DOI : 10.17577/IJERTV3IS100084
- Open Access
- Total Downloads : 959
- Authors : Z. S Johnson , G. Y Pam , K. M Peter
- Paper ID : IJERTV3IS100084
- Volume & Issue : Volume 03, Issue 10 (October 2014)
- Published (First Online): 18-10-2014
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
Conceptual Design and Performance Prediction of a Thermosyphon Solar Water Heating System using TRNSYS
Z. S Johnson a, G.Y Pam b K. M Peter c
-
Department of Mechanical Engineering Plateau State Polytechnic Barki Ladi Jos Nigeria
-
Department of Mechanical Engineering, Ahmadu Bello University Zaria. Nigeria
-
Department of Mechanical Engineering, University of Jos. Nigeria
Abstract – This study is the design and performance simulation of a solar domestic hot water thermosyphon system for Zaria Nigeria latitude 11.2 oN and longitude 7.8oN. The design method employed is the simulation based method, where detailed mathematical models representing the design procedure of each component and whole system design is coded into a computer program using MATLAB programming language. The program was used to calculate collector design parameters and system characteristics. The effect of some collector design parameters such collector tube diameter, absorber plate thickness and collector tube center to center distance on the heat removal factor were studied through an optimization program written in Matlab programming language to determine their optimal values using . The performance of the system was simulated using TRNSYS 16 software based on the optimal design parameters to predict the storage tank and collector temperature at the end of an average recommended day for each month of the year. The final system configuration and size adopted (Table 2) based on the result of the optimisation, reveals that storage tank water temperature varies between 59 to 82 degrees Celsius at the end of each day for all year round performance for this location. This implies that a very significant fraction of the system load of a monthly average daily hot water demand of 0.1m3 set at 90oC is made by the solar water heater indicating potentials in reduction of family utility bill for heating water.
Keywords: Tank Storage Temperature; Flat-plate collectors; Solar fraction; TRNSYS
-
INTRODUCTION
The Sun emits energy at a rate of 3.8 x 1023 KW, of which, approximately 1.8 x 1014 KW is intercepted by the earth, which is located about 150 million km from the sun. About 60% of this amount reaches the surface of the earth. The rest is reflected back into space and absorbed by the atmosphere. About 0.1% of this energy, when converted at an efficiency of 10% would generate four times the worlds total generating capacity of about 3000 GW [1]. It is also worth noting that the total annual solar radiation falling on the earth is more than 7500 times the worlds total annual
primary energy consumption of 450 EJ [1]. The annual solar radiation reaching the earths surface, approximately 3,400,000 EJ, is an order of magnitude greater than all the estimated (discovered and undiscovered) non-renewable energy resources, including fossil fuels and nuclear energy [1]. However, 80% of the present worldwide energy used is based on fossil fuels. Risks associated with their use are that they are all potentially vulnerable to adverse weather conditions or human acts. World demand for fossil fuels (starting with oil) is expected to exceed annual production, probably within the next two decades. International economic and political crisis and conflicts can also be initiated by shortages of oil or gas. Moreover, burning fossil fuels release harmful emissions such as carbon dioxide, nitrogen oxides, aerosols, etc. which affect the local, regional and global environment.
The heat converted from solar radiation, is well suited to provide domestic hot water and space heating. However satisfactory performance and reliability of a solar water heating system requires proper design to adequately size its components as well as accurate prediction of the delivered useful energy and outlet water temperature [2] .
There has been, extensive work on the analysis of the performance of thermosyphon solar water heaters, both experimentally and analytically, by numerous researchers: Belessiotis and Mathioulakis, [3] developed an efficient and simple simulation approach for thermosyphon solar water heaters and used the proposed methodology for energy optimization of the system in the design phase and for evaluation of test results of an existing system in order to improve it further. Shariah and Shalabi [4] have studied optimization of design parameters for a thermosyphon solar water heater for two regions in Jordan represented by two cities, namely Amman and Aqaba through the use of TRNSYS simulation program. Their results indicate that the solar fraction of the system can be improved by 10 to 25% when each studied parameter is chosen properly.
Zerrouki et al. [6] and Belessiotis and Mathioulakis [3] conducted their work on thermosiphon solar water heaters without heat exchanger. The first researchers took, as parameters of their study, the storage tank average
temperature and the water mass flow rate in the system. No allusion is, however, made to the inlet and outlet water temperatures from the collector and also the inlet and outlet temperatures of the storage tank, which are essential parameters to evaluate the energy of the system. Subsequent researchers undertook numerical and experimental studies with the aim of exploiting the results to bring a better comprehension of the basic operation of the system and also in order to optimize and improve its design.
