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

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

3. From the previous class View (shape) factors
For closed envelope – such as room

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

5. Boundary Conditions at External Surfaces

6. External Boundaries

7. 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:

8. 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)

9. 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

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

11. Solar radiation
Direct
Diffuse
Reflected (diffuse)

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

13. Solar Angles

14. Direct and Diffuse Components of Solar Radiation

15. 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:

16. 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.

17. HW1 part 1