Lecture Objectives:

• Finish with External Boundary Conditions

• Introduce Internal Surface Energy Balance

External Boundaries

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. 84CC)(0. 527 + 0. 161e[8.45(1 − 273/ Tair)] + 0. 84CC)

Tsky = 9. 365574 · 10−6(1 − CC) Tair6+ Tair

4CC·clouds

Emissivity of clouds:

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

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

Boundary Conditions at Internal Surfaces

Internal Boundaries

Room

F

C

L R

1

1

11

2

2

22

3

3

33

A air node

internal surface node

external surface node

element-inner node

Co

nve

ctio

n

Rad iati on

Window

TransmittedSolar radiation

Internal sources

Surface to surface radiation

ψi,j - Radiative heat exchange factor

Exact equations for closed envelope

44,, jiijiiji TTAQ

n

kkikjkjijji FF

1,,,, 1

nji ,...,2,1,

nji ,...,2,1, Closed system of equations

Ti TjFi,j - View factors

Internal Heat sourcesOccupants, Lighting, Equipment

• Typically - Defined by heat flux – Convective

• Directly affect the air temperature

– Radiative• Radiative heat flux “distributed” to surrounding surfaces

according to the surface area and emissivity

radiationsourceiiiiiisource QAreaSUMAreaQ _)]}([/)({

Internal Heat sources

• Lighting systems– Source of convective and radiative heat flux – Different complexity for modeling

above structure

lamp surf ace A , T surf

Plamp

qshort_wave

qlong_wave qconvection

P la mp

qsh or t_w a ve

ql on g_ w av eq co n ve ctio n

qsh o rt_w ave

ql on g_ wav e

qco n ve ctio n

Pla m pP la m p

Distribution of transmitted solar radiationDIRECT solar radiation

diffuse reflectionfi rst refle

ct ion

third reflect ion

s econd refle ct ion

di rect s un r adiatio

n

Floor absorpt ion

absorpt ion

abso

rptio

n

diffuse reflection

diff

use

refle

ctio

n

totally absorbed

iiiii ARAAASF 321floorfloorA 1

)()1(2 ,_ iiiFfloorfloorisurfaces FA

.....3 A

Distribution of transmitted solar radiationdiffuse solar radiation

diffuse sunradiat ion

sec on d re fle ction

absorpt ion

abso

rptio

n

lighting

window

diff

use

emis

sio

n

diffuse reflection

diff

use

refle

ctio

n

Air balance - Convection on internal surfaces + Ventilation + Infiltration

h1

Q1

h2

Q2

Affect the air temperature- h, and Q as many as surfaces- maircp.air Tair= Qconvective+ Qventilation

miTs1

Tair

Uniform temperature Assumption

Qconvective= ΣAihi(TSi-Tair)

Qventilation= Σmicp,i(Tsupply-Tair)

Tsupply

HW1 Problem

10 m 8 m

2.5 m

Internal surfaces

You will need Austin weather data:http://www.caee.utexas.edu/prof/Novoselac/classes/ARE383/handouts.html

Solar angles andSolar radiation components calculation