SOLAR SYSTEMS IN THE ECO VILLAGE AT THE UNIVERSITY OF MANITOBA. Heather King

Transcription

1 SOLAR SYSTEMS IN THE ECO VILLAGE AT THE UNIVERSITY OF MANITOBA Heather King

2 SOLAR SYSTEMS IN THE ECO VILLAGE AT THE UNIVERSITY OF MANITOBA Heather King A thesis submitted in conformity with the requirements for the degree of BACHELOR OF SCIENCE (MECH. ENG) at the University of Manitoba Supervisor: Dr. E. Bibeau Department of Mechanical and Manufacturing Engineering University of Manitoba 2007

3 ABSTRACT Solar technologies are vastly emerging across the globe as a renewable, environmentally acceptable alternative to fossil fuels and other non renewable energy resources. The eco village, an old straw bale barn located on the University of Manitoba s Ft. Garry campus, is currently being used to study solar technologies; more specifically, to examine the use and efficiency of solar air and water collectors. Once installed, data must be logged from these solar collectors to enable the energy output and instantaneous efficiency for each collector to be determined. This report discusses, in detail, the various types of solar collectors that are to be installed at the eco village. Calculations are carried out to determine the optimum location and position the solar collectors should be installed at in order to maximize the amount of solar radiation received by the collectors throughout the year. Research into the transfer of heat throughout each collector allowed for instantaneous efficiency models to be created for each collector, in which a user simply has to enter the required variable input data and the efficiency of the collector is calculated. The report concludes by examining the economical and environmental benefits of installing a system of solar collectors on the University of Manitoba s Ft. Garry campus and the capabilities this proposed system of solar collectors would have in supplementing the university s current district heating system. ii

4 ACKNOWLEDGEMENTS I would like to thank the following people for their assistance during the course of this undergraduate research project: Dr. Eric Bibeau Assistant Professor, Department of Mechanical Engineering, University of Manitoba G. Paul Zanetel, P.Eng Associate Professor, Engineer in Residence, Department of Mechanical Engineering, University of Manitoba Daniel Friesen, P. Eng Mike Ferley, P.Eng Stephanie Zubriski Dr. Kris Dick, P.Eng Consultant, Daniel Lepp Friesen Consulting Energy Advocate, Physical Plant, University of Manitoba Graduate Student, Faculty of Engineering, University of Manitoba Adjunct Professor, Engineer in Residence, Design Engineering, University of Manitoba iii

5 NOMENCLATURE h s = specific enthalpy of evaporation of steam at working pressure I = the direct radiation received by the collector b I = the effective solar radiation on the collector eff I N = the normal terrestrial solar radiation received at ground level m s = steam mass flow rate T a = ambient air temperature Q = heat transferred from the steam Q. L = thermal energy lost to the environment U L = the overall heat loss coefficient = Stefan Boltzmann constant = 5.67 x 10 8 W/m² K 4 = density of the heat transfer fluid = viscosity of the heat transfer fluid Σ = tilt angle of the flat plane of the collector Φ = direction of the angle of tilt Evacuated Tube Collector nomenclature: A c, i = inner tube diameter times collector length A c, o = outer tube diameter times collector length A h, i = heat pipe inner diameter times collector length A h, o = heat pipe inner diameter times collector length D c, i = inner diameter of the collector tube D c, o = outer diameter of the collector tube D, = outer diameter of the heat transfer condenser cond o D h, i = inner diameter of the heat transfer pipe D h, o = outer diameter of the heat transfer pipe F evac = the shape factor between the selectively coated outer surface of the heat pipe and the inner surface of the collector tube F r = flow rate factor h = heat transfer coefficient of the outer surface of the collector tube c h = heat transfer coefficient of the inner surface of the collector tube e h hm = heat transfer coefficient between the heat pipe fluid and the manifold fluid iv

6 h ph = heat transfer coefficient between the fin plate and the heat transfer pipe fluid k = thermal conductivity of the glass collector tube c k = thermal conductivity of the copper heat transfer tube h k fin = thermal conductivity of the fin plate L = the length of the heat transfer pipe m f = flow rate of the fluid through the manifold Pr m = Prandtl number of the heat transfer fluid in the manifold Pr = Prandtl number of the fluid within the heat transfer pipe p Re m = Reynolds number of the heat transfer fluid in the manifold Re p = Reynolds number of the fluid within the heat transfer pipe T c = mean temperature of the collector plate T = mean temperature of the heat pipe h T, = temperature of the fluid in the manifold before heating occurs f i Q. hm = thermal energy transferred from the heat pipe fluid to the manifold fluid U = mean velocity of the fluid within the heat pipe m V = mean velocity of the air flowing over the evacuated tube collector = kinematic viscosity of the liquid in the heat transfer pipe = emissivity of the collector tube c = emissivity of the heat transfer pipe h Flat Plate Collector nomenclature: A c = flat plate collector area D = outer diameter of the fluid tube F ' = collector efficiency factor F R = collector heat removal factor h = convective heat transfer coefficient from the inner fluid tube to the fluid k = thermal conductivity of the fluid tube m = flow rate of the heat transfer fluid through the heat transfer tubes T f = mean temperature of the heat transfer fluid W = distance between centre of two fluid tubes δ = thickness of the fluid tube = heat transfer tube absorptance ε = heat transfer tube emittance v

7 TABLE OF CONTENTS ABSTRACT...ii ACKNOWLEDGEMENTS... iii NOMENCLATURE... iv LIST OF FIGURES... viii LIST OF TABLES... ix 1 INTRODUCTION Purpose and Scope Layout of Thesis REVIEW OF LITERATURE Solar Energy Solar Collectors Solar Evacuated Tube Collector Solar Water Flat Plate Collector Solar Air Flat Plate Collector Solar Wall Air Heating Solar Collector SOLAR COLLECTOR LOCATION Geographical Location Incident Angle Methodology Calculations Solar Irradiance Methodology Calculations Chapter Summary HEAT TRANSFER ANALYSIS Evacuated Tube Collector Efficiency Methodology Calculations Flat Plate Collector Efficiency Methodology Calculations vi

8 5 ECONOMIC ANALYSIS Background Boiler Energy Analysis Collector Energy Analysis Cost Analysis Chapter Summary DISCUSSION OF RESULTS Benefits of Installing Solar Collectors Possible Collector Locations Evacuated Tube or Flat Plate? CONCLUSIONS AND RECOMMENDATIONS Solar Collector Location Instantaneous Efficiency Calculators Economic Analysis Final Recommendations REFERENCES APPENDIX A COLLECTOR SPECIFICATIONS APPENDIX B RETSCREEN DATA FOR WINNIPEG INT. AIRPORT APPENDIX C OPTIMUM TILT ANGLES AND DIRECTIONS: JAN DEC vii

9 LIST OF FIGURES Figure 1: Earth's Energy Budget... 3 Figure 2: Flat Plate Collector... 5 Figure 3: "Eco Village" Evacuated Tube Collector... 6 Figure 4: Single Evacuated Tube Model... 7 Figure 5: Heat Pipe Schematic... 8 Figure 6: Heat Transfer Schematic... 8 Figure 7: EnerWorks Flat Plate Collector... 9 Figure 8: Flat Plate Collector Schematic Figure 9: Sunsiaray Northern Comfort Flat Plate Collector Figure 10: Solar Wall Schematic Figure 11: Solar Geometry Figure 12: Angle of Elevation of the Sun Sept 15/ Figure 13: Azimuth Angle of the Sun Sept 15/ Figure 14: Direct Radiation Received with a Tilt Angle of 45 Sept 15/ Figure 15: Varying Degrees of Tilt Angle Figure 16: Comparison of Tilt Angles Figure 17: "Eco Village" Collector Schematic Figure 18: Equivalent Thermal Circuit Figure 19: Evacuated Tube Efficiency Calculator Figure 20: Flat Plate Collector Efficiency Calculator Figure 21: Distribution of Powerhouse Boiler Usage Figure 22: University of Manitoba Campus Map Figure 23: Hybrid Map of the University Figure 24: Rooftop Solar Collector Locations viii

10 LIST OF TABLES Table 1: Hour Angle Sept 15/ Table 2: Angle of Elevation of the Sun above the Eco Village Sept 15/ Table 3: Azimuth Angle of the Sun Sept 15/ Table 4: Direct Radiation Received by the Collector Sept 15/ Table 5: Summary of Location Results Table 6: Days of Operation in 2006 Boilers 5 and Table 7: Theoretical Collector Efficiencies Table 8: SRCC Heating Applications Table 9: Solar Radiation Values Table 10: Quantity of Collectors Needed Table 11: Collector Area Needed Table 12: Cost to Substitute Boiler 5 with Solar Energy Table 13: Economic Analysis of a System of 10 Collectors Table 14: Rooftop Availability Table 15: Optimum Tilt Angle January Table 16: Optimum Tilt Angle February Table 17: Optimum Tilt Angle March Table 18: Optimum Tilt Angle April Table 19: Optimum Tilt Angle May Table 20: Optimum Tilt Angle June Table 21: Optimum Tilt Angle July Table 22: Optimum Tilt Angle August Table 23: Optimum Tilt Angle September Table 24: Optimum Tilt Angle October Table 25: Optimum Tilt Angle November Table 26: Optimum Tilt Angle December ix

