christopher jantai boniface master of engineering (mechanical) study on radiant times series (24...
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A Study on Radiant Times Series (RTS) Based Method for Calculating
Cooling Load in Equatorial Climates
Christopher Jantai Boniface
Master of Engineering
(Mechanical)
2016
A Study on Radiant Times Series (RTS) Based Method for Calculating
Cooling Load in Equatorial Climates
Christopher Jantai Boniface
A thesis submitted
infulfilment of the requirements for the degree of Master of Engineering
Faculty of Engineering
UNIVERSITI MALAYSIA SARAWAK
2016
ii
Specially dedicated to
My beloved parents, Boniface Nyambong and Law Sega
And my siblings Michael Anggie and wife, George Intai and wife,
Josef Damu and John Lengin who have encouraged and
Inspired me through the journey in education
iii
ACKNOWLEDGEMENT
Firstly I would like to thank GOD for the blessings and allowing me to complete my Master in
Mechanical Engineering. I would like to express my sincere gratitude and appreciations to my
supervisor Ir. Dr. Mohd Danial Ibrahim for his continue support, generous guidance, help,
patience and encouragement in the duration of research until its completion. I would like to thank
everyone who are involved and my highest gratitude to those who have given me guidance and
support and also advice upon the completion of this research especially to Mr. Zuraimi B.Hj
Alias from Department Occupational Safety and Health, Malaysia for the assisting in the
sampling of Indoor Air Quality. Besides, special thanks to my family for the never ending
encouragement and moral support. Finally, everyone who are involved directly or indirectly upon
completing this research, I am really grateful for it. All of your contribution and effort are well
appreciated and well remembered. May GOD bless all of you. Thank you.
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ABSTRACT
Human being appreciate the relief from discomfort afforded by a modern air conditioning system.
In the present day, many houses, offices and commercial buildings or facilities would not be
comfortable to stay in without control of the indoor air environment. Air conditioning refers to
the control of air temperature, moisture content, cleanliness, air quality and air circulation as
required by an occupant, a process or a product in the space. The study was divided into three
major parts which consists of cooling load calculation method, Indoor Air Quality (IAQ) and
flow simulation. The first part involved the comparison of various methods of cooling load
calculation for equatorial climates (hot and humid), cooling load calculation suitable for peak
load calculation and cooling load energy analysis, implication of under size air conditioning
system and cooling load per square meter for specific building (Building functionality).The
results on the first part of the study shows that for building with high ceiling and high volume of
occupants, it is recommended that the peak cooling loads per square meter shall be between
0.121kW/m2
and 0.159kW/m2.As for offices, it is recommended that the peak cooling load for
high efficient buildings are from 0.058kW/m2
to 0.106kW/m2. The second part of the research is
on Indoor Air Quality (IAQ) sampling which was conducted during UNIMAS Convocation in
year 2012. The sampling of IAQ was successfully completed with collaborations Department of
Occupational Safety and Health (DOSH) Ministry Of Human Resources, Malaysia. Then, the
sampling results were compared against Industry Code of Practice on Indoor Air Quality 2010 by
DOSH. Based on the result of the sampling the air movement is below the minimum range
specified by DOSH Malaysia. Finally, the model of the existing DeTAR PUTRA Convocation
hall UNIMAS was simulated. All the initial parameters were included in the flow simulation. The
flow simulation was experimented by using three types of diffuser namely; typical diffuser,
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nozzle diffuser and modified nozzle diffuser. Based on the simulation, nozzle type diffuser gave
better results due to the characteristic of the nozzle that was able to throw the air much further as
compared to the typical diffuser which depends on the terminal air flow. In conclusion, Radiant
Times Series (RTS) is suitable for energy analysis for regions with equatorial climates as it can
gives accurate building cooling load profile which will help designers to select the suitable
system to suite the conditions.
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Kajian bagi kaedah pengiraan beban penyejukan berasaskan "Radiant Time Series (RTS)"
untuk kawasan beriklim khatulistiwa
ABSTRAK
Manusia menghargai kesan kelegaan daripada ketidakselesaan dengan kemampuan sistem
penyaman udara moden. Pada hari ini, banyak rumah, pejabat dan bangunan atau kemudahan
komersial tidak akan selesa untuk dihuni tanpa kawalan kepada persekitaran udara dalaman.
