This document discusses various topics related to engineering thermodynamics and heat transfer including Nusselt's theory of condensation, correlations for boiling and condensation, film condensation on vertical plates and radial systems, dropwise condensation, and classifications of pool boiling and flow boiling. It provides explanations, diagrams, and equations for analyzing different heat transfer processes involving phase changes.

1. Engineering Thermodynamics And
Heat Transfer
Prepared By:
140080125017 Rohan Master
140080125018 Ronak Modi
140080125019 Parth Thakkar
140080125020 Atri Patel
Guided by:
Prof. Manish Mehta
Production Engineering Department

2. Topic
• Nusselt’s Theory of condensation- pool
boiling, flow boiling
• Co-relations in boiling and condensation

3. Condensation
• Condensation occurs when the
temperature of a vapor is reduced below
its saturation temperature.
• Only condensation on solid surfaces is
considered in this chapter.
• Two forms of condensation:
– Film condensation,
– Dropwise condensation.

4. Film condensation
• The condensate wets the
surface and forms a liquid
film.
• The surface is blanketed
by a liquid film which
serves as a resistance to
heat transfer.
Dropwise condensation
• The condensed vapor
forms droplets on the
surface.
• The droplets slide down
when they reach a certain
size.
• No liquid film to resist
heat transfer.
• As a result, heat transfer
rates that are more than
10 times larger
than with film
condensation
can be achieved.

5. Dropwise Condensation
• One of the most effective mechanisms of heat
transfer, and extremely large heat transfer
coefficients can be achieved.
• Small droplets grow as a result of continued
condensation, coalesce into large droplets, and
slide down when they reach a certain size.
• Large heat transfer
coefficients enable designers
to achieve a specified heat
transfer rate with a smaller
surface area.

6. Dropwise Condensation
• The challenge in dropwise condensation is not
to achieve it, but rather, to sustain it for
prolonged periods of time.
• Dropwise condensation has been studied
experimentally for a number of surface–fluid
combinations.
• Griffith (1983) recommends these simple
correlations for dropwise condensation of steam
on copper surfaces:
0 0
0
51,104 2044 22 100
255,310 100
sat sat
sat
T C T C
hdropwise
T C
 + < <
= 
>

7. General Considerations
General Considerations
• Heat transfer to a surface occurs by condensation when the surface temperature
is less than the saturation temperature of an adjoining vapor.
• Film Condensation
 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.
 Thermal resistance is reduced through use of short vertical surfaces
and horizontal cylinders.
 Characteristic of clean, uncontaminated surfaces.
• Dropwise Condensation
 Surface is covered by drops ranging from
a few micrometers to agglomerations visible
to the naked eye.

8. General Considerations (cont).
 Thermal resistance is greatly reduced due to absence of a continuous film.
 Surface coatings may be applied to inhibit wetting and stimulate
dropwise condensation.

9. Film Condensation: Vertical Plates
Film Condensation on a Vertical Plate
• Distinguishing Features
 Generally, the vapor is superheated
and may be part of a mixture
that includes noncondensibles.
( ),v satT T∞ >
 A shear stress at the liquid/vapor
interface induces a velocity gradient
in the vapor, as well as the liquid.
• Nusselt Analysis for Laminar Flow
Assumptions:
 A pure vapor at .satT
 Negligible shear stress at liquid/vapor interface.
0
y
u
y δ=
∂→ =
∂
 Thickness and flow rate of
condensate increase with increasing x
( )m
g
( )δ

10. Vertical Plates (cont)
 Negligible advection in the film. Hence, the steady-state x-momentum
and energy equations for the film are
2
2
2
2
1
0
l l
pu X
y x
T
y
µ µ
∂∂ = −
∂ ∂
∂ =
∂
 The boundary layer approximation, may be applied to the film.0/ ,p y∂ ∂ =
Hence,
v
p dp
g
x dx
ρ
∂
= =
∂
 Solutions to momentum and energy equations
Film thickness:
( )
( )
( )
1 4
4
/
l l sat s
l l v fg
k T T x
x
g h
µ
δ
ρ ρ ρ
 −
=  
− 

11. Vertical Plates (cont)
Flow rate per unit width:
( ) 3
3
l l v
l
gm
b
ρ ρ ρ δ
µ
−
Γ ≡ =
g
Average Nusselt Number:
( )
( )
1 43
0 943
/
.L
l l v fgL
l l l sat s
g h Lh LNu
k k T T
ρ ρ ρ
µ
′ −
= =  
− 
( )
( )
1 0 68
Jakob number
.fg fg
p sat s
fg
h h Ja
c T T
Ja
h
′ = +
−
≡ →
Total heat transfer and condensation rates:
( )L sat s
fg
q h A T T
q
m
h
= −
=
′
g

