1. Lecture Objectives: Finish with External Boundary Conditions Introduce Internal Surface Energy Balance

2. External Boundaries

3. Ground and sky temperatures Sky temperature Swinbank (1963, Cole 1976) model -Cloudiness CC [0-1] 0 – for clear sky, 1 for totally cloud sky -Air temperature T air [K]  clouds = (1 − 0. 84CC)(0. 527 + 0. 161e[8.45(1 − 273/ T air )] + 0. 84CC) T sky = 9. 365574 · 10 −6 (1 − CC) T air 6 + T air 4 CC·  clouds Emissivity of clouds: For modeled T sky the  sky =1 (Modeled T sky is for black body)

4. Ground and sky temperatures Sky temperature Berdahl and Martin (1984) model  Clear = 0.711 + 0.56(T dp /100) + 0.73 (T dp /100) 2 - emissivity of clear sky T clear_sky = T air (  Clear 0.25 ) - Cloudiness CC [0-1] 0 – for clear sky, 1 for totally cloud sky - Air temperature T air [K] - Dew point temperature T dp [C] !!! T sky = (Ca) 0.25 * T clear_sky Ca = 1.00 +0.0224*CC + 0.0035*CC 2 + 0.00028*CC 3 – effect of cloudiness  sky =1

5. For ground temperature: - We often assume: T ground =T air -or we calculate Solar-air temperature -Solar-air temperature – imaginary temperature - Combined effect of solar radiation and air temperature T solar = f (T air, I solar, ground conductivity resistance) Ground and sky temperatures

6. Boundary Conditions at Internal Surfaces

7. Internal Boundaries Window Transmitted Solar radiation Internal sources

8. Surface to surface radiation ψ i,j - Radiative heat exchange factor Exact equations for closed envelope Closed system of equations Ti Tj F i,j - View factors

9. 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

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

11. Distribution of transmitted solar radiation DIRECT solar radiation

12. Distribution of transmitted solar radiation diffuse solar radiation

13. Air balance - Convection on internal surfaces + Ventilation + Infiltration h1 Q1 h2 Q2 Affect the air temperature - h, and Q as many as surfaces - m air c p.air  T air = Q convective + Q ventilation mimi Ts1 Tair Uniform temperature Assumption Q convective = ΣA i h i (T Si -T air ) Q ventilation = Σm i c p,i (T supply -T air ) Tsupply

14. HW1 Problem 10 m 8 m 2.5 m Internal surfaces You will need Austin weather data: http://www.caee.utexas.edu/prof/Novoselac/classes/ARE383/handouts.html Solar angles and Solar radiation components calculation