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
Lecture Objectives:
• Finish with Review – Radiation
• Boundary Conditions at External Surfaces
Raiation
Radiation wavelength
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
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
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
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
View factor relations
F11=0, F12=1/2
F22=0, F12=F21
F31=1/3, F13=1/3
A1
A2A3 A1=A2=A3
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
,
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
Boundary Conditions at External Surfaces
External Boundaries
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
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
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
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
Solar radiation
• Direct • Diffuse• Reflected (diffuse)
Externalsurface
Sky DiffuseDirect Normal
radiation
Reflected
n
Solar Angles
Vertical surface
Normal to verticalsurface
S
E
NSun beam
W
S
z
- Solar azimuth angle– Angle of incidence
Direct and Diffuse Components of Solar Radiation
Window
External wall
Horizontal shading
Ver
tical
sha
ding
Ver
tical
sha
ding
Ashaded
Aunshaded
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
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
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
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