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 –Glass is transparent –Does not depend on surface temperature Long-wave – surface or temperature radiation – >3  m –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  – emissivity of surface  – Stefan-Boltzmann constant A - area

Surface properties Emission (  is same as Absorption (  ) for gray surfaces Gray surface: properties do not depend on wavelength Black surface:   Diffuse surface: emits and reflects in each direction equally absorbed (α), transmitted (  ), and reflected (ρ) radiation

View (shape) factors For closed envelope – such as room

View factor relations F 11 =0, F 12 =1/2 F 22 =0, F 12 =F 21 F 31 =1/3, F 13 =1/3 A1 A2 A3A1=A2=A3

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

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

Boundary Conditions at External Surfaces

External Boundaries

Radiative heat exchange at external surfaces View (shape) factors for: 1) vertical surfaces: - to sky 1/2 - to ground1/2 2) horizontal surfaces: - to sky 1 - to ground 0 3) Tilted surfaces - to sky (1+cos  )/2 - to ground (1-cos  )/2 General equations:  ground surface

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 T air [K]  clouds = (1 − 0.84·CC)( *exp[8.45·(1 − 273/ T air )]) CC Emissivity of clouds: For modeled T sky the  sky =1 (Modeled T sky is for black body) T sky 4 = · 10 −6 (1 − CC) T air 6 + T air 4 CC·  clouds

Ground and sky temperatures Sky temperature Berdahl and Martin (1984) model  Clear = (T dp /100) (T dp /100) 2 - emissivity of clear sky T clear_sky = T air (  Clear 0.25 ) - Cloudiness CC [0-1] 0 – for clear sky, 1 for totally cloud sky - Air temperature T air [K] - Dew point temperature T dp [C] !!! T sky = (Ca) 0.25 * T clear_sky Ca = *CC *CC *CC 3 – effect of cloudiness  sky =1

For ground temperature: - We often assume: T ground =T air -or we calculate Solar-air temperature -Solar-air temperature – imaginary temperature - Combined effect of solar radiation and air temperature T solar = f (T air, I solar, ground conductivity resistance) Ground and sky temperatures

Solar radiation Direct Diffuse Reflected (diffuse)

Solar Angles zz  - Solar azimuth angle  – Angle of incidence

Direct and Diffuse Components of Solar Radiation

Solar components Global horizontal radiation I GHR Direct normal radiation I DNR Direct component of solar radiation on considered surface: Diffuse components of solar radiation on considered surface: Total diffuse solar radiation on considered surface: zz

Velocity at surfaces that are windward: Velocity at surfaces that are leeward : U -wind velocity u u Convection coefficient : windwardleeward External convective heat flux Presented model is based on experimental data, Ito (1972) Primarily forced convection (wind): surface

Boundary Conditions at External Surfaces 1. External convective heat flux Required parameters : - wind velocity - wind direction - surface orientation U windward leeward Energy Simulation (ES) program treats every surface with different orientation as separate object. Consequence : N

Wind Direction Wind direction is defined in TMY database: “Value: 0 – 360 o 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.” U windward leeward Wind direction: ~225 o N