of
the size of these particles. Increasing levels of air pollution limit solar energy incidence
on the earth’s surface.
The absorption of solar energy mostly occurs due to the absorption of radiation by
the ozone layer. However, many other atmospheric components absorb solar energy as
well. These components target certain wavelengths of solar radiation. While ozone tends
to absorb ultraviolet radiation (wavelengths shorter than 0.29 mµ ), carbon dioxide and
water vapor absorb infrared radiation.

- 12 -
2.1. Actual data
The radiation data for Kazakhstan is obtained from the World Radiation Data
Centre, which is maintained by the Russian Federal Service for Hydrometeorology and
Environmental Monitoring.
The radiation measuring station closest to Astana is located in Semipalatinsk,
which was the nuclear weapons testing area for the former USSR, located 500 km from
the city. The coordinates of this station are at 50.21° N and 80.15° E while the elevation
is 206 meters above sea level. The accessible data for this particular location are as
follows:
- Global radiation, from 1964 to 1992;
- Diffuse radiation, from 1990-1993;
- The number of hours of sunshine, from 1962 to 1992;
- The net total radiation, from 1964 to 1992.
Global radiation is the total radiation (beam and diffuse) on a horizontal surface.
Obviously, diffuse radiation is a part of global radiation; however, there is no information
on the ground reflectivity of the measurement area, which influences diffuse radiation
and other parameters of measurements. Figure 5 compares the mean monthly sums of
global and diffuse radiation on a horizontal surface.
Net total radiation is the difference between global radiation on a horizontal
surface and the amount of radiation emitted by the earth at this point. Net total radiation
is measured by placing two pyranometers, one facing the earth and one facing the sky, in
order to record the differences. This data is designated as meteorological study and is
useless for radiation estimation in terms of solar energy usage.

- 13 -
The number of hours of sunshine was measured by placing special paper next to a
lens that burns into the paper, making a trace line of sunshine with respect to time.
Figure 5: Mean monthly sums of global and diffuse radiation on a horizontal surface
(Data for diffuse radiation covers 2 years from 1990 to 1992, for global radiation covers
28 years from 1964 to 1992)
An example of a data file is listed in Appendix B. The data is provided in the form
of a text file with columns of numbers. The specification for the file explains particular
numbers by their position in the line. There are several different specifications for
different types of data. The first column of data file contains the type of data form, the
location code, the date, and the radiation code. The radiation code is specified by the
method by which radiation data were measured. The following columns depend on the
data form and can be filled, for example, with the daily means of global radiation
incidence on a horizontal surface in MJ/m2.

- 14 -
The first challenge was collecting the data and studying the specification in order
to decipher the data. The data is kept on perfo-cards, which can be understood by
consideration of the format of the data and the time it was measured. Putting the data into
a Microsoft Excel spreadsheet for further manipulation was the easiest way to sort the
values, provided that the data are global and diffuse radiation is on a horizontal surface.
Data regarding global radiation cover 27 consecutive years of measurements from 1964
to 1990 while data regarding diffuse radiation are available for only 3 years from 1990 to
1993.
Using Microsoft Excel's 'mid' function, we can separate the data into lines
according to the position they occupy. Then, using 'AutoFilter Data' we can sequentially
apply a particular template to a specific line to subtract the needed values. For example,
mean monthly sums of global radiation on a horizontal surface can be used for global
radiation values.
2.2. Solar radiation estimation using computer programming
A computer program has been developed that simulates solar radiation incidence
on Earth. The initial conditions are discussed in the introduction. A complete listing of
the Matlab code for the main program and subprograms is included in Appendix A. A
description of the program structure is described in the following paragraphs. Figure 6 is
a flow diagram of the computer program. All units for solar energy calculations are
specified in SI.

- 15 -
2.3. Extraterrestrial Radiation
Extraterrestrial radiation is radiation that would be incident on a horizontal plane
on Earth with the absence of atmosphere. For engineering purposes, it is useful to know
extraterrestrial radiation for comparison with measured and calculated values.
We need to know the extraterrestrial radiation value for comparison with the
actual data listed in Appendix B. First of all, the value of radiation incident on a
horizontal surface with respect to the atmosphere can never be higher than the
extraterrestrial radiation value. If it is higher, it shows that the data is erroneous or that
there is a mistake in the calculations.
Duffie & Beckman [7] recommend the following formula for calculating
extraterrestrial radiation
sc
o
2
G 360 (n)
H =(24 3600 ) (1+0.033 cos cos X cos( (n)) sin( (n))+ (2.1)
365 180
J
sin X sin( (n))
m
n× ×
Where:
- n is the day of the year;
- X is the latitude;
- is the declination;
- is an hour angle;
- scG is a solar constant.

- 16 -
Figure 6: Solar radiation program flow diagram
Initial data
Reading actual
daily radiation on
a horizontal
surface from file
Calculating daily
extraterrestrial
radiation on a
horizontal surface
Connecting 24
hours of radiation
data to the amount
of daylight
Juxtaposing data
(Figures 7-10)
Clear-sky
radiation on a
horizontal
surface
Calculating the
clearness index Kt
Calculating isotropic-
sky radiation on a
sloped surface
(45 degrees).
Calculating KT model
radiation on a sloped
surface (45 degrees).
Estimating radiation
on a sloped surface
from the actual data
(45 degrees).
Comparison, Figure 13

- 17 -
Note:
(n)
180
×
converts degrees to radians. Matlab works with radians by default;
therefore, simple functions were developed to convert degrees to radians and back again.
These functions are listed in Appendix A ('rd', 'dr').
Figure 7: Extraterrestrial radiation on a horizontal surface
Figure 7 shows the change of extraterrestrial solar radiation in 2
MJ
m
with respect
to the number of days in a year. Figure 8 has been included here to show relationships
between extraterrestrial radiation and actual data.
2.4. Clear-sky radiation
The clear-sky radiation model is a method of estimating clear-sky solar radiation
with respect to the zenith angle and altitude for a standard atmosphere. This method
distinguishes four different types of standard climates.

- 18 -
Figure 8: Mean monthly sums of extraterrestrial and actual global radiation on a
horizontal surface (Data covers 11 years from 1964 to 1991)
Duffie & Beckman [7] named these types as: tropical, midlatitude, subarctic
Clear-sky beam radiation on a horizontal surface is
coscb on b zG G= (2.2)
Where:
- onG is normal extraterrestrial radiation;
- b is the atmospheric transmittance for beam radiation;
- cos z is a zenith angle.
The atmospheric transmittance for beam radiation is presented as

- 19 -
0 0 1 exp
cos
b k
z
k
a r a r r= + (2.3)
Where:
- 0r , 1r , kr is the correction factors for climate types;
- 0a , 1a , k is the functions of altitude;
- cos z is a zenith angle.
Due to the fact that b is a function of z , which changes with the time of day,
the atmospheric transmittance must be computed for beam radiation for each daylight
hour of each day of a year. Knowing the sunset hour angle s is important since the
sunset hour angle is the opposite of the sunrise hour angle. The sunset hour angle can be
found from the following formula:
sin sin
cos (2.4)
cos cos
or
cos tan tan (2.5)
s
s
Lat
Lat
Lat
=
=
Where:
- Lat is a latitude;
- is the declination;

- 20 -
The double value of this angle gives us the angle of sun movement from sunrise
to sunset. It is also known that one hour equals 15o
of sun movement. Therefore, the
number of daylight hours is:
( )
2
tan tan
15
N Lat= (2.6)
The values for 0r , 1r , kr are [7]:
0
1
0.99
0.99
1.01k
r
r
r
=
=
=
(2.7)
The values for 0a , 1a , k can be found as
2
0
2
1
2
0.4237 0.00821 (6 )
0.4237 0.00595 (6.5 )
0.2711 0.01858 (2.5 )
a A
a A
k A
=
= +
= +
(2.8)
Where:
- A is an altitude , m.
The result of the calculation of the clear-sky model is shown in Figure 9. We can
visualize the difference between 'ideal' extraterrestrial radiation on a horizontal surface
and clear-sky model results, which are shown in Figure 10. Even though the clear-sky
model can give a good approximation of global radiation values, it considerably
underestimates global radiation (Figure 11). Switching to different types of climate did
not improve the clear-sky model.

- 21 -
Figure 9: Clear-sky radiation on a horizontal surface
Figure 10: Extraterrestrial and clear-sky radiation on a horizontal surface

- 22 -
Figure 11: Mean monthly sums of global, global clear-sky and diffuse radiations on a
horizontal surface
The clear-sky model is easy to understand but not precise enough for use in the
estimation of radiation. Correction factors for four different types of climate do not take
into account many factors that cause the scattering and absorption of beam radiation.
2.5. Radiation on a sloped surface
2.5.1. Isotropic sky
The isotropic-sky model implies that global radiation is isotropic, which means
that that the sum of diffuse and beam radiation does not depend on the angle of attack.
Diffuse radiation data retrieved from WRC [8] contain a lesser number of years than that

- 23 -
of global radiation data. Hence, the Collares-Pereira and Rabal correlation for separation
diffuse radiation from global radiation can provide more reliable values.
The Collares-Pereira and Rabal describes the values of beam and diffuse radiation
as a function of TK [7].
2 3 4
0.17 0.99
0.17 0.75 (1.188 2.27 9.473 21.865 14.648 )
0.75 0.80 ( 0.54 0.632) (2.11)
0.80 (0.2)
T d
T d T T T T
T d T
T d
if K H H
if K H H K K K K
if K H K H
if K H H
=
< = + +
< < = +
=
Figure 12 juxtaposes the results calculated with this correlation and actual data
for the year 1992. The Average Clearness index TK was derived from 23 years of data
for global radiation and extraterrestrial radiation on a horizontal surface.
2.5.2. KT method
KT stands for Klein and Theilacker, who developed a more detailed computation
of the estimation of solar radiation. This method assumes that diffuse and ground
reflected radiations are isotropic. This method shows better results than the isotropic-sky
method.

- 24 -
Figure 12: Comparison of diffuse radiation calculated with the Collares-Pereira and
Rabal correlation and actual data (1992).
The monthly average radiation on a collector is
KTH H R= (2.12)
Where:
- R is the ratio of the total radiation on the tilted surface to the total radiation on
a horizontal surface;
- H is the total radiation on a horizontal surface.
The ratio of a total radiation on the tilted surface to the total radiation on a
horizontal surface can be found by:

- 25 -
( ) ( )( )cos( )
sin cos sin cos 2 cos
cos( ) 2
1 1
(2.13)
2 2
d
s s s s s s s
d
g
HLat b
R a
d Lat H
H
H
! ! !! ! ! ! !!= + +
+
+ +
1
1
1
0.409 0.5016 sin( 60)
0.6609 0.4767 sin( 60)
sin cos
cos ( tan tan )
min (2.14)
cos ( tan( ) tan )
cos ( tan ( ) tan )
s
s
s s s
s
s
a
b
d
Lat
Lat
Lat
!= +
!=
! ! !=
! =
!! =
Where:
- g is the ground reflectance;
- Lat is the Latitude;
- H is the total radiation on a horizontal surface;
- dH is the diffuse radiation on a horizontal surface;
- is the surface slope;
- s
! is the hourly angle.
Figure 13 shows the comparison among radiation values obtained from actual
data, the KT mode, and the isotropic-sky model. We can see that both KT and clear-sky
models show a plausible approximation of solar radiation on a sloped surface.

- 26 -
Figure 13: Comparison of actual radiation on a horizontal surface with isotropic-sky and
KT model radiation on a sloped surface (45 degrees)
2.6. Optimal slope
The optimal slope is a slope that allows the surface to receive the maximum
amount of incident radiation. Using the Matlab optimization function 'fminsearch' we can
find the optimal slope angle for receiving the maximum amount of solar radiation on a
sloped surface. We assume that the surface azimuth angle is zero, which means that the
collector should be placed along the north-south axis.
Figure 14 graphically shows that change with respect to the time of the year. As
we can see for the coldest month, the optimal slope is very high (up to 80 degrees) since
the latitude of the location is high. This fact corresponds to some researchers'
recommendations [7] for installing solar collectors on walls as a way to improve solar
energy absorption at wintertime and eliminating precipitation influence on performance.

- 27 -
Empirical values for the optimal slope are latitude value plus 15 degrees in the
winter and latitude value minus 15 degrees in the summer [9]. The effect of the slope on
the absorption of solar radiation is discussed below.
Figure 14: Comparison of optimal slopes for maximum incident radiation and maximum
absorbed radiation (azimuth angle is zero).
2.7. Absorbed radiation
Absorbed radiation is a function of plate and cover characteristics and the incident
angle of radiation. Since glass is the most common material for cover, all characteristics
of cover are assumed to be independent of wavelength, which is a good assumption for
glass. Glass with low iron content ('water white') is a good material for cover since it has
high transmittance.
For application as solar collectors it is convenient to use a transmittance
absorptance product ( )" for the calculation of the amount of radiation that is

- 28 -
transmitted to the absorber plate. The transmittance absorptance product ( )" is a figure
of merit that tells us how much energy passing through the cover is reflected by the
absorber plate and reflected back by the cover.
( )
1 (1 ) d
"
"
"
= (2.15)
Where:
- is the transmittance of the cover;
- " is the absorptance of the cover;
- d , is the reflectance of the absorber plate for diffuse radiation.
Reflectance of the absorber plate contributes a great deal to the overall
performance of a solar collector. The absorber plates of modern solar collectors have two
major characteristics: high absorptance of solar radiation and low emmitence in a long-
wave spectrum (i.e., selective surfaces).
A Matlab code for solar radiation estimation (Appendix A) includes transmittance
absorptance product ( )" calculations (Figure 15). Assuming unpolarized radiation, we
can calculate perpendicular and parallel components of unpolarized radiation to obtain
the transmittance absorptance product.
2
2 1
2
2 1
2
2 1
2
2 1
1 1
2
sin ( )
sin ( )
tan ( )
tan ( )
sin
sin
r
r
n
# =
+
=
+
=
(2.16)
Where:

- 29 -
- r# ,is the perpendicular component of incident radiation;
- r is the parallel component of incident radiation;
- 1 is the angle of incident radiation;
- 2 is the refraction angle of incident radiation.
The average transmittance of glass cover is the average transmittance of two
components:
1 11
2 1 1
r
r r
r r
#
#
= +
+ +
(2.17)
Where 'r' stands for refraction losses;
2
exp
cos
a
KL
= (2.18)
Where:
- K is the extinction coefficient assumed to be 4 1
m for low iron glass;
- L is the glass thickness, m;
- The subscript 'a' stands for absorption losses.
Overall transmittance of a single cover can be found as:
a r$ (2.19)
Absorptance of a solar collector cover can be found as:
1 a" = (2.20)
Reflectance of a single cover can be found as:
a= (2.21)

- 30 -
Important assumptions were made for the calculation of beam radiation( )" . The
function of incident angle ( )" varies diurnally; therefore, complex calculations are
required. However, using an incidence angle that occurs 2.5 hours after the solar noon on
an average day of the month, we can calculate ( )" close to a real value of ( )" [7].
This empirical assumption is valid for space heating applications and does not give
acceptable results for other applications due to its narrow specialization of the
application. Transmittance absorptance products for diffuse radiation and ground
reflected radiation are the functions of the collector's slope and do not change with time.
The isotropic-sky model was used to take into account transmittance absorptance
products.
Figure 15: Average transmittance absorptance product fluctuation.
The following formula differs from the original formula (2.9) with transmittance-
absorptance products.

