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Lecture Objectives:

This lecture covers the basics of radiation heat exchange between surfaces and introduces simplified equations for non-closed and closed envelope systems. It also discusses view factors, boundary conditions at external surfaces, and models for ground and sky temperatures. Additionally, the lecture covers solar radiation components, including direct and diffuse radiation.

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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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