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BLDG 476-‐ Building Thermal Analysis
Concordia University Project # 1
Modeling Indoor Thermal Conditions in Urban Heat Island Areas
Submitted to:
Professor Haghighat September 24 2013
Submitted by:
Name: Rupali Patel
ID: 9578587
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1. Introduction In terms of urbanization and development, Montreal is one of Canada’s oldest cities with an everyday growing population. With many residential buildings and houses built in the 1950s, an issue under concern is rising: Retrofitting the buildings to comply with today’s building standards and codes as economically and ecologically as possible. Another issue is also underhand and it is climate change. Greener areas in the cities are becoming less common and housings, businesses and highways are popping up in underdeveloped towns. The rising temperatures during the summer have led to the Heat Alert and Response System in buildings due to urban heat islands. The Health Office of Quebec initiated this system because many older buildings do not have an air conditioning or mechanical ventilation systems and its residents are prone to many health issues. The system estimates indoor thermal characteristics of a building with respect to its building materials, the temperatures, outdoor issues etc. 1.1 Scope In this project, I will act as the HOQ and using Matlab, determine the temperature distributions through each wall and the indoor temperatures of a 3 story residential building in Montreal. The intention and thought process behind modeling this building is designing it for the worst possible case. Meaning using low efficient building materials, low performing windows, temperatures recorded during heat waves and assuming no air conditioning or ventilation system. 1.2 Objective To predict the hourly room air temperature in consideration with various real life factors. (Plotted on graph) To predict hourly temperature distributions in the north, east, west and south walls and in the roof all while neglecting the thermal mass of the building itself. (Plotted on graph) To take into consideration estimated heat gains and losses from:
-‐ Solar radiation -‐ Temperature difference
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-‐ Heat generated by occupants -‐ Air exchange
To take into consideration calculated heat gains and losses from:
-‐ Solar radiation intensities on different surfaces -‐ Ambient air temperatures -‐ Heat gains from the source in the room -‐ Air exchanges
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1. Methodology 1.1 Building Considerations 1) Building Location: The building must be of a high construction density built in Montreal. Therefore we will use building materials such as high-‐density insulation, brick or concrete exterior and standard gypsum board. We will consideration the month of July since it has the highest recorded temperatures. We must omit all wind sources but take into consideration heat emissions from surrounding buildings which. This type of heat will come from convection from the HVAC systems of the surrounding buildings. 2) Building System: For this project, we will consider the building with no air conditioning or mechanical ventilation whatsoever. This will force us to find an optimal solution in the most severe conditions and we can later add HVAC as improvements if needed. 3) Building Envelope: For the purpose of this project, inefficient and low performing materials will be used to put emphasis on the worst case scenario and due to the fact that the building was built in the 1950s. The building will have low exterior material surface albedo (brick / stone cladding), low thermal mass (wood / steel framing, not CMUs), poor natural ventilation (not a lot of windows) , low thermal insulation ( low density fiberglass insulation, type of window) and poor shading (flat roof, no louvers, no blinds on windows). 4) Room Location: The room to be studied will be located on the top floor and is therefore the most critical due to the exposure of environment from the roof and windows and as with the simple notion that heat rises. 5) Space Use: For the project we will consider cooking as the main human activity and energy generated in the room since it creates the most heat. 1.2 Building Data 1) Room Dimensions: Width: 10 meters Depth: 8 meters Height: 2.2 meters Third floor of a detached triplex building with a flat roof.
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2) Fenestration: South Wall: 1 x 2m x 1.5m double glazed single pane window (sliding). East & West walls: 1 x 1.5m x 1m double glazed single pane window (sliding). Factors to consider:
-‐ Window frame (conductivity) -‐ Thermal transmittance -‐ Solar heat gain coefficient -‐ Glass type – double glazed -‐ Glass: clear / tempered -‐ Insulating glass -‐ Filling between panes : air / argon -‐ Low E-‐coating -‐ Weather-‐stripping around frames
3) Outdoor conditions: -‐ Ongoing heat wave -‐ Maximum outdoor temperature: 34 degrees Celsius at 3 pm -‐ Minimum outdoor temperature: 23 degrees Celsius at 3 am -‐ Equivalent sky temperature = 5 degrees Celsius below ambient air temperature This will be used as the temperature for the roof design. 4) Solar Radiation: Use month of July 2012. See Table 1 in Appendix. 5) Air exchange rate: 0.5 when windows and doors are closed. Formula: a) !"# = ! !"#$%& !" !"#!$%&'%!("
! (!"#$%& !" !"#!$%&'%!(")
b) !!"# = !"# ! !"#$!" ! !!"# 6) Indoor activity: Cooking will occur for 2 hours per day, from 7-‐8 am and then 6-‐7 pm. 1 occupant will be home all day while the other will be at work from 8 am to 5p
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2. Modeling Procedure 1. Plan of the building