Penyamanan udara merujuk kepada kawalan suhu udara, kelembapan, kebersihan, kualiti udara
dan peredaran udara seperti yang dikehendaki oleh penghuni, proses atau produk dalam ruang
tersebut. Kajian ini terbahagi kepada tiga bahagian utama yang terdiri daripada kaedah
pengiraan beban penyejukan, Kualiti Udara Dalaman (IAQ) dan simulasi aliran. Bahagian
pertama melibatkan perbandingan di antara pelbagai kaedah pengiraan beban penyejukan untuk
kawasan beriklim khatulistiwa (panas dan lembap), pengiraan beban penyejukan yang sesuai
untuk beban penyejukan puncak dan analisis tenaga beban penyejukan, implikasi bagi kapasiti
penyejukan yang tidak mencukupi, dan beban penyejukan setiap meter persegi untuk bangunan
tertentu (fungsi bangunan). Keputusan bahagian pertama kajian menunjukkan bahawa untuk
bangunan dengan siling yang tinggi dan jumlah penghuni yang banyak, adalah disyorkan
bahawa beban penyejukan setiap meter persegi adalah dari 0.121kW/m2
ke 0.159kW/m2. Untuk
bagunan pejabat pula, adalah disyorkan bahawa beban penyejukan setiap meter persegi adalah
dari 0.058kW/m2
ke 0.106kW/m2. Bahagian kedua kajian adalah berkaitan dengan Kualiti Udara
Dalaman (IAQ). Persampelan IAQ telah dilaksanakan semasa Majlis Konvokesyen UNIMAS
pada tahun 2012. Persampelan IAQ telah Berjaya diselesaikan dengan kerjasama Jabatan
Keselamatan dan Kesihatan Pekerjaan (JKKP), Kementerian Sumber Manusia. Perbandingan
vii
telah dibuat di antara keputusan persampelan dengan Tataamalan Industri Kualiti
UdaraDalaman 2010 oleh JKKP. Berdasarkan keputusan persampelan, adalah didapati bahawa
pergerakan udara adalah di bawah julat minimum yang telah ditetapkan oleh JKKP, Malaysia.
Akhir sekali, simulasi telah dijalankan keatas model DeTAR PUTRA Dewan Konvokesyen
UNIMAS sedia ada. Semua parameter awalan telah diambilkira dalam simulasi aliran tersebut.
Simulasi aliran telah dilakukan dengan menggunakan tiga jenis peresap iaitu; penyebar biasa,
peresap jenis muncung dan peresap jenis muncung yang telah diubahsuai. Berdasarkan
keputusan simulasi aliran, peresap jenis muncung memberikan hasil yang lebih baik kerana cirri
muncung yang berkeupayaan menghantar udara lebih jauh berbanding peresap biasa yang
bergantung kepada pengaliran udara terminal. Kesimpulanya, "Radiant Times Series (RTS)"
adalah sesuai digunakanuntuk analisis tenaga dikawasan beriklim khatulistiwa kerana
kemampuannya untuk memberikan pengiraan beban penyejukan bangunan yang akan membantu
pereka-pereka memilih sistem yang sesuai terhadap kerperluan keadaan tersebut.
viii
TABLE OF CONTENTS PAGE
CHAPTER I .................................................................................................................................... 1
INTRODUCTION ........................................................................................................................... 1
1.0 BACKGROUND OF RESEARCH .................................................................................. 1
1.1 DEWAN TUNKU ABDUL RAHMAN PUTRA (DeTAR PUTRA) .............................. 7
1.2 PROBLEM STATEMENT ............................................................................................... 9
1.3 AIMS OF RESEARCH .................................................................................................. 12
1.4 OBJECTIVES ................................................................................................................. 12
1.5 SCOPE OF RESEARCH ................................................................................................ 13
CHAPTER II ................................................................................................................................. 14
LITERATURE REVIEW .............................................................................................................. 14
2.0 FUNDAMENTALS OF HEAT TRANSFER ................................................................ 14
2.1.1 Conduction .............................................................................................................. 14
2.1.2 Convection .............................................................................................................. 15
2.1.3 Radiation ................................................................................................................. 16
2.2 AIR CONDITIONING PROCESS ................................................................................. 17
2.3 AIR CONDITIONING SYSTEM .................................................................................. 18
2.3.1 All Air System ......................................................................................................... 18
2.3.2 Air And Water System ............................................................................................ 20
2.3.3 All Water System .................................................................................................... 20
2.3.4 Unitary, refrigeration based system ........................................................................ 20
2.4 SUMMARY OF PREVIOUS STUDY........................................................................... 21
2.5 RADIANT TIMES SERIES METHOD ......................................................................... 24
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2.6 RADIANT TIME SERIES COOLING LOAD CALCULATION ................................. 28
2.6.1 Cooling Load Calculation Principles ...................................................................... 28
2.6.2 RTS Procedure ........................................................................................................ 29
2.6.3 Heat Gain Calculations Using Standard Air Values ............................................... 29
2.6.4 Fenestration Direct Solar, Diffuse Solar, And Conductive Heat Gains .................. 33
2.6.5 Heat Gain through Exterior Surfaces ...................................................................... 35
2.6.6 Calculating Conductive Heat Gain Using Conduction Time Series ....................... 36
2.6.7 Heat Gain through Interior Surfaces ....................................................................... 38
2.7 CALCULATING CLEAR SKY RADIATION ............................................................. 39
2.7.1 Solar Constant and Extraterrestrial Solar Radiation ............................................... 39
2.7.2 Equation of Time and Solar Time ........................................................................... 40
2.7.3 Declination .............................................................................................................. 41
2.7.4 Sun‟s position .......................................................................................................... 43
2.7.5 Air Mass .................................................................................................................. 45
2.7.6 Clear-Sky Solar Radiation ....................................................................................... 45
2.7.7 Solar Angles Related to Receiving Surfaces ........................................................... 46
2.7.8 Clear-Sky Solar Irradiance Incident on Receiving Surface .................................... 47
2.8 CODE OF PRACTICE ON INDOOR AIR QUALITY 2005 - OVERVIEW ............... 50
2.8.1 Sources of Poor IAQ ............................................................................................... 52
2.8.2 Health Effects Due To Poor IAQ ............................................................................ 53