- 31 -
1 1
( ) ( ) ( )
2 2
b b b d d g gS H R H H" " "
+
= + + (2.22)
Note: subscripts b, d and g stand for beam diffuse and ground.
Where:
- Sbar daily is the absorbed radiation on a sloped surface corresponding to the
optimal angle for incident radiation, MJ/m2;
- Global daily and diffuse daily are the average vales of radiation on a horizontal
surface, MJ/m2;
- Sbar daily fixed is the absorbed radiation corresponding to a fixed angle of 70
degrees, MJ/m2;
- Sbar optimum is the absorbed radiation corresponding to the optimal angle for
absorbed radiation, MJ/m2.
This model was used in the Matlab simulation as a function 'absorbed'. The result
of this computation is shown in Figure 16.
Figure 17 is a replica of Figure 16 and represents the relationship between daily
radiation and the number of sunshine hours. The lines are concaved up since the number
of hours of sunshine is greater in the summer. Conversion to watts is made as a function
of ‘absorbed’ (Appendix A).
The separation of diffuse radiation from beam radiation has been described
previously (the Collares-Pereira and Rabal correlation). Diffuse radiation is assumed to
be constant all day. In the same manner, beam radiation is assumed to be incident on a
surface only during bright sunshine hours. We need to know this information in order to
use the concept of utilizability.

- 32 -
2.8. Utilizability
The amount of energy absorbed is as important as the period when this energy is
being absorbed. Being a function of the loss coefficient, the useful gain must be greater
than losses to the environment. Therefore, there is a minimum value of absorbed
radiation that cannot be reached in order to avoid losing energy that is stored. This is
called a “critical radiation level” or “threshold radiation.” This level depends on the
transmittance-absorptance product and overall loss coefficient.
Figure 16: Comparison of daily radiation on a horizontal surface to absorbed radiation
on sloped surfaces with different angles.
This level can be found by:
( )
( )
l p a
cr
U T T
H
"
= (2.23)
or

- 33 -
( )cr l p aS U T T= (2.24)
Where:
- crH is the critical radiation level, MJ/m2;
- lU is the overall loss coefficient, W/m C;
- ( )" is the transmittance-absorptance product;
- pT is the plate temperature, C;
- aT is the ambient temperature, C;
- crS is the critical absorbed radiation level, MJ/m2.
Figure 17: Comparison of values of absorbed radiation on sloped surfaces with different
angles (W/m2).

- 34 -
Due to the lack of actual radiation and ambient temperature values we cannot use
this concept and must rely on a control system that will shut pumps down when the solar
radiation level is less then its losses. However, in the computer program this concept is a
condition that checks if the outflow temperature from the collector is lower than the
inflow temperature. In that case, the system considers the solar collector as offline.

- 35 -
3. Solar Collectors
Usually the category name of a solar collector is determined by its working fluid
(water, air). Several types of flat-type solar collectors are available for use in residential
buildings. General categories are:
- Unglazed flat-type liquid-type solar collectors;
- Evacuated tube solar collectors;
- Glazed flat-type liquid-type solar collectors;
- Air-type collectors.
Unglazed flat-type liquid-type solar collectors are primarily used for the heating
of swimming pools since they cannot provide high water temperatures in severe climates.
Glazed flat-type liquid-type solar collectors are the most common type of solar
collectors available. They allow solar energy to be used in severe climates since their
glass covers can significantly reduce convective heat losses.
Air-type collectors have less efficiency compared to liquid-type collectors, but
they have fewer problems with operation and maintenance since air is a less aggressive
substance than water or other liquids.
In addition, there are other types of solar collectors, such as evacuated tube solar
collectors and parabolic trough solar collectors.
Evacuated tube solar technology has eliminated conductive heat losses. The
efficiency of evacuated tube solar collectors is very high. However, due to their fragility
and difficulties with snow removal from space between the tubes, the evacuated tube
solar collectors are not considered a viable option for this project. Parabolic trough solar

- 36 -
collectors are a technology that allows the concentration of solar energy incident on a
reflective parabolic surface to a certain point such that the concentrated energy can be
converted to heat. This technology is still too expensive and cumbersome for use in
residential heating.
The residential house previously described in the introduction has an orientation
such that the two slopes of the roof face west and east. This complicates placing solar
collectors since the optimum direction of the solar collector slope in most cases is south.
In order to avoid losing solar energy at sunset and sunrise and placing solar collectors on
the roof, the orientation of the house should be constructed along the west to east axis.
This means that the surface azimuth angle is zero. Since the project has not yet been built,
the orientation can be easily modified.
The flat-type liquid-type solar collector is used as the basic unit in this thesis. The
differences among flat-type solar collectors are subtle; therefore, a common type will
cover all the advantages and disadvantages of this type of device. The choice of solar
collector was made according to the specifications provided by the manufacturer.
The Canadian manufacturers of the model G32-P series solar collectors (Figure
18), Thermal Systems LTD [10] have a great deal of information on performance of their
products. They have been certified by the Solar Rating & Certification Corporation and
have a high degree of efficiency [4]. A full description of this solar collector is given in
Appendix C. The major advantage that differentiates this solar collector from the average
solar collector is the “Solarstrips TM
“ tubes, which are embedded in the absorber plate
and which allow thermal resistance between the absorber and the tube walls to be
disregarded.

- 37 -
Figure 18: G series solar collector, Thermal systems LTD.
3.1. Energy balance in a flat-type solar collector
Energy balance in a single covered collector is presented in Figure 19.
( )u c L pm aQ A S U T T= (3.1)
Where:
- uQ is useful gain, MJ/m2;
- cA is the collector area, 2
m ;
- S is absorbed energy, W/m2;

- 38 -
- LU is the overall loss coefficient, W/m2-C;
- pmT , aT is the plate mean temperature and ambient temperature, C.
Figure 19: Heat transfer processes in a single glass solar collector.
3.1.1. Assumptions
The following assumptions are often used in solar collector simulations:
- The properties of all materials are constant;
- The covers are opaque to infrared radiation;
- 1D Heat flux is [experienced] through a cover;
- The sky is a black body with an equivalent sky temperature;
- The dust effect on the solar collector's performance is negligible.

- 39 -
3.2. Overall loss coefficient
The overall loss coefficient is a key value in the study of the performance of a
solar collector. It consists of several components, namely:
- The top loss coefficient;
- The edge loss coefficient;
- The back loss coefficient.
The top loss coefficient has two parts: the losses from plate to cover and from
cover to the ambient or wind convection coefficient. Loss from cover to plate can be
found as a function of the Rayleigh number and slope. Figure 20 shows the iteration
process in Matlab function 'Ul' (Appendix A).
1/3
1/ 4
1/3
max
1708 sin(1.8 )1708 cos
1 1.44 1 1 1
cos cos 5830
75 90
sin
1,0.288 ,0.039(sin )
Ra
Nu
Ra Ra
gB T
Ra
for
Ra
Nu Ra
A
%"
++
& '
= + + ( )
* +
=
=
(3.2)
Where:
- Nu is a Nuselt number;
- Ra is a Rayleigh number;
- is an inclination;
- B , is a reciprocal of temperature (assuming air is Ideal Gas);
- %" is viscosity and thermal diffusivity;

- 40 -
- A is the ratio of the length of the collector to space between the absorber and
the cover.
Figure 20: Flow chart of solar collector simulation.
Input initial data
Calculate overall loss coefficient.
Estimate mean plate temperature and
cover temperature
Calculate cover temperature
Compare to initial cover temperature
Temperatures match
Temperatures do not match
Calculate actual useful gain and new
absorber plate temperature

- 41 -
Knowing the Nuselt number, the heat transfer coefficient from plate to glass becomes:
c
K
h Nu
L
= (3.3)
Where:
- K is the thermal conductivity of air estimated at film temperature W/m K;
- L is the space between cover and absorber, m.
The wind convection coefficient for the calculation of convection heat transfer on
the cover of a flat collector mounted on a house can be found by using this empirical
correlation [7]:
2.8 3wh V= + (3.4)
Where:
- wh , wind loss coefficient, W/m C;
- V, Wind speed, m/s.
The Radiation coefficient form plate to glass is:
4 4
r eff
Tp Tg
h
Tp Tg
,= (3.5)
Where:
- Tp and Tg are the glass and plate temperatures, K;
- is the Stefan-Boltzmann constant, W·m-2
·K-4
;
- eff, is the effective emissivity of the plate-glazing system.
1
1 1
1eff
p g
,
, ,
= + (3.6)
Where p, and g, are plate and glass emmisivities.

- 42 -
The radiation coefficient from the glass to the ambient can be estimated from the
sky temperature ( aT , Co
):
sky aT =T -6 (3.7)
4 4
r sky g
Tg Ts
h
Tg Ta
,= (3.8)
Where:
- Ts, Tg are the sky and glass temperatures, K;
- g, ,is the emissivity of the glass and Stefan-Boltzmann coefficient; aT is
the ambient temperature, K.
Combining the top loss coefficient of all components becomes:
1
1 1
t
c r w r sky
U
h h h h
= +
+ +
(3.9)
The back loss coefficient can be found by:
b
k
U
L
= (3.10)
Where:
- k is the insulation thermal conductivity, W/m C;
- L is the insulation thickness, m.
Edge loss coefficient
e b
Ae
U U
Ac
= (3.11)
Where:
- Ae is the edge area, m;

- 43 -
- Ac is the collector area, m.
Finally lU can be found as a sum of previously discussed terms:
l e b tU U U U= + + (3.12)
It is convenient to find collector heat removal and collector efficiency factors.
Collector efficiency can be found as [9]:
[ ]
1/
1 1 1
( )
tanh[ ( ) / 2]
[ ( )/ 2]
L
L b i fi
L
b
U
F
W
U D W D F C D h
m W D
F
m W D
U
m
k
kb
C
/
! =
+ +
+
=
=
=
(3.13)
Where:
- W is the spacing among tubes, m;
- LU is the overall loss coefficient, W/m C;
- F! is the collector efficiency;
- F is the standard fin efficiency for straight fins with a rectangular profile;
- D is the tube diameter, m;
- k is the thermal conductivity of the bond between the tube and the absorber
plate ,W/m C;

- 44 -
- is the thickness of the absorber plate, m;
- bC is the bond conductance, which is a function of bond conductivity, width,
and average thickness (since in this particular solar collector tubes are
metallurgically bonded into the absorber plate, bC is very big; therefore, it can
be disregarded);
- fih is the heat transfer coefficient inside of tubes, W/m C.
3.3 The heat transfer coefficient
The heat transfer coefficient inside of the solar collector tubes can be
approximated as a heat transfer coefficient with uniform heating of the tube. In other
words, heat flux to the fluid is an overall constant of the tube surface [11]. Calculating the
heat transfer for propylene glycol is not convenient since the thermodynamic properties
of propylene glycol are not widely spread. There is some information on material
properties at certain temperatures and concentration, but this information is not enough
for curve fitting for use as a reference. Consequently, the thermodynamic properties of
propylene glycol are assumed to be constant (Table 4). On the other hand, the
thermodynamic properties of air and water are widely spread and were used as a way to
approximate the simulation to real conditions [12, 13].
The heat transfer coefficient in solar collector tubes can be found by:
2
0.7 Pr 160
Re 10000
/ 10
(0.79ln(Re ) 1.64)
D
D
L D
f =

- 45 -
0.5 2/3
( /8)(Re 1000)Pr
1 12.7( /8) (Pr 1)
D
D
fi D
f
Nu
f
k
h Nu
D
=
+
=
(3.14)
Where:
- F is the Darcy friction coefficient;
- Pr, Nu, Re are the Prandtl, Nuselt and Reynolds numbers;
- fih is the heat transfer coefficient, W/m C.
Note: subscript d stands for hydraulic diameter which is used to calculate the Re number.

- 46 -
4. Solar heating system simulation
Figure 21: Solar space heating system.
Figure 21 shows the schematic diagram of the solar heating system of the
residential building that is simulated in this study. This system has a typical configuration
and showed good results in a number of studies [7].
The roof dimensions allow us to place up to 24 solar collectors (72 meters of solar
collectors) in two rows. Common practice is to use a mixed connection of solar collectors
to improve solar heating system performance [9]. We can use panels of 4 collectors
connected in parallel and 6 panels connected in a series (Appendix C: Typical double tier
solar collector array). The slope of the collectors is assumed to be fixed at 70 degrees for
all months since changing the slope requires some kind of control system which the small
increase of absorbed radiation cannot justify.

- 47 -
4.1. Heat exchangers
A water/glycol heat exchanger has been chosen as recommended by the
manufacturer. Following the manufacturer selection guide, the area of the heat exchanger
is found (a worksheet can be found in Appendix C). The heat transfer load can be found
as: 72 meters of solar collector multiplied by 850 2
W/m (maximum absorbed radiation:
Figure 17), which provides 205 MBtu/hr. The shell side fluid is propylene glycol. The
rest of the computation is in Appendix C. The operation cost is estimated separately in
the program (Appendix A). An air glycol heat exchanger is a typical air-type heat
exchanger with common parameters ( Table 3).
Table 3: Heat exchanger characteristics
Type
Property
Finned-tube heat exchanger Shell-tube heat exchanger
U ( 2
/W m K ) 200 216
Working
fluids
-shell side
-tube side
Air
propylene glycol
Propylene glycol
Water
Area, m 8 8
4.2. Thermal energy storage
There are numerous methods of storing thermal energy. The thermal capacity of a
solar collector should be as small as possible since this energy will be lost to the
environment. Therefore, we have to store thermal energy outside of the collector. The
effectiveness and feasibility of these methods depend on the object's designation and cost.