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2. Select Design 1) Walls (exterior to interior): -‐ Brick cladding -‐ 152 mm Fiberglass insulation (batt insulation) -‐ 12 mm Interior Gypsum Board For simplicity, we will neglect the air and vapor barriers and furring strips in the compositions. Also, we will neglect the wood / metal framing. The insulation goes in between the framing. 2) Floor (top to bottom): -‐ Finished floor : Hardwood -‐ 152 mm Fiberglass insulation -‐ 12 mm Interior gypsum board For simplicity, we will neglect the framing, furring strips, barriers and components needed for the finished floor. Also, we will neglect all acoustic components. To simplify the equations, we will consider the entire floor composition as one component and the conduction through the entire composition as one. 3) Roof (top to bottom): -‐ Standard built up roofing membrane -‐ 300 mm fiberglass insulation -‐ 12 mm interior gypsum board For simplicity, we will neglect the air and vapor barriers and furring strips in the compositions. Also, we will neglect the wood / metal framing. The insulation goes in between the framing. Also, we will assume the built up roof membrane to simply be felt
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3. Draw electrical Walls
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Roof
Floor
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4. Determine Equations Walls Point 1: Energy law with solar radiation, conduction and convection
!" × ! × !" − !1 + !"×! + (!"!" × !2− !1 = 0
Point 2: Energy law with conduction
!×!"!" × !1− !2 + !×
!"!" × !3− !2 = 0
Point 3: Energy law with conduction
!×!"!" × !2− !3 + !×
!"!" × !4− !3 = 0
Point 4: Energy law with conduction and convection
!×!"!" × !3− !4 + (!"×!× !" − !4 ) = 0
Roof Point 1: Energy law with solar radiation, conduction and convection
!" × ! × !" − !1 + !"×! + (!"#$!"#$ × !2− !1 = 0
Point 2: Energy law with conduction
!×!"#$!"#$ × !1− !2 + !×
!"!" × !3− !2 = 0
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Point 3: Energy law with conduction
!×!"!" × !2− !3 + !×
!"!" × !4− !3 = 0
Point 4: Energy law with conduction and convection
!×!"!" × !3− !4 + (!"×!× !" − !4 ) = 0
Floor Energy law with conduction through floor composition (assumed to be constant), convection and solar radiation from the windows.
(Q×Awindow×Trans)!
!!!
+ !"×!"#$$%× !" − !"#$$%
+!"#!" × !"#$%&"'(#$ − !"#$$% = 0
Room Temperature Energy law with convection, air exchange rate and input energies from occupants and cooking.
Hi×A× T4− Ti + !"#$%&' + !"##$%&' +!!!! !"#$×!"× !" − !" = 0
See Matlab program (Appendix 2)for a listing and description of thermal conduction values, thicknesses, areas, solar radiation values etc.
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5. Create Matrix To solve for temperatures, we need to create a matrix. The matrix will be composed of a coefficient matrix, an unknown variable matrix and the solution matrix. The coefficient matrix will be a 22x22 matrix and will be composed of the constants of thermal conduction, areas, widths etc. that are multiplied with the unknowns (T1, T2, T3…). The unknown variable matrix will be a 1x22 matrix composed of the temperature variables at each point in each wall, the room temperatures , the roof temperatures and floor temperatures. Finally, the solution matrix will be composed of the constants multiplied by the outdoor temperatures that are known for each hour. See Table 5 in the Appendix 1.
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3. Results 3.1 Temperature Distribution – North Wall
3.2 Temperature Distribution – South Wall
0 5 10 15 20 25 30 35 40 45
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Temperature (F)
Time (Hour)
North Wall
Point 1
Point 2
Point 3
Point 4
0
20
40
60
80
100
120
1 3 5 7 9 11 13 15 17 19 21 23
Temperature (F)
Time (Hour)
South Wall
Point 1
Point 2
Point 3
Point 4
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3.3 Temperature Distribution – East Wall
3.4 Temperature Distribution – West Wall
0
10
20
30
40
50
60
70
80
90
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Temperature (F)
Time (Hour)
East Wall
Point 1
Point 2
Point 3
Point 4
0
20
40
60
80
100
120
140
160
1 3 5 7 9 11 13 15 17 19 21 23
Temperature (F)
Time (Hour)
West Wall
Point 1
Point 2
Point 3
Point 4
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3.5 Temperature Distribution – Roof
0 10 20 30 40 50 60 70 80 90 100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Temperature (F)
Time (Hour)
Roof Temperature Distributions
Point 1
Point 2
Point 3
Point 4
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3.6 Temperature Distribution – Floor
3.7 Temperature Distribution -‐ Room
0
5
10
15
20
25
30
35
40
45
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Temperature (F)
Time (Hour)
Floor Temperature Distribution
0
5
10
15
20
25
30
35
40
45
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Temperature (F)
Room Temperature Distribution
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4. Discussion North Wall Analyze: From the curve, we can see that the 4 points in the wall show more or less the same trend. The temperature distributions for the exterior face brick and interior of brick are almost identical to each other. There are temperature spikes mainly in Point 2 and Point 4. These spike occurs within the two hours of cooking. From the tables, we can see that the lowest temperature is 19 degrees Celsius at 3 am and the highest occurs at 38 at 5 pm in terms of the interior temperature of surface of walls. The temperatures at point 4 rise substantially during the hours of occupant activity. The North Wall experiences peak temperatures at the surfaces at 6 am and at 6 pm. Explain: The trend lines of a regular temperature distribution curve should follow each other more or less depending on factors such as seasons, activities, location etc. Also keep in note that there is no mechanical ventilation/ air conditioning system to regulate temperature fluctuations. During the summer, point 1 should experience the highest temperature due to solar radiation, convection and conduction. From the given information, the highest temperature should occur at 3 pm and the lowest at 3 pm. According to Table 1 in the Appendix, the peak solar radiation value