1. Lecture Objectives: Discus HW 1 Finish with Solar Radiation Components
Solar angles
Solar components calculation process
Learn about Internal and External Surface Convection

2. 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.

3. Solar radiation
Direct
Diffuse
Reflected (diffuse)

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

5. Solar Angles

6. Calculation of Solar Angles
g – surface azimuth (from 0 to ±180°, east negative and west positive)
f - Latitude
d - Declination (function of a day in a year)
- Hour angle (function of Longitude defined distance from local meridian
Austin’s Latitude = ° N
Austin’s Longitude ° W
What is v ?
HW1a Part 3) Calculate q for two surfaces in your HW1a for each hour:
Use equation from the handouts.
NOTE: When you use excel be careful about degree and radian mode.
Default is radian ! 1
1 radian = 180/ degrees.

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. Convection
How to calculate h ? What are the parameters that affect h ? What is the boundary layer ?

12. Laminar and Turbulent Flow forced convection

13. Forced convection governing equations
1) Continuity
2) Momentum
u, v – velocities
n – air viscosity
Non-dimensionless momentum equation
Using
L = characteristic length and U0 = arbitrary reference velocity
ReL
Reynolds number

14. Forced convection governing equations
Energy equation for boundary layer 
T –temperature, a – thermal diffusivity a=k/rcp,
k-conductivity, r - density, cp –specific cap.
Non-dimensionless energy equations
Air temperature outside
of boundary layer
Wall temperature
Reynolds number
Prandtl number
Momentum diffusivity
Inertial force
Thermal diffusivity
Viscous force

15. Simplified Equation for Forced convection
General equation
For laminar flow:
For turbulent flow:
For air: Pr ≈ 0.7, n = viscosity is constant, k = conductivity is constant
Simplified equation:
Or:

16. Natural convection

17. GOVERNING EQUATIONS Natural convection
Continuity
Momentum which includes gravitational force
Energy
u, v – velocities , n – air viscosity , g – gravitation, b≈1/T - volumetric thermal expansion
T –temperature, – air temperature out of boundary layer, a –temperature conductivity

18. Characteristic Number for Natural Convection
Non-dimensionless governing equations
Using
L = characteristic length and U0 = arbitrary reference velocity Tw- wall temperature
The momentum equation become Gr
Multiplying by Re2 number Re=UL/n

19. Grashof number Characteristic Number for Natural Convection
Buoyancy forces
Viscous forces
The Grashof number has a similar significance for natural convection
as the Reynolds number has for forced convection, i.e. it represents a
ratio of buoyancy to viscous forces.
General equation

20. Natural convection simplified equations
For laminar flow:
For turbulent flow:
For air: Pr ≈ 0.7, n = constant, k= constant, b= constant, g=constant
Simplified equation:
Even more simple
Or:
T∞ - air temperature outside of boundary layer, Ts - surface temperature

21. Forced and/or natural convection
In general, Nu = f(Re, Pr, Gr)
natural and forced convection
forced convection
natural convection

22. Combined forced and natural convention
Churchill and Usagi approach :
This equation favors a dominant term (h1 or h2), and exponent coefficient ‘n’ determines
the value for hcombined when both terms have the same order of value

23. Example of general forced and natural convection
Equation for convection at cooled ceiling surfaces n

24. 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

25. 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

26. 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