2.8.3 Health Effects of Environmental Tobacco Smoke .................................................. 53
2.8.4 Sick-Building Syndrome ......................................................................................... 54
2.8.5 Building Related Illnesses ....................................................................................... 54
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2.9 ANSI/ASHRAE Standard 55-2004 ................................................................................ 55
2.10 ANSI/ASHRAE Standard 62.1....................................................................................... 56
2.11 SUMMARY OF MATLAB AND SIMULINK .......................................................... 56
CHAPTER III ................................................................................................................................ 58
METHODOLOGY ........................................................................................................................ 58
3.0 PROJECT METHODOLOGY ....................................................................................... 58
3.1 Cooling Load Calculation Method ................................................................................. 58
3.1.1 Information Gathering and Literature Review ........................................................ 59
3.1.2 Cooling Load Calculation ....................................................................................... 60
3.1.3 Data and related equation preparation ..................................................................... 60
3.1.4 Generating Command by Using Matlab and Simulink Software ............................ 60
3.1.5 Validation of Software Simulation .......................................................................... 62
3.1.6 Documentation of Thesis and Presentation ............................................................. 63
3.2 INDOOR AIR QUALITY (IAQ) ................................................................................... 65
3.2.1 Information Gathering and Literature Review ........................................................ 65
3.2.2 Investigation ............................................................................................................ 66
3.2.3 Walk Through Inspection ........................................................................................ 66
3.2.4 Initial Finding .......................................................................................................... 67
3.2.5 Assessment of Indoor Air Quality ........................................................................... 67
3.2.6 Analyzing Result and Data Analysis ....................................................................... 73
3.2.7 Documentation of Thesis and Presentation ............................................................. 73
3.3 SIMULATION ............................................................................................................... 74
3.3.1 Information Gathering and Literature Review ........................................................ 74
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3.3.2 Modeling and Simulation ........................................................................................ 75
3.3.3 Analyzing Result and Data Analysis ....................................................................... 78
3.3.4 Documentation of Thesis and Presentation ............................................................. 79
CHAPTER IV ............................................................................................................................... 80
RESULTS AND DISCUSSION ................................................................................................... 80
4.0 COOLING LOAD CALCULATION ............................................................................. 80
4.1.1 Initial Conditions For Radiant Times Series (RTS) Cooling Load Calculation ..... 80
4.1.2 DeTAR PUTRA Cooling Load Calculation Results ............................................... 85
4.1.3 Initial Conditions for Radiant Times Series (RTS) Cooling Load Calculation (15%
Safety factor) . .........................................................................................................................94
4.1.4 Cooling Load Energy Analysis Based On RTS Method ......................................... 99
4.2 INDOOR AIR QUALITY ............................................................................................ 104
4.2.1 Indoor Air Quality Standard by DOSH Malaysia ................................................. 104
4.2.2 Sampling Results ................................................................................................... 105
4.3 SIMULATION ............................................................................................................. 113