should be at 12 pm in the North Wall. Justify: The lowest temperature in the North Wall does occur at 3 am however the temperature spike at 5 pm instead of 3 pm may be due to occupant activity (2 people) increasing. The 2 peaks at 6 am and 6 pm for solar radiation on the exterior face brick have an identical solar radiation value of 57. The reasoning of these peaks is unknown, however they probably are related to the sunset and sunrise times. South Wall Analyze: From the curve, we notice that the shape of the trends are very similar. We also notice that the point 4 curve temperature distributions are much lower and the slope is almost flat. At point 4 (inside surface), the lowest temperature occurs at 3 am and it is 21 degrees Celsius and the highest temperature occurs at 5 pm and it is 41 degrees Celsius. On the exterior façade at point 1, the lowest temperature occurs at 3 am and it is 49 degrees Celsius and the highest one occurs at 12 pm and is 108
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degrees Celsius. As noticed earlier like the north wall, the curve rises in temperature during occupancy increase and peaks at cooking times in point 2. Explain The temperatures at point 3 and 4 should be very similar because the thickness of the gypsum board is small in comparison and because the temperatures are mainly affected by minor changes such as indoor convection. The south wall should experience the higher temperature distribution than the other walls due to the higher solar radiation values at each hour during the summer. Justify The main issue in the south wall comes from the minimum and maximum temperatures that hit the brick façade. The minimum temperature of 49 degrees and the max temperature of 108 seems highly unusual even though brick has a high thermal conductivity value. This may be due to the fact that considerations such as shadings, overhangs, surrounding buildings, trees etc. were not taken. Also it may be due to erroneous temperature values. The inside temperatures are viable because the south wall contains a large window which increases solar heat gains. East Wall Analyze: From a first glance, the trend of the curves on the east wall does not match at all and contain large gaps between. Another major error noticed is that point 2 is below point 4 and its values are extremely low. There is a large temperature peak on the exterior wall at 8 am with a temperature of 80 degrees Celsius. The interior temperature curve (T4) is fairly similar to the other walls and the temperatures are fairly average. Explain: The east wall experiences spikes in solar radiation especially between 6 am to 11 pm. A proper reasoning to this is may be due to orientations. According to the Canada Mortgage and Housing Corporation’s article on Solar Energy for Buildings: “Buildings with east and west facing orientations have greater potential for overheating in the non-‐heating season.” Justification: Since the other walls do not have the issue of point 2 being lower than point 4, the error must either come from solar radiation values or computation/input errors in Matlab.
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West Wall Analyze: From the graph, the trend of the curves seems to follow fairly through. Point 3 and point 4 are almost identical. There is a large gap that varies from the exterior surfaces to the interior ones. Also at first glance, we can see that the west wall is almost symmetrical to the east wall. The west wall records the highest temperature on the exterior surface as opposed to the other walls. The highest recorded temperature is at 4 pm and it reads 140 degrees Celsius. Explain & Justify: The gap between the exterior surfaces and the interior surfaces may be due to solar radiation values. Only the north wall does not have this issue because of its lower solar radiation values during the summer time. The reason for the east and west curves being symmetric are due to the solar radiation values. The readings on the east wall are an inverse of the west wall. Also we can use the simple notion that the sun rises north or south of due east and sets north or south of due west. The reason why the west wall reaches the highest temperature is due to a combination of solar heat gains and outdoor temperature readings. The west and east wall have the highest solar radiation values (up to 679W/m^2). When this occurs at 4 pm, the temperature is already around 33 degrees which is almost 34 (the maximum outdoor temperature). Floor & Room Analyze: The floor and indoor temperature distributions are very similar to each other. The highest temperatures occur at 5 pm and are around 40 degrees Celsius. The lowest temperatures occur at 3 am and are around 19 degrees Celsius. The two peaks occur when both the occupants are at home and at high solar radiation values. The cooking hours have a low impact on these temperatures. Both graphs resemble the T4 curves of each wall, since it is the indoor surfaces. Explain & Justify: The reason for both graphs being similar to each other have to do with the fact these formulas indicates similar convection values. For example:
Hi ∗ A ∗ (T4− Ti) ≅ (Hi ∗ A ∗ Ti− Tf ) Where T4 is almost equal to Tfloor (for indoor surfaces) Also take note that the areas are identical
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We also note that the 0.5 ACH value does not have a big impact on thermal heat gains in the summer. It might have a larger impact in the winter with heat losses. With peak temperatures reaching 34 at 3 pm, the curve should reach a peak at 3 pm instead of 5 pm. However, when taking into consideration solar heat gain from windows, increasing occupant activity, high outdoor temperature and cooking, it is reasonable. Roof The roof graph resembles the temperature distributions for the walls. The curves are more dependent on the solar radiation values rather than interior activities and materials. We can see that the curve for the roof surface is mainly active during the hours of sunlight.
