1. Lecture Objectives:
Introduce Internal Surface Energy Balance

2. HW1 Problem
10 m
2.5 m
Internal surfaces
East
South
South
West

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

4. 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.

5. Direct and Diffuse Components of Solar Radiation

6. 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:

7. Boundary Conditions at Internal Surfaces

8. Internal Boundaries Window Internal sources Transmitted
Solar radiation

9. 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

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

11. Internal Heat sources Lighting systems
Source of convective and radiative heat flux
Different complexity for modeling

12. Distribution of transmitted solar radiation DIRECT solar radiation

13. Distribution of transmitted solar radiation diffuse solar radiation

14. Air balance - Convection on internal surfaces + Ventilation + Infiltration
Uniform temperature Assumption
Affect the air temperature
- h, and Q as many as surfaces
- maircp.air DTair= Qconvective+ Qventilation
Tsupply
Qconvective= ΣAihi(TSi-Tair)
Ts1 mi
Qventilation= Σmicp,i(Tsupply-Tair) Q1 Q2
Tair h1 h2

15. HW1b Problem Steady State Energy Model 2.5 m Internal surfaces 8 m