-
SYSTEM DESCRIPTION (THERMOSYPHON): The system consists of a flat plate solar collector, tilted from the horizontal, a thermally insulated horizontal storage tank and interconnecting pipes connecting the solar collector and the storage tank. The flat plate collector casing is made of dry wood to minimize heat loss. The flat plate collector has evenly spaced copper pipes called risers embossed by semi-circular grooves formed in the flat plate absorber. The casing is covered at the top with a 4 mm
thick glass sealed with a rubber gasket. The absorber plate is painted with black fine matte paint to achieved high absorption coefficient. The underside of the absorber insulated with dry wood to reduce conduction losses. The hot water storage tank made from PVC material is properly lagged with saw dust to minimize heat loss to the surroundings. The hot water storage tank is linked to a source of water from the mains water supply through the cold water inlet as seen in figure 1. Control valves to control the inflow of water into the storage tank from the main supply are incorporated along the length of the pipe linking the mains water supply to the storage tank. To prevent draining back of water into the collector when the temperature in the collector is lower than that in the tank, especially in the night when there is no solar radiation, another control valve is put between the pipe connecting the collector hot water outlet and storage tank hot water inlet. The hot water to meet the domestic load is collected through the hot water outlet.
collector, the collector heat removal factor is expressed as [8].
= 1 (1)
Where:
= 1/
1 + 1 + 1
(2)
+
F is the standard fin efficiency for straight fins with rectangular profile, given as:
Fig. 1. Exploded view of the thermosyphon water heating system.
=
2
2
Where : =
(3)
(4)
-
Copper Grid
-
Supporting Frame
-
Collector Absorber Plate. 4-Collector Outlet Pipe
-
System Design theory.
-
Flat Plate Solar Collector Design Equations
-
Collector heat removal factor: In designing a flat plat collector one important design parameter
that need to be determined is the heat removal
-
Thermal Losses in a Flat-Plate Collector
Heat losses from any solar water heating system take the three modes of heat transfer: radiation, convection and conduction. The conduction heat losses occur from sides and the back of the collector plate. The convection heat losses take place from the absorber plate to the glazing cover and can be reduced by evacuating the space between the absorber plate and the glazing cover and by optimizing the gap between them [9].
An approximate relation for collector top loss coefficient (Utop) given by [8] is expressed as:
=
+
1 ( 2+ 2) +
1 2 + 1+0.133
factor . is analogous to the heat exchanger effectiveness. For a header-riser flat-plate
1
+ +
+0.00591 +
(5)
Where:
= 1 + 0.089 0.1166 1 + 0.07866
(6)
= 520 1 0.0000512 (7)
-
Convective Heat Transfer Coefficient in tubes
The general correlation for obtaining the convective heat transfer coefficient in tubes which is a useful parameter for the calculation of the heat removal factor is expressed as
[11] := 0.430 1
100
(8)
=
(14)
A reasonable guess for for liquid heating collector operated at typical flow rates of 0.01 to 0.02kg/m2s is [8].
= + 10 ( ) (9)
However, the Nusset number is a function of the Reynolds number. For the evaluation of the Nusselt number for a laminar flow where Reynold number. is less than 2200 as in the case of thermosyphon system, Fallziah at el [12] correlated Nusset number as:
1.15
The energy loss through the bottom of the collector is made up of conductive loss to heat flow through the insulation
0.0534
= 3.7 +
0.82
and convection and radiation resistance to the environment. The magnitude of the conduction and radiation loss
(15)
1+0.0335
compared to the radiation loss is such that the radiation is negligible [8]. Thus the back loss coefficient is estimated as [8].
Where is the Reynolds number expressed by Incropera, et al. [13]. as:
=
(10)
= 4
(18)
The edge loss coefficient is the ratio of the thermal
conductivity of the insulation at edge to it thickness; times
is the Prandtl number expressed by Duffie and Beckman [8] as:
the ratio of the area of edge to the collector effective aperture area. Tabor (1958) recommends edge insulation of about the same thickness as the bottom insulation. The
=
2.2 System Load Calculation
(19)
edge loss estimated by assuming one-dimensional sideway heat flow around the perimeter of the collector system is expressed as: [10] .
In this system design, the load is calculated by summing the amount of energy needed to heat water to the desire temperature (sensible heat requirement) and any heat loss from the storage tank and piping system [14] (Annas
=
(11)
1998).
