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Lecture Objectives:

Lecture Objectives:. Finish with Review Radiation Boundary Conditions at External Surfaces. Raiation. Radiation wavelength. Short-wave & long-wave radiation. Short-wave – solar radiation <3 m m Glass is transparent Does not depend on surface temperature

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Lecture Objectives:

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  1. Lecture Objectives: • Finish with Review • Radiation • Boundary Conditions at External Surfaces

  2. Raiation

  3. Radiation wavelength

  4. Short-wave & long-wave radiation • Short-wave – solar radiation • <3mm • Glass is transparent • Does not depend on surface temperature • Long-wave – surface or temperature radiation • >3mm • Glass is not transparent • Depends on surface temperature

  5. Radiation emission The total energy emitted by a body, regardless of the wavelengths, is given by: Temperature always in K ! - absolute temperatures • – emissivity of surface • – Stefan-Boltzmann constant A - area

  6. Surface properties • Emission ( e ) is same as Absorption ( a ) for gray surfaces • Gray surface: properties do not depend on wavelength • Black surface: e = a = 1 • Diffuse surface: emits and reflects in each directionequally absorbed (α), transmitted (t), and reflected (ρ) radiation

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

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

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

  10. 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

  11. Boundary Conditions at External Surfaces

  12. External Boundaries

  13. 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:

  14. 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)

  15. 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

  16. 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)

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

  18. Solar Angles qz • - Solar azimuth angle • – Angle of incidence

  19. Direct and Diffuse Components of Solar Radiation

  20. 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:

  21. 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

  22. 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

  23. 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

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