Lecture Objectives: Define Solar Radiation Components Introduce Internal Surface Energy Balance

External Boundaries

Solar radiation Direct Diffuse Reflected (diffuse)

Solar Angles zz  - Solar altitude angle  – Angle of incidence

Direct and Diffuse Components of Solar Radiation

Solar components Global horizontal radiation I GHR Direct normal radiation I DNR Direct component of solar radiation on considered surface: Diffuse components of solar radiation on considered surface: Total diffuse solar radiation on considered surface: zz

Global horizontal radiation I GHR and Diffuse horizontal radiation measurements zz

Measurement of Direct Solar Radiation

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)( e[8.45(1 − 273/ T air )] CC) T sky = · 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)

Ground and sky temperatures Sky temperature Berdahl and Martin (1984) model  Clear = (T dp /100) (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 = *CC *CC *CC 3 – effect of cloudiness  sky =1

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

Velocity at surfaces that are windward: Velocity at surfaces that are leeward : U -wind velocity u u Convection coefficient : windwardleeward External convective heat flux Presented model is based on experimental data, Ito (1972) Primarily forced convection (wind): surface

Boundary Conditions at External Surfaces 1. External convective heat flux Required parameters : - wind velocity - wind direction - surface orientation U windward leeward Energy Simulation (ES) program treats every surface with different orientation as separate object. Consequence : N

Wind Direction Wind direction is defined in TMY database: “Value: 0 – 360 o 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.” U windward leeward Wind direction: ~225 o N

HW1 Problem 10 m 8 m 2.5 m Internal surfaces You will need Austin weather data: Solar angles and Solar radiation components calculation

Boundary Conditions at Internal Surfaces

Internal Boundaries Window Transmitted Solar radiation Internal sources

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

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

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