12. Vertical Plates (cont)
• 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
δ
ρ δ
µ µ µ
Γ≡ = =
g

13. Vertical Plates (cont)
 Wave-free laminar region ( )Re 30 :δ <
( )
1 32
-1/3
1 47 Re
/
/
.
L l
l
h g
k
δ
ν
=
( ) 3
2
4
Re
3
l l v
l
g
δ
ρ ρ ρ δ
µ
−
=
 Wavy laminar region( )30 Re 1800 :δ< <
(10.37)
( )
1 32
1.22
Re
1.08 Re 5 2
/
/
.
L l
l
h g
k
δ
δ
ν
=
−
(10.38)
 Turbulent region( )Re >1800 :δ
(10.39)
( )
( )
1 32
-0.5 0 75
Re
8750 +58 Pr Re 253
/
.
/L l
l
h g
k
δ
δ
ν
=
−

14. Vertical Plates (cont)
 Calculation procedure:
– Assume a particular flow regime and use the corresponding expression for
(Eq. 10.37, 10.38 or 10.39) to determineLh Re .δ
Reδ– If value of is consistent with assumption, proceed to determination of
and .q m
g
– If value of is inconsistent with the assumption, recompute its value
using a different expression for and proceed to determination of
Reδ
Lh
and .q m
g

15. Film Condensation: Radial Systems
Film Condensation on Radial Systems
• A single tube or sphere:
( )
( )
1 43 /
l l l fg
D
l sat s
g k h
h C
T T D
υρ ρ ρ
µ
′ −
=  
− 
Tube: C =0.729 Sphere: C=0.826

16. Film Condensation: Radial Systems (cont).
• A vertical tier of N tubes:
( )
( )
1 4
3
0 729
/
, . ll l fg
D N
l sat s
g k h
h
N T T D
υ
ρ ρ ρ
µ
 ′−
=  
−  
 Why does decrease with increasing N?,D Nh
 How is heat transfer affected if the continuous sheets (c) breakdown and the
condensate drips from tube to tube (d)?
 What other effects influence heat transfer?

17. Film Condensation: Internal Flow
Film Condensation for a Vapor Flow in a Horizontal Tube
• If vapor flow rate is small, condensate flow is circumferential and axial:
,iRe 35 000
,
, :
m
i
u Dυ υ
υ
υ
ρ
µ
 
= < ÷
 
( )
( )
1 43
0 555
/
. l l l fg
D
l sat s
g k h
h
T T D
υρ ρ ρ
µ
′ −
=  
− 
( )0 375.fg fg sat sh h T T′ ≡ + −
• For larger vapor velocities, flow is principally
in the axial direction and characterized by
two-phase annular conditions.

18. Dropwise Condensation
Dropwise Condensation
• Steam condensation on copper surfaces:
dc
51100 2044 22 C< 100 C
255 500 100 C
,
,
dc sat sat
sat
h T T
h T
= + <
= >
o o
o
( )dc sat sq h A T T= −

19. Problem: Condensation on a Vertical Plate
Problem 10.48 a,b: Condensation and heat rates per unit width for saturated
steam at 1 atm on one side of a vertical plate at 54˚
C if
(a) the plate height is 2.5m and (b) the height is halved.
KNOWN: Vertical plate 2.5 m high at a surface temperature Ts = 54°C exposed to steam at
atmospheric pressure.
FIND: (a) Condensation and heat transfer rates per unit width, (b) Condensation and heat rates if
the height were halved.
ASSUMPTIONS: (1) Film condensation, (2) Negligible non-condensables in steam.
SCHEMATIC:

20. Problem: Condensation on a Vertical Plate (cont)
PROPERTIES: Table A-6, Water, vapor (1 atm): Tsat = 100°C, ρv = 0.596 kg/m3
, hfg = 2257
kJ/kg; Table A-6, Water, liquid (Tf = (100 + 54)°C/2 = 350 K): = 973.7 kg/m3
, = 0.668
W/m⋅K, = 365 × 10-6
N⋅s/m2
, = 4195 J/kg⋅K, = 2.29.
ANALYSIS: (a) The heat transfer and condensation rates are given by Eqs. 10.32 and 10.33,
(1,2)
where, from Eq. 10.26, with Ja = (Tsat − Ts)/hfg ,
.
Assuming turbulent flow conditions, Eq. 10.39 is the appropriate correlation,
(3)

21. Problem: Condensation on a Vertical Plate (cont)
Not knowing Reδ or , another relation is required. Combining Eqs. 10.33 and 10.35,
. (4)
Substituting Eq. (4) for into Eq. (3), with A = bL,
. (5)
Using appropriate properties with L = 2.5 m, find
(6)
.
Since Reδ > 1800, the flow is turbulent, and using Eq. (4) or (3), find
.

22. Problem: Condensation on a Vertical Plate (cont)
From the rate equations (1) and (2), the heat transfer and condensation rates are
<
. <
(b) If the height of the plate were halved, L = 1.25 m, and turbulent flow was still assumed to
exist, the LHS of Eq. (5) may be reevaluated and the equation solved to obtain
.
Since 1800 > Reδ , the flow is not turbulent, but wavy-laminar. The procedure now follows that
of Example 10.3. For L = 1.25 m with wavy-laminar flow, Eq. 10.38 is the appropriate
correlation. The calculation yields
. <
COMMENT:
Note that the height was decreased by a factor of 2, while the rates decreased by a factor of 2.2. Would you
have expected this result?

