Lecture Objectives: Summarize heat transfer review Define Solar Radiation Components Introduce Internal Surface Energy Balance

Radiative heat flux between two surfaces Simplified equation for non-closed envelope Exact equations for closed envelope ψi,j - Radiative heat exchange factor

Summary Convection Conduction Radiation Boundary layer Laminar transient and turbulent flow Large number of equation for h for specific airflows Conduction Unsteady-state heat transfer Partial difference equation + boundary conditions Numerical methods for solving Radiation Short-wave and long-wave View factors Simplified equation for external surfaces System of equation for internal surfaces

External Boundaries

Solar radiation Direct Diffuse Reflected (diffuse)

Solar Angles qz - Solar altitude angle – Angle of incidence

Direct and Diffuse Components of Solar Radiation

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:

Global horizontal radiation IGHR and Diffuse horizontal radiation measurements qz

Measurement of Direct Solar Radiation

Ground and sky temperatures Swinbank (1963, Cole 1976) model Cloudiness CC [0-1] 0 – for clear sky , 1 for totally cloud sky Air temperature Tair [K] Tsky = 9. 365574 · 10−6(1 − CC) Tair6+ Tair4CC·eclouds Emissivity of clouds: eclouds = (1 − 0. 84CC)(0. 527 + 0. 161e[8.45(1 − 273/ Tair)] + 0. 84CC) For modeled T sky the esky =1 (Modeled T sky is for black body)

Ground and sky temperatures Berdahl and Martin (1984) model - Cloudiness CC [0-1] 0 – for clear sky , 1 for totally cloud sky Air temperature Tair [K] Dew point temperature Tdp [C] !!! Tclear_sky = Tair (eClear0.25) eClear = 0.711 + 0.56(Tdp/100) + 0.73 (Tdp/100)2 - emissivity of clear sky Ca = 1.00 +0.0224*CC + 0.0035*CC2 + 0.00028*CC3 – effect of cloudiness Tsky = (Ca)0.25 * Tclear_sky esky =1

Ground and sky temperatures For ground temperature: - We often assume: Tground=Tair or we calculate Solar-air temperature Solar-air temperature – imaginary temperature Combined effect of solar radiation and air temperature Tsolar = f (Tair , Isolar , ground conductivity resistance)

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

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

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 http://rredc.nrel.gov/solar/pubs/tmy2/ http://rredc.nrel.gov/solar/pubs/tmy2/tab3-2.html leeward U windward Wind direction: ~225o

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

Boundary Conditions at Internal Surfaces

Internal Boundaries Window Internal sources Transmitted Solar radiation

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

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