- 48 -
In this thesis we use flat-plate-type liquid-type solar collectors coupled with a radiant
heating system which is embedded within a concrete slab. The slab is 4 inches thick, and
does not have enough storage capacity to store and distribute the required amount of
thermal energy for an adequate period. Hence, additional storage is required to provide
backup at night and on cloudy days.
Liquid-type solar collectors in cold climates require the use of antifreeze. In the
same manner, the use of water in a radiant heating system is a common practice.
Therefore, the heating system must have a heat exchanger to transfer energy from
antifreeze to water.
Table 4: Propylene glycol thermodynamic properties [14]
The most common, simple, and sensible thermal storage is a water tank. A multi-
tank system configuration provides as much energy storage as a single storage tank of
Properties Value Notes
Boiling point 187 °C (lit.)
Melting point U60 °C (lit.)
Density 1.036 g/mL at 25 °C(lit.)
Price 16 $/gallon.
Specific heat 3.806 kcal/(kg-C) (50% concentration)
Thermal Conductivity 0.34
W/m-K 50% H2O @90°C
Viscosity 3.1 g/m s

- 49 -
twice the volume [15]. In addition, a multi-tank system configuration can be presented as
single tank storage of twice the volume.
Any water tank with heat inflow and outflow experiences stratification to some
degree [16]. A stratified tank can be represented by several mathematical models. All of
them can be classified as a multimode model. Even a well-mixed storage tank model can
be called a multimode model since it implies a one-node tank model. Experimental data
does not verify improvement of the mathematical model with the increase of the numbers
of nodes since high stratification in a small capacity storage tank is unlikely [7]. Hence, a
two-node model has been used in the simulation.
Hot water from a solar collector does not change the tank temperature
immediately. The time after which heat collected by the solar collector reaches the
bottom of the storage tank and changes the performance of the system is called a turnover
period. Collected heat from the solar collector is equal to the heat required to raise the
temperature of the storage from siT to soT .
( ) ( )t w w fo fi s s w so siQ m C T T t M C T T= =& (4.1)
Assuming a two-node tank we can say ;fo so fi siT T T T= = . Hence, the turnover
period can be calculated as:
w w
t
s w
m C
t
M C
=
&
(4.2)
Where:
- wm& is the water flow rate, kg/s;
- wC is the specific heat of water
J
,
kg K
;

- 50 -
- sM is the storage capacity, kg;
- foT , is the temperature of the water leaving the water/glycol heat exchanger,
C;
- fiT is the temperature of the water entering the water/glycol heat exchanger,
C;
- soT is the temperature of the first node, C;
- siT is ,the temperature of the second node, C.
The new water temperature after a turnover is:
u
so si
s s
Q
T T
m C
= +
&
(4.3)
Where:
- soT is the storage outlet temperature, C;
- siT is the storage inlet temperature, C;
- uQ is the useful gain, W;
- s sm C& are the water parameters.
4.3. Radiant heating
Radiant heating is an efficient way to heat a house. The main advantages of
radiant heating compared to conventional heating systems are efficiency and comfort for
the inhabitants. These characteristics make it attractive and feasible to implement this
heating technique coupled with solar collectors.

- 51 -
The computer program in Appendix A includes a function that computes heating
loads for inputted ambient temperatures. This program works with the heating load
calculations program.
Heated space is divided into three zones with separate radiant heating inputs. This
is a common practice in order to avoid high temperatures at the beginning of the loop and
low temperatures at the end of the loop. Also, it takes into account room designations. A
three-zone system will give us a good approximation of water temperature that is
required to input into the radiant heating system's manifold.
Assuming water is used as a working fluid, upward heat flux can be calculated as
[17]:
u
designheat load of space
q
availible floor areaof space
= (4.4)
And downward heat flux as: 2
Btu hr
ft
:
4.17( )( )
( 5)
e slab outside
d
edge
P T T
q
R A
=
+
(4.5)
Where:
- P is the exposed perimeter of the slab, ft;
- slabT is the estimated operating temperature of the floor slab at design
conditions, F;
- outsideT is the ambient temperature, F;
- edgeR is the R-value of edge, 2
Btu hr
ft
;

- 52 -
- A is the available floor area of the space, 2
ft .
The outlet water temperature can be estimated as:
( )
500
1
1
b
out roomair in roomair
d
s ff air film u
T T T T e
a L
b
f
q
a
R R R q
= +
=
= + +
+ +
(4.6)
Where:
- inT is the room temperature, 68 F;
- sR is the slab resistance o
, Btu/(h ft F) ;
- ffR is the total thermal resistance of the finished floor
materials o
, Btu/(h ft F) ; air filmR is the air film resistance on the surface of the
floor o
, Btu/(h ft F) ; L is the length of the piping circuit, ft; f is the flow rate
through the circuit, usgpm.
4.3.1. Ventilation
Even though radiant heating is a better way to heat space than more common
means of space heating, it does not provide fresh air for the house; therefore, a small
ventilation system must be installed. An ASHRAE requirement for the amount of fresh
air per person is 15 cubic feet per minute (cfm) [6]. Assuming there are four people in
the family, the ventilation flow rate is 55 cfm (30 % fresh air, 70% reused). To provide
for the heating of 18 cfm of air to the house, an additional heat exchanger and fan have
been added to the system.

- 53 -
4.4. Programming
Figure 22: Flow chart of the simulation
The flow chart of the main program is presented in Figure 22. Several Matlab
functions are not included in the flow chart since their influence on the final results is
indirect. The main script of the simulation calculates the useful heat that is produced by
the solar heating system and, in case of insufficient radiation levels, activates the electric
heating system that plays the role of a backup system in this event.
The available solar radiation data for simulation are the mean monthly [and] daily
global radiation for 22 years from 1969 to 1991, and the average number of hours of
bright sunshine. The available temperature data are the average temperatures for Astana,
Kazakhstan (Appendix E).
4.5 Economy
Economic considerations are important in terms of evaluating the solar heating
system performance. The value of money changes overtime; therefore, we have to
consider the factors that influence the total cost of the system. Present worth is the
Main Script: Final
Input: year, month
Output: Total cost
Function: storage
Input: year, month
Output: cost
Function: Collector
Function: radiant floor
Function: House
Function: pump

- 54 -
difference between the project cost and the heating load worth. The present worth factor
can be found as [18]:
(4.7)
Where:
- I is the interest rate;
- dr is the discount rate;
- yr is the life of project.
The capital cost was estimated based upon the solar collectors' manufacturer price
guides. Operation and maintenance cost are assumed to be negligible.
Table 5: Economic parameters [1]
Parameter Value
electricity cost, $ 0.05
discount rate 0.1
life of the project, years 22
general inflation rate 0.08
fuel inflation rate 0.013
The present worth for this particular project can be found by:
load
load
solar Q equipment electr
electric Q equipment electr
Pw Pw Pw Pw
Pw Pw Pw Pw
=
=
(4.8)
Where:
- solarPw is the present worth of a solar space heating system;

- 55 -
- electricPw is the present worth of an electric space heating system;
- loadQPw is the present worth of heating loads;
- equipmentPw is the present worth of the equipment;
- electrPw is the present worth of the consumed electricity.

- 56 -
5. Analysis and Results
The simulation of the solar heating system (Figure 21, Figure 22) showed that
acceptable trends were met. From the beginning it was assumed that a solar heating
system would reduce electricity consumption. Figure 23 compares the consumed
electricity price trends of a solar space heating system and an electric heating system of
the same size for an average year. At this point it is clear that solar heating system
consumes less electricity for its needs, which is expected.
Figure 23: Cost comparison for an average year
According to the results of the simulation, the outside air temperature influenced
the operating cost in an obvious way in Figure 23. Even though February is the coldest
month [6], the January heating load is larger due to the lower average temperature used in
heating load calculations. Hence, the operating cost is the highest in January ($325/175).

- 57 -
In summary the resulting savings showed that total savings during the time of the
simulation (22 years) due to solar energy implications was $ 22,660. Calculations of the
capital cost showed that the current retail price of the G series solar collectors is in the
same range as the total savings for 22 years (the capital cost is $ 22,976). These numbers
illustrate the present high price of solar collector arrays that halt development of this
technology on a larger scale.
The most useful objective function for estimating the performance of asolar
heating system is the present worth of the heating system. The present worth of a
residential heating system is always negative since it does not produce energy for sale.
Table 6 represents the present worth values for solar and electric heating systems.
Table 6: Present worth of heating systems
Electricity cost, $/kWh 0.05
Present worth of solar heating system, $ -17,093
Present worth of electric heating system, $ -15,778
The current price of the G series solar collector is too high for use as an
alternative to conventional heating systems. However, performance of this type of
collector can be considered as one of the best in the class of flat-type solar collectors (due
to Solarstrips technology). In addition, the availability of this type of solar collector in
Kazakhstan is questionable. The closest manufacturers of solar collectors to Kazakhstan
are located in China. Considering the low labor costs in China, Chinese solar collectors
can provide less expensive alternatives and, consequently, improve the feasibility of a
flat-type solar collector heating system.

- 58 -
Table 7 shows that results of capital cost optimization and the critical price for the
solar heating system with current electricity costs (0.05$/kWh). The critical cost of 700
$/collector means that a solar heating system is more feasible than an electric heating
system of the same size if the cost solar collectors is less than 700 $ per collector.
Table 7: Present worth of heating systems
Present worth, $Collector price,
$ /collector
Electric heating system Solar heating system
840 -15778 -17093
700 -15778 -14693
600 -15778 -12293
The other important parameter for estimating the performance of solar heating
systems is the need for a back up system. Figure 24 shows the relationship between solar
heating systems and electric backup systems. The ratio of the backup system load to the
solar heating load can help us to measure the backup system. Overestimating the load of a
backup system is a common mistake that leads to the increased capital cost and the
overall cost inefficiency of the heating system.
According to Figure 24, the size of the backup system should provide 50 % of a
heating load on January (the upper line value). For instance, the heating load in January is
50,000 Btu/h (the heating load does not change since ambient temperatures are assumed
to be the same); therefore, the backup system should provide 25,000 Btu/h (7.33 kW).

- 59 -
Figure 24: Ratios of back up system load to solar heating system load (22 years of
simulation)
The backup system can be designed to completely supply the heating load in case
of bad weather conditions that cause low solar energy input into the system. However,
storing thermal energy makes the system more reliable and independent of weather
conditions. A 1000 kg sensible thermal storage tank has been used in simulation. In
reality, a storage tank can consist of several tanks connected in a series. Several research
studies have been done on simulating sensible thermal storage [7, 9, 15], the results of
which verify that three thermal storage collectors connected in a series can provide the
same thermal storage capacity as one storage tank of three times size [15].
The fact that the cost of electricity tends to increase the present worth of a solar
heating system was analyzed with different electricity costs. Figure 25 was made based
on data in Table 8 to show trends in present worth values for different electricity costs.

- 60 -
The present worth of heating systems drastically increases with the increase of
electricity rates; however, an electricity cost greater than 0.2 $/kWh is highly unlikely
since a quadrupled electricity price will likely initiate the development of alternative
technologies that will halt the increase.
Figure 26: Present worth of a solar space heating system and an electric heating system
with different electricity costs.
Table 9: Present worth of solar space heating system and electric heating systems
Electricity cost
$/kWh
System
0.05 0.1 0.2
Electric heating
system -15,778 -31,556 -80,667
Solar heating system -17,093 -34,186 -75,336

- 61 -
Figure 25 and Table 8 show that this simulated solar heating system would be
feasible if the electricity rate were to increase as high as 0.13 $/kWh. This price is already
a reality of the megapolises of the world; however, considering coal resources and
population, Kazakhstan will probably not arrive at this point in the near future.

- 62 -
6. Conclusion
A study of flat-type solar space heating for a residential building has been done.
The results show that flat-type solar collectors can perform well under the severe weather
conditions and the radiation levels of Astana. However, the simulation of a solar space
heating system compared to an electric resistance heating system showed that the solar
heating system that is simulated cannot provide enough heating capacity to heat the
building without 50 % backup system. In addition, the cost analysis showed that the
present worth of the solar heating system can be greater than the electric heating system
if the price of solar collectors is less than their current value.
The purpose of this study was to test if the implications of a flat-type liquid-type
solar heating system of a typical residential building would be feasible with current
electricity. The simulation disproved that statement and showed that the current savings
and capital cost of a solar heating system is in the same price range which means that not
many home owners will risk installing a solar heating system.
In addition, the electricity rate analysis demonstrated that the present worth of the
simulated solar heating system is influenced by electricity rates. One of the ways of
canceling this relationship is by combining several alternative energy technologies, such
as ground-coupled heat pumps, wind power and biogas, with solar space heating systems.
This would set aside the present worth of a solar heating system from electricity rates so
that the only factor that would need to be improved would be the capital cost.
Solar space heating technology cannot provide an adequate heating load for a
residential building in arid, cold climates without a significant increase in efficiency and

- 63 -
size of solar collectors or thermal storage, all of which would lead to increasing the
capital cost of the system.
Despite the simulation results, more comprehensive simulations and possibly full
scale tests should be performed to verify or disprove these results.
6.1. Future work
The residential building that is used in the simulation is a typical residential house
without any modifications for improving energy efficiency; therefore, better results could
be achieved by improved insulation technologies or passive solar energy technologies.
Computer simulations of solar space heating can provide good approximations
and ways of improving efficiency. However, nothing can replace carefully performed
experimentation. Experimental work and the collection of detailed data is a priority for
future investigation. There is a lot of work on the collection of solar radiation and other
types of data that must be done on a larger scale in order to justify solar energy use
(creating online solar and wind maps, improving the accessibility of this information, and
so on.).
The example of the developed countries, such as the USA, shows that the
promotion of alternative technologies, which is an important part of the proliferation of
solar energy use, has to be supported by the government. Henceforth, the propagation of
alternative energy technologies in Kazakhstan will depend on the lobbying efforts of
interested parties and leaders.

