1. Lecture Objectives: Finish with review of radiation Learn about
External long wave radiation
Soar radiation components

2. Radiation wavelength

3. Short-wave & long-wave radiation
Short-wave – solar radiation
<3mm
Glass is transparent
Does not depend on surface temperature
Long-wave – surface or temperature radiation
>3mm
Glass is not transparent
Depends on surface temperature

4. 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

5. Surface properties
absorbed (α), transmitted (t), and reflected (ρ) radiation
Emission ( e ) is same as Absorption ( a ) for gray surfaces
Gray surface: properties do not depend on wavelength
Black surface: e = a = 1
Diffuse surface: emits and reflects in each direction equally

6. View (shape) factors http://www.me.utexas.edu/~howell/
For closed envelope – such as room

7. View factor relations F11=0, F12=1/2 F22=0, F12=F21 F31=1/3, F13=1/3
A1=A2=A3 A1

8. Radiative heat flux between two surfaces
Simplified equation for non-closed envelope
Exact equations for closed envelope
ψi,j - Radiative heat exchange factor

9. Boundary Conditions at External Surfaces

10. External Boundaries

11. Radiative heat exchange at external surfaces
View (shape) factors for:
1) vertical surfaces:
- to sky 1/2
to ground 1/2
2) horizontal surfaces:
- to sky
- to ground
3) Tilted surfaces
- to sky (1+cosb)/2
- to ground (1-cosb)/2
surface b
ground
General equations:

12. Ground and sky temperatures
Swinbank (1963, Cole 1976) model
Cloudiness CC [0-1] 0 – for clear sky , 1 for totally cloud sky
Air temperature Tair [K]
Tsky4 = · 10−6(1 − CC) Tair6+ Tair4CC·eclouds
Emissivity of clouds:
eclouds = (1 − 0.84·CC)( *exp[8.45·(1 − 273/ Tair)]) CC
For modeled T sky the esky =1 (Modeled T sky is for black body)

13. Ground and sky temperatures
Berdahl and Martin (1984) model
- Cloudiness CC [0-1] 0 – for clear sky , 1 for totally cloud sky
Air temperature Tair [K]
Dew point temperature Tdp [C] !!!
Tclear_sky = Tair (eClear0.25)
eClear = (Tdp/100) (Tdp/100) emissivity of clear sky
Ca = *CC *CC *CC3 – effect of cloudiness
Tsky = (Ca)0.25 * Tclear_sky
esky =1

14. Ground and sky temperatures
For ground temperature:
- We often assume: Tground=Tair

15. Solar radiation
Direct
Diffuse
Reflected (diffuse)

16. Solar Angles qz - Solar altitude - Angle of incidence - Azimuth
b - Inclination

17. Solar Angles

18. Direct and Diffuse Components of Solar Radiation

19. Solar components Global horizontal radiation IGHR
Direct normal radiation IDNR
Direct component of solar radiation on considered surface:
Diffuse components of solar radiation on considered surface: qz
Total diffuse solar radiation on considered surface:

20. HW1
1) Using the equations provided in the attached paper sheet and the basic properties of view factors calculate the view factors for internal characteristic surfaces:
FSS , FSE , FSI
FES , FEE , FEI
FIS , FIE , FII
2) Using the geometry of the building, period of the year, and provided data in the excel file calculate:
- incident angle of direct solar radiation on all external surfaces for period of 24 hours,
- direct (ID) and diffuse (Id) components of solar radiation for period of 24 hours.
For the ground surface assume reflectivity of rground = 0.2.
3) Using both a) Swinbank Cole model and b) Berdahl and Martin model (provided in class notes) and data provided in the excel file calculate the equivalent sky temperature for the period of 24 hours.

21. HW1 part 1