Transcript Chapter7

Condensation and
Boiling
 Until now, we have been considering
convection heat transfer in homogeneous
single-phase (HSP) systems
 Boiling and condensation, however,
provide much higher heat transfer rates
than those possible with the HSP systems
Condensation
 Condensation occurs when the temperature of a vapor is reduced
below its saturation temperature
 Condensation heat transfer
Film condensation
Drop wise condensation
 Heat transfer rates in drop wise condensation may be as much as
10 times higher than in film condensation
Laminar Film condensation on a
vertical wall (VW)
y
y
y
x
x
Tsat
y
A
g
T
 (x)


u
 
l y  y
A
A
Condensate Film
(  v )gAy
l

 u 
l y  yy
A
Laminar Film condensation on a
vertical wall (cont..)
1/ 4
3 1/ 4
l
 4xkl (Tsat  Tw ) l 
 h fg g(l  v )k 
( x )  
 h(x)  

 4x (Tsat  Tw ) l 
 h fg g(l  v ) 
Averagecoeff.
 h fg g(l   v )k
h L  0.943
 L(Tsat  Tw ) l
3
l
where L is theplatelength.
T otalheat trans
fer rate:
q  h L A(Tsat  Tw )
Condensation rate:
h L A(Tsat  Tw )
q
 
m

h fg
h fg



1/ 4
Example
Laminar film condensation of steam
Saturated steam condenses on the outside of a 5 cm-diameter
vertical tube, 50 cm high. If the saturation temperature of the
steam is 302 K, and cooling water maintains the wall temperature
at 299 K, determine: (i) the average heat transfer coefficient, (ii)
the total condensation rate, and (iii) the film thickness at the
bottom of the tube.
Given: Film condensation of saturated steam
Required: (i) Average heat transfer coefficient, (ii) total
condensation rate, (iii) and film thickness
1. Effect of tube curvature negligible
2. Effect of liquid sub cooling negligible
3. Laminar
Example (contd...)
y
x
The Average heat trasn sfer coefficent is given by :
Tsat
y
A
1/ 4
g
_
h
 '
3
 h g(  v )k 
l
l
 0.943 fg
L(Tsat  Tw )v 

l


T
 (x)
Condensate Film
Evaluate hfg at the saturation temperature of
302 K
From Table of water properties :
h
fg
 2.432 106 J / kg
v  0.03kg / m3
Example (contd...)
Also, for water
k l  0.611W/mK
 l  996 kg/m3
 l  0.87 10-6 m 2 /s
 h fh g  l   v k l3 
h  0.943



L
T

T

sat
w
l 

1/ 4
 ( 2.432  10 )(9.81)996  0.03(0.611)
 0.943
6
(
0
.
5
)(
3
)(
0
.
87

10
)

6
3



1/ 4
 7570 W/m2 K
(ii) T he totalcondensation rateis :
Q
h AT (7570)(3) (0.05)(0.5)
4
m 



7
.
33

10
kg/s
6
h fg
h fg
( 2.432  10 )
Example (contd...)
(iii) T hefilm thicknessis
1/ 3
 3 l  

  
 v   l
 l g 
T hemass flow rate per unit widthof film  is :
m
(7.33  104 )


 4.67  103 kg/ms
D
( )(0.05)
 3(0.87 10 )(4.67  10 ) 

Hence,   
(996)(9.81)


-6
3
1/ 3
 1.08  104 m
Boiling
 Boiling occurs when the surface temperature Tw exceeds
the saturation temperature Tsat corresponding to the liquid
pressure
Heat transfer rate: qs  h(Tw  Tsat )  hTe
where Te  Tw  Tsat (excess temperatu
re)
 Boiling process is characterized by formation of vapor
bubbles, which grow and subsequently detach from the
surface
 Bubble growth and dynamics depend on several factors such
as excess temp., nature of surface, thermo physical
properties of fluid (e.g. surface tension, liquid density, vapor
density, etc.). Hence, heat transfer coefficient also depends
on those factors.
Pool Boiling Curve
qs
Te  
Modes of Pool Boiling

 Free convection boiling Te  5 C
 Nucleate boiling
 Transition boiling
 Film boiling
5 C  Te  30 C


30 C  Te  120 C

Te  120 C