Film Condensation on vertical surface Source: Convective heat transfer, Bejan

1. Condensation on
vertical surface
Convective Heat Transfer Seminar
Mostafa Ghadamyari
M. SC. Student
Spring 2014 - Tarbiat Modares university

2. Outline
 Here, We will discuss about:
 Condensation definition
 Different types of condensation
 Film Surface Condensation
 Laminar film equation derivation
 Laminar film heat transfer coefficient diagram
 Turbulent Film heat transfer coefficient diagram
2/12

3. Condensation definition
 A phase is a region of space (a
thermodynamic system), throughout
which all physical properties of a material
are essentially uniform.
 A phase transition is the transformation of
a thermodynamic system from one phase
or state of matter to another one by heat
transfer.
 Condensation is the change of the
physical state of matter from gas phase
into liquid phase, and is the reverse of
vaporization
3/12

4. Modes of condensation
 Condensation modes:
 (a &b). Surface condensation
 (a). Film
 (b). Dropwise
 (c) Homogeneous condensation
 (d) Direct Contact condensation
 We’ll focus on Film Surface condensation
4/12

5. Dropwise and Film Surface condensation
 (a) Dropwise condensation occurs if the
surface is coated with a substance that
inhibits wetting, Silicones, Teflon,
assortment of waxes and fatty acids
 (b) Film condensation is generally
characteristic of clean, uncontaminated
surfaces
 The condensate provides a resistance to
heat transfer between the vapor and the
surface
 It’s desirable but difficult to maintain
dropwise condensation, so calculations
are often based on Film condensation
5/12

6. Film condensation
 Film condensation has Three distinct regions:
 1. Laminar region, near the top, the film is
relatively thin
 2. Wavy region, The film becomes thick enough
to show the signs of transition
 3. Turbulent region, Ripples appear irregular in
both space and time
 Laminar Region complexities:
 Flow of liquid interacts with layer of vapor
 Tinterface= Saturation temperature of local P
 Tw < Saturation temperature < Tvapor
6/12

7. Laminar Film – Momentum Equation
 Momentum equation for simplified laminar film:
 Because of slenderness of the film:
 Substituting:
 Assuming negligible Inertia [Solved by Nusselt]:
  
   
        
2
2
(1) l l l
v v dP v
u v g
x y dy x
   

   
       
2
2
(3) ( )l l l v
Sinking Effect
FrictionInertia
v v v
u v g
x y x
(2) / vdP dy g
 



 
    
2 21
(4) ( , ) ( ) ( )
2
l g
l
g x x
v x y 7/12

8. Laminar Film – First thermodynamics law
 The first law of thermodynamics:
 Substituting conduction & (2):
 Substituting (1)
 Integrating from y=0
 Local mass flow rate:
 Vertical enthalpy inflow:
 Assume linear temperature distribution:
 
   

   
3
0
(1) (y) ( )
3
l
l l v
l
g
vdx

   ,0
(2) [ ( )]l f P l satH v h c T T dx
      ''
(3) 0 ( ) hg wH H dH d q dy

  
'
,
3
[ ( )]
8
(4) ( )
fg
fg P l sat ts
h
a w
l
w h c T T
k
T T dy d
 
 



3
'
( )
(5)
( )
l l sat w
fg l v
kv T T
dy d
h g

 
 
  
  
1/4
'
4 (T T )
(6) ( )
( )
l l sat w
fg l v
kv
y y
h g


 

1sat
sat w
T T x
T T
8/12

9. Laminar flow – Results
 Now we can calculate Heat transfer
coefficients:
 Similar results can be obtained by Scale
Analysis (Similar to laminar boundary
layer natural convection)
 Rohsenow refined preceding analysis by
discarding linear profile assumption and
performing an integral analysis.
 Rohsenow recommends:
 Jacob number = relative measure of
subcooling:
 To summarize:
 

 
    
  
1/43 '''
( )
(1)
4 ( )
l fg l vl
y
sat w l sat w
k h gq k
h
T T yv T T

4
(2)
3
L y Lh h
  
   
 
1/43 '
( )
(3) 0.943
( T )
fg l vL
L
l l l sat w
L h gh L
Nu
k kv T
    '
,(4) 0.68 ( ) (1 0.68 )fgfg p l sat w fgh h c T h JaT

 , ( )
(5) P l sat w
fg
c T T
Ja
h
  '
(6) ( ) ( )l
sat w L
fg
k
L T T Nu
h
  '
(7) ( ) (1 0.68 )fgq L h Ja 9/12

10. Laminar Film - Diagram
 In the preceding analysis were derived
by Nusselt, based on negligible inertia
assumption
 The complete momentum equation used
by Sparrow & Gregg in similarity solution.
 Their solution for Nu falls below Nusselt’s
solution -> Effect of Inertia
 Chen abandoned the assumption of zero
shear at interface, retaining effect of
inertia
 His results for Nu are smaller than Sparrow
& Gregg’s solution -> Effect of restraining
drag of vapor
 Better agreement with experimental data 10/12

11. Turbulent Film - Diagram
 Reynolds number of liquid film:
 Experimental observations:
 Laminar: Re < 30
 Wavy: 30 < Re < 1800
 Turbulent: Re > 1800
 Experiments revealed that heat transfer
rate in wavy and turbulent regions is
considerably larger than laminar section
 Following relation developed by Chen for
wavy and turbulent region:
4
(1) Re (y)y
l
 
  
  
2
1/3 0.44 6 0.8 1.3 1/2
(2) ( ) (Re 5.82 10 Re Pr )
L l
L L L
l
h
k g
11/12

12. Summary
 Condensation is phase change from Gas to Liquid
 There’re different types of condensation:
 Surface (Film, Droplet), Homogeneous, Direct contact
 Film surface condensation has three regions:
 Laminar, Wavy, Turbulent
 Laminar film condensation first solved by Nusselt by neglecting Inertia effect
 Complete momentum equation used by Sparrow and Gregg in similarity solution
 Chen Solution for laminar film contains vapor drag effect and inertia effect of liquid
 Chen reviewed and developed a relation for Wavy and Turbulent regions
12/12

13. Thank you!
13