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. Direct and Diffuse Components of Solar Radiation

14. 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: