condensation heat transfer -...
TRANSCRIPT
Condensation Heat Transfer
Condensation on a Vertical Surface
Heat transfer to a surface occurs by condensation when the surface temperature is less than the saturation temperature of an adjoining vapor.
• Film Condensation
o Entire surface is covered by the condensate, which flows continuously from the surface and provides a resistance to heat transfer between the vapor and the surface.
o Thermal resistance is reduced through use of short vertical surfaces and horizontal cylinders
o Characteristic of clean, uncontaminated surfaces.
Dropwise Condensation
• Dropwise Condensation
• Surface is covered by drops ranging from a few micrometers to agglomerations visible to the naked eye
• Thermal resistance is greatly reduced due to absence of a continuous film
• Surface coatings may be applied to inhibit wetting and stimulate dropwise condensation.
Film Condensation – Nusselt AnalysisRefer to Class Notes
Film Condensation on a Vertical Plate Refer to class notes for derivations of
momentum and energy equations
Derived expressions
Film thickness:
1 4
4/
l l sat s
l l v fg
k T T xx
g h
Flow rate per unit width:
3
3
l l v
l
gm
b
Average Nusselt Number:
1 43
0 943
/
.L
l l v fgL
l l l sat s
g h Lh LNuk k T T
1 0 68
Jakob number
.fg fg
p sat s
fg
h h Ja
c T TJa
h
Vertical Plates (cont)
Total heat transfer and condensation rates:
L sat s
fg
q h A T T
qm
h
• Effects of Turbulence:
Transition may occur in the film and three flow regimes may be identified and delineated in terms of a Reynolds number defined as
44 4Re l m
l l l
um
b
Wave-free laminar region Re 30 :
1 3
2
-1/31 47 Re
/
/.
L l
l
h g
k
3
2
4Re
3
l l v
l
g
Wavy laminar region 30 Re 1800 :
1 3
2
1.22
Re
1.08 Re 5 2
/
/
.
L l
l
h g
k
Turbulent region Re >1800 :
1 32
-0.5 0 75
Re
8750 +58 Pr Re 253
/
.
/L l
l
h g
k
Correlations – Laminar to Turbulent
Calculation procedure:
Assume a particular flow regime and use the corresponding expression for h to determine Re
If value of Re is consistent with assumption, proceed to determination of h and q
If value of Re is inconsistent with the assumption, recompute its value using a different expression for h, and proceed to determination of q
Film Condensation on Radial Systems
• Single tube or sphere:
1 43 /
l l l fgD
l sat s
g k hh C
T T D
Tube: C =0.729 Sphere: C=0.826
• Vertical stack of N tubes
1 43
0 729
/
, . ll l fg
D N
l sat s
g k hh
N T T D
Dropwise Condensation
• Steam condensation on copper surfaces [Griffith]:
dc
51100 2044 22 C< 100 C
255 500 100 C
,
,
dc sat sat
sat
h T T
h T
dc sat sq h A T T
Boiling Heat Transfer
When does boiling occur?
When heat is added to a liquid from a submerged solid surface which is at a temperature higher than the saturation temperature of the liquid it is usual for a part of the liquid to change phase and become vapour. This change of phase is called BOILING.
Pool boiling
(a) Heat transfer through heater plate at bottom
q”Tw
Tsat
q” Tw
Tsat
(b) Heat transfer through immersed heater coil
Flow Boiling
• Liquid is forced to move by an external agency like a pump
Liquid
TsTw
Boiling Curve
Nukiyama’s Experiment
Nukiyama’s Curve – Hysteresis Effect
Pool Boiling - pictures
Nucleate Boiling
Film Boiling
Pool Boiling Modes
1. Natural Convection Boiling: Te≤5 C
2. Nucleate Boiling: 5C ≤ Te ≤ 30 C
3. Transition Boiling: 30C ≤ Te ≤ 120 C
4. Film Boiling: Te ≥120 C
Correlation – Natural Convection Regime
Natural Convection Boiling: all single phase natural convection correlations are valid
For horizontal wire or cylinder inside a pool of liquid:
9/816/9
6/1
9/416/9
4/1"
Pr559.01
387.060.0
Pr559.01
518.036.0
Dsw
Dsw
RaTT
D
k
RaTT
D
kq for 10-6<RaD<109
for 109<RaD<1012
Correlation: Nucleate boiling
• Rohsenow’s correlation is used for horizontal wires, tubes and plates
• Cs,f depends on surface fluid combination• all properties evaluated at liquid saturation temp
3
)Pr
(])(
[,
,2/1"
n
lfgfs
swlpvlfgls
hC
TTcghq
Rohsenow Correlation
n = 1.0 for water
= 1.7 for other liquids
3"
sws TTq
Correlation: Critical Heat Flux
Infinite horizontal surface facing up (Kutateladze, Zuber)
2/1)(])(
[24
4/1
2
"
max
v
vl
v
vlvfg
ghq
4/1
2
"
max ])(
[149.0v
vlvfg
ghq
1
If the plate is finite size (Lienhard and Dhir)
Correlation – Transition regime
4/1
2
"
min ])(
)([
vl
vlvfg
gChq
Transition Boiling – no suitable correlation
Leidenfrost point
Correlation – Stable Film boiling
Film Boiling (similar to film condensation)
)(8.0 , swvpfgfg TTChh
For cylinders or spheres
If ,
0.75
conv rad
conv rad
h h
h h h
The cumulative (and coupled effects) of convection and radiation acrossthe vapor layer
4 / 34 / 3 1/ 3conv radh h h h
Geometry
Cylinder(Hor.) 0.62
C
Sphere 0.67
4/1
3'
])(
)([
swvv
fgvlv
v
convD
TTk
DhgC
k
DhNu
sw
swrad
TT
TTh
44
Summary
• Studied different regimes of pool boiling
• Looked at correlations governing heat transfer at each region
• Learnt the concept of Critical or Peak Heat Flux (CHF)
Example Problem
Known: Boiling from outer surface of horizontal cylinder in water
Find: Power dissipation per unit length for the cylinder, qs’
Schematic:
Example (cont.)
Assumptions: Steady-state, Water exposed to 1 atm, at uniform Tsat
Properties: Saturated water, liquid at 100C: l=1/vf=957.9 kg/m3,
hfg=2257kJ/kg. Saturated water vapor (Tf=450K): v=1/vv=4.808 kg/m3,
cp,v=cp,g=2.56kJ/kgK, kv=kg=0.0331W/mK, μv= μg=14.85x10-6Ns/m2.
Analysis:
Te = Ts-Tsat = 255 -100 = 155C >120 C
Pool film boiling conditions are met
Example (cont.)
Heat transfer rate per unit length is:
ess TDhDqq "'
3/13/43/4
hhhh radconv
For combined heat transfer by convection + radiation
KmWTD
Tchgkh
ev
evpfgvlvv
conv
24/1,
3
/238])8.0()(
[62.0
KmWTT
TTh
sats
satsrad
244
/3.21)(
Example (cont.)
KmWh 2/1.254
mWTDhDqq ess /742"'
3/13/43/4
3.21238 hh
Solve for h
Thank You!