- 64 -
REFERENCES
[1] Kazakhstan: General information (n.d.). Retrieved January 07, 2007, from
http://missions.itu.int/~kazaks/eng/kazak01.htm
[2] Kazakhstan: General information (n.d.). Retrieved January 07, 2007, from
http://www.powerexpo.kz/en/2005/desc/
[3] World Map of the Köppen-Geiger climate classification updated. Retrieved May 13,
2007, from http://koeppen-geiger.vu-wien.ac.at/
[4] Summary of SRCC Certified Solar Collector and Water Heating System Ratings
(n.d.). Retrieved May 07, 2007, from http://solar-rating.org/ratings/ratings.htm
[5] Residential house drawings and supplementary information are provided by Russell
Walters, Ph.D., P.E. Iowa State University.
[6] ASHRAE Handbook (2005). Fundamentals Volume. American Society of
Heating, Refrigeration and Air-conditioning Engineers. NY: 2005.
[7] Duffie, J., & Beckman, W. (2006). Solar engineering of thermal processes, 3rd Ed.,
New York: John Wiley & Sons
[8] Radiation data for Kazakhstan. Retrieved January 10, from
http://www.worldclimate.com/cgi-bin/data.pl?ref=N51E071+2100+35188W
[9] Tiwari G.N. (2002). Solar Energy: Fundamentals, Design, Modeling and
Applications. New Delhi: Narosa Publishing House
[10] G series solar collectors: specifications. Retrieved April 1, 2007, from
http://www.thermo-dynamics.com/technical_specs/G_series_technical.html
[11] Incropera, P., &DeWitt, D. (1996). Introduction to Heat transfer, 3rd Ed., New
York: John Wiley & Sons

- 65 -
[12] Water properties: Matlab function. Retrieved May 13, 2007, from http://www.x-
eng.com
[13] Air properties: Matlab function. Retrieved May 13, 2007, from
http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=
5165&objectType=file
[14] Propylene glycol: Properties. Retrieved May 13, 2007, from
http://www.sigmaaldrich.com/catalog/search/ProductDetail/SIAL/P4347
[15] Experimental analysis of stratified multi-tank thermal storage configurations for
solar heating systems. Retrieved May 13, 2007, from
http://www.solar2006.org/presentations/tech_sessions/t23-a046.pdf
[16] Dincer, I., & Rosen, M. (2002).Thermal energy storage., NY: John Wiley & Sons
[17] Siegenthaler, J.,(1995). Modern hydronic heating for residential and light
commercial buildings. New York: Delmar Publishers
[18] Burmeister, L., (1998).Elements of thermal-fluid system design., NJ:Prentice-Hall

- 66 -
Appendix A. Computer program
A.1. Final script
%Economical parameters
Cload=.05;% worth of load
elec=0.3; % electricity cost $/kwh,
dr=0.1; % discount rate
yr=22; % life project
ig=0.08; % general inflation rate
ifu=0.013; % fuel inflation rate
%no loans no salvage values.
pwf=(1/(dr-ig))*(1-((ig+1)/(1+dr))^yr); % present worth factor
%Capital cost
Nc=24; % number of collectors
Ccol=800; % $ collector cost
HxC=1000; % Heat exchangers estimated cost, $.
Hxa=500; % estimate air glycol cost
Fanc=200; % fan cost
Csto=300; % Storage estimated cost, $
Cc=Nc*Ccol; %Collectors cost, $
Cpg=5*40;% proplelene glycol price $40/gallon
Cpumps=2*504;% 2 pump cost, $
% electric heat cost. 50,000 BTU/h=14.65 KW
Ceh=(550+40*14.65)/2;%electric heater cost.(50%capacity)
CCs=HxC+Csto+Cc+Cpg+Cpumps+Ceh+Hxa+Fanc;%capital cost of solar heating
system
CCe=(Ceh*2)+Cpumps+Hxa+Fanc; %capital cost of electric heating
system
[Diffuse,Global,Hcb,Ho,Ht_bar,Kt,Hkt,Global_dayly,Diffuse_dayly,Average
persunsh,Na,Rad]=Solar;
cnt1=0;
for y=69:92
cnt1=cnt1+1;
%heating season months
for j=1:4;
%Calculating
n=24-(ceil(Averagepersunsh(j+1)));
con=0;
[Cost_elec_1,Cost_auxilary_1,pfan,air_cost,q_load]=storage(y,j,n,con,el
ec) ;
%function storage input year and month
%n- number of hours
%con-control function,= 1 for radiation
% or zero for night hours
n=(ceil(Averagepersunsh(j+1)));
con=1;%con-control function,= 1 for radiation
[Cost_elec,Cost_auxilary,pfan,air_cost,q_transf]=storage(y,j,n,con,elec
) ;
Cost_auxilary_total(cnt1,j)=30*((sum(Cost_auxilary)+sum(Cost_auxilary_1
)...
+(pfan+mean(air_cost))*24*elec));%$/day
Cost_solar(cnt1,j)=30*(sum(Cost_elec_1)+sum(Cost_elec)+(pfan+...

- 67 -
(sum(air_cost))))*elec;%$/day
Costload(cnt1,j)=q_load*24*30*Cload*pwf; %worth of heating load
end
cnt=9;
for j=5:7;
cnt=cnt+1;
[Diffuse,Global,Hcb,Ho,Ht_bar,Kt,...
Hkt,Global_dayly,Diffuse_dayly,Averagepersunsh,Na,Rad]=Solar;
n=24-(ceil(Averagepersunsh(cnt+1)));
con=0;
[Cost_elec_1,Cost_auxilary_1,pfan,air_cost,q_load]=storage(y,cnt,n,con,
elec) ;
%function storage input year and month
%n- number of hours
%con-control function,= 1 for radiation
n=(ceil(Averagepersunsh(cnt+1)));
con=1;
[Cost_elec,Cost_auxilary,pfan,air_cost,q_transf]=storage(y,cnt,n,con,el
ec);
Cost_auxilary_total(cnt1,j)=30*((sum(Cost_auxilary)+sum(Cost_auxilary_1
)+(pfan+mean(air_cost))*24*elec));%$/day
Cost_solar(cnt1,j)=30*(sum(Cost_elec_1)+sum(Cost_elec)+(pfan+(sum(air_c
ost))))*elec;%$/day
Costload(cnt1,j)=q_load*24*30*Cload*pwf; %worth of heating load
end
end
PW_Sol=((mean(Costload))*7)-((mean(Cost_solar))*pwf*7)-CCs;
PW_elec=((mean(Costload))*7)-((mean(Cost_auxilary_total))*pwf*7)-CCe;
Solar radiation computation program
function [Diffuse,Global,Hcb,Ho,Ht_bar,Kt...
,Hkt,Global_dayly,Diffuse_dayly,Averagepersunsh,Na,Rad]=Sol
ar
%%Initial data.
% Site Location
Lat=53.15; % LAtitude
Alt=350; % Altitude, meters
Gsc=1367; % Solar Constant W/m^2
%%%%%%%%%%%%%Annual Extraterrestial Radiation on a
horizontal surface%%%%%%%
beta=0; % horizontal plane
gamma=0; % surface azimuth angle (orientation to south
north axe)

- 68 -
%%%%%%%Reading Data file for Number of hours of sunshine
1962- 1992 %%%%%
fid_data=fopen('DAta Sunshine 69-92.txt','r'); %%%
open file for reading
A=fscanf(fid_data,'%e%e%e%e ', [4 inf]);
B11=A';
% Defining arrays
omegas=(1:365); % sunset hour angle
N=(1:365); % number of days a yeaer
sunset=(1:365);
sunrise=(1:365);
Ho=(1:365);
% Ho - daily extraterrestial radiation on a horizontal
surface
for h=1:365
omegas(h)=rd(acos(-tan(dr(Lat))*tan(sigma(h)))); % sunset
hour angle degree
N(h)=(2/15)*omegas(h) ; % number of daylight hours
sunset(h)=(omegas(h))/15; % sinset hour angle
sunrise(h)=sunset(h)*(-1);% sunrise hour angle
Ho(h)=(24*3600*Gsc/pi)*(1+0.033*((cos(dr(360*h/365)))))*...
((
(cos(dr(Lat))))*((cos(sigma(h))))*((sin(dr(omegas(h)))))+..
.
(dr(omegas(h)))*((sin(dr(Lat))))*((sin(sigma(h)))));
% Ho - daily extraterrestial radiation on a horizontal
surface
end
f=Ho; %%Intermidate variable
Ho=f*10^(-6); %%Converting to MJ/m^2
i=0;j=0;
for h=1:22 % 22 is a number of years of data
j=j+1;
mon(h,1)=B11(j,1);
for k=2:13
i=i+1;
mon(h,k)=B11(i,4);
end
j=j+12;
end
% Monthly average daily hours of bright sunshine
[m,n] = size(mon);
for h=2:13
mon(23,h)=(mean(mon(1:m,h)));

- 69 -
end
% Monthly average of maximum possible daily hours of bright
sunshine
Avedays=[17,47,75,105,135,162,198,229,259,288,318,344];%AVe
rage days of months
for h=1:12
Na(h)=(2/15)*(rd(acos(-
tan(dr(Lat))*tan(sigma(Avedays(h)))))) ;
noverN(1,h)=mon(23,h+1)/Na(h);
noverN(2,h)=noverN(1,h)*100; % percents
end
for i=2:13%from 2 since first row is a year
Averagepersunsh(i)=mean(mon(1:23,i)); %% average number of
hours of sunshine.
end
%%%%%%Estimation of clear sky radiation%%%%%%%%%%
a0=0.4237-0.00821*(6-(Alt*10^(-3)))^2;
a1=0.5055+0.00595*(6.5-(Alt*10^(-3)))^2;
ks=0.2711+0.01858*(2.5-(Alt*10^(-3)))^2;
%correction factors for Climate Types (subarctic
summer.)
R0=0.99;
R1=0.99;
Rk=1.01;
for n=1:365
%%%Extraterrestial radiation incident on the plane
normal to the
%%%radiation on the nth day of year
B=(n-1)*360/365;
Gon(n)=Gsc*(1.000110+0.31221*cos(dr(B))+0.001280*sin(dr(B))
+...
0.000719*cos(2*dr(B))+0.000077*sin(2*dr(B)));
sunsetrise=round(sunset(n)); % rounding number of
hours before/after solar noon
om=-7.5 ;%half an hour after the sunrise
for i=1:sunsetrise
omega=om;
cosz=(cos(dr(Lat))*cos(sigma(n))*cos(dr(omega))+sin(dr(Lat)
)...
*sin(sigma(n)));

- 70 -
%%% Atmospheric transmittence for beam radiation
tb=a0*R0+a1*R1*exp(-ks*Rk/cosz);
om=omega-15; %% step one hour
taub(i)=tb;
%%%%%%% The beam radiation on a horizontal plate
Gcnb(n,i)=Gon(n)*taub(i);
Gcb(n,i)=Gon(n)*taub(i)*cosz;
taud(n,i)=0.271-0.294*taub(i);
Gcd(n,i)=Gon(n)*cosz*taud(n,i);
Icnb(n,i)=Gcnb(n,i)*3600; %%Mj/m2
Icb(n,i)=Gcb(n,i)*3600;
Icd(n,i)=Gcd(n,i)*3600;
end
%%%% Daily beam radiation clear sky.
%%%% Mj/m2!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Hcb(n)=(2*(sum(Icb(n,1:sunsetrise))))*10^(-6);
end
%Reading Global Radiation from file
fid_data=fopen('Global.txt','r'); %%% open file
C1=fscanf(fid_data,'%d',[4 inf]);
C=C1.';
clear ('C1');
[g,n]=size(C);
% Average for years
for i=1:12
d=0;cnt=0;
for k=1:g
if C(k,2)==i
d=d+C(k,4);
cnt=cnt+1;
end
end
d1=d/cnt;
Global(i)=0.01*d1; % monthly sums MJ/m2
end
clear ('C');
%Organize data. Mean values
%Extraterretrial rad sums
f3(1)=sum(Ho(1:31));f3(2)=sum(Ho(32:59));f3(3)=sum(Ho(60:90
));
f3(4)=sum(Ho(91:120));f3(5)=sum(Ho(121:151));f3(6)=sum(Ho(1
52:181));

- 71 -
f3(7)=sum(Ho(182:212));f3(8)=sum(Ho(213:243));f3(9)=sum(Ho(
244:273));
f3(10)=sum(Ho(274:304));f3(11)=sum(Ho(305:334));f3(12)=sum(
Ho(335:365));
%%%Clear sky
clear ('f');
f(1)=sum(Hcb(1:31));f(2)=sum(Hcb(32:59));f(3)=sum(Hcb(60:90
));
f(4)=sum(Hcb(91:120));f(5)=sum(Hcb(121:151));f(6)=sum(Hcb(1
52:181));
f(7)=sum(Hcb(182:212));f(8)=sum(Hcb(213:243));f(9)=sum(Hcb(
244:273));
f(10)=sum(Hcb(274:304));f(11)=sum(Hcb(305:334));f(12)=sum(H
cb(335:365));
%%%%Comparison. F3 and T
% Reading diffuse radiation from file
fid_data=fopen('diffuse 90- 92.txt','r'); %%% open file
C=C1.';
clear ('C1');
[g,n]=size(C);
% one year
for i=1:12
d=0;cnt=0;
for k=1:g
if C(k,2)==i
d=d+C(k,3);
cnt=cnt+1;
end
end
d=d/cnt;
Diffuse(i)=0.01*d; % monthly sums MJ/m2
end
clear ('C');
% Monthly average isotropic-sky radiation on a sloped
surface.
rho_g=[.7,.7,.7,.4,.2,.2,.2,.2,.2,.2,.4,.7,.7]; %Ground
reflectance (Assumed)

- 72 -
% %%%Clearness index
Kt=Global./f3;
for m=1:12
if m==1
n=17;
elseif m==2
n=47;
elseif m==3
n=75;
elseif m==4
n=105;
elseif m==5
n=135;
elseif m==6
n=162;
elseif m==7
n=198;
elseif m==8
n=228;
elseif m==9
n=258;
elseif m==10
n=288;
elseif m==11
n=318;
elseif m==12
n=344;
end
om1=acos(-tan(dr(Lat-beta ))*tan((sigma(n))));
om2=acos(-tan(dr(Lat))*tan((sigma(n))));
SUnset_angle_on_collec=min(om1,om2);
R_b(m)=((cos(dr(Lat-beta))*cos(sigma(n))*...
sin(SUnset_angle_on_collec)) +...
(pi*((rd(SUnset_angle_on_collec))/180)*sin(dr(Lat-
beta))*sin(sigma(n))))/...
((cos(dr(Lat))*cos(sigma(n))*...
sin(SUnset_angle_on_collec)) +...
(pi*((rd(SUnset_angle_on_collec))/180)*sin(dr(Lat))*sin(sig
ma(n))));

