Lecture Objectives:

Finish with Solar Radiation and Wind

Define Boundary Conditions at Internal Surfaces

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

Measurement of Direct Solar Radiation

Global horizontal radiation IGHR

and Diffuse horizontal radiation measurements

)cos( DNRGHRationzontalRadiDifusseHoi III

HW1 Problem

8 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 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

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

Surface Balance

Conduction

All radiation components

Convection

Convection + Conduction + Radiation = 0

For each surface – external or internal :

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

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