11 1 INTRODUCTION The following chapter introduces the reader to this report, with the aim of clarifying the purpose, scope, and layout the following undergraduate thesis presents. 1.1 Purpose and Scope The purpose of this thesis is to examine and discuss the energy potential of installing solar collectors at the University of Manitoba. The primary intention of this report is to conclude on whether it would be beneficial for the University of Manitoba to install solar collectors on campus. If installed, these collectors would either 1) provide hot water that would tie into the university s district heating system or 2) heat air that could be circulated as a heating source through campus buildings. The eco village, a straw bale barn located on the University of Manitoba s Fort Garry campus, currently has a single evacuated tube collector installed onto its south facing wall. Plans to install two flat plate collectors, both a solar water collector and a solar air collector, as well as a solar wall collector, are in the works. Using manufacturer data for the evacuated tube collector and the solar water flat plate collector, theoretical efficiencies have been calculated. The results from these analyses were then applied to a hypothetically larger quantity of collectors in order to study the economic potential of installing a system of solar collectors on campus. The scope of this project is limited to evacuated tube collectors and solar water flat plate collectors. Solar air collectors, such as the second flat plate collector and the solar wall collector, and photo voltaic (PV) systems could also be analyzed in the same manner; however time and equipment constraints limited this report to the two solar technologies mentioned. December 4 th, Heather King

12 1.2 Layout of Thesis Following the introduction to this report, a basic overview of solar energy and solar energy technologies is provided. The schematics of the evacuated tube collector that is currently mounted on the eco village and the proposed solar water flat plate collector are provided and discussed in detail. Brief overviews of the solar air collector and solar wall collector that the university plans to install along with the solar water collectors are also given, however the scope of this thesis limits the discussion of these solar air collectors, and therefore no analysis will be carried out on these collectors at this time. The first calculation to be discussed is that of the optimal collector location on campus in regards to the sun. Methodology and calculations related to this objective are stated and explained. A heat transfer analysis is then applied to both the evacuated tube system and the flat plate collector system in order to determine the theoretical efficiencies of these collectors. Finally, an economic analysis is conducted on the proposed systems of collectors. Discussion in this section includes the number of collectors needed, the proposed location for these collectors on campus, and the potential energy they would provide in relation to the amount of energy currently used to heat water on campus. A recommendation is then presented on whether or not installing a system of evacuated tube collectors at the University of Manitoba is economically and environmentally advantages. December 4 th, Heather King

13 2 REVIEW OF LITERATURE In order to provide the reader with an introductory lesson on solar collector technologies, the following background section and literature review has been provided. This section will discuss current solar technologies, with specific focus on the collectors that are to be installed at the University of Manitoba s eco village. 2.1 Solar Energy Solar energy is, in the simplest of descriptions, energy from the sun. This energy travels to the earth in the form of electromagnetic radiation and is used to support virtually all life on earth. Approximately 1367 W/m² of energy is available from the sun outside the Earth s atmosphere; however some of this energy is absorbed as it passes through the Earth s atmosphere. For instance, on a clear day, the amount of solar energy available from the sun is in the region of 1000 W/m² [1]. The schematic below shows how the incoming solar radiation from the sun is divided as it enters the Earth s atmosphere [2]. Figure 1: Earth's Energy Budget December 4 th, Heather King

14 As the diagram shows, the majority of the incoming solar energy is absorbed by land and oceans; this is a large amount of free, renewable energy which could be converted to heat energy or stored for later use. Heat and light, direct forms of energy from the sun, and solar based resources account for more than 99.9 percent of the available flow of renewable energy [3]. Solar based resources include wind power, hydroelectricity, biomass and solar collectors. This thesis report will further discuss solar energy collection by the use of solar collectors, such as evacuated tube collectors and flat plate collectors. Further discussion on these different types of collectors follows in the proceeding sections. December 4 th, Heather King

15 2.2 Solar Collectors A solar collector is a device that extracts energy from the incident radiation of the sun and converts it into a more useful form of energy, such as heat. Solar collectors can be used to heat air or water and are often seen atop of homes and industrial buildings. The image below shows a flat plate collector mounted to the roof top of a house in Australia [4]. Figure 2: Flat Plate Collector The two most commonly found solar collectors are flat plate collectors and evacuated tube collectors. A flat plate collector generally consists of a weatherproofed and durable insulated box, containing an absorber sheet and built in heat transfer pipes. The collector is placed in the path of sunlight, which allows the radiation incident on the plate to heat up the water within the heat transfer pipes, causing it to circulate through the system by natural convection. This heated water is usually then accumulated in a storage tank above the collector. Evacuated tube collectors operate on the same general principle as the flat plate collector; however these collectors use evacuated tubes to absorb the sun s incident rays. More detail is provided on evacuated tube collectors and flat plate collectors in the following sections. December 4 th, Heather King

16 Evacuated tube collectors and flat plate collectors are referred to as solar water heating devices. However, solar collector technology is not limited to water heating; solar air heating technology is also commonly seen. Solar air heating collectors operate with the same general principles as water heating collectors, the only difference between the two technologies being that air is the medium to be heated, not water or a heat transfer fluid Solar Evacuated Tube Collector The image below shows the evacuated tube collector that is currently installed on the eco village. This collector was manufactured by Apricus Solar Co. and is installed at a tilt angle of 45 on the buildings south facing wall. Collector specifications for the Apricus solar collector are given in Appendix A. Figure 3: "Eco Village" Evacuated Tube Collector December 4 th, Heather King

17 The evacuated tube collector works by absorbing radiation from the sun through a system of 30 evacuated tubes. Each evacuated tube consists of two glass tubes made from extremely strong borosilicate glass. The outer tube is transparent, which allows light rays to pass through with minimal reflection and maximum absorption. The inner tube is coated with a special selective coating, in this case Al N/Al, which gives the collector excellent solar radiation absorption and minimal reflection properties. A vacuum is created by fusing the top of these two tubes together and pumping out the air contained in the space between the two layers of glass. A schematic of a single evacuate tube is given below. Figure 4: Single Evacuated Tube Model As you can see from the above figure, a copper heat pipe is inserted into the inner borosilicate tube. This heat pipe works as a condenser, based on this principle that liquids boil at a lower temperature when the surrounding air pressure is decreased. The liquid used in the heat pipe is purified water. The heat pipes used in Apricus solar collectors have a boiling point of only 30 C, allowing any liquid in the heat pipe to vaporize if the heat pipe is heated above 30 C. This water vapor rapidly rises to the top of the heat pipe, transferring heat along the heat pipe and exchanging it into the propylene glycol/water heat transfer fluid flowing in the manifold. As the heat is lost at the top of the condenser, the water vapor condenses to form a liquid December 4 th, Heather King

18 and returns to the bottom of the heat pipe to once again repeat the process. The heat transfer fluid used in our application is a 50:50 propylene glycol water solution, in order to achieve the lower freezing point necessary for northern winters. diagramed in Figure 5. This process is Figure 5: Heat Pipe Schematic Figure 6: Heat Transfer Schematic December 4 th, Heather King

19 The figure shown on the previous page illustrates the flow of heat through the evacuated tube collector, from the incident solar energy from the sun collected by the evacuated tubes, to the transfer of heat from the condenser into the water running through the copper header. Once heated, the water in the copper header will be collected in a storage tank for future distribution into the university s district heating system Solar Water Flat Plate Collector At the time of completion of this thesis, an EnerWorks solar water flat plate collector had been ordered by the university, for installation in the Eco Village. The EnerWorks flatplate collector is a high performance collector that boasts an absorbance rate of 94% of the sun s energy [14]. The figure below shows two EnerWorks flat plate collectors mounted to a home in North America. Figure 7: EnerWorks Flat Plate Collector Solar hot water flat plate solar collectors follow the same general principle as an evacuated tube collector; however, the heat transfer process within the collector is much simpler than that of the evacuated tube collector. The diagram on the following page illustrates how the flat plate collector works. December 4 th, Heather King

20 Figure 8: Flat Plate Collector Schematic Energy from the sun strikes the flat, glazed surface of the collector, travelling through the glass surface to be absorbed by the absorber plate. The heat obtained from this energy absorption warms up the heat transfer fluid that is flowing through the collector. This fluid flow enters the collector through an inlet pipe on one corner of the collector, travels through the fluid flow tubes, and exits the collector through an outlet tube located at the opposite corner of the collector. From the outlet tube, heat is transferred through a heat exchanger into a water flow. This heated water is collected in a storage tank for future use. Detailed product specifications for the EnerWorks solar hot water flat plate collector to be installed on at the Eco Village can be found in Appendix A Solar Air Flat Plate Collector The solar air flat plate collector works with exactly the same principles are the solar water flat plate collector, the one and only difference being that the fluid that circulates through the collector is air, not a heat transfer fluid such as water or a propylene glycol solution. December 4 th, Heather King

21 A Sunsiaray Inc. Northern Comfort flat plate collector is to be installed at the eco village. An image of this collector can be seen in Figure 9 below. Figure 9: Sunsiaray Northern Comfort Flat Plate Collector Solar Wall Air Heating Solar Collector The solar wall is a solar system for heating or pre heating ventilation air for buildings. If you were to look at a building which contained a solar wall, it would simply look like the building was composed of conventional metal cladding. This metal cladding, however, contains thousands of tiny perforations which allow fresh air to pass through on the way to the building s heating and ventilation (HVAC) system. As the air passes through these holes into the building, it accumulates free heat from the cladding, which has been warmed by the sun during the day. Ventilation fans installed inside the building create negative pressure to draw air in through the perforations. Once the warmed up air has passed through the solar wall it rises up to be collected into a distribution ducting system. One of the biggest benefits of solar walls is that they even work at night, as the heat that December 4 th, Heather King