- 73 -
Ht_bar(m)=(Global(m)-
Diffuse(m))*R_b(m)+Diffuse(m)*rho_g(m)*(1+cos(dr(beta))/2)+
...
Global(m)*(1-cos(dr(beta))/2); %
MJ/m2
end
beta=70;
%%%%KT model
Hkt=KT(Lat,beta,Ho,Diffuse,Global,Kt,gamma);
%Absorbed radiation
%param=[Lat,Global,Diffuse];
%Reading monthly daily mean
fid_data=fopen('Global.txt','r'); %%% open file
C=C1.'; %transposition
clear ('C1','d','cnt');
[g,n]=size(C);
for i=1:12
d=0;cnt=1;
for k=1:g-12
if C(k,2)==i
C1(cnt)=C(k,3);
cnt=cnt+1;
end
end
Global_dayly(i)=0.01*(mean(C1)); % monthly dayly
means MJ/m2
end
%Collare-Pereira and Rabl correlation for diffuse radiation
estimation
%page 77,[3]
for i=1:12
if Kt(i)<=0.17
Diffuse_dayly(i)=Global_dayly(i)*0.99;
elseif ((Kt(i) > 0.17) && (Kt(i) < 0.75))
Diffuse_dayly(i)=Global_dayly(i)*(1.188-
2.272*Kt(i)+9.473*Kt(i)*...
Kt(i)-21.865*(Kt(i))^3+14.648*(Kt(i))^4) ;
elseif ((Kt(i) > 0.75) && (Kt(i) < 0.80))
Diffuse_dayly(i)=Global_dayly(i)*(-
0.54*(Kt(i))+0.632);
elseif Kt(i) >= 0.80
Diffuse_dayly(i)=Global_dayly(i)*0.2;

- 74 -
end
end
%%%DEfining arrays of GLobal radiation 1964-1991
% converting data from MJ/m2 to W/m2
% B11- sunshine hours
% C- global radiation
[m1,n1] = size(C);
[m2,n2] = size(B11);
cnt=0;
for i=61:m2
cnt=cnt+1;%counter
if C(i,1)==B11(cnt,1) && C(i,2)==B11(cnt,2)%matching
availible data for
%radiation nad number of hours of sunshine and
converting global
%radiation to instantenious values, W
%%Separating diffuse froom global radiation using
Collare-Pereira correlation
if Kt(C(i,2))<=0.17 % average values of Kt
Diffuse_d(i)=C(i,3)*0.99;
elseif ((Kt(C(i,2)) > 0.17) && (Kt(C(i,2)) < 0.75))
Diffuse_d(i)=C(i,3)*(1.188-
2.272*Kt(C(i,2))+9.473*Kt(C(i,2))*...
Kt(C(i,2))-
21.865*(Kt(C(i,2)))^3+14.648*(Kt(C(i,2)))^4) ;
elseif ((Kt(C(i,2)) > 0.75) && (Kt(C(i,2)) < 0.80))
Diffuse_d(i)=C(i,3)*(-0.54*(Kt(C(i,2)))+0.632);
elseif Kt(C(i,2)) >= 0.80
Diffuse_d(i)=C(i,3)*0.2;
end
%%Combined values for global radiation and diffuse
radiation average
% daily sums, MJ/m2.
Rad (cnt,2) =Diffuse_d(i);
Rad (cnt,1) =C(i,3);
Rad (cnt,3) =B11(cnt,1);
end
end

- 75 -
A.2. Radiant floor program
function [Tout,f,Q]=radiant_floor(i,Tin)% month,
temperature, F
Sei=11; %Slab edge insulation R-11
t=4; %slab thickness ,inches
Rff=0.21; %%floor finish vinil tile
R_air_film=0.61; % assumed
Rs=0.795; %Slab resistance, graph.
A1=1534; %Area
A=A1*0.7; %aproximate open floor. 70% of the floor is not
covered
%Outside temperature
F =[-6.8,-6.6,4.6,28,42.4,52.3,56.3,51.8,41.4,28.6,12,-1];
%°F
% Radiant floor
L=61; %feet
W=25; %feet
f=1.5; % flow rate gpm
%3/4 in plastic tubing spaced 12 ins on center
Np=23; % number of pipes ASsumed from the geometry of the
building
qload=house(i); % heating load, BTU/h
q_u=(qload)/A; % Upward heat flux.
p=1; % initial guess
while (q_u-p)>1
Tw=68+q_u*(Rs+Rff+R_air_film); %Average water temperature
required in a circle, F.
q_d=(4.17*(L+W)*(Tw-F(i)))/((Sei+5)*(1534));
a=(1/((Rs+Rff+R_air_film)))*(1+(q_d/q_u));
b=a*60*Np/(500*f);
Tout=68+(Tin-68)*exp(-b);
Q=500*f*(Tin-Tout); % total heat flux, Btu/h
p=(Q-q_d);
f=f-0.1;% new flow rate
end

- 76 -
A.3. Calculation of overall heat loss coefficient, useful gain, and outlet
water temperature.
function [U_l,Tmp,Q_u,Tfo]=U_l(i,Tin,beta,Sbar_w_per_m2)
Tmp=Tin+50; % mean plate , initial guess, C
Cel =[-21.6,-21.5,-15.2,-2.2,5.8,11.3,13.5,11,5.2,-1.9,-
11.1,-18.4]; % °C
sigma=5.6*10^(-8); %Stefan-boltzman constant
V=10; % Wind speed Assumed m/s
e_p=0.95; %plate emmitance
e_g=0.88; %glass emmitance
t_b=0.025; %m
k_b=0.036;%W/mC
p_c_t=0.025; %m
rho_gl=1036;% kg/m3
m_dot=2.5; %Assumed flow rate in the collector, L/m
mdot_gl=m_dot*rho_gl/3600; % flow rate , kg/s
A_coll=4*2.96; % Area of a collector ,m
Coll_length=2.47; %m
h_fi=300;% initial guess heat transfer coefficient
D_h=4*120/36;% hydraulic diameter
Ta=Cel(i); % ambient temperature
Tsky=Ta-6;% sky temperature
Tg=Ta+20; %Assumed glass temperature,C
Tg1=Tg+15; %Tg1 always bigger to get results.
e_eff=((1/e_p)+(1/e_g)-1)^(-1 ); %effective emmisivity of
plate glasing system;
while (Tg-Tg1)<2 % Loop break condition
Tg=Tg1;
h_r_1=e_eff*sigma*( (Tmp+273)^4-(Tg+273)^4 )/(Tmp-Tg);
% radiation transfer coefficient, plate to cover
h_r_2=e_g*sigma*( (Tg+273)^4-(Tsky+273)^4 )/(Tg-Ta);
%radiation transfer coefficient, cover to sky
% Air properties @ film temperature
T_film=(((Tmp+273)+(Tg+273))/2);
kond_a=airProp2(T_film ,'k' );
ny=airProp2(T_film, 'ny');
alfa_a=kond_a/(airProp2(T_film, 'rho')*airProp2(T_film,
'cp'));
Ra=9.81*(Tmp-
Tg)*(1/T_film)*(0.025)^3/(alfa_a*ny);%rayleigh number
if beta<=75
B1=1-(1708/(Ra*cos(dr(beta))));
B2=((Ra*cos(dr(beta))/5830)^(1/3))-1;

- 77 -
if B1<0
B1=0;
end
if B2<0
B2=0;
end
Nu=1+1.44*B1*(1-
(sin(dr(1.8*beta)^(1.6)))*1708/(Ra*cos(dr(beta))))+B2;
elseif beta>75
A=Coll_length/p_c_t;%ratio of plate length to space
to absorber
B1=0.288*(Ra*sin(dr(beta))/A)^(1/4);
B2=0.039*(Ra*sin(dr(beta)))^(1/3);
Nu=max(B1,B2);
if B1<1 && B2<1
Nu=1;
end
end
h_c_1=Nu*kond_a/p_c_t;
h_c_2=2.8+3*V;
U_t=((1/(h_r_1+h_c_1))+(1/(h_r_2+h_c_2)) )^(-1);
Tg1=Tmp-(U_t/(h_c_1+h_r_1))*(Tmp-Ta);
U_b=k_b/t_b; %back loss coefficient,W/m2C
A_e=(1.20+2.47)*2*0.086; %edge area
U_e=U_b*(A_e/A_coll); %edge loss coefficient,W/m2C
U_l=U_t+U_b+U_e; %Overall top loss coefficient,
W/m2C
Cp_gl=3806; %specific heat poly glycol
J/kgK
S=Sbar_w_per_m2; %absorbed radiation, W/m2
m=(U_l/(0.0005*385))^(1/2); % plate thermal conductivity
and thickness
F=(tanh(m*(0.143-0.012)/2 ))/(m*(0.143-0.012)/2 );
F_r_s=(1/U_l)/(0.143*(1/(U_l*(0.012+(0.143-
0.012)*F))+1/(pi*0.04*h_fi)));
F_r=(mdot_gl*Cp_gl/(A_coll*U_l))*(1-exp(-
(A_coll*U_l*F_r_s/(mdot_gl*Cp_gl))));
Q_u=A_coll*F_r*(S-U_l*(Tin-Ta)); %%actual
useful gain
Tmp=(Tin+((Q_u/A_coll)/(F_r*U_l))*(1-F_r));% mean plate
temperature , C
Tfo=((Q_u/U_l)+Ta)+(Tin-Ta-(Q_u/U_l))*exp(-
A_coll*U_l*F_r_s/(mdot_gl*Cp_gl));%output water temperature
mu_gl=3.1*10^(-3); %m2/s
nu_gl=mu_gl/rho_gl;
k_gl=0.34 ; %W/m-K 50% H2O @90°C

- 78 -
alfa=k_gl/(rho_gl*Cp_gl); % thermal diffusivity
Pr=nu_gl/alfa; % Prandtl Number
Re=4*mdot_gl/(pi*D_h*10^(-3)*mu_gl); %Reynolds NUmber
f=(0.79*log(Re)-1.64)^(-2);% Darcy friction factor
Nu_gl=(f/8)*(Re-1000)*Pr/(1+12.7*((f/8)^.5)*((Pr^(2/3))-
1));
h_fi=Nu_gl*k_gl/(D_h*10^(-3));% heat transfer coefficient
inside tubes, w/mC
end
A.4. Absorbed radiation program.
function
[Sbar,Sbar_w_per_m2]=absorbed(beta,param,Averagepersunsh,Na
)
Lat=param(1);
Global(1:12)=param(2:13);
Diffuse(1:12)=param(14:25);
rho_g=[.7,.7,.7,.4,.2,.2,.2,.2,.2,.2,.4,.7,.7]; %Ground
N=1;%number of covers
l_g=0.0038; %glass thickness, m
KL=4*l_g;
for m=1:12
if m==1
n=17;
elseif m==2
n=47;
elseif m==3
n=75;
elseif m==4
n=105;
elseif m==5
n=135;
elseif m==6
n=162;
elseif m==7
n=198;
elseif m==8
n=228;
elseif m==9
n=258;

- 79 -
elseif m==10
n=288;
elseif m==11
n=318;
elseif m==12
n=344;
end
[tau_alfa_g,tau_alfa_d,tau_alfa_b]=transmittence(beta(m),N,
KL);
om1=acos(-tan(dr(Lat-beta(m) ))*tan((sigma(n))));
R_b(m)=((cos(dr(Lat-
beta(m)))*cos(sigma(n))*sin(SUnset_angle_on_collec))+...
SUnset_angle_on_collec*sin(dr(Lat-
beta(m)))*sin(sigma(n)))/...
(cos(dr(Lat))*cos(sigma(n))*sin(SUnset_angle_on_collec)
+...
SUnset_angle_on_collec*sin(dr(Lat))*sin(sigma(n)));
Sbar(m)=(Global(m)-
Diffuse(m))*R_b(m)*tau_alfa_b(m)+Diffuse(m)*tau_alfa_d*...
((1+cos(dr(beta(m))))/2)+Global(m)*tau_alfa_g*rho_g(m)*((1-
cos(dr(beta(m))))/2);
Sbar_w_per_m2(m)=((Global(m))*(10^6/(Averagepersunsh(m+1)*3
600))-...
Diffuse(m)*(10^6/(Na(m)*3600)))*R_b(m)*tau_alfa_b(m)+Diffus
e(m)*(10^6/(Na(m)*3600))*tau_alfa_d*...
((1+cos(dr(beta(m))))/2)+Global(m)*(10^6/(Na(m)*3600))*tau_
alfa_g*rho_g(m)*((1-cos(dr(beta(m))))/2);
% absorbed radiation for
end
A.5. Calculation of an optimum slope for incident radiation Isotropic-sky
model.
function Hmax=sloped_iso(beta,param,month)
m=month;
%param=[Kt,Lat,Global,Diffuse];
Lat=param(1);

- 80 -
rho_g=[.7,.7,.7,.4,.2,.2,.2,.2,.2,.2,.4,.7,.7]; %Ground
if m==1
n=17;
elseif m==2
n=47;
elseif m==3
n=75;
elseif m==4
n=105;
elseif m==5
n=135;
elseif m==6
n=162;
elseif m==7
n=198;
elseif m==8
n=228;
elseif m==9
n=258;
elseif m==10
n=288;
elseif m==11
n=318;
elseif m==12
n=344;
end
R_b(m)=((cos(dr(Lat-
beta))*cos(sigma(n))*sin(SUnset_angle_on_collec))+...
(SUnset_angle_on_collec*sin(dr(Lat-
beta))*sin(sigma(n))))/...
((cos(dr(Lat))*cos(sigma(n))*sin(SUnset_angle_on_collec))
+...
(SUnset_angle_on_collec*sin(dr(Lat))*sin(sigma(n))));
Ht_bar=(Global(m)-
Diffuse(m))*R_b(m)+Diffuse(m)*((1+cos(dr(beta)))/2)+...

- 81 -
Global(m)*rho_g(m)*((1-cos(dr(beta)))/2);
Hmax=1/Ht_bar;
A.6. Calculation of transmittance of glass.
function
[tau_alfa_g,tau_alfa_d,tau_alfa_b]=transmittence(beta,N,KL)
theta_g=dr(90-0.5788*beta+0.002693*beta^2);
theta_d=dr(59.7-0.1388*beta+0.001497*beta^2);
theta2=asin(sin(dr(beta)) /1.526); %rad
r_perpen_g=(sin (( theta2- theta_g)))^2/(sin (( theta2+
theta_g)))^2;
%refractive index to surface.
r_perpen_d=(sin (( theta2- theta_d)))^2/(sin (( theta2+
theta_d)))^2;
r_paral_g=(tan (( theta2- theta_g)))^2/(tan (( theta2+
theta_g)))^2;
tau_a=exp( -KL /(cos((theta2)))) ;
r_paral_d=(tan (( theta2- theta_d)))^2/(tan (( theta2+
theta_d)))^2;
tau_d=tau_a/2*( (1- r_paral_d)/(1+(2*N-1)* r_paral_d )+
((1- r_perpen_d)/(1+(2*N-1)* r_perpen_d ))) ;
tau_g=tau_a/2*( (1- r_paral_g)/(1+(2*N-1)* r_paral_g )+
((1- r_perpen_g)/(1+(2*N-1)* r_perpen_g ))) ;
rho_d=tau_a-tau_d;
rho_g=tau_a-tau_g;
alfa_p=1-tau_a;
tau_alfa_g=tau_g*alfa_p/(1-(1-alfa_p)*rho_g);
tau_alfa_d=tau_d*alfa_p/(1-(1-alfa_p)*rho_d);
Lat=53.15;
% mean day of the month
for m=1:12
if m==1
n=17;
elseif m==2
n=47;
elseif m==3
n=75;
elseif m==4
n=105;

- 82 -
elseif m==5
n=135;
elseif m==6
n=162;
elseif m==7
n=198;
elseif m==8
n=228;
elseif m==9
n=258;
elseif m==10
n=288;
elseif m==11
n=318;
elseif m==12
n=344;
end
omega=dr(-2.5*15) ; %radians % [2],page 229
theta_b=acos(cos(dr(Lat-beta) )
*cos(sigma(n))*cos(omega)+...
sin (dr(Lat-beta) )* sin(sigma(n)) );
theta2=asin((sin(theta_b)) /1.526); %rad
%%%beam radiation tau_alfa
r_perpen_b=(sin (( theta2- theta_b)))^2/(sin (( theta2+
theta_b)))^2;
r_paral_b=(tan (( theta2- theta_b)))^2/(tan (( theta2+
theta_b)))^2;
tau_a=exp( -KL /(cos((theta2)))) ;
tau_b=1/2*((1-r_paral_b)/(1+(2*N-1)* r_paral_b )+ ((1-
r_perpen_b)/(1+(2*N-1)* r_perpen_b ))) ;
alfa_p=.90; %absorber plate absorptance independant of
angle
rho_d=tau_a-tau_b;
tau_alfa_b(m) = tau_b*alfa_p/(1-(1-alfa_p)*rho_d) ;
end
A.7. Heating load calculations
function Qload=house(month)
%%%Input desired month

- 83 -
i=month;
Ceiling=1534; %FT2
doors=2*73; %ft2
Windows=211;%ft2
Garage_Walls=446.4;%ft2
Floor=1534;%ft2
FloorP=214.5;%ft2
exposed_area=2797.2;%ft2
Volume=12272;%ft3
Basement=1534;%ft2
%Design conditions ASHRAE (2005)
Cl=4840;%Air latent factor, Btu/h*cfm
Cs=1.1;%Air sensible heat factor, Btu/h*cfm*F
Ct=4.5;% air total heat factor, Btu/hrcfm(Btu/lb)
Hro=1.6; % average winter outside Humidity ratio grains of
moisture per lb of dry air.
% WInter
WIndoorT=68;
WIndoorRH=30;%
WOutdoorT=-17.8;
WdeltaT=85.8;
WBasementT=8.9;
WgarageT=-17.8;
%Summer
SIndoorT=75;
SIndoorRH= 30;%
SOutdoorT=85.7;
SDaily_range=19.1;
SOutdoor_wb=62.9;
SdeltaT=10.7;
SMoistureD=0.001;
%%%These values are calculated by ASHRAE method
%%%Heating loads
Al=116.2; %Ventilation and infiltratioin flow
Qvi=45.34; %%Combined infiltration/ventilation flow rate.
cfm
deltaW=0.0052;%indoor/outdoor HUmidity ratio difference
gr/lb
hrv_erv=0.7;%heat recovery ventilators and energy recovery
ventilators (HRV/ERVs) effectivness.
%Average minimum Temperatures
%Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
%C =[-21.6,-21.5,-15.2,-2.2,5.8,11.3,13.5,11,5.2,-1.9,-
11.1,-18.4]; % °C
F =[-6.8,-6.6,4.6,28,42.4,52.3,56.3,51.8,41.4,28.6,12,-1];
%°F

- 84 -
Fmax =[ 10.4 ,11.7, 23.5 ,48.6 ,67.1 ,77.4 ,80.6 ,76.1,
65.5 ,47.5, 26.8 ,14.4 ,45.9 ];
Tif=68;%Internal Temperature °F
Tic=20;%Internal Temperature °C
deltaT=68-F(i);
IDF=(698+8*deltaT*(0.81+0.53*(0.016/116.2)))/1000;%%Infiltr
ation driving force (ASHRAE 2005,p29.5)
Qi=Al*IDF; %Infiltration airflow rate, cfm
ACH=60*Qi/(2905*8) ;%Air exchange per hour
qvi=Cs*Qvi*deltaT; % Infiltration ventilation load BTU/hr
U_walls_1_floor=0.073;
U_roof=0.049;
U_window=0.35; %%Low-e High solar
% Areas, ft2
% South
SWalls=271.67+289.699; %ft2
SWindows=7.0486+19.3164;
Qload_south_walls=(SWalls-SWindows)*U_walls_1_floor*deltaT;
Qload_south_wind=SWindows*U_window*deltaT;
% East
EWalls=486.39837+95.2444;
EWindows=12.1528+43.5521+29.2917+20;
EDoors=42.25;
Qload_east_walls=(EWalls-EWindows-
EDoors)*U_walls_1_floor*deltaT;
Qload_east_wind=EWindows*U_window*deltaT;
% North
NWalls=527.6586+38.236;
Qload_North_walls=(NWalls)*U_walls_1_floor*deltaT;
% West
% Neglect garage
WWalls=468.733+79.9874+62.5;
WWindows=40+40;
WDoor=30;
Qload_West_walls=(WWalls-WWindows-
WDoor)*U_walls_1_floor*deltaT;
Qload_West_wind=WWindows*U_window*deltaT;
%Roof
U_roof=0.049;
Roof_Area=1655; % roof Area , ft2
deltaT_roof=68-((68-F(i))/2); %% Unheated attic mean T
between outside and inside T
Qload_roof=U_roof*Roof_Area*deltaT_roof;
%Total envelope loads
Qload=qvi+Qload_south_walls+Qload_south_wind+Qload_east_wal
ls+...

- 85 -
Qload_east_wind+Qload_North_walls+Qload_West_walls+...
Qload_West_wind+Qload_roof; % Btu/hr
A.8. Degree to radians conversion
function s = dr(d)
s = (pi/180) * d;
A.9. Radians to degree conversion
function s = rd(d)
s = (180/pi) * d;
A.10. Calculation of optimal degree for absorbed radiation.
function Smax=optimal_beta_absorbed(beta,param,month)
m=month;
%Optimal angle for absorbed radiation
% Absorbed radiation
Lat=param(1);
rho_g=[.7,.7,.7,.4,.2,.2,.2,.2,.2,.2,.4,.7,.7]; %Ground
N=1;%number of covers
l_g=0.0038; %glass thickness, m
KL=4*l_g;
[tau_alfa_g,tau_alfa_d,tau_alfa_b]=transmittence(beta,N,KL)
;
if m==1
n=17;
elseif m==2
n=47;
elseif m==3

- 86 -
n=75;
elseif m==4
n=105;
elseif m==5
n=135;
elseif m==6
n=162;
elseif m==7
n=198;
elseif m==8
n=228;
elseif m==9
n=258;
elseif m==10
n=288;
elseif m==11
n=318;
elseif m==12
n=344;
end
R_b(m)=(cos(dr(Lat-
beta))*cos(sigma(n))*sin(SUnset_angle_on_collec) +...
SUnset_angle_on_collec*sin(dr(Lat-
beta))*sin(sigma(n)))/...
((cos(dr(Lat))*cos(sigma(n))*sin(SUnset_angle_on_collec))
+...
SUnset_angle_on_collec*sin(dr(Lat))*sin(sigma(n)));
Sbar=(Global(m)-
Diffuse(m))*R_b(m)*tau_alfa_b(m)+Diffuse(m)*tau_alfa_d*...
((1+cos(dr(beta)))/2)+Global(m)*tau_alfa_g*rho_g(m)*((1-
cos(dr(beta)))/2);
Smax=1/Sbar;
A.10. Pump power calculation
function p=pump(rho,mwin,mu,pR,pD,Npump,pL)
Area=(pi*pD^2)/4;
V=mwin/rho/Area;

- 87 -
Re=rho*V*pD/mu;
A=(2.457*log(1/((7/Re)^.9+.27*pR/pD)))^16;
B=(37530/Re)^16;
ff=8*((8/Re)^12+1/(A+B)^(3/2))^(1/12);
d=(ff*(pL/pD)*(1/2)*rho*V^2); %
p=(mwin*d)/(Npump*rho*1000);

- 88 -
Appendix B. Solar radiation data
B.1. Diffuse radiation
2361770901002 595 502 648 469 314 154 530 254 478 391 02
2361770901002 298 394 473 656 451 456 410 427 344 296 03
2361770901002 435 458 201 275 261 285 446 253 414 210 467 12245 04
2361770901102 247 01
2361770901102 305 470 165 261 184 299 405 384 293 279 02
2361770901102 95 250 249 224 170 133 231 171 179 179 03
2361770901102 192 255 107 302 325 277 335 365 183 148 02 7415 04
2361770901202 192 01
2361770901202 156 168 211 138 222 125 55 97 176 157 02
2361770901202 274 205 205 210 125 120 244 180 226 147 03
2361770901202 164 177 295 138 216 247 242 189 287 247 294 5937 04
2361770910102 274 01
2361770910102 128 306 286 246 283 167 306 321 186 334 02
2361770910102 349 207 91 203 247 344 319 380 368 183 03
2361770910102 395 290 413 157 242 338 240 235 369 324 232 8489 04
2361770910202 485 01
2361770910202 316 376 394 273 384 430 460 502 552 397 02
2361770910202 438 613 577 553 604 506 468 338 305 322 03
2361770910202 550 502 436 681 546 760 515 772 0 0 0 13570 04
2361770910302 763 01
2361770910302 957 949 841 632 888 593 553 552 718 550 02
2361770910302 753 728 563 883 714 770 733 673 1007 727 03
2361770910302 774 1049 1065 1028 587 486 551 873 683 999 02 23642 04
2361770910402 676 01
23617709104021012 844 403 913 419 1165 530 588 558 408 02
2361770910402 451 769 957 502 568 900 918 639 568 911 03
2361770910402 898 670 585 589 541 534 539 841 531 533 0 20284 04
2361770910502 765 01
2361770910502 556 901 556 979 1033 983 726 663 696 802 02
2361770910502 690 981 957 1360 1208 750 901 620 763 564 03
2361770910502 664 485 1007 559 513 456 1056 574 567 472 662 23704 04
2361770910602 861 01
2361770910602 657 830 461 428 1024 659 987 752 1107 1071 02
2361770910602 850 1008 795 828 677 968 1402 986 1025 1205 03
23617709106021053 943 1045 776 604 566 937 450 861 880 0 25835 04
2361770910702 925 01
23617709107021208 1134 1143 1206 960 938 862 959 825 1029 02
2361770910702 955 1187 703 497 464 623 828 1237 1097 1176 03
2361770910702 738 962 759 1019 635 646 582 771 1144 1056 1333 28676 04
2361770910802 735 01
2361770910802 677 723 938 655 929 866 823 744 487 915 02
2361770910802 682 986 885 858 507 911 907 986 592 625 03
2361770910802 863 631 581 414 549 02 762 841 469 702 556 22799 04
2361770910902 533 01
2361770910902 750 708 646 232 835 525 653 785 397 405 02
2361770910902 876 529 02 490 512 525 402 02 325 354 03
2361770910902 510 514 339 378 388 585 649 584 630 408 0 16001 04
2361770911002 426 01
2361770911002 265 419 459 318 572 387 369 552 648 618 02
2361770911002 508 513 237 648 470 620 523 396 526 407 03
2361770911002 544 309 429 227 335 285 292 460 328 300 256 13220 04
2361770911102 289 01
2361770911102 500 351 166 443 454 290 287 295 258 218 02
2361770911102 176 267 234 279 292 241 304 207 346 245 03
2361770911102 216 254 260 391 185 293 228 362 308 312 0 8662 04
2361770911202 221 01
2361770911202 283 120 122 288 237 308 166 193 282 180 02

- 89 -
2361770911202 150 128 125 272 203 257 187 229 103 294 03
2361770911202 247 232 263 251 236 213 247 273 243 256 277 6865 04
2361770920102 282 01
2361770920102 236 246 331 169 222 148 205 145 238 297 02
2361770920102 81 237 266 316 354 272 366 355 334 257 03
2361770920102 236 376 368 268 225 475 396 271 306 353 393 8742 04
2361770920202 489 01
2361770920202 359 335 545 391 349 341 451 439 418 379 02
2361770920202 512 507 625 602 639 567 444 466 499 475 03
2361770920202 411 457 623 478 208 669 777 584 618 0 0 14168 04
2361770920302 862 01
2361770920302 705 751 804 901 681 1095 710 883 964 752 02
2361770920302 963 935 908 828 933 1005 1077 851 885 789 03
2361770920302 900 832 839 740 804 768 754 952 759 993 950 26711 04
2361770920902 669 01
2361770920902 867 687 673 830 716 652 737 911 361 725 02
2361770920902 804 638 535 725 801 566 870 775 836 345 03
2361770920902 401 735 621 906 490 603 492 371 593 812 0 20078 04
2361770921002 493 01
2361770921002 383 777 446 455 667 594 552 658 453 445 02
2361770921002 515 576 401 673 722 638 569 582 453 451 03
2361770921002 342 449 561 397 359 351 237 395 209 02 02 15297 04
B.2. Number of hours of sunshine
2361770690104 930 30 01
2361770690204 1270 45 01
2361770690304 2060 66 01
2361770690404 2000 67 01
2361770690504 2340 75 01
2361770690604 3440 115 01
2361770690704 3300 106 01
2361770690804 2770 89 01
2361770690904 2390 80 01
2361770691004 820 26 01
2361770691104 1360 45 01
2361770691204 1170 38 01
Skipping lines for years from 1970 to 1991
2361770920104 800 26 01
2361770920204 1790 62 01
2361770920304 2200 71 01
2361770920804 2720 88 01
2361770920904 1260 42 01
2361770921004 1980 64 01
B.3. Global Radiation 1964 to 1991
2361770640501 2350 01
23617706405012679 2763 1821 1946 2666 2675 2817 2851 2620 2595 02
23617706405011180 2114 2901 1921 1071 2118 1980 1649 2524 1833 03
23617706405012733 2671 2474 2646 2809 1825 2541 983 3169 3098 3190 72850 04
2361770640601 2294 01
23617706406012855 2114 2097 2553 2181 3119 3131 1971 2700 1276 02
2361770640601 950 2285 1574 2491 3207 3161 2440 1620 2754 2189 03
23617706406012097 1842 1620 2038 2742 2574 2562 1942 2344 2411 02 68820 04
2361770640701 2502 01

- 90 -
23617706407012436 2177 2775 2537 3286 2495 2784 2629 1649 2855 02
23617706407011821 2867 2038 2600 2901 2934 2177 2193 3144 2738 03
23617706407012909 2796 2696 2499 2763 1540 2466 2453 1967 2085 2352 77562 04
2361770640301 1281 01
23617706403011197 761 1268 1373 1318 686 1469 1565 937 1662 02
23617706403011264 699 1699 841 711 418 1687 1607 1189 1909 03
23617706403011925 1913 1858 1716 347 749 422 1369 1825 1800 1532 39711 04
2361770640401 1857 01
23617706404011000 1858 1632 2043 1105 975 1038 1557 1607 2064 02
23617706404011147 2357 2281 2315 2105 2072 1708 2126 1900 2348 03
23617706404012373 1875 1875 2281 2181 975 2369 1339 2600 2633 02 55710 04
2361770640501 2350 01
23617706405012679 2763 1821 1946 2666 2675 2817 2851 2620 2595 02
23617706405011180 2114 2901 1921 1071 2118 1980 1649 2524 1833 03
23617706405012733 2671 2474 2646 2809 1825 2541 983 3169 3098 3190 72850 04
2361770640601 2294 01
23617706406012855 2114 2097 2553 2181 3119 3131 1971 2700 1276 02
2361770640601 950 2285 1574 2491 3207 3161 2440 1620 2754 2189 03
23617706406012097 1842 1620 2038 2742 2574 2562 1942 2344 2411 02 68820 04
2361770640701 2502 01
23617706407012436 2177 2775 2537 3286 2495 2784 2629 1649 2855 02
23617706407011821 2867 2038 2600 2901 2934 2177 2193 3144 2738 03
23617706407012909 2796 2696 2499 2763 1540 2466 2453 1967 2085 2352 77562 04
2361770640801 2088 01
23617706408012742 1997 2683 2520 2399 2185 2302 2633 1448 2181 02
23617706408012038 2302 2093 2252 2143 1122 2495 2486 2281 2156 03
23617706408011285 1528 1398 2055 2185 2227 1498 2114 1532 2231 2244 64728 04
2361770640901 1484 01
23617706409012160 778 1934 2018 1050 1771 1963 1980 2055 1779 02
23617706409011616 2030 1930 1783 1867 1934 1444 1147 397 1193 03
2361770640901 406 1515 1712 1532 1507 619 1557 1674 607 573 02 44520 04
2361770641001 7511 01
23617706410011574 1452 1444 1457 1260 1327 422 259 699 628 02
2361770641001 460 628 795 1080 10251 4771 2631 5101 69511076 03
23617706410011029 351 460 180 364 464 347 519 690 715 648 232811 04
2361770641101 4631 01
2361770641101 519 280 410 142 803 837 774 644 745 66 02
2361770641101 477 711 309 669 418 7411 5941 2301 1801 4011 03
2361770641101 4351 452 1921 79 452 565 531 422 431 406 02 138901 04
2361770641201 305 01
2361770641201 418 154 163 154 263 150 351 414 498 230 02
2361770641201 355 163 255 205 368 439 468 431 209 213 03
2361770641201 251 259 188 263 167 159 473 355 506 594 339 9455 04
Skipping lines from 1965 to 1990
2361770910101 443 01
2361770910101 483 307 366 396 409 167 306 331 509 425 02
2361770910101 434 208 91 433 247 426 368 529 534 571 03
2361770910101 401 494 592 665 685 553 608 580 372 600 639 13729 04
2361770910201 775 01
2361770910201 720 715 634 744 690 524 637 502 676 844 02
2361770910201 803 679 652 628 618 888 903 1081 1097 1095 03
2361770910201 793 961 436 1093 1167 829 515 787 0 0 0 21711 04
2361770910301 1399 01
23617709103011023 1030 915 1287 1160 1472 1491 1517 1503 1559 02
23617709103011553 1290 1606 1079 1547 1157 736 1387 1062 727 03
23617709103011608 1530 1496 1595 1902 2020 1999 1699 1914 1109 02 43372 04
2361770910401 2026 01
23617709104011425 1942 403 1277 2181 1225 562 1885 2306 2310 02
23617709104012371 2155 1407 2428 2326 1179 1920 2385 2418 2168 03
23617709104012189 2412 2417 2508 2480 2449 2662 2126 2475 2801 0 60792 04
2361770910501 2515 01
23617709105012694 916 2627 2204 1862 2449 2738 2652 2708 2636 02
23617709105012692 2502 2377 1915 1382 2762 1517 2774 2670 2898 03
23617709105012841 2988 1745 2828 3034 3063 2242 3147 3087 3031 2987 77968 04
2361770910601 2619 01
23617709106012955 2593 3009 3086 2339 2862 2780 2755 1394 1979 02

- 91 -
23617709106013071 2146 2768 2560 3078 2632 1911 2578 1998 1921 03
23617709106012690 2515 2508 3033 3093 3116 2748 3161 2683 2596 0 78558 04
2361770910701 2290 01
23617709107012070 2579 2422 2547 2665 1107 2406 2669 2825 1403 02
23617709107012563 1273 2958 2865 3060 2928 2313 1584 2191 1772 03
23617709107012538 1681 1909 2638 2677 2631 2756 2610 1645 1774 1917 70976 04
2361770910801 1888 01
23617709108011120 1408 1931 2481 1141 2201 2335 2335 2622 2016 02
23617709108012240 2118 1827 2062 2449 2103 2137 1705 2333 706 03
2361770910801 989 632 2143 2185 2100 021791 1496 2038 1874 2112 58518 04
2361770910901 1440 01
23617709109011695 804 1928 232 907 1932 1826 1836 1930 1901 02
23617709109011182 1787 021806 1721 1594 653 021790 1711 03
23617709109011506 1512 1666 1653 1587 1101 737 823 1020 1466 0 43185 04
2361770911001 870 01
23617709110011497 1406 1238 1370 1191 1270 1232 580 937 715 02
2361770911001 510 634 237 816 610 691 973 983 933 961 03
2361770911001 574 309 917 991 787 948 950 753 765 300 877 26955 04
2361770911101 502 01
2361770911101 578 364 166 740 578 717 728 641 688 713 02
2361770911101 708 636 647 546 555 590 520 596 427 245 03
2361770911101 543 443 317 460 185 295 228 406 400 413 0 15073 04
2361770911201 309 01
2361770911201 348 120 122 288 402 348 166 193 445 456 02
2361770911201 150 128 125 311 445 270 197 371 103 403 03
2361770911201 439 444 385 356 433 447 433 277 411 274 280 9570 04
B.4. Specifications for Form 4 and the File of Instantaneous Values of
Direct Solar Radiation
____________________________________________________________
__________________
No.of Posi- Num- Content of record, table Comments
record tion ber line, punch card
on MT, No. of
table posi-
line, tions
punch
card
_____________________________________________________________________________
1 2 3 4 5
_____________________________________________________________________________
1 1 1 "4"- instantaneous va-
lues file identifier
2-7 6 Station synoptic index
8-9 2 Year
10-11 2 Month
12-13 2 Radiation parameter code
14-16 3 Degree | station
17-18 2 Minutes | latitude
19-22 4 Degrees | station
23-24 2 Minutes | longitude

- 92 -
25-28 4 Elevation above sea
level (m)
29 1 Parameter T Parameter T should
take the following
value : "0"-if the
table indicates the
true solar time of ob-
servation, "1"-if the
sun's altitude is in-
dicated
30-31 2 Parameter L (the total
number of lines filled
up in a sheet ( or
sheets) of Form 4 for
the given station)
32-78 47 Blanks
79-80 2 "01" - the order num-
ber of record on MT,
table line, punch card
- 29 -
_____________________________________________________________________________
1 2 3 4 5
_____________________________________________________________________________
2 1 1 "4"- instantaneous values
file identifier
8-9 2 Year
10-11 2 Month
14-15 2 Date
16-17 2 Hours | true solar
18-19 2 Minutes | time of ob-
| servation
or
16-18 3 the sun's altitude in
10th degrees
19 1 Parameter Z Parameter Z can have the
following values: "0"- if
measurement was made be-
fore noon; "1" - at true
noon; "2"- in the after-
noon.
20-22 3 Direct solar radiation
value
23 1 Quality flag of direct
solar radiation value
24-27 4 True solar time of ob- *
servation or the sun's
altitude

- 93 -
value
31 1 Quality flag
32-35 4 True solar time of ob- *
servation or the sun's
altitude
value
39 1 Quality flag
. .
. .
. .
- 30 -
_____________________________________________________________________________
1 2 3 4 5
_____________________________________________________________________________
64-67 4 True solar time of obser-
vation or the sun's alti-
tude
68-70 3 Direct solar radiation If less than 7 measu-
value rements were made dur-
ing one day, the corres-
ponding positions should
not be filled in
71 1 Quality flag
72-78 7 Blanks
79-80 2 "02" - the order number
of record on MT, table
line, punch card
. . The order number of the
. . last record should be
. . equal to parameter value
L (see record 1)
* Positions are filled in similarly to positions 16-19.
B.5. Specifications for Forms 1A & lB and Description File
_____________________________________________________________________________
No.of Posi- Num- Content of record,table Comments
record tion ber line, punch card
on MT, No. of
table posi-
line, tions
punch

- 94 -
card
_____________________________________________________________________________
1 2 3 4 5
_____________________________________________________________________________
1 1 1 "1" - description file
identifier
2-7 6 Station synoptic index For stations with
the WMO synoptic in-
dex, bytes 2-6 are
filled in, byte 7
is filled in with
zero; the six-digit
index assigned by
the WRDC is record-
ed in positions
2-7
8-9 2 Year The last two figu-
res of the year are
recorded
10-11 2 The number of lines
filled up in a sheet
(or sheets) of Form 1A
(parameter LA)
12-13 2 The total number of li-
nex filled up in sheets
Forms 1A and 1B
(parameter LB)
14-16 3 Degrees | station The sign "-" means
17-18 2 Minutes | latitude the southern hemi-
sphere
23-24 2 Minutes | longitude the western hemis-
phere
25-28 4 Station elevation
above sea level (m)
29-78 50 Blanks
- 14 -
_____________________________________________________________________________
1 2 3 4 5
_____________________________________________________________________________
79-80 2 "01" - the order num-
ber of record on MT,
table line, punch
card
_____________________________________________________________________________
identifier
8-9 2 Year
10-22 13 Reference instrument Plain language
type

- 95 -
23-32 10 Series number of refe-
rence instrument
33-40 8 Calibration factor of
reference instrument
41-56 16 Units of calibration Plain language
factor
57-60 4 Year Date of refe-
61-62 2 Month rence instru-
63-64 2 Day ment calibra-
tion
65-78 14 Place of reference in- Plain language
strument calibration
79-80 2 "02" - the order number
record, table line,
punch card
______________________________________________________________________________
identifier
8-9 2 Year
10-78 69 Station history - com- Plain language
ments on different
changes at station
- 15 -
______________________________________________________________________________
1 2 3 4 5
______________________________________________________________________________
79-80 2 "02" - the order num- The number of these
ber of record on MT, records is equal to
table line, punch card the number of "com-
ments" lines and is
variable
______________________________________________________________________________
LA+1 1 1 "1"- description file The beginning of
identifier Form 1B records
8-9 2 Year
10-11 2 Code of radiation para-
meter
12,13,14 3 Codes of the time reso-
lution of parameter
measured
15-40 26 Instrument type The receiving sur-
face colour can be
indicated,e.g.
"black and white
pyranometer"
41-50 10 Instrument series,

- 96 -
number
51-66 16 Manufacturer
67-70 4 Instrument manufacturer
year
71-72 2 Year | Beginning of
73-74 2 Month | measurements
| with the in-
| strument
75-76 2 Year | Discontinuance
77-78 2 Month | of measurements
| with the instru-
| ment
79-80 2 The order number of re-
cord on MT, table line,
punch card
______________________________________________________________________________
LA+2 1 1 "1"- description file
identifier
- 16 -
______________________________________________________________________________
1 2 3 4 5
______________________________________________________________________________
2-7 6 Station synoptic
index
8-9 2 Year
10-11 2 Code of radiation
parameter
12-24 8 Calibration factor
before the first
calibration in the
given year
25-39 15 Units Plain language
40-41 2 Month | Date of the
42-43 2 Day | 1st calibrati-
| on in the gi-
| ven year
44 1 Calibration type 1 - calibration by
the sun
2 - calibration by
lamp
53-54 2 Month | Date of the se- If the 2nd and the
55-56 2 Day | cond calib- 3rd calibrations
| ration were not made, the
position are not
filled in
57 1 Calibration type

- 97 -
66-67 2 Month | Date of the
68-69 2 Day | 3rd calibra-
| tion
70 1 Calibration type
79-80 2 The order number of re-
cord on MT, table line,
punch card
- 17 -
B.6. 4.2. Specifications for Form 2 and Daily Sums File
____________________________________________________________
__________________
No.of Posi- No.of Content of record, table Comments
record tion posi- line, punch card
on MT, No. tions
table
line,
punch
card
______________________________________________________________________________
1 2 3 4 5
______________________________________________________________________________
1 1 1 "2"- daily sums file iden-
tifier
8-9 2 Year
10-11 2 Month
17-18 2 Minutes | latitude the southern hemi-
sphere
23-24 2 Minutes | longitude the western hemi-
sphere
25-28 4 Station elevation above
sea level (m)
29-32 4 Monthly mean of daily
sums
33 1 Quality flag of monthly
mean of daily sums
34-37 4 Monthly sum of sunshine
duration
sum of sunshine duration
39-41 3 Monthly mean of sunshine
duration
mean of sunshine duration
79-80 2 "01"- the order number of
record on MT, table line,
punch card
______________________________________________________________________________