The overall heat loss coefficient for a flat plate collector is composed of the top loss coefficient, the edge loss coefficient and the back loss coefficient. A relation for collector overall heat loss coefficient UL is expressed as [8]:
= + + (12)
2.1.3 Collector useful energy: In steady state, the performance of a flat-plate solar collector can be described by the useful gain from the collector, , which is defined as the difference between the absorbed solar radiation and the thermal loss expressed as [8]:
= + (13)
The + superscript indicates that only positive values of the terms in the square brackets are to be used. Thus, to produce useful gain greater than zero the absorbed radiation must be greater than the thermal losses.
= + + (20)
For satisfactory performance of the system, the collector useful energy gain should be greater than the system total load. i.e >
-
Sensible Heat Requirement.
The sensible heat requirement is the energy needed to raise the temperature of water to desire temperature. If water of volume is to be heated from a mains supplied temperature to a desire temperature, the energy requirement over a specified time horizon may be expressed as follows [15]:
= (21)
When the storage tank temperature is less than the load (desired) temperature (Tst < TL), the desired load temperature requirement can be met by an auxiliary heater. The duty of auxiliary heater is given by the formula [15].
= (22)
-
Pipe/Ducts Losses.
These can be estimated by conventional methods. For any well-designed system the losses from ducts should be small and can be approximated to an adequate degree of accuracy in terms of the inlet and outlet temperatures as [8] :
= + (23)
-
Storage Tank Losses.
Losses from the storage tanks may be significant. The rate of tank losses is estimated from the tank loss coefficient- area product and the ambient temperature surrounding the tank, as [15] :
= (24)
2.3 System Performance Evaluation
2.3.1 System Solar Fraction:
Solar fraction is the fraction of the total hot water energy need that is supplied by solar system, is calculated using the equation from Buckles and Klein [16].
to obtain monthly average daily values of: Ambient temperature, wind velocity and total radiation on tilted surface, for typical recommended day of each month of the year as shown in table 1 [7]. The month with the worst amount of total radiation on collector surface tilted at angle equal to latitude of Zaria (11. 2) is considered as the design month. System design parameters optimization and characteristics would be calculated based on the solar radiation and weather data of the design month.
3.2 Design Calculation and Optimisation Procedure
To determine the flat plate design parameters and system characteristics, required to provide 0.1m3 of hot water set at 90oC at the end of each day, equations (1) to (28) were coded using Matlab programming language in a way that represents the design sequence calculations. Solar radiation and weather data for the design month served as input to these calculations. To optimize the collector design parameters, an optimization program written in Matlab programming language was use to study the sensitivity and effect of varying some of the selected design parameters on the objective function (the heat removal factor). The results
=
(27)
for the optimizations are not shown in this publication. Table 2 shows the results of the design calculations and the
is the total auxiliary energy supplied to the system to support the portion of the total load that is not provide by the solar energy. The solar fraction is a better indicator of the system performance compared to the other parameters such as collector efficiency or heat removal factor, since it manifests the overall performance of the entire system not a component Buckles and Klein [16] .
2.3.2 Collector Efficiency
The Hottel-Whillier equation defines the efficiency for a solar collector in terms of the collector heat removal factor R, given in equation form as [17]:
system characteristics from the optimization results used for the performance simulation.
3.3 System Performance Prediction
The annual performance of the system was evaluated by simulating the collector and storage tank water temperatures for typical average recommended day of the months using TRNSYS 16 software based on the system characteristics and optimal design parameters as presented in table 2.
= = +
(28)
-
-
-
-
Design Approach and Methodology
The bulk of the design of this solar water heating system is to appropriately size the flat plate solar collector to meet the system load and remain within the operating parameters of the materials through numerical simulation.
-
Weather Data and the Design Month:
Solar radiation and meteorological data which are very important driving functions for all solar system design often seem to be highly random and irregular. However, long-term statistical analysis indicates that these variables are predictable to some degree. The dynamic nature of solar data can therefore be smoothed out by formulating a representative data which can characterized the mean-value behavior of any location over a long period [7]. Based on this method, the Typical Meteorological Year (TMY) weather data obtained from www.weatheranalytic.com for the location (Zaria) latitude 11.2o N and longitude 7.8oE will be processed using the type 109 TRNSYS component
-
-
Results And Discussion
Table1 shows the monthly average daily total solar radiation on tilted surface (11.2o) and weather data of Zaria, Nigeria (lat. 11.2o N and Long. 7.8o E) for recommended average day of the months obtained by processing the Typical Meteorological Year (TMY) weather data using the Type 109 solar radiation processor
of TRNSYS 16 software . The The table shows that the month of August has the worst amount of solar radiation. This month is used as the design month. The solar radiation and weather data of this month (August) served as the input for the calculations of system designs parameters and parametric study to determine the optimum system parameters for the performance simulation of the system.