22 would otherwise escape freely from the building is captured within the face of the metal cladding and reused for ventilation pre heat. The image below shows a schematic of the principle of solar wall operation [16]. Figure 10: Solar Wall Schematic December 4 th, Heather King

23 3 SOLAR COLLECTOR LOCATION The absolute value of solar radiation available for utilization in a particular site on Earth is dependent on the relation between the location of the site and the location of the sun. In order to maximize the amount of solar radiation available we must optimize the variables in this relation. The diagram below shows the variables that must be optimized [6]: Figure 11: Solar Geometry December 4 th, Heather King

24 Where: A = the angle of elevation of the sun Z = the azimuth angle of the sun Φ = the azimuth angle from due south θ = the incident angle of the collector Ψ = the elevation angle Σ = the tilt angle of the plane In order to show the variation in optimal solar collector location throughout the year, each variable has been calculated for the 1 st of each month for the year Appendix C shows the results of these calculations. Step by step calculations for September 15 th, 2007 are shown in the proceeding sections. 3.1 Geographical Location The first variable that must be specified is the position coordinates of the solar collector. For calculation purposes we will use the coordinates of the eco village. The eco village has the following coordinates [5]: 3.2 Incident Angle Location Latitude Longitude Elevation Above Sea Level Straw Bale Building Service Street 1 SW University of Manitoba Winnipeg, MB Canada N W 238 m (781 ft) Table 3.1 Location of the Eco Village The following section discusses the methodology for calculating the incident angle upon the evacuated tube collector installed on the eco village. Sample calculations for September 15 th, 2007 are also included. The incident angle calculated in the following December 4 th, Heather King

25 sections will apply to both evacuated tube and flat plate collectors mounted on the University of Manitoba campus Methodology The incident angle of the collector, θ, is the angle between the sun s rays and the normal to the plane surface of the collector. This angle is given by the following relation: cos (sin A )(cos ) (cos A)(sin )[cos( Z )] [3 1] By calculating the incident angle we can determine the optimum solar collector position relative to the sun. The following are the steps that must be followed to determine the incident angle of the sun in relation to a solar collector located at the University of Manitoba. For example purposes, calculations will be done for each step of the process for the date of September 15 th, Step 1: Calculate D, the angle of declination. The angle of declination, D, represents the amount by which the Earth s north polar axis is tilted towards the sun. This value varies on a daily basis and can be approximated by the following equation: 360 D 23.45sin (284 n) [3 2] 365 Where: n = the n th day of the year Step 2: Calculate H, the hour angle. The hour angle, H, expresses the time of day in which one 24 hour day is represented as 360 degrees of angle. December 4 th, Heather King

26 Where: H 15t [3 3] t = the time in hours (decimally) from solar noon Step 3: Calculate A, the angle of elevation of the sun. The angle of elevation of the sun above the eco village can be calculated, on an hourly basis, by the following equation: sin A (cos D)(cos H )(cos L) (sin D)(sin L) [3 4] Where: D = the declination angle, calculated above. H = the hour angle, calculated above. L = the latitude of the collector site. The angle of elevation will be positive above the horizon and negative below the horizon. Step 4: Calculate Z, the azimuth angle of the sun. The azimuth angle of the sun, Z, can be calculated as follows: cos D sin H sin Z [3 5] cos A Where: D = the declination angle, calculated above. H = the hour angle, calculated above. A = the angle of elevation of the sun, calculated above. The azimuth angle will be positive to the east and negative to the west, if measured from the south. December 4 th, Heather King

27 Step 5: Determine the optimum tilt angle of the plane, Σ, and the optimum direction of the angle of tilt, Φ, to maximize the incident angle, θ. In order to maximize the amount of solar irradiance we want to get the incident angle between the sun's rays and the normal to the plane surface of the collector to as close to zero as possible. Using equation [3 1], where cos (sin A )(cos ) (cos A)(sin )[cos( Z )], we can see that, in order to make equal to zero, we must set cos equal to 1. By setting cos equal to 1, the solver function in Excel can be used to optimize Σ, the tilt angle of the plane, and Φ, the direction of the angle of tilt Calculations The following computations use the methodology outlined in section to optimize Σ, the tilt angle of the plane, and Φ, the direction of the angle of tilt, for September 15 th, Complete, tabulated data is available in Appendix C for the 1 st of every month from January 2007 to December Step 1: Calculate D, the angle of declination. September 15 th, 2007 is the 258 th day of the year, therefore n 258. Using equation [3 2], D 23.45[2 ( )] D [degrees] Hour t H 12:00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00AM :00AM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM Table 1: Hour Angle Sept 15/07 December 4 th, Heather King

28 Step 2: Calculate H, the hour angle. On September 15 th, 2007, solar noon occurred at 1:24 pm [7]. Using equation [3 3], the hour angle can be calculated. The table to the on the previous page shows the values of the hour angle, in degrees, for each hour of the 24 hour clock for September 15 th, Step 3: Calculate A, the angle of elevation of the sun. From Table 1, the latitude of the eco village is N. By substituting values for D, H, and L into equation [3 4] we can obtain a numerical result for sina, and thus are able to calculate the angle of elevation of the sun above the ecovillage, A for September 15 th, The following table shows these results: Hour sina A 12:00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 AM Table 2: Angle of Elevation of the Sun above the Eco Village Sept 15/07 December 4 th, Heather King

29 The graph shown on the following page shows how the sun rises and falls during the 24 hour period of September 15 th, Sunrise occurs when the angle of elevation of the sun crosses the zero axes from a negative value to a positive one. Likewise, sunset occurs when the angle of elevation of the sun crosses the zero axes from a positive value to a negative value. Figure 12: Angle of Elevation of the Sun Sept 15/07 December 4 th, Heather King

30 Step 4: Calculate Z, the azimuth angle of the sun. By substituting values for D, H, and A into equation [3 5] we can obtain a numerical result for sinz, and thus are able to calculate the azimuth angle of the sun, Z, for September 15 th, The table below shows these results. Hour sinz Z 12:00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 AM Table 3: Azimuth Angle of the Sun Sept 15/07 December 4 th, Heather King

31 Figure 13: Azimuth Angle of the Sun Sept 15/07 The graph shown above shows the oscillation of the azimuth angle of the sun for a 24 hour period on September 15 th, It can be seen that the azimuth angle is at a maximum to the east at sunrise, as the sun rises from the east. Likewise, the azimuth angle is at a maximum to the west at sunset, as the sun sets to the west. Step 5: Determine the optimum tilt angle of the plane, Σ, and the optimum direction of the angle of tilt, Φ, to maximize the incident angle, θ. Using equation [3 1], the values for A, the angle of elevation of the sun, and Z, the azimuth angle of the sun, which were calculated above, and the solver function in Microsoft Excel, it was possible to determine optimum values for the tilt angle of the plane, Σ, and the direction of the angle of tilt, Φ. The optimum values for Σ and Φ for September 15 th, 2007 are shown in the table on the following page. December 4 th, Heather King

32 Hour Opt Σ Opt φ Max cosθ Max θ 12:00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM Table 3.4 Optimizing the Tilt Angle and Direction of the Tilt Angle of the Evacuated Tube Collector on the Eco Village If we were to plot the curves of the optimum tilt angle and the direction of the tilt angle as the day progressed, we would see curves similar to the ones plotted on the following page for September 15 th, The first plot shows the variation in optimum tilt angle. Please note that this graph only shows the values of the tilt angle that are equal to or less than 90. An angle greater than 90 occurs when the sun is below the horizon; a time when irradiance levels are zero. The second plot shown is that of the change in the optimum direction of the angle of tilt as the day progresses. It can be seen from the plot that the optimum tilt direction is 0 ; the time at which the optimum direction of the collector is to face directly south. December 4 th, Heather King

33 Figure 3.4 Optimum Tilt Angle: Sept 15/07 Figure 3.5 Optimum Direction of the Tilt Angle: Sept 15/07 Determining the most beneficial, constant tilt angle for the evacuated tube collector however is not as simple. The optimization of this constant angle will be discussed to further depth in the following section. December 4 th, Heather King

34 3.3 Solar Irradiance The following section discusses the methodology for calculating the solar irradiance directed upon a collector installed at the eco village. Sample calculations for September 15 th, 2007 are also included Methodology The amount of solar irradiance that reaches either the installed evacuated collector or the proposed flat plate collector throughout the day is related to the incident angle of the collector, θ. The incident angle of the collector is the angle that a direct beam of light from the sun makes with the line normal to the plane of the collector, as seen in Figure 3.1. As discussed in Section 3.2, in order to receive optimum solar radiation on the plane of the collector, this angle should be set as close to zero as possible. However, due to the fact that the sun is not a stationary object and rises and falls throughout the day, it is not possible to keep this angle constantly at zero unless a pivoting solar collector was probable, which is not the case. Thus, in order to optimize the amount of radiation received by the collector, we must determine the tilt angle that accumulates the most incident rays onto the plate throughout the day. The following two formulas are utilized in the proceeding section to determine the best tilt angle for the evacuated tube collectors. The first equation that we will use is Equation [3 1], cos (sin A )(cos ) (cos A)(sin )[cos( Z )] [3 1] In this equation A and Z are known values. The direction of the tilt angle, Φ, will be set to 0, as discussed in Section This leaves us with two variables, Σ, the tilt angle of the plane, and θ, the incidence angle of the collector. December 4 th, Heather King

