1. Lecture Objectives: Discuss –solar radiation and heat transfer through windows –Internal heat loads Introduce Homework Assignment 1b –solve 1/3 of the problem

2. Internal Boundaries Window Transmitted Solar radiation Internal sources

3. Distribution of transmitted solar radiation DIRECT solar radiation

4. Distribution of transmitted solar radiation diffuse solar radiation

5. Transmission for single and double glazed window,,,

6. Heat transfer for double glazed window

7. 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

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

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

10. Air balance - Convection on internal surfaces + Ventilation + Infiltration h1 Q1 h2 Q2 What affects the air temperature? - h and corresponding Q - as many as surfaces mimi Ts1 Tair Uniform Air Temperature Assumption! Q convective = ΣA i h i (T Si -T air ) Q ventilation = Σm i c p,i (T supply -T air ) Tsupply -m air c p.air Δ T air = Qc onvective + Q ventilation Energy balance:

11. Air balance – steady state Convection on internal surfaces + Infiltration = Load h1 Q1 h2 Q2 - h, and Q surfaces as many as surfaces - infiltration – mass transfer (m i – infiltration) Q air = Q convective + Q infiltration mimi Ts1 Tair Uniform temperature Assumption Q convective = ΣA i h i (T Si -T air ) Q infiltration = Σm i c p (T outdoor_air -T air ) Q HVAC = Q air = m·c p (T supply_air -T air ) T outdoor air HVAC In order to keep constant air Temperate, HVAC system needs to remove cooling load

12. Homework assignment 1b West 10 m 2.5 m South conduction T air_in I DIR I dif Glass T inter_surf T west_i T west_o T south_i T south_oi T air_out Styrofoam I DIR I dif Surface radiation Surface radiation Top view

13. Homework assignment 1 Surface energy balance 1) External wall (west) node 2) Internal wall (west) node Q solar =  solar ·(I dif +I DIR ) A Q solar +C 1 ·A(T sky 4 - T west_o 4 )+ C 2 ·A(T ground 4 - T west_o 4 )+h ext A(T air_out -T west_ o )=Ak/  (T west_o -T west_in ) C 1 =  ·  surface  long_wave ·  ·F surf_sky Q solar_to west_surf =  portion of transmitted solar radiation that is absorbed by internal west surface C 3 A(T _in 4 - T internal_surf 4 )+C 4 A(T west_in 4 - T west_in 4 )+ h int A(T west_in -T air_in )= =kA(T west_out-- T west_in )+Q solar_to_west_surf C 3 =  niort_in ·  ·  north_in_to_ internal surface

14. Howe to solve system of equation by Using MathCad