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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 :