ASRAE Student Branch meeting Speaker: Kenneth Simpson USGBC – LEED rating system Today at 5 pm ECJ 5.410
Jan 03, 2016
ASRAE Student Branch meeting
Speaker: Kenneth Simpson
USGBC – LEED rating systemToday at 5 pm
ECJ 5.410
Lecture Objectives:
• Review - Heat transfer
– Convection
– Conduction
– Radiation
Simplified Equation for Forced convection
Pr) (Re, fNu
LU
LRe 3/1PrRe LCNu
5/4PrRe TCNu
For laminar flow:
For turbulent flow:
For air: Pr ≈ 0.7, = viscosity is constant, k = conductivity is constant
k
hLNu
General equation
mnmforced UCLUfh ),(
Simplified equation:
mforced ACHCh
Or:
RoomVolumeACH
rate flow Volume
Natural convection
GOVERNING EQUATIONSNatural convection
Continuity
• Momentum which includes gravitational force
• Energy
v2
2
y
uvTTg
y
u
x
uu
0 v
yx
u
2
2 v
y
T
y
T
x
Tu
u, v – velocities , – air viscosity , g – gravitation, ≈1/T - volumetric thermal expansion T –temperature, – air temperature out of boundary layer, –temperature conductivity T
Characteristic Number for Natural Convection
TT
TTTUU
uuLyyLxxw
***** ;v v;; ;
2*
*2*
2*
**
*
**
Re
1 v
y
uT
U
LTTwg
y
u
x
uu
L
Non-dimensionless governing equations
Using
L = characteristic length and U0 = arbitrary reference velocity Tw- wall temperature
The momentum equation become
2
3
LTTg w
Multiplying by Re2 number Re=UL/
Gr
2*
*2*2
*
**
*
** )Re/1()Re/( v
y
uTGr
y
u
x
uu LL
Grashof number Characteristic Number for Natural Convection
2
3
LTTwg
Gr
The Grashof number has a similar significance for natural convection as the Reynolds number has for forced convection, i.e. it represents a ratio of buoyancy to viscous forces.
Buoyancy forces
Viscous forces
Pr) ,( GrfNu
General equation
Even more simple
Natural convection simplified equations
4/1Pr GrCNu L
3/1Pr GrCNu T
For laminar flow:
For turbulent flow:
For air: Pr ≈ 0.7, = constant, k= constant, = constant, g=constant
),(),)(( nmnmnatural LTfLTTwfh
Simplified equation:
mnatural TCh
Or:
T∞ - air temperature outside of boundary layer, Ts - surface temperature
Forced and/or natural convection
Gr) Pr, (Re, 1Re2 fNuGr LL
Pr) (Re, 1Re2 fNuGr LL
Pr) ,( 1Re2 GrfNuGr LL
In general, Nu = f(Re, Pr, Gr)
natural and forced convection
forced convection
natural convection
Example of general forced and natural convection
8.019.1 ACHh forced
3/138.0333.0 )19.1()12.2( ACHThcombinbed
333.0 )12.2( Thnatural
Equation for convection at cooled ceiling surfaces
n
Conduction
Conductive heat transfer
• Steady-state
• Unsteady-state
• Boundary conditions
– Dirichlet Tsurface = Tknown
– Neumann
)(/ 21 SS TTLkq
sourcep
qx
T
c
kT
2
2
)( surfaceair TThx
T
L
Tair
k - conductivity of material
TS1 TS2
h
0 1 2 3 4 5 6 7 8 9 100.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Analytical solution Numerical -3 nodes, =60 min Numerical -7 nodes, =60 min Numerical -7 nodes, =12 min
(T-T
s)/(
To
-Ts)
hour
Ts
0
T
-L / 2 L /2
h
h
h
To
T
h omogenous wa ll
L = 0.2 mk = 0 . 5 W/ m Kc = 9 20 J/kgK
= 120 0 k g/mp
2
Importance of analytical solution
What will be the daily temperature distribution profile on internal surface
for styrofoam wall?
A.
B.
External temperature profile
T
time
What will be the daily temperature distribution profile on internal surface
for tin glass?
A.
B.
External temperature profile
T
time
Conduction equation describes accumulation
Radiation
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 (τ), 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
Example: 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
Building components