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5. Conclusion 5.1 Real Life Scenario After conducting this experiment, I have found that the occupants are not thermally comfortable especially from 2pm to 5 pm. The maximum indoor temperature reaches 38 degrees Celsius which is about 4 degrees higher than the maximum outdoor temperature. This is taking into consideration only cooking activities and not equipment such as refrigerators, televisions, computers etc. that might be on for a long time. A ventilation system is required to exhaust the indoor air out at least even if there isn’t an air conditioning system. 5.2 Room for Improvement Suggest techniques to improve the thermal comfort without the use of a mechanical ventilation system. Various techniques can be used to improve the thermal comfort without using a mechanical ventilation system or an air conditioning system. To minimize heat gains from the windows, we can begin by adding shading systems (roller shades and venetians) as opposed to curtains that can be heavier. This will cut the radiation coming from the sun especially through the south wall. Energy efficient windows can also be added. For the sake of the project, we used double glazed windows without an airspace. There are now double glazed windows available with low emissivity coating. This coating is a thin metal film applied to the glass that blocks enough solar radiation in the summer but also allows enough heat gains in the winter. Triple glazed windows with an airspace and insulated spacers are also available however they are more of an advantage in the winter time as they provide a higher R-‐value. Modifying building materials is also another way to improve thermal comfort. Materials with a lower thermal conductivity will provide lower heat gains through the walls. Facades that are made of stucco or of concrete finishing systems are a good choice because they have a higher thermal mass; meaning that they are cooled at night and they release this coolness into the building during the day. Also note that a proper air and vapor barrier are crucial to an overall proper envelope system. Another solution would be proper roof design. An overhang would help in shading the building to decrease solar radiation. Heat islands from roofs are being eliminated today with lighter surfaces, which as a result induce a higher surface reflectance. Green roofs are also a technique used to reduce heat islands.
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6. References 1. http://www.greenbuildingadvisor.com/blogs/dept/musings/all-‐about-‐thermal-‐mass 2. http://energy.gov/energysaver/articles/insulation-‐materials 3.http://www.awwd.ca/images/pdfs/Selecting_Energy_Efficient_Windows%5B1%5D.pdf 4. http://www.europeanconcrete.eu/publications/energy-‐efficiency/121-‐concrete-‐for-‐energy-‐efficient-‐buildings-‐the-‐benefits-‐of-‐thermal-‐mass 5.http://www.cmhcschl.gc.ca/en/inpr/bude/himu/coedar/upload/OAA_En_aug10.pdf 6. http://solar-‐center.stanford.edu/AO/sunrise.html 7.http://highered.mcgrawhill.com/sites/dl/free/0073398128/835451/Chapter16.pdf
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7. Appendix 1 Table 1-‐Solar Radiation Values in (W/m2)
Time (Hour) North East South West Roof
5 32 71 5 5 9 6 57 472 38 38 119 7 83 651 68 63 286 8 87 679 107 82 454 9 97 606 209 97 595 10 107 457 318 107 704 11 114 252 394 114 772 12 116 126 420 126 795 13 114 114 394 252 772 14 107 107 318 457 704 15 97 97 209 606 595 16 87 82 107 679 454 17 83 63 68 651 286 18 57 38 38 472 119 19 32 5 5 71 9