4.3.1 Boundary Condition .............................................................................................. 113
4.3.2 Graphical simulations Results ............................................................................... 114
4.3.3 Graphical simulations Results ............................................................................... 116
4.4 APPLICATION ............................................................................................................ 120
4.4.1 Wisma Bapa Malaysia (WBM) Cooling Load ...................................................... 120
4.4.2 Wisma Bapa Malaysia (WBM) Cooling Load With No Occupants. .................... 127
4.5 SUMMARY OF FINDINGS ........................................................................................ 129
4.5.1 Radiant Times Series (RTS) Cooling Load Calculation. ...................................... 129
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CHAPTER V ............................................................................................................................... 132
CONCLUSION ........................................................................................................................... 132
5.1 CHALLENGES FACED .............................................................................................. 135
5.2 FUTURE APPLICATION/ STUDY ............................................................................ 136
5.3 RECOMMENDATIONS.............................................................................................. 136
REFERENCES ............................................................................................................................ 138
LIST OF PUBLICATIONS ........................................................................................................ 144
APPENDICES ............................................................................................................................. 145
APPENDIX A-1 RTS METHOD (EXAMPLE OF MANUAL CALCULATION) ............... 145
APPENDIX A-2 NON-RESIDENT COOLING LOAD TABLES ......................................... 155
APPENDIX A-3 FENESTRATION ....................................................................................... 158
APPENDIX A-4 CLIMATIC DESIGN INFORMATION ..................................................... 160
APPENDIX A-5 RTS MATLAB SIMULINK PROGRAMME ............................................. 162
APPENDIX A-6 DeTAR PUTRA COOLING LOAD (15% SAFETY FACTOR) ............... 166
APPENDIX B-1 FLOW SIMULATION ................................................................................ 167
APPENDIX B-2 FLOW TRAJECTORY................................................................................ 170
APPENDIX B-3 DIFFUSER CONSTRUCTION ................................................................... 175
xiii
LIST OF FIGURE PAGE
Figure 1.1: Typical Energy Breakdown In A Building 5
Figure 1.2: Dewan Tunku Abdul Rahman Putra ( DeTAR PUTRA) UNIMAS 8
Figure 1.3: Schematic Intake Diagram Of DeTAR PUTRA Air Conditioning System. 11
Figure 2.1: Fundamental Air Conditioning Processes In Psychometrics Chart 17
Figure 2.2: Reheat System 19
Figure 2.3: Variable Air Volume (VAV) System 19
Figure 2.4: Overview Of Radiant Time Series Method 27
Figure 2.5: Motion of Earth Around The Sun 42
Figure 2.6: Solar Angles For Vertical And Horizontal Surfaces 43
Figure 2.7: Thermal Comfort Based On ANSI/ASHRAE Standard 55-2004 55
Figure 3.1: Overall RTS Matlab Simulink Program 62
Figure 3.2: Flow chart of Cooling Load Calculation methodology 64
Figure 3.3: DeTAR PUTRA Side View Cross Sectioned 68
Figure 3.4: DeTAR PUTRA Front View Cross Sectioned 68
Figure 3.5: Arrangements of Sampling Equipments 72
Figure 3.6: DOSH MALAYSIA Officers Collecting IAQ Data 73
Figure 3.7: Flow chart of Indoor Air Quality methodology 74
Figure 3.8: Simulation – Cross Section View Towards Audience 77
Figure 3.9: Simulation – Cross Section Ceiling Diffuser 77
Figure 3.10: Simulation – Cross Section Of nozzle diffuser 78
Figure 3.11: Simulation – Cross Section Of modified nozzle diffuser 78
xiv
LIST OF FIGURE PAGE
Figure 3.12: Flow chart of Indoor Air Quality methodology 79
Figure 4.1: DeTAR PUTRA Main Hall Level 2 Air Conditioning System 82
Figure 4.2: DeTAR PUTRA Main Hall Upper Level 3 Air Conditioning System 83
Figure 4.3: DeTAR PUTRA Main Hall Lower Level 4 Air Conditioning System 83
Figure 4.4: DeTAR PUTRA Main Hall Upper Level 4 Air Conditioning System 84
Figure 4.5: DeTAR PUTRA Cooling Load, kW Vs Respective Area (5% Safety Factor) 86
Figure 4.6: DeTAR PUTRA Cooling Load per Square Meter,kW/m2 Vs Respective Area 87
Figure 4.7: DeTAR PUTRA Cooling Load Refrigerant Tonne, RT Vs Respective Area 90
Figure 4.8: DeTAR PUTRA Cooling Load, kW Vs Respective Area (15% Safety Factor) 97
Figure 4.9: DeTAR PUTRA Cooling Load per Square Meter, kW/m2
Vs Respective Area (15% Safety Factor)
99
Figure 4.10: Refrigerant Tonne, RT Vs Hour
100
