Lecture Objectives:

• Finish with Review – Radiation

• Boundary Conditions at External Surfaces

Raiation

Radiation wavelength

Short-wave & long-wave radiation

• Short-wave – solar radiation– <3m– Glass is transparent – Does not depend on surface temperature

• Long-wave – surface or temperature radiation– >3m– 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

4ATQemited

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

1

n

absorbed (α), transmitted (), and reflected (ρ) radiation

View (shape) factors

jijiji FAFA

i jA A

jiji

iij dAdA

lAF

2

coscos1

http://www.me.utexas.edu/~howell/

1j

ijF

For closed envelope – such as room

n

jijiniii FFFFF

1321 1... ni ,...,2,1

View factor relations

F11=0, F12=1/2

F22=0, F12=F21

F31=1/3, F13=1/3

A1

A2A3 A1=A2=A3

Radiative heat flux between two surfaces

44,, BAABABABA TTAFQ

ψi,j - Radiative heat exchange factor

Exact equations for closed envelope

Simplified equation for non-closed envelope

44,, jiijiiji TTAQ

n

kkikjkjijji FF

1,,,, 1 nji ,...,2,1,

BB

B

ABAAA

A

BABA

AFAA

TTQ

111

44

,

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

)(2/)cos1( 44_ skysurfskysurfskysurf TTAQ

T ground

Tsurface T air

T sky

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+cos)/2 - to ground (1-cos)/2

General equations:

)(2/)cos1( 44_ groundsurfgroundsurfgroundsurf TTAQ

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 Tair [K]

clouds = (1 − 0.84·CC)(0.527 + 0.161*exp[8.45·(1 − 273/ Tair)]) + 0.84CC

Emissivity of clouds:

For modeled T sky the sky =1 (Modeled T sky is for black body)

Tsky4 = 9. 365574 · 10−6(1 − CC) Tair

6+ Tair4CC·clouds

Ground and sky temperatures• Sky temperature

Berdahl and Martin (1984) model

Clear = 0.711 + 0.56(Tdp/100) + 0.73 (Tdp/100)2 - emissivity of clear sky

Tclear_sky = Tair (Clear0.25)

- Cloudiness CC [0-1] 0 – for clear sky , 1 for totally cloud sky - Air temperature Tair [K]- Dew point temperature Tdp [C] !!!

Tsky = (Ca)0.25 * Tclear_sky

Ca = 1.00 +0.0224*CC + 0.0035*CC2 + 0.00028*CC3 – effect of cloudiness

sky =1

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)

Ground and sky temperatures

Solar radiation

• Direct • Diffuse• Reflected (diffuse)

Externalsurface

Sky DiffuseDirect Normal

radiation

Reflected

n

Solar Angles

Vertical surface

Normal to verticalsurface

S

E

NSun beam

W

S

z

- Solar azimuth angle– Angle of incidence

Direct and Diffuse Components of Solar Radiation

Window

External wall

Horizontal shading

Ver

tical

sha

ding

Ver

tical

sha

ding

Ashaded

Aunshaded

Solar components

cosDNRDIR II

2/)cos1()cos(_ DNRGHRskydif III2/)cos1(_ groundGHRreflecteddif II

reflecteddifskydifdif III __

• Global horizontal radiation IGHR

• Direct normal radiation IDNRDirect component of solar radiation on considered surface:

Diffuse components of solar radiation on considered surface:

Total diffuse solar radiation on considered surface:

z

m/s 2for U 0.25

m/s 2for U 0.5

U

u

05.03.0 Uu

uh 6.55.3

Velocity at surfaces that are windward:

Velocity at surfaces that are leeward :U -wind velocity

u u

Convection coefficient :

windward leeward)( surfaceair TThAQ

External convective heat fluxPresented 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 – 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.”

U

windward

leeward

Wind direction: ~225o

N

http://rredc.nrel.gov/solar/pubs/tmy2/http://rredc.nrel.gov/solar/pubs/tmy2/tab3-2.html