Table 2-‐ Surface Conductances for Air
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Table 3 – Thermal Properties of Materials
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Table 4 – Outside Hourly Temperatures
Time Temperature 0 23.41866257 1 23.73686028 2 24.13655663 3 24.6109127 4 25.15181214 5 25.75 6 26.39524112 7 27.07649525 8 27.78210594 9 28.5 10 29.21789406 11 29.92350475 12 30.60475888 13 31.25 14 31.84818786 15 32.3890873 16 32.86344337 17 33.26313972 18 33.58133743 19 33.81259204 20 33.95294674 21 34 22 33.95294674 23 33.81259204 24 33.58133743
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Table 5-‐Matrix
T1N T2N T3N T4N T1S T2S T3S T4S T1E T2E T3E T4E T1W T2W-‐Anw*(-‐Kb/Xb+ho) Anw(Kb/Xb) 0 0 0 0 0 0 0 0 0 0 0 0
Anw*Kb/Xb -‐Anw*(Kb/Xb+Ki/Xi) Anw*Ki/Xi 0 0 0 0 0 0 0 0 0 0 00 Anw*Ki/Xi -‐Anw*(Ki/Xi+Kg/Xg) Anw*Kg/Xg 0 0 0 0 0 0 0 0 0 00 0 (Anw*Kg/Xg) -‐Anw(Kg/Xg+Hi) 0 0 0 0 0 0 0 0 0 00 0 0 0 -‐Asw*(-‐Kb/Xb+ho) Asw(Kb/Xb) 0 0 0 0 0 0 0 00 0 0 0 Asw*Kb/Xb -‐Asw*(Kb/Xb+Ki/Xi) Asw*Ki/Xi 0 0 0 0 0 0 00 0 0 0 0 Asw*Ki/Xi -‐Asw*(Ki/Xi+Kg/Xg) Asw*Kg/Xg 0 0 0 0 0 00 0 0 0 0 0 (Asw*Kg/Xg) -‐Asw(Kg/Xg+Hi) 0 0 0 0 0 00 0 0 0 0 0 0 0 -‐Aew*(-‐Kb/Xb+ho) Aew(Kb/Xb) 0 0 0 00 0 0 0 0 0 0 0 Aew*Kb/Xb -‐Aew*(Kb/Xb+Ki/Xi) Aew*Ki/Xi 0 0 00 0 0 0 0 0 0 0 0 Aew*Ki/Xi -‐Aew*(Ki/Xi+Kg/Xg) Aew*Kg/Xg 0 00 0 0 0 0 0 0 0 0 0 (Aew*Kg/Xg) -‐Aew(Kg/Xg+Hi) 0 00 0 0 0 0 0 0 0 0 0 0 0 -‐Aww*(-‐Kb/Xb+ho) Aww(Kb/Xb)0 0 0 0 0 0 0 0 0 0 0 0 Aww*Kb/Xb -‐Aww*(Kb/Xb+Ki/Xi)0 0 0 0 0 0 0 0 0 0 0 0 0 Aww*Ki/Xi0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 Hi*Anw 0 0 0 Hi*Asw 0 0 0 Hi*Aew 0 0
T3W T4W TIROOF T2ROOF T3ROOF T4ROOF TFLOOR Ti TEMP-‐VALUES SOLUTIONS0 0 0 0 0 0 0 0 T1 (north) -‐(Ho*A*To+Qsn*A)0 0 0 0 0 0 0 0 T2 (north) 00 0 0 0 0 0 0 0 T3 (north) 00 0 0 0 0 0 0 Hi*Anw T4 (north) 00 0 0 0 0 0 0 0 T1 (south) -‐(Ho*A*To+Qsn*A)0 0 0 0 0 0 0 0 T2 (south) 00 0 0 0 0 0 0 0 T3 (south) 00 0 0 0 0 0 0 Hi*Asw T4 (south) 00 0 0 0 0 0 0 0 T1 (east) -‐(Ho*A*To+Qsn*A)0 0 0 0 0 0 0 0 T2 (east) 00 0 0 0 0 0 0 0 T3 (east) 00 0 0 0 0 0 0 Hi*Aew T4 (east) 00 0 0 0 0 0 0 0 T1 (west) -‐(Ho*A*To+Qsn*A)
Aww*Ki/Xi 0 0 0 0 0 0 0 T2 (west) 0-‐Aww*(Ki/Xi+Kg/Xg) Aww*Kg/Xg 0 0 0 0 0 0 T3 (west) 0
(Aww*Kg/Xg) -‐Aww(Kg/Xg+Hi) 0 0 0 0 0 Hi*Aww T4 (west) 00 0 -‐Ar*(-‐Kb/Xb+ho) Ar(Kb/Xb) 0 0 0 0 T1(roof) (-‐Ho*A*To)-‐(Qsn*A)0 0 Ar*Kb/Xb -‐Ar*(Kb/Xb+Ki/Xi) Ar*Ki/Xi 0 0 0 T2(roof) 00 0 0 Ar*Ki/Xi -‐Ar*(Ki/Xi+Kg/Xg) Ar*Kg/Xg 0 0 T3(roof) 00 0 0 0 (Ar*Kg/Xg) -‐Ar(Kg/Xg+Hi) 0 Hi*Ar T4(roof) 00 0 0 0 0 0 (-‐Hi*Af)-‐(Kso/Xf) Hi*Af Tfloor (-‐Kso/Xf)*(Tcon)-‐(Qe*Aew*Trans)-‐(Qs*Asw*Trans)-‐(Qw*Aww*Trans)0 Hi*Aww 0 0 0 Hi*Ar Hi*Af (Hi)*(-‐Anw-‐Asw-‐Aew-‐Aww-‐Ar-‐Af)-‐(Ma*Cp) Ti (-‐Qperson)-‐(Qcooking)-‐(Ma*Cp*To)
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Table 6: Results
North Wall - 1st Iteration
#1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
POINT 1 27.1234 26.62514 26.42584 26.62514 27.35042 28.52695 30.15511 31.30563 32.80262 34.28296 35.7143 36.80974 37.70735 38.1694 38.2835 37.98234 37.42378 36.49765 34.92401 33.30186 31.90672 30.51159 29.21611 28.02028
POINT 2 32.99645 32.50116 32.30305 32.50116 33.25024 34.61829 36.68749 37.5354 39.08558 40.59048 41.9962 43.06109 43.97733 44.45368 44.53368 44.17217 43.55832 42.88277 40.77852 39.13793 37.75115 36.36436 35.07663 33.88795