35 The second formula utilized relates the daily solar radiation values for Winnipeg to the incidence angle of the collector [6]. This equation allows us to determine the irradiance upon the collector as it varies throughout the day. I cos [3 6] b I N Where: I = the direct radiation received by the collector b I = the normal terrestrial solar radiation received at ground level N Values for I N can be obtained from RETScreen. International Airport is included in Appendix B. The RETScreen data for Winnipeg Calculations The evacuated tube collector that is currently installed on the eco village is mounted so that it faces directly south and has a tilt angle of 45. Therefore, Σ = 45 and Φ = 0. From the RETScreen data in Appendix B we can see that, for the month of September, the daily solar radiation, I N, is 3.61 kwh/m²/d or kwh/m²/h. Using Equations [3 1] and [3 6] with the values of Σ, Φ, and I N noted above and the values of A and Z as calculated in the previous sections, a curve of the direct radiation received by the collector, throughout the day can be plotted for September 15 th, This plot can be seen on page 27. I b, December 4 th, Heather King

36 Hour A Z Σ φ cosθ θ In [kwh/m²/h] Ib [kwh/m²/h] 12:00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 AM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM :00 PM Table 4: Direct Radiation Received by the Collector Sept 15/07 December 4 th, Heather King

37 The plot below shows how the incident radiation upon the evacuated tube collector increase as the day moves towards mid day, then falls again as the afternoon progresses. Figure 14: Direct Radiation Received with a Tilt Angle of 45 Sept 15/07 One of the aims of this thesis was to determine the optimum tilt angle; the angle in which the most irradiance would be collected by the evacuated tube collector throughout the period of one day. In order to compare the potentials of different tilt angles, the above calculations were done while varying the tilt angle, Σ. As with the example above, the direction of tilt, Φ, was set to 0. The plot on the following page shows the direct radiation received by the evacuated tube collector, I b, as the day of September 15 th, 2007 progresses for tilt angles of 5, 15, 25, 35, 45, 55 and 65. From this it can be concluded that the optimum tilt angle is 50, however any tilt value in the range of 45 to 55 would produce optimal results. December 4 th, Heather King

38 Figure 15: Varying Degrees of Tilt Angle Figure 16: Comparison of Tilt Angles December 4 th, Heather King

39 3.4 Chapter Summary Analysis on the location of the sun with regards to the evacuated tube collector currently installed on the eco village has allowed me to determine the optimum mounting location for an evacuated tube or flat plate collector. The following table summarizes these results: Flat, horizontal surface, such Location as a roof top or an empty field. Tilt Angle, Σ 50 Direction of Tilt Angle, Φ 0 (South Facing) Table 5: Summary of Location Results December 4 th, Heather King

40 4 HEAT TRANSFER ANALYSIS The following section examines the transfer of heat through the Apricus evacuated tube collector and the EnerWorks flat plate collector. A heat transfer model is created for each collector and the overall efficiencies of the individual collectors are determined. 4.1 Evacuated Tube Collector Efficiency The proceeding section discusses and outlines the methodology used to calculate the working efficiency of the Apricus evacuated tube collector that is installed at the ecovillage at the University of Manitoba. In order for these calculations to be accurately applied, the necessary data must be acquired from the solar collector system, through the use of data acquisition equipment Methodology Figure 17 below shows a schematic of a single evacuated tube, comparable to one of the tubes used in the collector currently mounted at the eco village. This tube consists of an outer glass cover which acts as an envelope around a fin plate, which is selectively coated and attached to a heat pipe absorber. The energy obtained from the solar radiation incident on the collector travels as heat and is transferred from the heat pipe evaporator fluid to the heat pipe condenser, and finally to the fluid flowing through the manifold. Figure 17: "Eco Village" Collector Schematic December 4 th, Heather King

41 The heat flow through the evacuated tube to the manifold can be modeled as a thermal circuit. This model allows us to simplify the system for use in the following calculations. Shown below is the thermal circuit equivalent of an evacuated tube [8], as seen in the eco village solar collector. Figure 18: Equivalent Thermal Circuit In the above diagram the nomenclature is as follows: A c, i = collector tube inner diameter times collector length A c, o = collector tube outer diameter times collector length A h, i = heat pipe inner diameter times collector length A h, o = heat pipe outer diameter times collector length h c, o = heat transfer coefficient of the outer surface of the collector tube h hm = heat transfer coefficient between the heat pipe fluid and the manifold fluid T a = ambient air temperature T c = mean temperature of the collector tube T = mean temperature of the heat pipe h T, = temperature of the fluid in the manifold before heating occurs = the effective solar radiation on the collector f i I eff Q. Q. L hm = thermal energy lost to the environment = thermal energy transferred from the heat pipe fluid to the manifold fluid December 4 th, Heather King

42 U L = the overall heat loss coefficient = the product of the absorptivity and transmitivity of the glass tube Assuming steady state conditions, Norton (1992) and Tiwari (2002) describe the rate of useful energy produced by the evacuated tube collector, in Watts, as:. Q u F A [( ) I U ( T T )] [4 1] r c, o eff L fi a Where: F, the flow rate factor, is equal to: r F 1 r U L Ac, o U [4 2] L ( ) ( 1) h A h hm h, o ph And, h ph = heat transfer coefficient between the fin plate and the heat transfer pipe Once the rate of useful thermal energy is determined, the efficiency of the evacuated tube collector can be calculated as:. Q u [4 3] I eff Ac, o The following outline the steps taken to calculate the efficiency of the evacuated tube collector installed at the eco village : Step 1: Calculate h c,o, the heat transfer coefficient of the outer surface of the collector tube. The heat transfer coefficient of the collector tube can be calculated as: December 4 th, Heather King

43 V c ( Tc Ta )( Tc Ta ) hc, o [4 4] Ac, o Ah, i Where: c = emissivity of the glass collector tube = Stefan Boltzmann constant = 5.67 x 10 8 W/m² K 4 V = mean velocity of the air flowing over the evacuated tube collector Step 2: Calculate h c,i, the heat transfer coefficient of the evacuated envelope (inner surface of the collector tube). The heat transfer coefficient of the inner surface of the collector tube can be calculated as: Where: D c, o kc hc, i [4 5] Dh, o Dc, o ln( ) D 2 c, i = outer diameter of the collector tube D c, i = inner diameter of the collector tube D h, o = outer diameter of the heat transfer pipe k c = thermal conductivity of the glass collector tube Step 3: Calculate h h,o, the heat transfer coefficient of the outer surface of the heat transfer pipe. The heat transfer coefficient of the outer surface of the heat transfer pipe can be calculated as: h h, o 2 2 ( Th Tc )( Th Tc ) [4 6] (1 h ) 1 (1 c ) Ah, i ( ) F Ac, i h evac c Where: c = emissivity of the collector tube = emissivity of the heat transfer pipe h December 4 th, Heather King

44 F evac = the shape factor between the selectively coated outer surface of the heat pipe and the inner surface of the collector tube Step 4: Determine the overall heat loss coefficient of the collector, U L. The overall heat loss coefficient of the collector can be calculated as: U L 1 [4 7] h h h h, o c, i c, o Where the heat transfer coefficients three steps. h h, o, c i h, and h c, o were calculated in the previous Step 4: Calculate h hm, the heat transfer coefficient between the heat pipe condenser and the fluid flowing through the manifold. The heat transfer coefficient between the heat pipe condenser and the fluid flowing through the manifold can be calculated as external flow over a cylinder in cross flow. This heat transfer can be expressed as: h hm Nu D D cond, o [4 8] k h Where: D cond, o = outer diameter of the heat transfer condenser k h = thermal conductivity of the copper condenser Nu = Nusselt number of the fluid flowing through the manifold D In order to calculate Nu, the Nusselt number of the fluid flowing through the manifold, D we first need to calculate the Reynolds number of that fluid. December 4 th, Heather King

45 The Reynolds number, Re m, can be calculated as follows: Re m 4 m [4 9] f Dcond, o f Where: m f = the flow rate of the fluid through the manifold f = dynamic viscosity of the fluid within the heat pipe Once the Reynolds number of the heat transfer fluid within the manifold has been determined, the value can be substituted into the following Churchill and Bernstein [15] correlation for a cylinder in cross flow: 1/ 2 1/ 3 5 / Re Pr Re D m D Nu D / 3 1/ 4 [4 10] [1 (0.4 / Pr) ] Where: Pr = Prandtl number of the heat transfer fluid in the manifold m 4 / 5 Substituting the value for the average Nusselt number obtained by the above correlation into equation [4 8], the heat transfer coefficient between the heat pipe condenser and the heat transfer fluid flowing through the manifold can be calculated. Step 5: Calculate h ph, the heat transfer coefficient between the fin plate and the heat transfer pipe fluid. Flow between the fin plate and the heat transfer pipe fluid can be considered as flow over a flat plate. This flow will be assumed to be laminar. The first step to calculating this value is to determine the Reynolds number of the liquid within the heat transfer pipe. December 4 th, Heather King

46 This can be done by using the following relations: Where: U L Re p [4 11] U = the velocity of the liquid within the heat transfer pipe L = the length of the heat transfer pipe = the kinematic viscosity of the liquid in the heat transfer pipe. Please note that since the velocity of the liquid within the heat transfer pipe, in this case purified water, is not known, we will assume it to be very small (~ m/s). Once the Reynolds number has been determined, the following relation can be used to find the heat transfer coefficient between the fin and the heat transfer pipe. Where: h ph 1/ 2 1/ Re p Prp k fin [4 12] L Pr p = the Prandtl number of the fluid within the heat transfer pipe k fin = the thermal conductivity of the fin plate Step 6: Calculate F r, the flow rate factor of the evacuated tube collector. Using equation [4 2], as shown below, and the values calculated above for h ph, the flow rate factor of the evacuated tube collector can be calculated. U L, h hm, and F 1 r U L Ac, o U [4 2] L ( ) ( 1) h A h hm h, o ph December 4 th, Heather King