23. Classification of boiling
Pool Boiling
• Boiling is called pool
boiling in the
absence of bulk fluid
flow.
• Any motion of the
fluid is due to natural
convection currents
and the motion of the
bubbles
under the
influence
of buoyancy.
Flow Boiling
• Boiling is called flow
boiling in the
presence of bulk fluid
flow.
• In flow boiling, the
fluid is forced to move
in a heated pipe
or over a
surface by
external
means such
as a pump.

24. Pool Boiling
Boiling takes different forms, depending on the ∆Texcess=Ts-Tsat

25. Heat Transfer Correlations in Pool
Boiling
• Boiling regimes differ considerably in their
character
different heat transfer relations need
to be used for different boiling
regimes.
• In the natural convection boiling regime
heat transfer rates can be accurately
determined using natural convection
relations.

26. Film Boiling
• The heat flux for film boiling on a horizontal
cylinder or sphere of diameter D is given by
• At high surface temperatures (typically above 300°C),
heat transfer across the vapor film by radiation becomes
significant and needs to be considered.
• The two mechanisms of heat transfer (radiation and
convection) adversely affect each other, causing the total
heat transfer to be less than their sum.
• Experimental studies confirm that the critical heat flux
and heat flux in film boiling are proportional to g1/4
.
( ) ( )
( )
( )
1
43
0.4v v l v fg pv s sat
film film s sat
v s sat
gk h C T T
q C T T
D T T
ρ ρ ρ
µ
  − + −  = −
−  
&

27. Enhancement of Heat Transfer in
Pool Boiling
• The rate of heat transfer in the nucleate boiling regime
strongly depends on the number of active nucleation
sites on the surface, and the rate of bubble formation at
each site.
• Therefore, modification that enhances nucleation on the
heating surface will also enhance heat transfer in
nucleate boiling.
• Irregularities on the heating surface, including roughness
and dirt, serve as additional nucleation
sites during boiling.
• The effect of surface roughness is
observed to decay with time.

28. Enhancement of Heat Transfer in
Pool Boiling
• Surfaces that provide enhanced heat transfer in
nucleate boiling permanently are being
manufactured and are available in the market.
• Heat transfer can be enhanced by a factor of up
to 10 during nucleate boiling, and the
critical heat flux by a factor of 3.
Thermoexcel-E

29. Flow Boiling
• In flow boiling, the fluid is forced to move by an
external source such as a pump as it undergoes
a phase-change process.
• The boiling in this case exhibits the combined
effects of convection and pool boiling.
• Flow boiling is classified as either
external and internal flow boiling.
• External flow ─ the higher the
velocity, the higher the nucleate
boiling heat flux and the critical
heat flux.

30. Flow Boiling ─ Internal Flow
• The two-phase flow in a
tube exhibits different
flow boiling regimes,
depending on the relative
amounts of the liquid and
the vapor phases.
• Typical flow regimes:
– Liquid single-phase flow,
– Bubbly flow,
– Slug flow,
– Annular flow,
– Mist flow,
– Vapor single-phase flow.
Axialpositioninthetube

31. Flow Boiling ─ Internal Flow
• Liquid single-phase flow
– In the inlet region the liquid is subcooled and heat transfer to the liquid
is by forced convection (assuming no subcooled boiling).
• Bubbly flow
– Individual bubbles
– Low mass qualities
• Slug flow
– Bubbles coalesce into slugs of vapor.
– Moderate mass qualities
• Annular flow
– Core of the flow consists of vapor only, and liquid adjacent to the walls.
– Very high heat transfer coefficients
• Mist flow
– a sharp decrease in the heat transfer coefficient
• Vapor single-phase flow
– The liquid phase is completely evaporated and vapor is superheated.

32. Film Condensation on a Vertical
Plate
• liquid film starts forming at the
top of the plate and flows
downward under the influence
of gravity.
• δ increases in the flow direction
x
• Heat in the amount hfg is
released during condensation
and is transferred through the
film to the plate surface.
• Ts must be below the saturation
temperature for condensation.
• The temperature of the
condensate is T at the

33. Vertical Plate ─ Flow Regimes
• The dimensionless parameter
controlling the transition between
regimes is the Reynolds number
defined as:
• Three prime flow regimes:
– Re<30 ─ Laminar (wave-free),
– 30<Re<1800 ─ Wavy-laminar,
– Re>1800 ─ Turbulent.
• The Reynolds number increases in
the flow direction.
( )
( )
}hydraulic diameter
4
Re
hD
l l
x
l
Vδ ρ
µ
=

34. Heat Transfer Correlations for Film
Condensation ─ Vertical wall
Assumptions:
1. Both the plate and the vapor are
maintained at constant temperatures
of Ts and Tsat, respectively, and the
temperature across the liquid film
varies linearly.
2. Heat transfer across the liquid film is
by pure conduction.
3. The velocity of the vapor is low (or
zero) so that it exerts no drag on the
condensate (no viscous shear on the
liquid–vapor interface).
4. The flow of the condensate is laminar
(Re<30) and the properties of the
liquid are constant.
5. The acceleration of the condensate
layer is negligible.
Height L and width b