POINT 3 161.8722 161.4423 161.2704 161.4423 162.7179 168.3197 180.1369 174.2986 177.0258 179.0748 179.9155 180.3062 181.635 182.4278 181.7544 180.0589 178.2227 183.0839 169.252 167.2026 165.999 164.7953 163.6776 162.6459
POINT 4 167.8465 167.4196 167.2489 167.4196 168.7199 174.5198 186.7929 180.642 183.4243 185.4989 186.3133 186.6724 188.0206 188.8282 188.1196 186.3616 184.4682 189.5884 175.2079 173.1393 171.9442 170.749 169.6392 168.6148
North Wall - 10th Iteration
#10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
POINT 1 23.73172 23.23172 23.03172 23.23172 23.96242 25.16362 26.8441 27.96816 29.47686 30.96587 32.40047 33.49727 34.40048 34.86589 34.97689 34.66819 34.10154 33.19742 31.56246 29.93175 28.53174 27.13173 25.83173 24.63172
POINT 2 23.78626 23.28626 23.08626 23.28626 24.05008 25.48514 27.69646 28.4725 30.05449 31.58293 32.9975 34.06605 34.99752 35.48298 35.55456 35.17259 34.53677 33.92102 31.65017 29.98634 28.58632 27.18631 25.88629 24.68628
POINT 3 24.99049 24.4904 24.29037 24.4904 25.98529 32.58421 46.51636 39.60821 42.80845 45.20748 46.17967 46.62471 48.18003 49.10819 48.30944 46.30942 44.14647 49.8979 33.58666 31.19161 29.79136 28.39111 27.09087 25.89066
POINT 4 25.04673 24.54664 24.3466 24.54664 26.07566 32.91577 47.39534 40.1283 43.40412 45.84381 46.79534 47.21125 48.79571 49.74455 48.90515 46.82956 44.59529 50.6441 33.67709 31.24789 29.84763 28.44737 27.14712 25.9469
South Wall - 1st Iteration
#1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
POINT 1 27.1234 26.62514 26.42584 26.62514 27.17596 28.40417 30.05819 31.43486 33.52633 35.64638 37.52358 38.7741 39.51663 39.53282 39.00721 38.11158 37.32685 36.37487 34.74954 33.30186 31.90672 30.51159 29.21611 28.02028
POINT 2 32.99645 32.50116 32.30305 32.50116 33.08256 34.5003 36.59433 37.6596 39.78113 41.90085 43.73507 44.949 45.7162 45.76404 45.22923 44.29637 43.46516 42.76477 40.61084 39.13793 37.75115 36.36436 35.07663 33.88795
POINT 3 161.8722 161.4423 161.2704 161.4423 162.7001 168.3072 180.127 174.3118 177.0996 179.214 180.1002 180.5066 181.8197 182.567 181.8282 180.072 178.2128 183.0714 169.2342 167.2026 165.999 164.7953 163.6776 162.6459
POINT 4 167.8465 167.4196 167.2489 167.4196 168.7091 174.5122 186.7869 180.65 183.4691 185.5833 186.4253 186.7941 188.1327 188.9127 188.1644 186.3696 184.4622 189.5808 175.1971 173.1393 171.9442 170.749 169.6392 168.6148
South Wall - 10th Iteration
#10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
POINT 1 23.73172 23.23172 23.03172 23.23172 23.78796 25.04084 26.74718 28.0974 30.20058 32.3293 34.20976 35.46164 36.20977 36.22931 35.7006 34.79743 34.00462 33.07465 31.38799 29.93175 28.53174 27.13173 25.83173 24.63172
POINT 2 23.78626 23.28626 23.08626 23.28626 23.8824 25.36714 27.6033 28.59671 30.75005 32.89331 34.7364 35.954 36.73642 36.79336 36.25012 35.29679 34.44362 33.80302 31.48249 29.98634 28.58632 27.18631 25.88629 24.68628
POINT 3 24.99049 24.4904 24.29037 24.4904 25.96748 32.57168 46.50647 39.6214 42.88232 45.34665 46.36434 46.82521 48.3647 49.24735 48.38331 46.32261 44.13658 49.88537 33.56885 31.19161 29.79136 28.39111 27.09087 25.89066
POINT 4 25.04673 24.54664 24.3466 24.54664 26.06486 32.90816 47.38934 40.13631 43.44895 45.92827 46.90742 47.33294 48.90779 49.82901 48.94998 46.83756 44.58928 50.63649 33.66628 31.24789 29.84763 28.44737 27.14712 25.9469
West Wall - 1st Iteration
#1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