47 Step 7: Calculate Q, the rate of useful energy produced by the collector. Using equation [4 1], as shown below, and the values calculated above for F r and the rate of useful energy produced by the evacuated tube collector can be calculated. U L,. Q u F A [( ) I U ( T T )] [4 1] r c, o eff L fi a Step 8: Calculate, the instantaneous efficiency of the evacuated tube collector. Using equation [4 3], as shown below, and the value of Q u calculated in step 7, the instantaneous efficiency of the evacuated tube can be calculated. u [4 3] I eff. Q A c, o The eight steps described in the preceding section can be used to calculate the instantaneous efficiency of the Apricus evacuated tube solar water collector that is currently installed at the University of Manitoba s eco village. As an alternative to manually calculating each step of the sequence, a Microsoft Excel spreadsheet has been derived which calculates the instantaneous efficiency of the Apricus evacuated tube collector based on the variable input parameters of the solar collector system (mass flow rate, wind velocity, collector temperature, ambient air temperature and manifold fluid temperature). This program can be found in the disk attached to the appendix of this thesis report. December 4 th, Heather King

48 4.1.2 Calculations As previously mentioned, a Microsoft Excel spreadsheet was created to calculate the instantaneous efficiency of the Apricus evacuated tube collector. This spreadsheet takes seven variable parameter inputs and, along with the known collector and heat transfer fluid parameters, calculates the efficiency of the Apricus evacuated tube collector. The seven variable inputs necessary for the spreadsheet to calculate the efficiency are: 1. The temperature of the ambient air surrounding the collector, in degrees K. 2. The temperature of the heat transfer fluid entering the manifold, in degrees K. 3. The mean temperature of the collector tube, in degrees K. 4. The mean temperature of the heat pipe, in degrees K. 5. The mass flow rate, in kg/s, of the liquid within the heat pipe. 6. The velocity of the air flow over the collector, in m/s. 7. The month of the year. A scroll down menu is available for the user to choose the month of the year that the preceding three parameters were collected. Once the month of the year is known, the spreadsheet can calculate the appropriate incident radiation value received by the collector. Unfortunately, since the data acquisition equipment necessary to log the required inputs from the Apricus evacuated tube collector have not been received at the eco village at this time, no data readings were available for the input values in order to run a test of the program. In lieu of entering obtained data as the input values, a theoretical calculation will be applied to test to efficiency calculator program. For this theoretical calculation, the following input parameters will be used: 1. T a = 293 K = 20 C 5. m = kg/s 2. T f = 288 K = 15 C 6. V = 0. 1 m/s 3. T tube = 298 K = 25 C 7. Month of the Year = September 4. T pipe = 303 K = 30 C December 4 th, Heather King

49 The image below shows the results of this calculation using the excel spreadsheet: Apricus Evacuated Tube Collector Efficiency Calculator Required Inputs: Ambient Air Temperature: 293 [K] Temperature of Fluid flowing into the Manifold: 288 [K] Mean Temperature of the Collector Tube: 298 [K] Mean Temperature of the Heat Transfer Pipe: 303 [K] Air Flow Velocity over the Collector: 0.1 [m/s] Flow Rate of Heat Transfer Fluid in the Heat Pipe: [kg/s] Month of the Year: September Known Collector Parameters: Collector Tube Length: [m] Heat Pipe Length: [m] Collector Tube Outer Diameter: [m] Collector Tube Inner Diameter: [m] Heat Pipe Outer Diameter: [m] Heat Pipe Inner Diameter: [m] Condenser Outer Diameter: [m] Shape Factor between Heat Pipe and Collector Surfaces: Emissivity of the Glass Collector Tube: Emissivity of the Copper Heat Transfer Pipe: Stefan Boltzmann Constant: 5.67E 08 [W/m² K^4] Thermal Conductivity of the Copper Fin Plate: 4.01E+02 [W/m K] Thermal Conductivity of the Condenser: 4.01E+02 [W/m K] Thermal Conductivity of the Glass Collector Tube: 1.4 [W/m K] Heat Transfer Fluid Kinematic Viscosity: [N s/m²] Prandtl Number of Manifold Heat Transfer Fluid: Prandtl Number of Heat Pipe Fluid: 5.5 Effective Radiation Incident on Collector: [W/m²] Velocity of Liquid in the Heat Transfer Pipe: [m/s] Kinematic Viscosity of Liquid in the Heat Transfer Pipe: 8.33E 07 [m²/s] Collector Absorptance: 0.94 Calculated Collector Parameters: Collector Tube Outer Surface Area: [m²] Collector Tube Inner Surface Area: [m²] Heat Transfer Pipe Inner Surface Area: [m²] Condenser Outer Surface Area: [m²] Collector Tube Outer Surface Heat Transfer Coefficient: [W/m² K] Collector Tube Inner Surface Heat Transfer Coefficient: [W/m² K] Heat Transfer Pipe Outer Surface Heat Transfer Coefficient: [W/m² K] Collector Overall Heat Loss Coefficient: [W/m² C] Manifold Heat Transfer Fluid Reynolds Number: Manifold Heat Transfer Fluid Nusselt Number: Heat Transfer Coefficient Between Heat Pipe Condenser and Manifold Fluid: E 05 [W/m² K] Reynolds Number of Fluid in the Heat Transfer Pipe: Heat Transfer Coefficient Between Fin Plate and Heat Pipe Fluid: [W/m² K] Flow Rate Factor: Rate of Useful Energy from the Collector: [W] Efficiency: % Figure 19: Evacuated Tube Efficiency Calculator December 4 th, Heather King

50 4.2 Flat Plate Collector Efficiency The proceeding section follows the same general principles in describing the methodology and calculations used to determine the working efficiency of the EnerWorks flat plate collector, as were used to determine the working efficiency of the Apricus evacuated tube collector. Variation, however, can be seen in the formulae utilized for the flat plate collector from those used in analyzing the efficiency of the evacuated tube collector. As mentioned in the previous section, the necessary data must be acquired for the flatplate system before any calculations can be carried out Methodology Assuming steady state conditions and pump forced flow, Norton (1992) and Tiwari (2002) describe the rate of useful energy from the collector, in Watts, as:. Q u F A [( ) I U ( T T )] [4 10] R c eff L f a Where: A = flat plate collector area c F R, the collector heat removal factor, is equal to: F R mc A U c f L ' A CU L F 1 exp [4 11] mc f ' F, the collector efficiency factor, is equal to: 1 F' U LW W ( ) ( ) hd D ( W D) F [4 12] December 4 th, Heather King

51 F, the fin efficiency, is equal to: F tanh[ m( W D)]/ 2 [4 13] [ m( W D)]/ 2 U L m [4 14] k In which, W = distance between centre of two tubes D = outer diameter of the tube k = thermal conductivity of the tube δ = thickness of the tube h = convective heat transfer coefficient from the inner tube to the fluid Once the rate of useful thermal energy is determined, the efficiency of the flat plate collector can be calculated as: Q. u [4 15] I eff A c Unlike with evacuated tube collectors, the overall heat loss coefficient of the flat plate collector, U L, is a known value. Tiwari and Ghosal (2005) state that the value of the overall heat transfer coefficient for a flat plate collector with a single glass cover at an inclination angle, in an operating range of ambient to 70 C, can be considered as U L = 7.5 W/m² C. Therefore, the only variable left to calculate is h, the convective heat transfer coefficient from the inner tube to the fluid. The steps needed to calculate this value are shown on the next page. December 4 th, Heather King

52 Step 1: Determine the tube. Re D, the Reynolds number of the heat transfer fluid within The Reynolds number within the inner heat transfer tubes of the flat plate collector can be determined using the following formula: Where: m Re D 4 [4 16] D m = flow rate of the heat transfer fluid through the heat transfer tubes = viscosity of the heat transfer fluid Step 2: Determine the Nusselt number of the heat transfer fluid within the tube. Fluid flow within the inner tubes of the flat plate collector can be described as laminar internal flow. In a circular tube that is characterized by a uniform surface heat flux and laminar, fully developed flow, the Nusselt number is a constant; it is independent of Pr, and axial location. Therefore, Nu 4.36 [4 17] Re D, Step 3: Determine h, the convective heat transfer coefficient from the inner tube to the heat transfer fluid. The convective heat transfer coefficient from the inner tube to the heat transfer fluid can be determined by combining equation [4 17] and the following relation. hd Nu D 4.36 [4 18] k December 4 th, Heather King