Table 1: Simulated monthly average daily solar and weather data for Zaria for typical average recommended of the months .
(m/s2)
(oC)
(J/m2.day)
JAN
2.60
38
26.8 x 106
FEB
2.57
38
27.5 x 106
MARCH
2.70
40
27.7 x 106
APRIL
2.31
32
26.8 x 106
MAY
2.80
35
26.1 x 106
JUNE
3.50
32
21.2 x 106
JULY
2.91
26
16.2 x 106
AUGUST
3.08
28
15.1x 106
SEPT
1.56
32
24.0 x 106
OCT
2.57
36
23.7 x 106
NOV.
3.39
35
24.9 x 106
DEC.
2.00
33
26.5 x 106
A. AV
2.67
33.75
23.1 x 106
Source: Researcher simulated result
4.2 System Optimum Design Parameters and Simulation
Table 2 shows the final optimum system design parameters and components sizes obtained from the optimization procedures of the system using solar radiation and weather data of the design month (August). These system characteristics (table 2) were used to evaluate and predict the performance of the system in August and other months. Figure 1 to figure 6 shows the predicted performance of the system at the end of the day based on the TMY solar radiation and weather data for each typical recommended average day of each month of the year. From these figures, the system is capable of heating water to temperature above 75oc from the months of January to April. This implies that the system is capable of meeting 83% of the designed load of 0.1 m 3 of hot water set at temperature of 90oC. The figures also indicate a drop in average tank temperature at the end of the day from the months of May to August, with
the worst condition in August (54oC). This may be due to poor weather conditions experience during these months as a result of high amount of rainfall resulting to high cloud cover reducing the amount of solar radiation received on the collector surface. The performance of the system again improved from the months of September to December due to less cloudy conditions leading to higher solar radiation as the rains is lesser in these months.
Table 2a: System components characteristics.
Description
Value/Type
Riser tubes material
Copper
Number of riser tubes
12
Absorber surface
Painted
matt black
Glass type
4 mm low
iron glass
Table 2b: System final optimum design parameters and components size used for the simulation.
Orientation:
Sloped towards true south
Parameter
Description
Values
Collector area (m2)
2.20
()
Heat removal factor-transmiittance-absorbttance product
0.63
Heat removal factor-collector loss coefficient product
14.26
Mass flow rate per unit collector area (kg/h m2)
16.00
Incidence angle modifier constant
0.10
Collector slope (degrees)
12.0
Number of parallel collector risers
12
Riser diameter (m)
0.02
Header diameter (m)
0.02
Header length (m)
1.4
Vertical distance between collector outlet and inlet (m)
0.33
Vertical distance between outlet of tank and inlet of collector (m)
0.37
Diameter of collector inlet pipe (m)
0.02
Length of collector inlet pipe (m)
2.0
Loss coefficient of collector inlet pipe plus insulation (kJ/h m2 oC)
0.625
Diameter of collector outlet piping (m)
0.02
Length of collector outlet piping (m)
0.80
2
Number of right angle bends (or equivalent) in collector outlet piping
2
Loss coefficient of collector outlet pipe plus insulation (kJ/h m2oC)
0.625
Tank volume (m3)
0.120
Tank height (if vertical) or diamete (if horizontal) (m)
0.40
Height of collector return to tank above bottom of tank (m)
0.39
Fluid specific heat (kJ/kg oC)
4.19
Fluid density at standard conditions (kg/m3)
1000
Tank inlet tempt
coll inlet tempt
Tank av. tempt Tempt to Load
80
Tank inlet tempt
coll inlet tempt
Tank av. tempt
Tem
pt to Load
90
Temperature in degrees celsius
70
Temperature in degrees celsius
80
60
70
50 60
50
40
40
30
30
20
8 9 10 11 12 13 14 15 16 17 18
Time in hours
20
8 9 10 11 12 13 14 15 16 17 18
Figure 1: Temperatures variation for a recommended average day in January. (17th January)
Time in hours
Figure 3: Temperatures variation for a recommended average day in March. (16th March)
Tank inlet tempt coll inlet tempt Tank av. tempt
Tank inlet tempt
coll inlet tempt
Tank av. tempt
Tempt to Load
90 90
Temperature in degrees celsius
Temperature in degrees celsius
80 Tempt to Load 80
70 70
60 60
50
50
40
40
30
30
20
