1. Lecture Objectives: Boundary Conditions at External Surfaces
Solar radiation

2. External Boundaries

3. 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:

4. 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)

5. 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

6. Ground and sky temperatures
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)

7. Solar radiation
Direct
Diffuse
Reflected (diffuse)

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

9. Direct and Diffuse Components of Solar Radiation

10. 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:

11. External convective heat flux Presented model is based on experimental data, Ito (1972)
Primarily forced convection (wind):
Velocity at surfaces that are windward:
Velocity at surfaces that are leeward :
U -wind velocity
Convection coefficient : u
surface u
windward
leeward

12. Boundary Conditions at External Surfaces
1. External convective heat flux
Required parameters:
- wind velocity
wind direction
surface orientation N
leeward
Consequence: U
Energy Simulation (ES) program treats every surface with different orientation as separate object.
windward

13. Wind Direction Wind direction: ~225o
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.” N
leeward U
windward
Wind direction: ~225o