- 98 -
2 1 1 "2"- daily sums file iden-
tifier
8-9 2 Year
10-11 2 Month
14-17 4 Daily sum for the 1st day
of the month
- 18 -
______________________________________________________________________________
1 2 3 4 5
______________________________________________________________________________
18 1 Quality flag of daily
sum for the first day
19-22 4 Daily sum for the second
day of the month
sum for the second day
. .
. .
. .
59-62 4 Daily sum for the 10th
day of the month
sum for the 10th day
64-78 15 Blanks
79-80 2 "02"- the order number of
record on MT Table line,
punch card
______________________________________________________________________________
3 1 1 "2"- daily sums file
identifier
8-9 2 Year
10-11 2 Month
day of the month
18 1 Quality flag of daily sum
for the 11th day
day of the month
. .
. .
. .
- 19 -

- 99 -
______________________________________________________________________________
1 2 3 4 5
______________________________________________________________________________
day of the month
64-78 15 Blanks
79-80 2 "03" - the order number Or
punch card
______________________________________________________________________________
4 1 1 "2" - daily sums file
identifier
8-9 2 Year
10-11 2 Month
14-17 4 Daily sum for the 21st
day of the month
sum for the 21st day
. .
. .
. .
64-67 4 Daily sum for the 31st
day of the month
sum for the 31st day
69-74 6 Monthly sum
sum
76-78 3 Blanks
79-80 2 "04" - the order number of
punch card

- 100 -
Appendix C. G series Solar Collectors
Product # Description Retail
G32-P 4' x 8' Grid collector, 3/4" hdr, selective paint $840
A. General Information
1.0 Product Description:
Thermo Dynamics G Series flat plate liquid collectors are single
glazed with low-iron tempered glass. The absorber is an
arrangement of parallel riser fins connected to top and bottom
headers. The fins are aluminum with integral copper riser tubes,
which are completely surrounded by the aluminum and are
metallurgically bonded together. The copper riser tubes are
soldered to internal manifolds (headers), which are available in
either 3/4" or 1" diameter copper pipe. The back and sides are
insulated with a 25 mm (1") layer of compressed fiberglass. The
collector frame is extruded aluminum with a baked-enamel
finish, (dark brown). Collector mounting is by way of a sliding
bolt-track. Flush and racked collector mounting formats are
easily accommodated.
1.1 Options
Factory installed temperature sensors; 3/4" and 1" headers; 12
mm (1/2") riser tubes; absorber coatings: selective Anodic-
Cobalt surface, or selective paint surface.
1.2 Dimensions and Volumes
1.20 m x 2.47 m x 0.086 m
(47-3/8 in x 97-3/8 in x 3-3/8 in)
Gross area: 2.96 m2 (31.9 ft2)
Aperture area: 2.78 m2 (30.0 ft2)
Absorber area: 2.87 m2 (30.9 ft2)
Volume (19 mm (3/4") header): 1.84 liter (0.40 IG) Volume (25
mm (1") header): 2.40 liter (0.53 IG)
1.3 Weight:

- 101 -
Net: 45 kg (99 lb)
Shipping: 64 kg (140 lb)
(includes wooden crate)
2.0 Product Use
2.1 Product Applications:
Residential and commercial domestic hot water, process hot
water, space heating, pool heating
2.2 Geographic and Climatic Limitations:
None.
3.0 Manufacturer's Experience
3.1 Background
Thermo Dynamics Ltd. (TDL) is a Canadian company engaged in
the research, development, production, distribution and
installation of solar thermal equipment. The company has been
involved in the solar thermal industry since 1981 and operates
from its head office and factory in Dartmouth, Nova Scotia,
Canada, the sister city of Halifax situated on the Atlantic coast.
The company's specialization is the glazed liquid-flat-plate (LFP)
collectors with metal absorbers. TDL is a fully integrated solar
thermal company with the ability to convert raw aluminum and
copper into a high technology solar water heating system.
Thermo Dynamics Ltd., as a world leader in solar technology,
manufactures and markets solar heating equipment from

- 102 -
complete systems to basic selective surface components for
O.E.M.'s licensees, dealers and distributors through out North
America, Europe, Africa, New Zealand, as well as 10 other
countries around the world.
3.2 Production:
3000 m2 per year for G32 collectors.
3.3 Projects:
Mount Saint Vincent Motherhouse, Halifax, Nova Scotia, Canada.
Largest SDHW system in Canada. Collector type and number:
224 - G32 Collector area: 675 m2 (7,265 ft2) 1.75 GJ/m2 /year
(154 MBtus/ft2 /year)
Top of the Mountain Apartments, Halifax, Nova Scotia, Canada.
Collector type and number: 49 - G32; 49 - G40 Collector area:
328 m2 (3,531 ft2) 1.78 GJ/m2 /year (156 MBtus/ft2 /year)
Somerset Place Apartments, Halifax, Nova Scotia, Canada
Collector type and number: 120 - G32 Collector area: 356 m2
(3,332 ft2) 2.10 GJ/m2 /year (185 MBtus/ft2 /year)
Thermo Dynamics Ltd. has installed thousands of solar
residential domestic hot water and pool heating systems.
B. Glazing System
1.0 General Description:
Glazing is a 3.2 mm (1/8") single sheet of low-iron tempered
glass with an EPDM rubber seal around the edges. Glazing is
secured by an aluminum capping fastened by stainless steel
screws around the perimeter.
1.1 Trade Names:
Solite
1.2 Chemical Composition:
Iron oxide content of 0.03%
1.3 Physical Treatment:

- 103 -
All glazing is tempered with swiped edges and has a shallow
stipple pattern to reduce specular reflectance.
1.4 Thickness:
3.18 mm (1/8")
1.5 Spacing:
Glazing to absorber: 20 to 25 mm (3/4" to 1")
1.6 Weight:
7.8 kg/m2 (1.6 lb/ft2)
1.7 Appearance:
Translucent; the inner surface is embossed with a stipple pattern
which produces a frosted effect.
2.0 Optical Performance
2.1 Spectral Transmittance:
Visible light 89.8% ASTM E424-71A Ultra violet light 51% ISO
9050 Solar light/energy 89.5% ASTM E424-71A
2.2 Energy Transmission:
Solar spectrum (0-3 micrometres) 89.5% Infrared spectrum (>3
micrometres) No data available
2.3 Refractive Index:
1.525
3.0 Structural Performance
3.1 Tensile Strength:

- 104 -
Design Pressure is 2.87 kPa (.416 psi) for 1/8 inch glass with a
design factor of 2.5. Tensile strength is 152 MPa (22,000 psi)
with a 2.5 safety factor.
3.2 Impact Resistance:
Glazing can withstand 542 J (400 ft-lb) soft-body impact, 3 to 5
times stronger than annealed glass.
3.3 Uniform Load Resistance:
Uniform load testing was conducted at the National Solar Test
Facility in May1986 as part of CSA-378. Positive load: 1.5 kPa
(0.22 psi) Negative load: 1.9 kPa (0.28 psi)
4.0 Thermal Performance
4.1 Coefficient of Thermal Expansion:
89.9 x 10-7 1/°C (49.9 x 10-7 1/°F)
4.2 Operating Temperature Range:
Min: below -46°C (-51°F); max: 260°C (500°F)
4.3 Thermal Conductivity:
No data available
5.0 Fire Behavior:
Non-combustible. Does not produce toxic fumes in a fire
situation.
6.0 Durability:
Glass is chemically inert to most chemical solvents and staining
agents, and is resistant to surface weathering, ultraviolet and
thermal degradation, and moisture damage.
C. Absorber System
The absorber consists of eight parallel aluminum fins with
integral copper riser tubes, which are bonded to and completely
surrounded by the aluminum by means of high-pressure cold-
rolling process. The absorber coating is Anodic-Cobalt selective
surface or black paint selective surface. The riser/header
connection has two parts, a short copper nipple brazed to the
header with the absorber fin soldered to the copper nipple.

- 105 -
1.1 Generic/Trade Names:
Absorber fins: "Sunstrip"
Tubes: copper
Headers: Type M copper
Coating: selective Anodic-Cobalt or paint
Solder/Brazing: 95/5 tin antimony/Silfos
Absorber fins: aluminum (AA 1350/0 alloy)
Tubes: copper (CDA 1220/0 alloy)
Headers: copper
Coating: anodized-cobalt pigmented, or semi-selective paint
Solder/Brazing: no data available
1.3 Physical Treatment:
None.
1.4 Dimensions:

- 106 -
Tube diameter: rhombic shape with an open area of about 120
mm2 (0.19 in2 )
Tube spacing: 143 mm (5.63")
Header diameter: 22.2 or 28.6 mm (3/4" or 1") nominal
Absorber thickness: 0.5 mm (0.02")
Coating thickness: no data available.
2.0 Optical Performance
2.1 Absorptivity of Solar Radiation:
Painted surface: a = 95%
Anodic-Cobalt surface: a = 92%
2.2 Emissivity of Infrared Radiation:
Painted surface: e = 25%
Anodic-Cobalt surface: e = 15%
3.1 Thermal Transfer:
Good thermal transfer due to the high conductivity of aluminum
and the bond between the aluminum fins and copper tubes.
Absorber: no data available
Tubes: no data available
To allow for thermal expansion, the absorber is free to float
within the collector container. EPDM gaskets prevent contact
between the copper headers and the aluminum container.
3.3 Thermal Capacity of Absorber System:
No data available.
Absorber: max. 300°C (572°F)
Tubes: max. 300°C (572°F)
Solder/Brazing: min. -50°C (-58°F); max. 400°C (752°F)
Coating: max. 300°C (572°F)
4.0 Mechanical Integrity:
The collector has completed 30-day stagnation testing at The
National Solar Test Facility (NSTF), Mississauga, Canada, with no
sign of degradation or loss in performance.
5.0 Durability:

- 107 -
The absorber and the selective surface are not affected by
normal aqueous solutions. Stagnation testing has shown no
thermal degradation.
D. Insulation
Collectors are insulated around the sides and back with
fiberglass board. Complies with ASTM-C-612 Classes 1 and 2.
1.1 Trade Names:
Sides: Fiberglas AF530
Back: Fiberglas AF530
Fibrous glass bonded by a thermosetting resin. Inorganic, will
not rot.
1.3 Density:
48 kg/m3 (3.0 lb/ft3)
1.4 Thickness:
Side: 25 mm (1")
Back: 25 mm (1")
2.1 Thermal Conductivity:
0.036 W/mI°C (0.25 Btu Iin/hrIft2I°F) at 24°C (75°F)
2.2 Thermal Resistance:
RSI 0.7 °CIm2/W (R 4 °FIft2Ihr/Btu) at 24°C (75°F)
No data available
Maximum continuous operating temperature is 232°C (450°F).
3.0 Fire Behavior
3.1 Surface Burning Characteristics:
Fiberglas AF530 is inherently fire safe. ULC Flame Spread rating
of 15. (compared to untreated Red Oak as 100 - test method
ULC S-102)

- 108 -
4.0 Durability:
No changes should occur to the insulation when subjected to
chemicals normally encountered in use conditions. No thermal
degradation has been found after prolonged stagnation testing.
Moisture adsorption is less than 0.2% by volume, 96 hours at
49°C (120°F) and 95% R.H. Inorganic therefore does not breed
or promote bacteria and fungus. Essentially odorless.

- 113 -
Appendix D. Building envelope surfaces areas.
Table D.1: South elevation Table D.2: East elevation
Angle
Surface
90° 27°
Walls 486.39837'
95.2444'
Windows 12.1528'
43.5521'
29.2917
20'
Door 42.25'
Roof 15809.2093'
174.133'
Angle
Surface
90° 27°
Walls 271.67'
289.699'
Windows 7.0486'
19.3164'
Roof 106'

- 114 -
Table D.3: North elevation Table D.4: West elevation
Angle
Surface
90° 27°
Walls
Brick wall
527.6586 '
38.236'
Roof 30.23'
149.19'
Angle
Surface
90° 27°
Walls 468.733'
79.9874'
Brick wall 62.5'
Windows 40'
40'
Door 30'
Garage doors 112'
60'
Part of the garage wall 95.8'
33.7'
Roof 249.7'
535.394'
412.438'

- 115 -
Appendix E. Climate data
The climate data retrieved from www.worldclimate.com which has been derived
from GHCN 1: The Global Historical Climatology Network version 1 and from GHCN 2
Beta: The Global Historical Climatology Network, version 2 beta respectively.
Weather station Celinograd (Astana) is at about 51.13°N 71.30°E.
Table E.1: 24-hr Average Temperature
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year
°C -16.7 -16.5 -10.1 2.9 12.9 18.5 20.7 17.9 11.4 2.5 -6.9 -13.8 2.0
°F 1.9 2.3 13.8 37.2 55.2 65.3 69.3 64.2 52.5 36.5 19.6 7.2 35.6
Source: CELINOGRAD data derived from GHCN 2 Beta. 1191 months between 1881
and 1989
Table E.2: Average Maximum Temperature
°C -12.0 -11.3 -4.7 9.2 19.5 25.2 27.0 24.5 18.6 8.6 -2.9 -9.8 7.7
°F 10.4 11.7 23.5 48.6 67.1 77.4 80.6 76.1 65.5 47.5 26.8 14.4 45.9
Source: CELINOGRAD data derived from GHCN 2 Beta. 817 months between 1900 and
1989
Table E.3: Average Minimum Temperature
°C -21.6 -21.5 -15.2 -2.2 5.8 11.3 13.5 11.0 5.2 -1.9 -11.1 -18.4 -3.6
°F -6.8 -6.6 4.6 28.0 42.4 52.3 56.3 51.8 41.4 28.6 12.0 -1.0 25.5

- 116 -
Source: CELINOGRAD data derived from GHCN 2 Beta. 1143 months between 1884
and 1989
Table E.4: Average Rainfall
mm 14.9 13.1 14.6 16.8 28.5 37.4 47.2 35.7 23.1 23.8 16.5 14.5 287.5
inches 0.6 0.5 0.6 0.7 1.1 1.5 1.9 1.4 0.9 0.9 0.6 0.6 11.3
Source: CELINOGRAD data derived from GHCN 1. 1196 months between 1881 and
1990

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