8 9 10 11 12 13 14 15 16 17 1
Time in hours
20
8 9 10 11 12 13 14 15 16 17 18
Figure 2: Temperatures variation for a recommended average day in February. (16th February)
Time in hours
Figure 4: Temperatures variation for a recommended average day in April. (15th April)
Tank inlet tempt
coll inlet tempt
Tank av. tempt
Tempt to Load
60
70
Tank inlet tempt
coll inlet tempt 55
Temperature in degrees celsius
65 Tank av. tempt
Temperature in degrees celsius
Tempt to Load
60
50
55
50 45
45
40
40
35 35
30
30
25
8 9 10 11 12 13 14 15 16 17 18
Time in hours
25
Figure 5: Temperatures variation for a recommended average day in May. (15th May)
8 9 10 11 12 13 14 15 16 17
Time in hours
Figure.8:Temperatures variation for a recommended average day in August. (16th Aug)
75
Tank inlet tempt 80
70 coll inlet tempt Tank av. tempt
Temperature in degrees celsius
Tempt to Load
65
60
Tank inlet tempt
coll inlet tempt
Tank av. tempt
Temperature in degrees celsius
70 Tempt to Load
55
50 60
45
40 50
35
30
40
25
8 9 10 11 12 13 14 15 16 17 18
Time in hours
Figure 6: Temperatures variation for a recommended average day in June. 30
(11th June)
80
Tank inlet tempt
coll inlet tempt
Tank av. tempt Tempt to Load
Temperature in degrees celsius
70
20
8 9 10 11 12 13 14 15 16 1
Time in hours
Figure 9: Temperatures variation for a recommended average day in September. (15th Sept.)
60
Tank inlet tempt coll inlet tempt
Tank av. tempt
Tempt to Load
75
50 70
Temperature in degrees celsius
65
40
60
55
30
50
20 45
6 8 10 12 14 16 18
Time in hours
Figure 7: Temperatures variation for a recommended average day in July. 40
th
(17 July) 35
30
25
8 9 10 11 12 13 14 15 16 17
Time in hours
Figure 10: Temperatures variation for a recommended average day in October. (15th Oct)
Tank inlet tempt coll inlet tempt
Tank av. tempt
Tempt to Load
75
70
Temperature in degrees celsius
65
60
55
50
45
40
35
30
25
8 9 10 11 12 13 14 15 16 17 18
Time in hours
Fig.11: Temperatures variation for a recommended average day in November. (14th Nov.)
Tank inlet tempt
coll inlet tempt
Tank av. tempt
Tempt to Load
80
Temperature in degrees celsius
70
60
50
40
30
20
8 9 10 11 12 13 14 15 16 17 18
Time in hours
Figure12: Temperatures variation for a recommended average day in
December. (10th Dec.)
-
CONCLUSIONS
-
Shariah AM, Shialabi B. Optimal design for a thermosyphon solar water heater. Renewable Energy;11:351-361. .( 1997):
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Kulkarni, G.N., Kedare, S.B., Bandyopadhyay, S. The concept of design space for sizing solar hot water systems. Solar Energy: 12:283-298. (2006).
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Zerrouki A, Boume´dien A, Bouhadef K . The natural circulation solar water heater model with linear temperature distribution. Renew Energy;26:549559. (2002).
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Qin L . Analysis modelling and optimum design of solar domestic hot water system. (Phd thesis, University of Wisconsin) Retrieved 13th march 2011 at http://sel.me.wisc.edu/theses. (1998)
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Duffie, J.A., Beckman, W.A., Solar Engineering of the Thermal Processes, second ed. John Wiley & Sons Inc., New York. (991).
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S.N. Agbo and E.C. Okoroigwe, Analysis of Thermal Losses in the Flat-Plate Collector of a Thermosyphon Solar Water heater. Research Journal of Physics, 1: 35-41. (2007).
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Rai G.D. Solar energy utilization: A text book for engineering students 5th Edition, Delhi, Khanna. (2008).
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Jaime B. Principles and Modern applications of mass transfer operations. New Jersy. (2009)
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Fallziah, S. Balbir S. M. Simulation of Convective Heat Transfer Coefficient in The Receiver Tube of a Parabolic Trough Concentrator. ( 2003)
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Incropera, F.P., DeWitt, D.P, Bergman, T.L., & Lavine, A.S., Fundamentals of heat and mass transfer, 6th Ed., Hoboken, NJ, John Wiley & Sons. (2007).
