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Lecture Objectives:

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.

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Lecture Objectives:

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

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

  3. Summary • Convection • 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

  4. External Boundaries

  5. Solar radiation • Direct • Diffuse • Reflected (diffuse)

  6. Solar Angles qz • - Solar altitude angle • – Angle of incidence

  7. Direct and Diffuse Components of Solar Radiation

  8. 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:

  9. Global horizontal radiation IGHRand Diffusehorizontal radiation measurements qz

  10. Measurement of Direct Solar Radiation

  11. 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 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 theesky =1 (Modeled T sky is for black body)

  12. Ground and sky temperatures Sky temperature 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

  13. 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)

  14. External convective heat fluxPresented 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

  15. 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 treatsevery surface with different orientation as separate object. windward

  16. Wind Direction 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

  17. 2.5 m Internal surfaces 10 m 10 m HW1 Problem Solar angles and Solar radiation components calculation You will need Austin weather data: http://www.caee.utexas.edu/prof/Novoselac/classes/ARE383/handouts.html

  18. Boundary Conditions at Internal Surfaces

  19. Internal Boundaries Internal sources Window Transmitted Solar radiation

  20. 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

  21. Internal Heat sourcesOccupants, 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

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

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