1. Lecture Objectives: Summarize heat transfer review
Define Solar Radiation Components
Introduce Internal Surface Energy Balance

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. Summary Convection Conduction Radiation 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

4. External Boundaries

5. Solar radiation
Direct
Diffuse
Reflected (diffuse)

6. Solar Angles qz
- Solar altitude angle
– Angle of incidence

7. Direct and Diffuse Components of Solar Radiation

8. 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:

9. Global horizontal radiation IGHR and Diffuse horizontal radiation measurementsqz

10. Measurement of Direct Solar Radiation

11. 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]
Tsky = · 10−6(1 − CC) Tair6+ Tair4CC·eclouds
Emissivity of clouds:
eclouds = (1 − 0. 84CC)( e[8.45(1 − 273/ Tair)] CC)
For modeled T sky the esky =1 (Modeled T sky is for black body)

12. 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

13. 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)

14. 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

15. 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

16. 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

17. HW1 Problem You will need Austin weather data: Solar angles and
Internal surfaces
Solar angles and
Solar radiation components calculation
You will need Austin weather data:

18. Boundary Conditions at Internal Surfaces

19. Internal Boundaries Window Internal sources Transmitted
Solar radiation

20. Surface to surface radiation
Exact equations for closed envelope Tj Ti
Fi,j - View factors
ψi,j - Radiative heat exchange factor
Closed system of equations

21. Internal Heat sources Occupants, Lighting, Equipment
Typically - Defined by heat flux
Convective
Affects the air temperature
Radiative
Radiative heat flux “distributed” to surrounding surfaces according to the surface area and emissivity

22. Surface Balance For each surface – external or internal :
All radiation components
Conduction
Convection
Convection + Conduction + Radiation = 0