53 Once the heat transfer coefficient between the inner tube and the heat transfer fluid has been determine, the fin efficiency, collector efficiency factor, and collector heat removal factor can be determined. This then allows for the rate of useful energy from the collector to be calculated, by utilizing equation [4 10], as shown.. Q u F A [( ) I U ( T T )] [4 10] R c eff L f a The instantaneous efficiency of the EnerWorks flat plate solar water collector can thus be determined by applying equation [4 15]: Q. u [4 15] I eff A c As an alternative to manually calculating each step of the sequence, a Microsoft Excel spreadsheet has been derived which calculates the instantaneous efficiency of the EnerWorks flat plate collector based on the variable input parameters of the solar collector system (mass flow rate, ambient air temperature, and heat transfer fluid temperature). This program can be found in the disk attached to the appendix of this thesis report Calculations As mentioned above, a Microsoft Excel spreadsheet was created to calculate the instantaneous efficiency of the EnerWorks flat plate collector. This spread sheet takes four variable parameter inputs and, along with the known collector and heat transfer fluid parameters, calculates the instantaneous efficiency of the EnerWorks flat plate collector. The four variable inputs necessary for the spreadsheet to calculate the efficiency are: 1. The temperature of the ambient air surrounding the collector, in degrees K. 2. The temperature of the heat transfer fluid entering the collector, in degrees K. 3. The mass flow rate, in kg/s, of the heat transfer fluid entering the collector. December 4 th, Heather King

54 4. The month of the year. A scroll down menu is available for the user to choose the month of the year that the preceding three parameters were collected. Once the month of the year is known, the spreadsheet can calculate the appropriate incident radiation value received by the collector. Unfortunately, since the EnerWorks flat plate collector and the necessary data acquisition equipment, have not been received and installed at the eco village at this time, no data readings were available for the input values in order to run a test of the program. In lieu of entering obtained data as the input values, a theoretical calculation will be applied to test to efficiency calculator program. For this theoretical calculation, the following input parameters will be used: 1. T a = 293 K = 20 C T f = 288 K = 15 C m = kg/s 4. Month of the Year = September The image on the next page shows the results of this calculation using the excel spreadsheet. December 4 th, Heather King

55 EnerWorks Flat-Plate Collector Efficiency Calculator Required Inputs: Mass Flow Rate of Heat Transfer Fluid: [kg/s] Ambient Air Temperature: 293 [K] Mean Heat Transfer Fluid Inlet Temperature: 288 [K] Month of the Year: September Known Collector Parameters: Outer Diameter of Heat Transfer Tube: 0.01 [m] Heat Transfer Tube Length: [m] Viscosity of Heat Transfer Fluid: [N s/m²] Nusselt Number of the Heat Transfer Fluid: 4.36 Thermal Conductivity of the Heat Transfer Tube: 401 [W/m K] Overall Collector Heat Loss Coefficient: 7.5 [W/m² C] Distance Between Centre of 2 Heat Transfer Tubes: 0.02 [m] Thickness of Heat Transfer Tube: [m] Specific Heat of the Heat Transfer Fluid: 795 [J/kg K] Effective Radiation Incident on the Collector: [W/m²] Collector Absorptance: 0.94 Calculated Collector Parameters: Flat Plate Collector Area: [m²] Reynolds Number of the Heat Transfer Fluid: Heat Transfer Coefficient from the Inner Tube to the Fluid: [W/m² K] Fin Efficiency: Collector Fin Efficiency: Collector Heat Removal Factor: Rate of Useful Energy from the Collector: [W] Collector Efficiency: 41.8 % Figure 20: Flat Plate Collector Efficiency Calculator From the efficiency calculator output shown in Figure 20, it can be seen that, during the month of September, if the ambient air surrounding the collector is at 25 C and the heat transfer fluid flowing through the collector at a mass flow rate of kg/s is measured to have a mean temperature of 45 C, the efficiency of the collector at that instant is 41.8%. December 4 th, Heather King

56 It should be noted that the heat transfer fluid used in the EnerWorks flat plate collector is a 50:50 propylene glycol water solution. All heat transfer fluid properties used in the efficiency calculator spreadsheet are for a 50:50 propylene glycol water solution. December 4 th, Heather King

57 5 ECONOMIC ANALYSIS In order to determine the energy potential of installing solar collectors on campus, an economic analysis must be undertaken. This analysis will look at the cost of purchasing and installing a system of solar collectors, the number of solar collectors needed to substantially affect the current district heating system at the University of Manitoba, and finally, the pay back period that installing a system of collectors would produce. 5.1 Background The University of Manitoba s powerhouse currently has 6 steam boilers in operation. These boilers are mainly used for domestic hot water and reheat, with the distribution being approximately as follows: Figure 21: Distribution of Powerhouse Boiler Usage Of the six boilers in operation at the powerhouse, boiler 5 and boiler 6 are summer boilers, each with an operating capacity of 15,000 lbs of steam per hour. In order to look at the potential of installing a system of solar collectors on campus, an analysis will be undertaken in which the cost of replacing one of these boilers with solar energy will be determined. December 4 th, Heather King

58 The following table summarizes the number of days boilers 5 and 6 were in operation in 2006, along with the quantity of steam produced each month [10]. Operating Days Boiler 5 Steam Produced [klbs] Operating Days Boiler 6 Steam Produced [klbs] JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC TOTAL Table 6: Days of Operation in 2006 Boilers 5 and 6 Both boilers 5 and 6 have an average operating efficiency of 81% and operate for roughly the same amount of days per month [10]. For analysis sake, the following discussion will determine the potential of replacing the heat obtained from boiler 5 with solar energy. By taking the total pounds of steam produced by boiler 5 in August, as is the dominant month for use of the boiler, it can be seen that the boiler produces, at most, 9879 lbs of steam per hour during August. The following shows the conversion used to obtain this value: Convert to lbs/hour: 1000lbs 1month 1day 7350klbs = 9879 lbs/hour klbs 31days 24hours December 4 th, Heather King

59 5.2 Boiler Energy Analysis In order to eliminate the use of boiler 5, the equivalent to 9879 lbs/hour of steam must be able to be produced by a system of solar collectors. The following relation is used to determine the amount of power, in KW, that this flow rate of steam produces: m s h Q e [5 1] 3600 Where: m s = steam flow rate (kg/h) h s = specific enthalpy of evaporation of steam at working pressure (kj/kg) Q = heat transferred from the steam (kw) Noting that 9879 lbs/hour is equivalent to 4481 kg/h, and that the specific enthalpy of evaporation of steam at 100 psi (the working pressure) is kj/kg [11], we can see that: (4481)(267.1) Q kw 3600 Therefore, a system of collectors must be able to produce ~332.5 kw in order for boiler 5 to be eliminated from the district heating system. 5.3 Collector Energy Analysis As the solar collectors have not yet been tested to determine their working efficiencies, all energy analysis calculations will be done using the theoretical efficiency of the collectors, as given on their respective product specification sheets. December 4 th, Heather King

60 These efficiencies are as follows: Product Efficiency Apricus Evacuated Tube Collector EnerWorks Flat Plate Collector 4.014( Ti Ta ) ( Ti I I Table 7: Theoretical Collector Efficiencies T ) a 2 The Solar Rating & Certification Corporation (SRCC) breaks the different heating applications into the following categories: (T inlet T ambient) Heating Application A 5 C Pool heating in warm climate. B 5 C Pool heating in cool climate. C 20 C Water heating in warm climate. D 50 C Water heating in cool climate. E 90 C Industrial process water heating. Table 8: SRCC Heating Applications During the summer months, when boiler 5 is operational, the climate in Winnipeg can be described as warm. Therefore, in order to determine the efficiency of the EnerWorks Flat Plate collector, T T ) will be set to 20 C. ( i a From the RETScreen data for Winnipeg International Airport, provided in Appendix B, the daily solar radiation, in W/m² can be calculated based on the average monthly hours of sunlight. These values can be seen in Table 9. December 4 th, Heather King

61 Daily Solar Radiation Month Average Monthly [kwh/m²/d] Hours of Sunlight [W/m²] JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC ANNUAL Table 9: Solar Radiation Values For the month of August, in which boiler 5 is most prominently used, it can be seen that the daily solar radiation value is W/m². In order to estimate the theoretical efficiency of the EnerWorks solar collector during August, I, the solar irradiance incident upon the collector, will be set as W/m². The efficiency can be calculated as: 4.014( Ti T I a ) ( Ti I (20) (20) T ) a 2 December 4 th, Heather King

62 The following table summarizes the number of solar collectors needed to obtain enough heat energy from solar radiation to eliminate the use of boiler 5. Collector Apricus Evacuated Tube Collector EnerWorks Flat Plate Collector Solar Radiation for August [W/m²] Efficiency Solar Energy Converted to Heat Energy [W/m²] Collector Absorber Area [m²] Solar Energy Converted to Heat Energy [W] Number of Collectors Needed to Produce kw of Heat Table 10: Quantity of Collectors Needed As Table 10 shows, 418 evacuated tube collectors, or 560 flat plate collectors, would need to be installed by the University of Manitoba in order for the powerhouse to eliminate the use of boiler 5. To put this value into perspective, the area required to house these collectors can be calculated. Table 11 shows a brief calculation of the area needed to house these theoretical solar collector systems. Please note that the area of a standard Canadian football field is approximately equal to 1 acre. Collector Apricus Evacuated Tube Collector EnerWorks Flat Plate Collector Number of Collectors Needed Area of Land Needed per Collector [m²] Total Area of Land Needed for Collector System [m²] Total Area of Land Needed for Collector System [acres] Equivalent Number of Football Fields ~ ~0.4 Table 11: Collector Area Needed From this calculation it can be seen that, if you were to take an area of land approximately the size of approximately half of a football field and fill it with side by side evacuated tube solar collectors, enough energy would be accumulated to eliminate the use of boiler 5. This land may seem like a slightly large area to put aside solely for use by solar collectors, however it is not unreasonable. December 4 th, Heather King

