Condensation Heat Transfer Overview of Four Lectures Contents

Condensation Heat Transfer
Dr Vishwas Wadekar
Technology Director, HTFS Research
Aspen Technology
Filmwise
Condensation
Overview of Four Lectures
• Lecture 1
– Condensation - I
• Lecture 2
– Condensation - II
– Enhancement of heat
transfer
• Lecture 3
– Pool boiling heat
transfer
– Flow patterns
– Flow boiling heat
transfer
• Lecture 4
– Enhancement of boiling
Contents
Modes of condensation
Dropwise/filmwise condensation
Direct/indirect/homogeneous
condensation
Filmwise condensation on
Flat plate
Outside/inside a tube
Other complex effects
Industrial equipment
Dropwise
Condensation
Filmwise

Filmwise Condensation
Condensed liquid forms a continuous liquid
film on the heat transfer surface
Examples of heat transfer surface can be
Flat plate (as in the diagram)
Outside/inside a tube
Plate of a plate heat exchanger
Heat transfer coefficient is lower (than
dropwise mode) but predictable and stable
Almost all industrial equipment is designed for
this mode of condensation
Dropwise Condensation
Condensed liquid forms droplets on the
heat transfer surface due to poor
wettability
Very high heat transfer coeff. (50-500
kW/m 2 K)! However, it can degrade to
filmwise values over time
This mode is promoted by
Surface coating (e.g. with PTFE)
Additives in vapour stream
Still an area of ongoing research to
make it work in industrial practice
Homogeneous Condensation
Small droplets forming as fog
Increase in pressure can lead to fog formation
Droplets often too small to separate
Fog and cloud formation are due to
homogeneous nucleation
Undesirable in industrial practice
Loss through venting system
Possible source of pollution

Direct Contact Condensation
Subcooled liquid is brought
in contact with vapour
Latent heat raises the
temperature of subcooled
liquid
Efficient form of heat
exchange
Sea water desalination
Power plants
Emergency core cooling in
nuclear reactors
Vapour
Liquid Spray
Vapour
Condensation
In the remaining lecture we now focus
on indirect contact filmwise
condensation
Filmwise
Condensation
Resistances to Heat Transfer
Pure vapour
Pure vapour
+
non-condensable
T i = T sat
T g
T i
vapour
vapour+gas
coolant
liquid
film
coolant
liquid
film
p v,b
p v,i

General Approach to
Condensation
Filmwise condensation is considered
Various geometries are covered
Flat plate (vertical and inclined)
Outside/inside a single tube
Outside multiple tubes (tube bundle)
Gravity controlled situations studied in
detail
Further complicating factors such as
inundation and vapour shear effects are
then examined briefly
General Approach to
Condensation
Condensation on Flat Plate
Nusselt analysed this case in
1916
Analysis is considered in detail
because -
Milestone in condensation work
Simplest geometry
Forms the basis of other
geometries

Nusselt Analysis -
Assumptions
Laminar condensate film
Gravitational and viscous forces only
Heat transfer by conduction through the
film
Thermodynamic equilibrium at the
interface
Uniform -
Physical properties
Wall temperature
Nusselt Analysis - I
From film analysis
V&
=
( ρ − ρ )
l
g
3η
gδ
3 W
T w
δ
T sat
We define the mass flow rate per
unit width as
V&
ρ
Γ =
W
l
ρ
=
l
( ρ − ρ )
l
3η
g
gδ
3
Nusselt Analysis - II
Liquid film flowrate, G, increases with distance,
x. If G c is condensation mass flux then from
mass balance G c = dΓ/ dx
T sat
As
ρ
Γ =
l
( ρ − ρ )
l
3η
g
gδ
3
T w
dx
dΓ
ρl
G
c=
=
dx
( ρ − ρ )
l
3η
g
g
3δ
2
dδ
dx

Nusselt Analysis - III
Condensation mass flux G c is related to
heat flux, q& c , by q&
= ∆h v
G c
(∆h v = latent heat of vaporisation)
T w
δ
T sat
Heat transfer through the film is by
conduction. Therefore the heat transfer
coefficient will be (λ l / δ)
λ
l
q&
=
δ
( Tsat
− Tw
) = ∆hvG
c
Combining….
Condensation mass flux G c and
heat transfer equation
G
λ
l
δ
c
( Tsat
− Tw
) = ∆hvG
c
ρ
=
l
( ρ − ρ )
l
η
g
g
δ
2
dδ
dx
Condensation mass flux G c and
film flow equation
δ 3
ηλ
dδ
=
ρ
l
( T − T )
dx
l sat w
( ρl
− ρ
g
) g∆hv
On integrating…..
x
δ
Local Coefficient
….On integrating
δ
4
4ηλ
=
ρ
l
( T − T )
x
l sat w
( ρl
− ρ
g
) g∆hv
Local heat transfer coefficient
( ρ − ρ )
1/ 4
3
λ ⎡λ
ρ g∆h
4 ( ) ⎥ ⎥ ⎤
l l l l g v
α = = ⎢
δ ⎢⎣
η Tsat
− Tw
x ⎦