POINT 1 27.1234 26.62514 26.42584 26.62514 27.17596 28.40417 30.02588 31.27332 32.80262 34.28296 35.7143 36.87436 38.59907 40.431 41.57251 41.80767 41.09402 39.17925 35.17602 33.30186 31.90672 30.51159 29.21611 28.02028
POINT 2 32.99645 32.50116 32.30305 32.50116 33.08256 34.5003 36.56328 37.50435 39.08558 40.59048 41.9962 43.12319 44.83434 46.62727 47.6947 47.84864 47.08574 45.46003 41.02072 39.13793 37.75115 36.36436 35.07663 33.88795
POINT 3 161.8722 161.4423 161.2704 161.4423 162.7001 168.3072 180.1237 174.2953 177.0258 179.0748 179.9155 180.3127 181.726 182.6587 182.0901 180.4493 178.5973 183.3576 169.2777 167.2026 165.999 164.7953 163.6776 162.6459
POINT 4 167.8465 167.4196 167.2489 167.4196 168.7091 174.5122 186.7849 180.64 183.4243 185.4989 186.3133 186.6764 188.0759 188.9683 188.3233 186.5986 184.6956 189.7545 175.2235 173.1393 171.9442 170.749 169.6392 168.6148
West Wall - 10th Iteration
#10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
POINT 1 23.73172 23.23172 23.03172 23.23172 23.78796 25.04084 26.71487 27.93586 29.47686 30.96587 32.40047 33.56189 35.2922 37.1275 38.26591 38.49355 37.77181 35.87905 31.81447 29.93175 28.53174 27.13173 25.83173 24.63172
POINT 2 23.78626 23.28626 23.08626 23.28626 23.8824 25.36714 27.57225 28.44145 30.05449 31.58293 32.9975 34.12816 35.85455 37.6566 38.71563 38.84911 38.06425 36.49831 31.89237 29.98634 28.58632 27.18631 25.88629 24.68628
POINT 3 24.99049 24.4904 24.29037 24.4904 25.96748 32.57168 46.50317 39.60492 42.80845 45.20748 46.17967 46.6313 48.27105 49.33903 48.64515 46.69987 44.52109 50.17161 33.61238 31.19161 29.79136 28.39111 27.09087 25.89066
POINT 4 25.04673 24.54664 24.3466 24.54664 26.06486 32.90816 47.38733 40.1263 43.40412 45.84381 46.79534 47.21526 48.85095 49.88465 49.1089 47.06653 44.82265 50.81022 33.6927 31.24789 29.84763 28.44737 27.14712 25.9469
East Wall - 1st Iteration
#1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
POINT 1 27.1234 26.62514 26.42584 26.62514 27.60243 31.20855 33.82536 35.13095 36.09162 36.54455 36.60602 36.87436 37.70735 38.1694 38.2835 37.95003 37.29454 36.37487 34.74954 33.30186 31.90672 30.51159 29.21611 28.02028
POINT 2 32.99645 32.50116 32.30305 32.50116 33.49244 37.19555 40.21491 41.21187 42.2466 42.76407 42.85322 43.12319 43.97733 44.45368 44.53368 44.14112 43.43411 42.76477 40.61084 39.13793 37.75115 36.36436 35.07663 33.88795
POINT 3 161.8722 161.4423 161.2704 161.4423 162.7436 168.5934 180.5115 174.689 177.3615 179.3057 180.0066 180.3127 181.635 182.4278 181.7544 180.0556 178.2095 183.0714 169.2342 167.2026 165.999 164.7953 163.6776 162.6459
POINT 4 167.8465 167.4196 167.2489 167.4196 168.7355 174.6859 187.0203 180.8789 183.6281 185.639 186.3685 186.6764 188.0206 188.8282 188.1196 186.3596 184.4602 189.5808 175.1971 173.1393 171.9442 170.749 169.6392 168.6148
East Wall - 10 th Iteration
#10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
POINT 1 23.73172 23.23172 23.03172 23.23172 24.21443 27.84524 30.51437 31.79352 32.76589 33.22748 33.29219 33.56189 34.40048 34.86589 34.97689 34.63589 33.97231 33.07465 31.38799 29.93175 28.53174 27.13173 25.83173 24.63172
POINT 2 23.78626 23.28626 23.08626 23.28626 24.29228 28.06243 31.22394 32.14903 33.21556 33.75655 33.85453 34.12816 34.99752 35.48298 35.55456 35.14153 34.41256 33.80302 31.48249 29.98634 28.58632 27.18631 25.88629 24.68628
POINT 3 24.99049 24.4904 24.29037 24.4904 26.01101 32.85792 46.89098 39.99866 43.14416 45.43832 46.27069 46.6313 48.18003 49.10819 48.30944 46.30612 44.13328 49.88537 33.56885 31.19161 29.79136 28.39111 27.09087 25.89066
