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Lecture Objectives:

Lecture Objectives:. Finish with review of radiation Learn about External long wave radiation S oar radiation components. Radiative heat flux between two surfaces. Simplified equation for non-closed envelope. Exact equations for closed envelope. ψ i,j - Radiative heat exchange factor.

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Lecture Objectives:

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  1. Lecture Objectives: • Finish with review of radiation • Learn about • External long wave radiation • Soar radiation components

  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. From the previous class View (shape) factors http://www.me.utexas.edu/~howell/ For closed envelope – such as room

  4. View factor relations F11=0, F12=1/2 F22=0, F12=F21 F31=1/3, F13=1/3 A2 A3 A1=A2=A3 A1

  5. Boundary Conditions at External Surfaces

  6. External Boundaries

  7. Radiative heat exchange at external surfaces View (shape) factors for: 1) vertical surfaces: - to sky 1/2 • to ground 1/2 2) horizontal surfaces: - to sky 1 - to ground 0 3) Tilted surfaces - to sky (1+cosb)/2 - to ground (1-cosb)/2 surface b ground General equations:

  8. 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] Tsky4 = 9. 365574 · 10−6(1 − CC) Tair6+ Tair4CC·eclouds Emissivity of clouds: eclouds = (1 − 0.84·CC)(0.527 + 0.161*exp[8.45·(1 − 273/ Tair)]) + 0.84CC For modeled T sky theesky =1 (Modeled T sky is for black body)

  9. 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

  10. Ground and sky temperatures For ground temperature: - We often assume: Tground=Tair

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

  12. Solar Angles qz • - Solar altitude • - Angle of incidence • - Azimuth b - Inclination

  13. Direct and Diffuse Components of Solar Radiation

  14. 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:

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