CAE 331/513 Building Science Fall 2016

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1 CAE 331/513 Building Science Fall 2016 Week 3: September 8, 2016 Heat transfer in buildings: Finish radiation, then solar radiation and windows Advancing energy, environmental, and sustainability research within the built environment Dr. Brent Stephens, Ph.D. Civil, Architectural and Environmental Engineering Illinois Institute of Technology

2 Last time Finished convection Convective heat transfer coefficients Radiation Theory for natural convection Gr = buoyancy vs. viscosity Ra = Gr x Pr Empirical measurements Simplified empirical relationships h c = f(temperature difference, velocity, orientation, roughness) q 1 2 = ( 4 T ) surf,2 4 σ T surf,1 1 ε 1 ε 1 + A 1 A 2 1 ε 2 ε F 12 4 q 1 2 = ε surf σ F 12 T surf,1 ( 4 T ) surf,2 2

3 Finish radiation heat transfer Today s objectives Understand solar radiation (short wave radiation) Basic solar geometry Understand heat transfer through windows Combined modes of heat transfer Assign HW #2 (due Tues Sep 13) Discuss Exam #1 (scheduled for Tues Sep 20) Should we move to Thurs Sep 22? 3

4 Solar radiation striking a surface (high temperature) Most solar radiation is at short wavelengths Solar radiation striking a surface: I solar! " # W m 2 $ % & Solar radiation: (opaque surface) Transmitted solar radiation: (transparent surface) q solar = αi solar q solar = τ I solar 4

5 Absorptivity (α) for solar (short-wave) radiation 5

6 Radiation heat transfer (surface-to-surface) We can write the net thermal radiation heat transfer between surfaces 1 and 2 as: A 1 σ ( T T ) 2 Q 1 2 = 1 ε 1 + A 1 ε q 1 2 = Q 1 2 A 1 ε 1 A 2 ε 2 F 12 where ε 1 and ε 2 are the surface emittances, A 1 and A 2 are the surface areas and F 1 2 is the view factor from surface 1 to 2 F 1 2 is a function of geometry only A 2, T 2, ε 2 A 1, T 1,ε 1 6

7 Emissivity ( gray bodies ) Real surfaces emit less radiation than ideal black ones The ratio of energy radiated by a given body to a perfect black body at the same temperature is called the emissivity: ε ε is dependent on wavelength, but for most common building materials (e.g. brick, concrete, wood ), ε = 0.9 at most wavelengths 7

8 Emissivity (ε) of common materials 8

9 Emissivity (ε) of common building materials 9

10 View factors, F 12 Radiation travels in directional beams Thus, areas and angle of incidence between two exchanging surfaces influences radiative heat transfer Some common view factors: A 1 F 1 2 = 0.5((ac + bd) (ad + bc)) Online radiation view factors textbook: 10

11 Typical view factors Other common view factors from the ASHRAE Handbook of Fundamentals: 11

12 Long-wave radiation example What is the net radiative exchange between the two interior wall surfaces below end of the room if the room is 5 m x 5 m x 3 m? 2 3 m 1 5 m 5 m T surf 2,in = 72 F = 22 C T surf 1,in = 76.6 F = 24.8 C 12

13 Simplifying surface radiation We can also often simplify radiation from: Q 1 2 = A 1 σ ( T T ) 2 1 ε 1 ε 1 + A 1 A 2 1 ε 2 ε F 12 To: Q 1 2 = ε surf A surf σ F ( 12 T T ) 2 Particularly when dealing with large differences in areas, such as sky-surface or ground-surface exchanges 13

14 Simplifying radiation We can also define a radiation heat transfer coefficient that is analogous to other heat transfer coefficients Q rad,1 2 = h rad A ( 1 T 1 T ) 2 = 1 A ( R 1 T 1 T ) 2 rad When A 1 = A 2, and T 1 and T 2 are within ~50 F of each other, we can approximate h rad with a simpler equation: h rad = 4σT 3 avg 1 ε ε 2 1 where T avg = T 1 +T

15 Radiation visualizations 15

16 SOLAR RADIATION 16

17 Solar radiation Solar radiation is a very important term in the energy balance of a building We must account for it while calculating loads This is particularly true for perimeter zones and for peak cooling loads Solar radiation is also important for daylighting design We won t cover the full equations for predicting solar geometry and radiation striking a surface in this class CAE 463/524 Building Enclosure Design goes into more detail But will discuss basic relationships and where to get solar data 17

18 Components of solar radiation Solar radiation striking a surface consists of three main components: I solar = I direct + I diffuse + I reflected! " # W m 2 $ % & Direct Diffuse Reflected 18