Figure 4.11: RTS For Lightweight Zone 101
Figure 4.12: RTS For Heavy Construction 101
Figure 4.13: Process Of Lighting Load 102
Figure 4.14: Conduction Times Series For Various Wall Construction 103
Figure 4.15: Concentration TVOC(ppm) Vs Time At Station A 108
Figure 4.16: Concentration TVOC(ppm) Vs Time At Station B 109
Figure 4.17: Relative Humidity Vs Time At Station A 109
Figure 4.18: Relative Humidity Vs Time At Station B 110
Figure 4.19: Air Movement Vs Time At Station A 112
xv
LIST OF FIGURE PAGE
Figure 4.20: Air Movement Vs Time At Station B 112
Figure 4.21: Fluid (Air) volume checks 114
Figure 4.22: Results and Geometry Resolution 115
Figure 4.23: Fluid temperature flow trajectory (0.16 m3/s) with typical diffuser 117
Figure 4.24: Fluid temperature flow trajectory (0.08 m3/s) with typical diffuser 117
Figure 4.25: Fluid temperature flow trajectory (0.16 m3/s) with Nozzle diffuser 118
Figure 4.26: Average Temperature of Typical Diffuser, °K Vs Iterations 118
Figure 4.27: Average Temperature Fluid, °K Vs Iterations 119
Figure 4.28: Wisma Bapa Malaysia 121
Figure 4.29: The WBM 5th Floor Plan. 122
Figure 4.30: WBM Cooling Load, kW/m2 Vs Location (Left) 123
Figure 4.31: WBM Cooling Load, kW/m2 Vs Location (Right) 124
Figure 4.32: WBM Cooling Load Refrigerant Tonne, RT Vs Location (Left) 125
Figure 4.33: WBM Cooling Load Refrigerant Tonne, RT Vs Location (Right) 125
Figure 4.34: WBM Cooling Load, kW/m2 Vs Location (Left) No Occupant 127
Figure 4.35: WBM Cooling Load, kW/m2 Vs Location (Right) No Occupant 127
xvi
LIST OF TABLE PAGE
Table 2.1: List Of Indoor Air Contaminants And The Maximum Limits 51
Table 3.1: Recommended Numbers Of Sampling Points 70
Table 3.2: Penetration Characteristics 71
Table 3.3: Manufacturer: ASLI Mechanical Sdn Bhd 76
Table 4.1: DeTAR PUTRA Cooling Load, kW Vs Respective Area (5% Safety Factor) 85
Table 4.2: DeTAR PUTRA Cooling Load per Square Feet, kW/m2
Vs Respective Area (5% Safety Factor)
87
Table 4.3: DeTAR PUTRA Cooling Load Refrigerant Tonne, RT Vs Respective Area
(5% Safety Factor)
89
Table 4.4: DeTAR PUTRA Cooling Load, kW Vs Respective Area (15% Safety Factor) 96
Table 4.5: DeTAR PUTRA Cooling Load per Square Meter, kW/m2
Vs Respective Area (15% Safety Factor)
98
Table 4.6: Acceptable Range for Specific Physical Parameters 104
Table 4.7: List Of Indoor Air Contaminants And The Acceptable Limits 105
Table 4.8: Baseline Results At Station A and Station B 106
Table 4.9 IAQ Data acquisition At Station A Actual Day 107
Table 4.10: IAQ Data acquisition At Station B on Actual Day 107
Table 4.11: WBM Cooling Load, kW/m2 Vs Respective Area 122
Table 4.12: WBM Cooling Load Refrigerant Tonne, RT Vs Respective Area 126
Table 4.13: WBM Cooling Load, kW/m2 Vs Respective Area (No Occupants) 128
xvii
NOMENCLATURE
ASHRAE American Society Of Heating, Refrigerating And Air Conditioning
RTS Radiant Times Series
HB Heat Balance
MVAC Mechanical, Ventilation And Air Conditioning
DeTAR PUTRA Dewan Tunku Abdul Rahman Putra Unimas
WBM Bangunan Tunku Abdul Rahman / Wisma Bapa Malaysia
CLTD Cooling Load Temperature Different
TFM Transfer Function Method
SBS Sick Building Syndrome
TETD/TA Total Equivalent Temperature Differential/ Time Averaging
SCL Solar Cooling Load
CLF Cooling Load Factor
MLY Malaysia
CTS Conduction Time Series
DB Dry Bulb
WB Wet Bulb
MCDB Mean Coincident Dry Bulb Temperature
MCWB Mean Coincident Wet Bulb Temperature
MCDBR Mean coincident dry bulb temp. range
MCWBR Mean coincident dry Wet temp. range
RT Refrigerant Tonne
xviii
NOMENCLATURE
Btu/hr British Thermal Unit per Hour
Btu/Hr.ft2 British Thermal Unit per Hour per Feet Square
taub Clear sky optical depth for beam irradiance
taud Clear sky optical depth for diffuse irradiance
MEP Mechanical Electrical Plant
FCU Fan Coil Units
AHU Air Handling Units
HEX Heat Exchanger
LEED Leadership in Energy and Engineering Design
met Metabolic
M Metabolic Rate
DOSH Department Of Occupational Safety and Health
CHWP Chilled Water Pump
CHWS Chilled Water Supply
CHWR Chilled Water Return
𝑄 Rate of heat flow, unit (W) or (Btu-ft)
A Cross sectional area normal to the heat flow, unit (m2) or (ft
2)
k Ratio of heat flow per unit area to the local temperature gradient,
unit (W/m.ºC) or (Btu- ft/hr-ft2-ºF)
𝑄𝑐𝑜𝑛𝑣 Rate of heat flow, unit (W) or (Btu-ft)
ℎ Convection heat transfer coefficient, unit (W/m2.ºC)
xix
NOMENCLATURE
𝐴𝑠 Surface area in which convection takes place, unit (m2) or (ft
2)
𝑇𝑠 Surface temperature, unit (ºC) or (ºF)
𝑇∞ Temperature of fluid sufficiently far from surface temperature from
surface, unit (ºC) or (ºF)
𝑄𝑒𝑚𝑖𝑡 ,𝑚𝑎𝑥 The maximum rate of radiation that can be transmitted, unit (W) or
(Btu-ft)
𝜎 Stefan-Boltzmann constant (5.670 x 10-8
W/m2.K
4) or (0.1714 x 10
-
8 Btu/h.ft
2.R
4)
𝐴𝑠 Surface area in which convection takes place, unit (m2) or (ft
2)
𝑇𝑠 Surface temperature, unit (ºC) or (ºF)
VAV Variable Air Volume
Qs Standard flow rate, kgda/m3
Δh Enthalpy difference
Ct 1.2 is the air total heat factor, in W/(L/s) per kJ/kg enthalpy h.