63 The University of Manitoba recently purchased the land on which the Southwood Golf and Country Club resides. This facility is located adjacent to the University of Manitoba and consists of roughly 120 acres of land, 240 times the area needed to house the solar collectors; land that could easily be home to a system of solar collectors. 5.4 Cost Analysis A brief cost analysis will be carried out to determine if there is any financial benefit for the university to install a system of solar collectors to replace boiler 5. This cost analysis will compare the cost of purchasing the solar collectors to the cost of running boiler 5. As this is a simplified cost analysis estimate, factors such as installation and maintenance costs are not included in the calculation. Carbon Finance Intel, a Canadian company which trades greenhouse gasses financial incentives for both Canadian and international customers, states the current trading prices of C0 2 reduction as ~ 22 per tonne of CO 2 (stated 28 Nov 2007 [17]). This value converts to approximately $32.40 CAD per tonne of CO 2. In order to determine the financial incentive the University of Manitoba would obtain by reducing their CO 2 emissions, it must be determined how much CO 2 boiler 5 releases during the month of august. Boiler 5 was in use for 31 days during august 2006 and produced a total of 247,380 kwh s of energy (332.5 kw x 31 days x 24 hours/day). As the boiler is only 81% efficient, 305,407.4 kwh s of energy from natural gas were used by the boiler to produce this steam output. For every kwh of energy from a greenhouse gas that is consumed, 0.21 kg s of CO 2 are released into the atmosphere. This means that boiler 5 released approximately 64,135.6 kg s (64.14 tonnes) of CO 2 into the surroundings during its operating period. Based on the current trading values of CO 2 ($32.40 CAD per tonne CO 2 ), the university would receive an incentive of approximately $2, during the month of august if boiler 5 was replaced with solar energy. Over the course of one year December 4 th, Heather King

64 this reimbursement would equal $24, This financial incentive will be taken into consideration in the following cost analysis. Apricus Evacuated Tube Collector EnerWorks Flat Plate Collector Cost Per Collector [$] Number of Collectors Needed Amount of Energy Produced [kw] Total Cost of Solar Collector System [$] Cost of Boiler 5 Operation [$] Carbon Dioxide Reduction Incentive [S] Annual Energy Savings ,013, , ,957 87,957 24,938 24, , ,895 Simple Payback 9.0 years 8.7 years Table 12: Cost to Substitute Boiler 5 with Solar Energy The values in Table 12 were determined as follows: 1. Cost per collector: Estimate quoted by Apricus and EnerWorks reference collector specifications. 2. Number of collectors needed: Calculated in Table Total cost of solar collector systems: Cost per collector x number of collectors needed. 4. Cost of Boiler 5 Operation: Calculated based on an average natural gas price in Winnipeg of $0.024/kWh. Boiler 5 used 305,407.4 kwh s during august 2006, at a cost of $ Over the course of one year this would equal $87, Carbon dioxide reduction incentive: As discussed above. December 4 th, Heather King

65 6. Annual Energy Savings: Equivalent to the cost of operating boiler 5 plus the CO 2 reduction incentive received by the university. 7. Simple payback: The cost to purchase the system divided by the annual energy savings, in years. From the results shown in Table 12, it can be seen that installing a system of solar collectors on campus to replace the use of boiler 5 is financially feasible. This conclusion is made for two reasons: 1) The average life span of a solar collectors averages around years, making the simple payback period of purchasing the solar collectors shorter than the life of the collectors themselves. This would mean that the university would finish paying off the purchasing cost of the collectors before their life span had ended, allowing the university to actually make a profit out of the use of solar collectors over natural gas steam boilers. 2) Other financial benefits for installing a system of solar collectors exist, beyond that of the CO 2 reduction incentive. Federal government incentives, such as the Renewable Energy Deployment Initiative (REDI). REDI provides funds for up to 25% of the purchase and installation cost of a system of collectors by a business or institution, up to a maximum value of $80,000. If the full spectrum of available government incentives is utilized in the installation of solar collectors on campus, the simple payback period will drop even further, creating more revenue for the university. Installing 418 evacuated tube collectors or 560 flat plate collectors on campus is a large risk for the university as no solar collector system is currently set up to test the results with. It is good, in this case, to look into the advantages of installing a smaller system of collectors on campus. Would the results, both financial and environmental, be the same? December 4 th, Heather King

66 The same analysis was carried out for a system of 100 solar collectors; both the Apricus evacuated tube collector and the EnerWorks flat plate collector. The results of this analysis are contained in Table 13. Apricus Evacuated Tube Collector EnerWorks Flat Plate Collector Cost Per Collector [$] Number of Collectors Total Cost of Solar Collector System [$] Average Annual Solar Radiation [kwh/m²/d] Average Annual Solar Radiation [kw/m²] Collector Absorber Area [m²] Average Annual Incident Radiation [kw] 242, , Collector Efficiency Amount of Energy Produced By One Collector [kw] Amount of Energy Produced By 100 Collectors [kw] % of District Heating System Supplemented Cost to Produce Equivalent Heat by District Heating System [$] Carbon Dioxide Prevented from Entering the Atmosphere [tonnes] Carbon Dioxide Reduction Incentive [S] Annual Energy Savings $13, $10, Simple Payback 17.8 years 17.2 years Table 13: Economic Analysis of a System of 10 Collectors December 4 th, Heather King

67 The results in Table 13 show the same type of results for the system of 100 solar collectors to that of the larger quantity of collectors; however the simple payback period is about double to length. It should be noted, however, that the results from Table 13 analyze a system of collectors over the course of one year and use the average annual daily solar radiation, whereas the larger system of collectors used to replace boiler 5 looked specifically at the summer months, where more solar radiation is available. 5.5 Chapter Summary This chapter examined the economic potential that installing a system of solar collectors at the University of Manitoba would produce. An analysis was carried out to determine how many solar collectors, either evacuated tube or flat plate, would be needed to eliminate the use of one of the smaller, summer load boilers, and what the economic value of installing this theoretical system would be. As the previous sections determined, it is both environmentally and financially advantages to replace one of the boilers from the university s powerhouse with solar energy. The payback period that installing a system of collectors induced would be much less than the lifespan of the collectors themselves, creating both a large reduction in CO 2 emissions and a long term profit for the university. December 4 th, Heather King

68 6 DISCUSSION OF RESULTS After analyzing the potential of installing solar collectors at the University of Manitoba s eco village, many distinctive results and debates arose. These results are discussed in the following sections. 6.1 Benefits of Installing Solar Collectors There are two ways to view the theoretical addition of a system of solar collectors to the University of Manitoba campus. The first view and most obvious view would be to look at the cost that installing a system of collectors ensues and compare it to the payback period installing the system of collectors holds. From the results seen in Section 5.4, it is apparent that the installation of a system of collectors on campus in economically advantages for the university in the long run, and should be highly regarded as an energy conservation method. The second view in which to regard the installation of solar collectors on campus is from an environmental standpoint. The use of steam boilers emits CO 2 into the atmosphere, adding to the Earth s already highly increasing level of greenhouse gasses and global warming. Solar energy, on the other hand, is a completely harm free, renewable energy source. Yes, the price we pay for these collectors now may be significantly higher than that of a steam boiler or natural gas, but what about 50 years from now? Somewhere down the line, whether our generation or the next, someone will have to pay the price for global warming and other easily preventable man made disasters. Many government incentives now exist in which funding for some, if not most, of the cost of purchasing and installing the collectors is provided. Incentives also exist for the reduction of CO 2 from the environment, with some emission trading markets stating exchange rates of up to $32.40 CAD per tonne of CO 2 reduced from release into the atmosphere. December 4 th, Heather King

69 It may be completely unreasonable to convert the entire University of Manitoba s heating system to solar energy, but how much would it really take to convert 5, or even 10% of the university s annual heating use? We can see from the example in Section 5.4 that substituting even 4% of the university s district heating system from boilers to solar energy would prevent around 93 tonnes of CO 2 from being released into the atmosphere per year, not to mention benefitting the University s appeal and environmental conformity from a green stance. 6.2 Possible Collector Locations The following page shows a map of the University of Manitoba. Also shown in the image is the Southwood Golf and Country Club. As mention previously, these 120 acres of land were recently purchased by the University of Manitoba and will be acquired for use by the University in In order to supplement around 4% of the district heating system, approximately 400m² (~0.1 acres) of land would be needed. Of the 120 acres about to be acquired by the university, it must certainly be possible to set aside a tenth of an acre for solar collectors. One could argue that that by designating a certain area of land for solar collectors, the University would be losing potential land for agriculture. This is not necessarily the case. The land underneath the collectors would still be cultivatable; it would just not receive as much sunlight as a fully exposed area of land. However, there are many plants and crops that do not need the sun to thrive. Fungi, such as mushrooms, do not need chlorophyll to grow, and potatoes, once their dormancy is broken, can be fully harvested in a shaded area. In addition, plants, such as hostas, astillbies, ferns, and impatients, will bloom to fully potential in a shaded environment. December 4 th, Heather King

70 Figure 22: University of Manitoba Campus Map December 4 th, Heather King

71 In order to show just how little land is needed to significantly contribute to the University of Manitoba s district heating system with solar energy, the results from the previous chapters have been used to estimate how much solar energy could be obtained from installing solar collectors on the engineering and agriculture building s rooftops. The image below shows a hybrid map of the agriculture building and the engineering building, on the left and the right of the view respectively. Engineering Building Architecture Building Figure 23: Hybrid Map of the University From the image above it can be seen that a majority of the rooftops of these buildings are flat and unused. The hatched red areas on the following image mark potential solar collector system locations on the Architecture and Engineering building s rooftops. December 4 th, Heather King