19 Components of solar radiation Direct solar radiation (I direct ) is a function of the normal incident irradiation (I DN ) on the earth s surface and the solar incidence angle of the surface of interest, θ Where I DN is the amount of solar radiation received per unit area by a surface that is always perpendicular to the sun s direct rays Function of day of the year and atmospheric properties I D = I DN cosθ Diffuse solar radiation (I diffuse ) is the irradiation that is scattered by the atmosphere Function of I DN, atmospheric properties, and surface s tilt angle Reflected solar radiation (I reflected ) is the irradiation that is reflected off the ground (it becomes diffuse) Function of I DN, solar geometry, ground reflectance, and surface tilt angle 19

20 Solar radiation: earth-sun relationships Earth rotates about its axis every 24 hours Earth revolves around sun every days Earth is titled at an angle of Therefore, different locations on earth receive different levels of solar radiation during different times of the year (and different times of the day) 20

21 Solar radiation striking an exterior surface The amount of solar radiation received by a surface depends on the incidence angle, θ This is a function of: Solar geometry (I DN ) Location Time Surface geometry Shading/obstacles Solar Altitude β Solar Azimuth φ γ θ Surface at Tilt of α ψ Surface Azimuth α N I D = I DN cosθ 21

22 Visualizing solar relationships 22

23 Downloading solar data For hourly sun positions, you can build a calculator or use one from the internet For solar position and intensity (from time and place) Output of interest = global irradiance on a tilted surface For actual hourly solar data (direct + diffuse in W/m 2 ) Output of interest = direct normal radiation à adjust using cosθ Note: typical meteorological years 23

24 Typical meteorological year (TMY) For heating and cooling load calculations and for hourly building energy simulations, we often rely on a collection of weather data for a specific location We generate this data to be representative of more than just the previous year Represents a wide range of weather phenomena for our location TMY3: Data for 1020 locations from 1960 to 2005 Composed of 12 typical meteorological months Each month is pulled from a random year in the range Actual time-series climate data Mixture of measured and modeled solar values Variables include: outdoor temperature, direct normal radiation, wind speed, wind direction, outdoor RH, cloud cover, and more 24

25 Typical meteorological year (TMY): Solar data Data for typical September 10 th at Midway, Chicago, IL Direct Normal Irradiance Cloud Cover IDN (W/m2) Cloud cover (0 to 10) Air temperature 6 Wind speed Air temperature (deg C) Wind speed (m/s)

26 What to do with solar data once you have it? Solar data can be used on exterior opaque surfaces to help determine exterior surface temperatures q solar = αi solar Solar data can also be used on exterior fenestration (e.g. windows and skylights) to determine how much solar radiation enters an indoor environment q solar = τ I solar 26

27 SOLAR RADIATION AND WINDOWS 27

28 Solar radiation and windows (i.e., fenestration) Solar radiation through a single glaze I solar U=k/L h conv+rad ε 100% incident 8% reflected 80% transmitted outside h conv+rad ε ρ τ Thus 12% absorbed 8% rad/conv outward 4% rad/conv inward 84% total transmitted inside α 28

29 Windows and total heat gain The total heat gain of a window is the sum of two terms: The amount of heat gain from solar radiation passing through Combined conductive/convective/lwr thermal heat gain or loss from the temperature difference between the interior and exterior In the summer, both terms are positive towards the interior and add to heat gains In the winter, solar is positive inwards (gain) but conduction/ convection/lwr is negative towards the exterior (loss) Net heat gain may be in either direction 29

30 Heat gain through windows Calculating the heat gain/loss through a window based on indoor/outdoor temperature differences is relatively easy: Q =UA(T in T out ) =UAΔT Accounting for solar heat gain is more complicated Need to include absorption of solar energy and re-radiation of thermal energy Need to include spectral and angular characteristics of radiation and glazing We can do this with a simplified metric The solar heat gain coefficient (SHGC): Q solar,window = ( I solar A)SHGC 30

31 Solar heat gain coefficient, SHGC For a single pane of glass: SHGC = τ +α U R = 1 h ext U = 1 + L glass + 1 h int k glass U=k/L h ext k glass = ~1 W/mK L glass = ~5 mm (0.2 ) * R glass is negligible (~0.005 m 2 K/W) h ext τ Q solar,window = ( I solar A)SHGC q solar,window = ( I solar )SHGC α 31

32 Solar heat gain coefficient, SHGC For double glazing with a small still air gap: SHGC = τ +α outer pane U! +α h inner pane U 1 # + ext " h ext 1 h airspace $ & % R = 1 U = 1 h int + L outer pane k outer pane + 1 h airspace + L inner pane k inner pane + 1 h ext * R outer pane and R inner pane are negligible It gets complicated quickly! 32