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Annas, H. Conceptual design of a solar-thermal heating system with seasonal storage for a vashon greenhouse. (Unpublished Masters thesis, University of Washington). Retrieved Jan 20th 2012 at http: faculty.washington.edu/malte/pubs/Anna_Thesis.pdf. (2006)
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Govind N. K, Shireesh B. K, Santanu B. Determination of design space and optimization of solar water heating systems. Solar Energy,32: 263-276. (2006)
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Buckles, W.E., Klein, S.A., Analysis of solar domestic hot water heaters. Solar Energy 25 (5), 417424. 1980.
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The solar system is capable of meeting 60% to 90% of the monthly average daily hot water need of 0.1m3 at 90 oC all year round with a collector area of 2.24 m2
-
The performance of a thermosyphon solar heating system depends on many parameters which have to be exploited through simulation and experimental studies. These studies are necessary to obtain a detailed understanding of the system behaviour which leads to more efficient designs.
-
Mirunalini T., Iniyan S, Ranko G. A review of solar thermal technologies. Renewable and Sustainable Energy Reviews ,14: 312322. (2010)
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Young-Deuk K et al. Thermal analysis and performance optimization of a solar hot water plant with economic evaluation. Solar Energy 86 : 13781395. (2012)
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Belessiotis V, Mathioulakis E . Analytical approach of thermosyphon solar domestic hot water system performance. Solar Energy; 72: 715. (2002)
5-Storage Tank Inlet Control Valve. 6- Mains Water Supply Pipe.
7-Hot Water Storage Tank 8- Glass Glassing
9- Tank Outlet Pipe 10- Roller.
A thermosyphon solar water heating system, designed to
NOMENCLATURE
Collector area (m2)
Edge insulation area (m2)
Tank surface area (m2)
Cb Contact resistance (KJ/hr.m.K).
meet a daily load of 100L of hot water at 90oC was designed and the performance of the system was evaluated
Fluid specific heat (KJ/kgK)
through simulation for Zaria using TRNSYS simulation Program. The simulated results lead to the following conclusions:
REFERENCES.
Di Diameter of collector inlet pipe (m)
Outer tube diameter (m)
Heat removal factor
F Collector efficiency factor
F Standard fin efficiency
hfi fluid heat transfer coefficient (KJ/hr.m2.K).
hw Wind heat transfer coefficient KJ/hr.m2.K).
Monthly average daily radiation on a horizontal surface ( kJ/.m2)
Thermal conductivity of fluid in the tank (kJ/h m
oC)
Thermal conductivity of insulation material (kJ/hr m oK)
Plate conductivity (kJ/hr m oK)
Thermal conductivity of edge insulation materials (kJ/hr m oK)
Thermal conductivity of back insulation materials (kJ/hr m oK)
Length of each pipe (m)
Number of glass covers
Collector fluid mass flow rate ( kg/hr.m2)
Heat required to meet load (kJ/hr )
Auxiliary heat to meet load (kJ/hr)
Load met by solar energy (kJ/hr)
Reynolds number
Monthly absorbed radiation (kJ/.m2)
Tpm Mean plate temperature (K)
Collector fluid inlet temperature (K)
Ta Ambient temperatures (K)
Collector fluid outlet temperature (K)
Desired load (hot water) temperature, oC
Thickness of insulation material (m)
Storage temperature (oc)
Collector means fluid temperature (k)
Storage tank inlet temperature (oc)
Loss coefficient edge of collector per unit aperture area (kJ/hr-m2-K)
Loss coefficient of collector outlet pipe plus insulation (kJ/hr m2 oK)
Tank volume (m3)
Overall Loss Coefficient (kJ/ m2hr.k)
Ut Collector top loss coefficient (KJ/hr.m2.K).
Back loss coefficient (KJ/hr.m2.K).
Tank loss coefficient (KJ/hr.m2.K).
Tube spacing (m)
Insulation thickness at the edge (m)
Greek Symbols
Absorber plate emittance
Absorptance of absorber plate
Collector slope (degrees)
Latitude of the location (Degrees)
Absorber plate thickness (m)
Emittance of glass (0.88)
Emittance of plate
Dynamic viscosity, (kg/m s)
Density of water (kg/m3)
Thermal cbic expansion coefficient
Collector efficiency