Lecture Objectives Finish with review of radiation Learn

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

Radiation wavelength

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

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

Surface properties absorbed (α), transmitted (t), and reflected (ρ) radiation • 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 direction equally

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

View factor relations A 2 A 3 A 1 F 11=0, F 12=1/2 F 22=0, F 12=F 21 F 31=1/3, F 13=1/3 A 1=A 2=A 3

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

Boundary Conditions at External Surfaces

External Boundaries

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

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 4 = 9. 365574 · 10− 6(1 − CC) Tair 6+ Tair 4 CC·eclouds Emissivity of clouds: eclouds = (1 − 0. 84·CC)(0. 527 + 0. 161*exp[8. 45·(1 − 273/ Tair)]) + 0. 84 CC For modeled T sky the esky =1 (Modeled T sky is for black body)

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 (e. Clear 0. 25) e. Clear = 0. 711 + 0. 56(Tdp/100) + 0. 73 (Tdp/100)2 - emissivity of clear sky Ca = 1. 00 +0. 0224*CC + 0. 0035*CC 2 + 0. 00028*CC 3 – effect of cloudiness Tsky = (Ca)0. 25 * Tclear_sky esky =1

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

Solar radiation • Direct • Diffuse • Reflected (diffuse)

Solar Angles qz a q g b - Solar altitude - Angle of incidence - Azimuth - Inclination

Solar Angles

Direct and Diffuse Components of Solar Radiation

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:

HW 1 1) Using the equations provided in the attached paper sheet and the basic properties of view factors calculate the view factors for internal characteristic surfaces: FSS , FSE , FSI FES , FEE , FEI FIS , FIE , FII 2) Using the geometry of the building, period of the year, and provided data in the excel file calculate: - incident angle of direct solar radiation on all external surfaces for period of 24 hours, - direct (ID) and diffuse (Id) components of solar radiation for period of 24 hours. For the ground surface assume reflectivity of rground = 0. 2. 3) Using both a) Swinbank Cole model and b) Berdahl and Martin model (provided in class notes) and data provided in the excel file calculate the equivalent sky temperature for the period of 24 hours.

HW 1 part 1