33 Manufacturer supplied SHGC Glazing manufacturers will measure and report SHGC values for normal incidence according to the methods of NFRC 200 National Fenestration Rating Council has developed methods for rating and labeling SHGC, U factors, air leakage, visible transmittance and condensation resistance of fenestration products In reality, SHGC is a function of incidence angle (θ) Simply: More accurately: Q solar,window = ( I solar A)SHGC Q solar,window = I direct SHGC(θ)A+ (I diffuse+reflected )SHGC diffuse+reflected A 33

34 Complex SHGC SHGC, solar transmittance, reflectance, and absorptance properties for glazing all vary with incidence angles of solar radiation (θ) The ASHRAE Handbook of Fundamentals 2013 Chapter 15 provides data for a large variety of glazing types 34

35 What about window assemblies? In addition to glazing material, windows also include framing, mullions, muntin bars, dividers, and shading devices These all combine to make fenestration systems 35

36 What about window assemblies? In addition to glazing material, windows also include framing, mullions, muntin bars, dividers, and shading devices These all combine to make fenestration systems Total heat transfer through an assembly: Q window =UA pf ( T out T ) in + I solar A pf SHGC Where: U = overall coefficient of heat transfer (U-factor), W/m 2 K A pf = total projected area of fenestration, m 2 T in = indoor air temperature, K T out = outdoor air temperature, K SHGC = solar heat gain coefficient, - I solar = incident total irradiance, W/m 2 36

37 Window U-factors U-values (or U-factors) for windows include all of the elements of the fenestration system Center of glass properties (cg) Edge of glass properties (eg) Frame properties (f) The overall U-factor is estimated using area-weighted U- factors for each: U = U cg A cg +U eg A eg +U f A f A pf 37

38 U-values and multiple layers of glazing We can separate glass panes with air-tight layers of air or other gases Center of glass U-values for double pane glazing Q: Why does argon filled have lower U value than air filled? k air = W/mK k argon = W/mK k krypton = W/mK 2013 ASHRAE Handbook of Fundamentals: Chapter 15 38

39 U-values and multiple layers of glazing We can separate glass panes with air-tight layers of air or other gases Center of glass U-values for triple pane glazing 2013 ASHRAE Handbook of Fundamentals: Chapter 15 39

40 Combined U-factor data: ASHRAE 2013 HOF 40

41 Shading devices, including drapes and blinds, can mitigate some solar heat gain We can attempt to describe this with an indoor solar attenuation coefficient (IAC) Heat gain through a window can be modified as follows: What about shading? Q window =UA pf ( T out T in ) + I direct A pf SHGC(θ)IAC(θ,Ω) + (I diffuse+reflected )A pf SHGC diffuse+reflected IAC diffuse+reflected IAC is a function of incidence angle, θ, and the angle created by a shading device Or more simply: Q window =UA pf ( T out T ) in + I solar A pf SHGC IAC 41

42 IAC for blinds and drapes: ASHRAE HOF

43 Summary: Modes of heat transfer in a building 43

44 Summary: Modes of heat transfer in a building Conduction Convection Radiation q conv = h conv ( T fluid T surf ) Long-wave 4 σ T surf,1 q= k ( L T T ) surf,1 surf,2 k L =U = 1 R R total = 1 U total R total = R 1 + R 2 + R 3 + For thermal bridges and combined elements: U total = A 1 A total U 1 + A 2 A total U Window (combined modes) ( T out T in ) + I solar A pf SHGC IAC Q window =UA pf R conv = 1 h conv q 1 2 = 4 ( T surf,2 ) 1 ε 1 ε 1 + A 1 A 2 1 ε 2 ε F 12 q rad,1 2 = h rad ( T surf,1 T surf,2 ) h rad = 4σT 3 avg 1 ε ε q 1 2 = ε surf σ F 12 T surf,1 Solar radiation: (opaque surface) Transmitted solar radiation: (transparent surface) R rad = 1 h rad 4 ( T surf,2 ) q solar = αi solar q solar = τ I solar 44

45 Where are we going? Building energy balances Taken altogether, each of the heat transfer modes we ve discussed can be combined with inputs for climate data, material properties, and geometry to make up a building s energy balance We will also revisit this for heating and cooling load calculations Cooling loads Heating loads Wall Gain Ceiling Gain Wall Loss Ceiling Loss Window Infiltration Floor Loss Door Infiltration Window Exfiltration Floor Loss Door Exfiltration 45

46 Next time HW #2 assigned today Due Tues Sep 13 46

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