qs Sensible heat
Δt Change of dry-bulb temperature
W Humidity ratio, kgw/kgda
ql Latent heat
ΔW Change of Humidity ratio (in kgw/kgda)
Cl 3010 is the air latent heat factor, in W/(L/s).
Cx,0 Any of the sea-level C values
xx
NOMENCLATURE
P/P0 (1– elevation× (2.25577 ×10–5)) 5.2559, where elevation is in
meters.
SHGC(θ) Beam solar heat gain coefficient as a function of incident angle θ
⟨SHGC⟩D Diffuse solar heat gain coefficient
Tin Inside temperature, °C or °F.
Tout Outside temperature, °C or °F.
U Overall U-factor, including frame and mounting orientation,
W/(m2·K)
IAC(θ.Ω) Indoor solar attenuation coefficient for beam solar heat gain
coefficient
IACD Indoor solar attenuation coefficient for diffuse solar heat gain
coefficient
α Absorptance of surface for solar radiation
Et Total solar radiation incident on surface, W/m2
ho Coefficient of heat transfer by long-wave radiation and convection
at outer surface, W/(m2·K)
to Outdoor air temperature, °C or °F.
ts Surface temperature, °C or °F.
ε Hemispherical emittance of surface
ΔR Difference between long-wave radiation incident on surface from
sky and surroundings and radiation emitted by blackbody at outdoor
xxi
NOMENCLATURE
air temperature, W/m2
qi,θ-n Conductive heat input for the surface n hours ago, W
Us Overall heat transfer coefficient for the surface, W/(m2·K)
te,θ-n Sol-air temperature n hours ago, °C or °F.
trc Presumed constant room air temperature, °C or °F.
qθ Hourly conductive heat gain for the surface, W
qi,θ Heat input for the current hour
qi,θ-n Heat input n hours ago
c0, c1 Conduction time factors
q Heat transfer rate, W
Uis Coefficient of overall heat transfer between adjacent and
conditioned space, W/(m2·K)
tb Average air temperature in adjacent space, °C or °F.
ti Air temperature in conditioned space, °C or °F.
Qr, θ Radiant cooling load Qr for current hour θ, W
qr, θ Radiant heat gain for current hour, W
qr,θ−n Radiant heat gain n hours ago, W
r0, r1 Radiant time factors
n Number of days in a year
Eo Extraterrestrial Radiant Flux, W/m2
Γ Expressed in minutes
xxii
NOMENCLATURE
AST Apparent solar time, decimal hours
LST Local standard time, decimal hours
ET Equation of time in minutes
LSM Longitude of local standard time meridian, °E of Greenwich
LON Longitude of site, °E of Greenwich
TZ Time Zone
DST Daylight Saving Time
δ Solar declination
H Hour angle
β Solar altitude angle
L Local latitude
Solar azimuth angle
m Air Mass
Eb Beam normal irradiance
Ed Diffuse horizontal irradiance
Eo Extraterrestrial normal irradiance
τb and τd Beam and diffuse optical depths
ab and ad Beam and diffuse air mass exponents.
Angle of incidence
Azimuth angle
xxiii
NOMENCLATURE
Tilt angle
Et,b Beam component
Et,d Diffuse component
Et,r Ground-reflected component
Y Ratio of clear-sky diffuse irradiance on a vertical surface to clear-
sky diffuse irradiance on the horizontal.
ρg Ground reflectance
TVOC Total Volatile Organic Compound
CMH Cubic Meter Hour
ppm Part Per Million
TVOC Total Volatile Organic Compounds