Lecture Objectives:

• Summarize heat transfer review

• Define Solar Radiation Components

• Introduce Internal Surface Energy Balance

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

External Boundaries

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 altitude 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

Global horizontal radiation IGHR

and Diffuse horizontal radiation measurements

)cos( DNRGHRationzontalRadiDifusseHoi III z

Measurement of Direct Solar Radiation

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

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

HW1 Problem

10 m 10 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

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

• Affects the air temperature

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

according to the surface area and emissivity

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

Surface Balance

Conduction

All radiation components

Convection

Convection + Conduction + Radiation = 0

For each surface – external or internal :