POINT 4 25.04673 24.54664 24.3466 24.54664 26.09128 33.08189 47.62271 40.36527 43.60787 45.98391 46.85058 47.21526 48.79571 49.74455 48.90515 46.82756 44.58728 50.63649 33.66628 31.24789 29.84763 28.44737 27.14712 25.9469
Roof - 1st Iteration
#1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
POINT 1 26.66911 26.16954 25.96971 26.16954 26.74354 28.45107 30.94393 33.20167 35.54697 37.67102 39.50511 40.74307 41.50339 41.56767 41.04224 39.89591 38.27637 36.39962 34.33701 32.86378 31.46498 30.06618 28.7673 27.56833
POINT 2 55.06101 54.57663 54.38288 54.57663 55.28166 57.74863 62.05727 62.76003 65.1881 67.30309 68.94633 70.01864 70.88384 71.08122 70.51625 69.25068 67.5737 66.99052 62.64419 61.06728 59.71102 58.35477 57.09539 55.93288
POINT 3 165.2838 164.8556 164.6844 164.8556 166.1321 171.8823 184.0127 178.0951 180.9194 183.0332 183.8915 184.2763 185.6042 186.3729 185.6292 183.8326 181.8808 186.8051 172.6403 170.5931 169.3942 168.1954 167.0821 166.0545
POINT 4 169.9174 169.4916 169.3213 169.4916 170.7924 176.6823 189.1456 182.9465 185.7878 187.9016 188.7267 189.0823 190.43 191.2229 190.4716 188.6523 186.6888 191.8472 177.2647 175.1974 174.0052 172.8129 171.7058 170.6839
Roof - 10th Iteration
#10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
POINT 1 23.77505 23.274 23.07358 23.274 23.85255 25.58068 28.11713 30.35313 32.70834 34.83977 36.67672 37.9159 38.68094 38.74799 38.21994 37.06727 35.44088 33.58222 31.46858 29.98813 28.58518 27.18222 25.87948 24.67695
POINT 2 23.98681 23.48649 23.28637 23.48649 24.24052 26.9296 31.70846 32.17614 34.71079 36.90494 38.57874 39.66408 40.58001 40.80741 40.21428 38.88039 37.12979 36.7422 31.84534 30.19074 28.78985 27.38896 26.08814 24.88738
POINT 3 25.02179 24.52166 24.32162 24.52166 26.02272 32.79424 47.09095 40.07783 43.38672 45.85913 46.85228 47.29288 48.85276 49.76008 48.88805 46.77945 44.49294 50.32869 33.62456 31.22329 29.82295 28.42261 27.12229 25.922
POINT 4 25.06572 24.56561 24.36556 24.56561 26.09838 33.04323 47.74407 40.41332 43.75508 46.23931 47.20356 47.61678 49.20401 50.14019 49.25632 47.11483 44.80557 50.90555 33.7001 31.26712 29.8668 28.46649 27.16619 25.96592
Floor - 1st Iteration
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
FLOOR 177.0263 176.6041 176.4353 176.6041 178.0923 185.0691 198.5067 192.0904 195.2123 197.464 198.1576 198.3602 199.8464 200.757 199.8563 197.7477 195.5482 200.6086 184.5095 182.2614 181.0793 179.8971 178.7995 177.7862
Floor - 10th Iteration
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
FLOOR 25.13355 24.63345 24.43341 24.63345 26.36497 34.44824 50.23282 42.62933 46.27612 48.91618 49.75569 50.01867 51.75609 52.81696 51.77722 49.33068 46.76858 52.81678 33.96649 31.33479 29.93451 28.53423 27.23397 26.03373
Room - 1st Iteration
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Room 177.0248 176.6026 176.4337 176.6026 177.941 184.047 197.0249 190.3909 193.2585 195.3726 196.1464 196.4569 197.8351 198.6657 197.9025 196.0482 194.0663 199.5865 184.3582 182.2598 181.0777 179.8956 178.7979 177.7847
Room - 10th Iteration
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Room 25.13355 24.63345 24.43341 24.63345 26.2152 33.42768 48.7525 40.93132 44.32383 46.82631 47.74593 48.11689 49.74633 50.72709 49.82493 47.63266 45.28826 51.79623 33.81672 31.33479 29.93451 28.53423 27.23397 26.03373
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8. Appendix 2 Matlab Programming