Average Coefficient
On integrating
⎡λ
ρ
( ρ − ρ )
3
α 1
= ∫ L
l l l g
αdx
= 0.943 ⎢
L 0
η( T − T ) L
sat w
⎢⎣
g∆h
v
⎤
⎥
⎥⎦
1/ 4
x = L
δ
OR
αZ
Nu = = 1.47 Re
λ
⎡
Z = ⎢
⎢⎣
ρ
l
l
η
2
−1/
3
⎤
4Γ
;Re =
⎥
( ρ − ρ ) g η
l
g
⎥⎦
1/ 3
where
Nusselt Analysis -
Assumptions
Laminar condensate film
Gravitational and viscous forces only
Heat transfer by conduction through
the film
Thermodynamic equilibrium at the
interface
Uniform -
Physical properties
Wall temperature
Verification of Nusselt
Analysis
Earlier attempts to experimental
verification were not successful because of
Presence of non-condensible gases
Presence of dropwise condensation
Forced convective effects (vapour shear)
Rippling, splashing and turbulence of the
film
Recent data under “Nusselt conditions”
validates the simple Nusselt theory

Extension of Nusselt Analysis
Condensate subcooling - Bromley
(1952); Rohsenov (1956)
Condensate inertia forces and convection
- Sparrow and Gregg (1959a, 1959b)
Shear stress at the interface - Koh et al
(1961); Chen (1961)
Uniform wall heat flux - Fuji et al (1972)
General Approach to
Condensation
W = πDi
Laminar Condensation in
Vert. Tubes
3
⎡λ
lρ
α = 0.924 ⎢
⎢⎣
l
( ρ − ρ )
l
ηΓ
l
g
g ⎤
⎥
⎥⎦
1/ 3
W = πDo

Condensation on Horizontal
Tubes
Gravity controlled
condensation on a single
horizontal tube is examined
The analysis is then extended
to industrial situation of
multiple tubes in a bundle
considering inundation effects
Single Horizontal Tube
3
⎡λ
lρl
α = 0.728 ⎢
⎢⎣
η
( ρ − ρ )
l
( T − T )
sat
g
w
g∆h
D
o
v
⎤
⎥
⎥⎦
1/ 4
In alternate form
3
⎡λ
lρ
α = 1.523 ⎢
⎢⎣
l
3
( ρ ) ⎤
1/
l
− ρ
g
1/ 3
η
2
⎥
⎥⎦
Re
−
l
Inundation Effects
Indundation - Condensate from
upper tubes falls on the lower
tubes
This increases the condensate
thickness, decreasing the
condensation coefficient
α
= α
− n
N
N 1/
1
n= 4 - Nusselt theory
n= 6 - Kern from experience

Condensation in Horizontal
Tube
Vapour
Film draining
under gravity
Liquid pool
Gravity controlled
case
Vapour shear
controlled case
Condensation in Horizontal Tube
φ
Coefficient for top region where film is
drained:-
α
Top
3
⎡λ
lρl
= β⎢
⎢⎣
η
( ρ − ρ )
l
( T − T )
sat
g
w
g∆h
D
i
1/ 4
β depends
v
on the
angle φ
⎤
⎥
⎥⎦
Average coefficient for the top and bottom region is:-
( ρ − ρ )
1/ 4
3
⎡λ
⎤
lρl
l g
g∆hv
φβ
α
Tube
= Ψ⎢
⎥ where,
Ψ =
⎢⎣
η( Tsat
− Tw
) Di
⎥⎦
π
Jaster and Kosky (1976) obtained Ψ from void fraction
Vapour Shear Effects
Vapour shear effects arise from forced
convective motion of the vapour
Vapour shear thins the liquid film,
thereby increasing the coefficient
Onset of laminar to turbulent
transition occurs at lower Reynolds
number
Shekriladze and Gomelauri (1966)
developed equations for vertical vapour
down flow

Industrial Equipment
Pure vapour
+
non-condensable
T g
• Drainage of condensate is
important. Condensation is
almost always carried out in
downflow manner
coolant
T i
vapour+gas
p liquid
v,b
film
p v,i
• Provision of a vent for noncondensable
gas at proper
location is of paramount
importance.
Enhanced Condensation Surfaces
Special surfaces enhance
condensation by
Localised thinning of the
condensate film using surface
tension effects
(‘Gegorrig surfaces’)
Easy condensate drainage
Enhanced condensation tubes
are commercially available
More often these are used as
“double enhancement” devices
Vapour
Cooling wall
Condensate
For a Convex Surface…
σ
pl
= psat
+
r
• Differentiating with
respect to distance
along a fin
( 1 r)
dp d
= σ
/
dz dz
• For a concave surface
( 1 r)
dp d
= −σ
/
dz dz