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Radiative Heat Transfer: External Boundary Conditions & View Factors

Learn the fundamentals of radiation, external surface boundary conditions, view factors, and radiative heat exchange. Understand the factors influencing radiation wavelengths, emissivity, and energy emission, and how they impact heat transfer. Explore equations for closed and non-closed envelopes, simplification for external surfaces, and system equations for internal surfaces.

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Radiative Heat Transfer: External Boundary Conditions & View Factors

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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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