72 Figure 24: Rooftop Solar Collector Locations By estimating the area, in m², of rooftop contained in the hatched areas, the following analysis was completed to determine the approximate percentage of the district heating system that could be supplemented by installing solar collectors in the available rooftop space. Engineering Building Roof Architecture Building Roof Evacuated Tube Collectors Flat Plate Collectors Evacuated Tube Collectors Flat Plate Collectors Roof top Area Available [m²] Area Needed Per Collector [m²] Max # of Collectors Possible Energy Produced by 1 Collector [kw] Energy Produced by Collector System [kw] % of District Heating System Supplemented Table 14: Rooftop Availability December 4 th, Heather King

73 This breakdown shows that, by installing a system of solar collectors in the un utilized space on top of one or more campus buildings, the university could easily obtain enough heat energy from the sun to significantly supplement the district heating system and drastically reduce CO 2 emissions. 6.3 Evacuated Tube or Flat Plate? The two types of solar collectors that were studied in detail throughout this report were evacuated tube collectors and flat plate collectors. Both operate on the same general principle utilizing energy from the sun to heat water. However, there are a few distinct differences between the collectors that must be discussed. 1. Evacuated tubes, in general, have a higher efficiency than flat plate collectors. This result was seen when the efficiency calculators were used for both the evacuated tube collector and the flat plate collector under the same conditions. The evacuated tube collector gave an efficiency of 76.24% while the flat plate collector gave an efficiency of 41.8%. These results match up to the efficiencies stated on both collectors specification sheets. The Apricus evacuated tube collector suggested a product efficiency of 71.77%, while the EnerWorks flat plate collector was estimated to have an efficiency of 47.78% in the summer months. 2. Of the two types of collectors, flat plate collectors tend to sell at a price reasonably less than evacuated tube collectors. The cost of an Apricus evacuated tube collectors is approximately $2425 per collector, while an EnerWorks flat plate collector would cost around $1750 per collector. 3. As for weathering the elements and surviving a winter in Winnipeg, both collectors should fair the same. However, if a problem were to occur, an evacuated tube collector may be easier to fix. For instance, if a hailstorm December 4 th, Heather King

74 was to damage a flat plate collector, it is most likely that the whole collector would have to be replaced. With an evacuated tube collector, however, only one or two of the tubes may have been damaged, allowing the individual tubes to be easily replaced. If the University of Manitoba were to install a system of solar collectors on campus, it is a matter of quantity over quality as to whether evacuated tube collectors or flat plate collectors should be installed. The calculations and analysis completed during this study confirmed that the payback periods for each system were equivalent; however maintenance costs were not included in those calculations. Therefore, it is suggested that evacuated tube collectors be installed over flat plate collectors, as they would save the university money in the long run. December 4 th, Heather King

75 7 CONCLUSIONS AND RECOMMENDATIONS The aim of this thesis report was to study and analyze the potential, both economic and environmental, that installing a system of solar collectors at the University of Manitoba could provide. This study began by proposing the installation of four solar collectors at the eco village ; an evacuated tube collector, two flat plate collectors (water and air), and a solar wall collector. The scope of this thesis project, unfortunately, was limited as eco village solar collector research project as a whole is in its beginning phase. The solar collectors have been purchased by the university but these collectors, along with the necessary data acquisition equipment, were not accessible for installation at the completion of this thesis project time period. Despite the lack of available equipment, this project studied and analyzed many aspects of a proposed installation of solar collectors on campus. The following conclusion and recommendations can be made upon the completion of this thesis project. 7.1 Solar Collector Location By utilizing the theories of Tiwari & Ghosal, and the work done by Ametek Inc., the optimum angular location of a solar collector at the University of Manitoba was determined. It was found that, in order to receive the maximum amount of solar radiation incident on the collector plane over the course of one year, the tilt angle of the plane should be set to 50 with a tilt angle direction of 0 (facing directly south). It is recommended to install the eco village collectors at these tilt angle coordinates. December 4 th, Heather King

76 7.3 Instantaneous Efficiency Calculators Analyzing the heat transfer flows through the Apricus evacuated tube collector and the EnerWorks flat plate collectors allowed for the creation of a Microsoft Excel spreadsheet for each collector. This collector requires the user to input the variable collector parameters, such as temperatures and fluid flow, and calculates the instantaneous efficiency of the collector. As there is currently no installed, operational solar collector, it was not possible to verify the accuracy of these calculators through experimentation. It is highly recommended that these formulae be verified once the applicable equipment is installed. From the efficiency calculator models created, it was determined that, during the summer months, an evacuated tube collector located at the eco village would have an efficiency of 76.2% while a flat plate collector would have an efficiency of 41.8%. These results are accurate when compared to the solar collector efficiencies stated by the respective manufacturers. 7.4 Economic Analysis A brief economic analysis was performed on several theoretical solar collector systems. This analysis showed both pros and cons to the installation of a system of solar collectors at the University of Manitoba. obtained. The following gives an overview of the conclusions By placing a system of evacuated tube collectors in 1000m² of empty space upon the rooftop of the Engineering Building, approximately 10% of the university s district heating load could be supplemented. This would decrease the amount of CO 2 released into the atmosphere by roughly 220 tonnes a year. December 4 th, Heather King

77 By placing a system of flat plate collectors in 1500m² of empty space upon the rooftop of the Architecture Building, approximately 16.8% of the university s district heating load could be supplemented. This would decrease the amount of CO 2 released into the atmosphere by roughly 372 tonnes a year. The cost for installing enough evacuated tube solar collectors on campus to eliminate the use of one of the U of M powerhouse s smaller, summertime boilers is approx. $1.013 million; installing enough flat plate collectors would cost approx. $0.98 million. If we take these costs, minus the financial incentives available for reducing CO 2 emissions, and compare them to the cost of running a boiler with natural gas, lead to payback periods of 9.0 and 8.7 years respectively. It was concluded that the switch from steam boiler heating to that of solar energy is beneficial to the university in the long run. Due to time constraints on this thesis project, different effects on solar radiation levels were not examined. Factors such as the amount of cloudy days per year, snow coverage on collectors, and collector maintenance should be studied before a system of solar collectors is installed at the University of Manitoba. 7.5 Final Recommendations This thesis report concluded that installing a system of solar collectors at the University of Manitoba is both an economically and environmentally viable project. Further research and analysis of the solar collectors to be installed at the eco village should be carried out to reinforce this claim, and a full, economic and financial cost evaluation should be initiated. December 4 th, Heather King

78 8 REFERENCES [1] About Solar Energy, Canadian Renewable Energy Network, [Online Document], 2000 Jul 10, [cited 2007 Oct 27], Available HTTP: [2] Cheaper and Efficient Energy, Solar Benefits, [Online Document], no date given, [cited 2007 Oct 27], Available HTTP: benefits.com/ [3] Solar Energy, Wikipedia, [Online Document], no date given, [cited 2007 Oct 27], Available HTTP: [4] The Facts about Solar Hot Water, World of Energy, [Online Document], 2007 Feb 27, [cited 2007 Oct 27], Available HTTP: [5] Winnipeg, Wikipedia, [Online Document], no date given, [cited 2007 Oct 28], Available HTTP: [6] Ametek, Inc., Solar Energy Handbook: Theory and Applications, 2 nd Edition, Chilton Book Company, [7] Sunrise and Sunset in Winnipeg, Time and Date AS, [Online Document], no date given, [cited 2007 Sept 29], Available HTTP: &obj=sun&afl= 11&day=1 [8] Tiwari, G. N., Solar Energy Technology Advances, 1 st Edition, Nova Science Publishers, [9] Technical Information, Apricus Solar Co., [Online Document], 2007, [cited 2007 Nov 15], Available HTTP: [10] University of Manitoba Powerhouse Annual Report 2006, University of Manitoba, [11] Çengel, Y.A. & Boles, M.A., Thermodynamics: An Engineering Approach, 4 th Edition, McGraw Hill Higher Education, [12] Solar Collector Efficiency, Energistic Systems, [Online Document], no date given, [cited 2007 Nov 21], Available HTTP: December 4 th, Heather King

79 [13] Profitability Index Calculator, MONEY zine.com, [Online Document], 2006, [cited 2007 Nov 22], Available HTTP: zine.com/calculators/investment Calculators/Profitability Index Calculator/ [14] Residential Products, EnerWorks Inc., [Online Document], 2007, [cited 2007 Nov 24], Available HTTP: [15] Incropera et al, Fundamentals of Heat and Mass Transfer, 6 th Edition, John Wiley & Sons, [16] World's Largest Solar Wall at Canadair Facility, Natural Resources Canada, [Online Document], 2005 Sep 26, [cited 2007 Nov 27], Available HTTP: tr=20 [17] Carbon Finance Intel, Carbon Finance Intel, [Online Document], 2006, [cited 2007 Nov 28], Available HTTP: December 4 th, Heather King

80 APPENDIX A COLLECTOR SPECIFICATIONS This appendix lists the technical specifications of the two collectors studied throughout this report. The Apricus Evacuated Tube Collector specifications can be found at the following site: APCollectorSpecificationsRev.1.6.pdf The EnerWorks Flat Plate Collector specifications can be found at the following site: December 4 th, Heather King

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91 EnerWorks Flat Plate Collector Specifications: December 4 th, Heather King

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93 APPENDIX B RETSCREEN DATA FOR WINNIPEG INT. AIRPORT This appendix gives the RETScreen data for Winnipeg International Airport that was utilized throughout this report. RETScreen International can be accessed at December 4 th, Heather King

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