lecture objectives:
DESCRIPTION
Lecture Objectives:. Finish with Review Radiation Boundary Conditions at External Surfaces. Raiation. Radiation wavelength. Short-wave & long-wave radiation. Short-wave – solar radiationTRANSCRIPT
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Lecture Objectives:
• Finish with Review – Radiation
• Boundary Conditions at External Surfaces
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Raiation
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Radiation wavelength
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Short-wave & long-wave radiation
• Short-wave – solar radiation– <3m– Glass is transparent – Does not depend on surface temperature
• Long-wave – surface or temperature radiation– >3m– Glass is not transparent – Depends on surface temperature
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Radiation emission The total energy emitted by a body, regardless of the wavelengths, is given by:
Temperature always in K ! - absolute temperatures
– emissivity of surface
– Stefan-Boltzmann constant
A - area
4ATQemited
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Surface properties
• Emission ( is same as Absorption ( ) for gray surfaces
• Gray surface: properties do not depend on wavelength
• Black surface: Diffuse surface: emits and reflects in each direction equally
1
n
absorbed (α), transmitted (), and reflected (ρ) radiation
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View (shape) factors
jijiji FAFA
i jA A
jiji
iij dAdA
lAF
2
coscos1
http://www.me.utexas.edu/~howell/
1j
ijF
For closed envelope – such as room
n
jijiniii FFFFF
1321 1... ni ,...,2,1
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View factor relations
F11=0, F12=1/2
F22=0, F12=F21
F31=1/3, F13=1/3
A1
A2A3 A1=A2=A3
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Radiative heat flux between two surfaces
44,, BAABABABA TTAFQ
ψi,j - Radiative heat exchange factor
Exact equations for closed envelope
Simplified equation for non-closed envelope
44,, jiijiiji TTAQ
n
kkikjkjijji FF
1,,,, 1 nji ,...,2,1,
BB
B
ABAAA
A
BABA
AFAA
TTQ
111
44
,
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Summary
• Convection– Boundary layer– Laminar transient and turbulent flow– Large number of equation for h for specific airflows
• Conduction – Unsteady-state heat transfer – Partial difference equation + boundary conditions– Numerical methods for solving
• Radiation – Short-wave and long-wave – View factors– Simplified equation for external surfaces– System of equation for internal surfaces
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Boundary Conditions at External Surfaces
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External Boundaries
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Radiative heat exchange at external surfaces
)(2/)cos1( 44_ skysurfskysurfskysurf TTAQ
T ground
Tsurface T air
T sky
View (shape) factors for:
1) vertical surfaces:- to sky 1/2- to ground 1/2
2) horizontal surfaces: - to sky 1 - to ground 0
3) Tilted surfaces - to sky (1+cos)/2 - to ground (1-cos)/2
General equations:
)(2/)cos1( 44_ groundsurfgroundsurfgroundsurf TTAQ
ground
surface
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Ground and sky temperatures
• Sky temperature
• Swinbank (1963, Cole 1976) model-Cloudiness CC [0-1] 0 – for clear sky , 1 for totally cloud sky -Air temperature Tair [K]
clouds = (1 − 0.84·CC)(0.527 + 0.161*exp[8.45·(1 − 273/ Tair)]) + 0.84CC
Emissivity of clouds:
For modeled T sky the sky =1 (Modeled T sky is for black body)
Tsky4 = 9. 365574 · 10−6(1 − CC) Tair
6+ Tair4CC·clouds
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Ground and sky temperatures• Sky temperature
Berdahl and Martin (1984) model
Clear = 0.711 + 0.56(Tdp/100) + 0.73 (Tdp/100)2 - emissivity of clear sky
Tclear_sky = Tair (Clear0.25)
- Cloudiness CC [0-1] 0 – for clear sky , 1 for totally cloud sky - Air temperature Tair [K]- Dew point temperature Tdp [C] !!!
Tsky = (Ca)0.25 * Tclear_sky
Ca = 1.00 +0.0224*CC + 0.0035*CC2 + 0.00028*CC3 – effect of cloudiness
sky =1
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For ground temperature:
- We often assume: Tground=Tair
-or we calculate Solar-air temperature
-Solar-air temperature – imaginary temperature
- Combined effect of solar radiation and air temperature
Tsolar = f (Tair , Isolar , ground conductivity resistance)
Ground and sky temperatures
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Solar radiation
• Direct • Diffuse• Reflected (diffuse)
Externalsurface
Sky DiffuseDirect Normal
radiation
Reflected
n
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Solar Angles
Vertical surface
Normal to verticalsurface
S
E
NSun beam
W
S
z
- Solar azimuth angle– Angle of incidence
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Direct and Diffuse Components of Solar Radiation
Window
External wall
Horizontal shading
Ver
tical
sha
ding
Ver
tical
sha
ding
Ashaded
Aunshaded
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Solar components
cosDNRDIR II
2/)cos1()cos(_ DNRGHRskydif III2/)cos1(_ groundGHRreflecteddif II
reflecteddifskydifdif III __
• Global horizontal radiation IGHR
• Direct normal radiation IDNRDirect component of solar radiation on considered surface:
Diffuse components of solar radiation on considered surface:
Total diffuse solar radiation on considered surface:
z
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m/s 2for U 0.25
m/s 2for U 0.5
U
u
05.03.0 Uu
uh 6.55.3
Velocity at surfaces that are windward:
Velocity at surfaces that are leeward :U -wind velocity
u u
Convection coefficient :
windward leeward)( surfaceair TThAQ
External convective heat fluxPresented model is based on experimental data, Ito (1972)
Primarily forced convection (wind):
surface
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Boundary Conditions at External Surfaces
1. External convective heat flux
Required parameters:- wind velocity- wind direction - surface orientation
U
windward
leeward
Energy Simulation (ES) program treats every surface with different orientation as separate object.
Consequence:
N
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Wind Direction
Wind direction is defined in TMY database:
“Value: 0 – 360o Wind direction in degrees at the hou
indicated. ( N = 0 or 360, E = 90, S = 180,W = 270 ). For calm winds, wind direction equals zero.”
U
windward
leeward
Wind direction: ~225o
N
http://rredc.nrel.gov/solar/pubs/tmy2/http://rredc.nrel.gov/solar/pubs/tmy2/tab3-2.html