Chapter 10

BOILING AND
CONDENSATION

Copyright © 2011 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
BOILING HEAT TRANSFER
• Evaporation occurs at the liquid–vapor interface when
the vapor pressure is less than the saturation pressure of
the liquid at a given temperature.
• Boiling occurs at the solid–liquid interface when a liquid
is brought into contact with a surface maintained at a
temperature sufficiently above the saturation
temperature of the liquid.

2
 Boiling heat flux from a solid surface to the fluid

excess temperature

Classification of 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.
• 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.
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 Subcooled Boiling
• When the
temperature of the
main body of the
liquid is below the
saturation
temperature.

Saturated Boiling
• When the
temperature of the
liquid is equal to the
saturation
temperature.

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 POOL BOILING
In pool boiling, the fluid is not forced to flow
by a mover such as a pump.
Any motion of the fluid is due to natural
convection currents and the motion of the
bubbles under the influence of buoyancy.

Boiling Regimes and

the Boiling Curve

Boiling takes different forms, depending on

the DTexcess = Ts  Tsat

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6
 Natural Convection Boiling
(to Point A on the Boiling Curve)
• Bubbles do not form on the heating surface until the liquid is heated a few
degrees above the saturation temperature (about 2 to 6°C for water)
• The liquid is slightly superheated in this case (metastable state).
• The fluid motion in this mode of boiling is governed by natural convection
currents.

• Heat transfer from the

heating surface to the fluid
is by natural convection.
• For the conditions of Fig.
10–6, natural convection
boiling ends at an excess
temperature of about 5°C.

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 Nucleate Boiling (between
Points A and C)
• The bubbles form at an increasing
rate at an increasing number of
nucleation sites as we move along
the boiling curve toward point C.

• Region A–B ─ isolated

bubbles.

• Region B–C ─
numerous continuous
columns of vapor in the
liquid.

Point A is referred to as
the onset of nucleate
boiling (ONB).
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• In region A–B the stirring and agitation caused by the entrainment of the liquid to
the heater surface is primarily responsible for the increased heat transfer
coefficient.
• In region A–B the large heat fluxes obtainable in this region are caused by the
combined effect of liquid entrainment and evaporation.
• For the entire nucleate boiling range, the heat transfer coefficient ranges from
about 2000 to 30,000 W/m2·K.

• After point B the heat

flux increases at a
lower rate with
increasing DTexcess, and
reaches a maximum at
point C.
• The heat flux at this
point is called the
critical (or maximum)
heat flux, and is of
prime engineering
importance.
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NUCLEATE POOL BOILING – BUBBLE FORMATION

• In nucleate boiling, bubbles are created by the expansion of entrapped gas

or vapor at small cavities in the surface.
• The bubbles grow to a certain size, depending on the surface tension at the
liquid-vapor interface and the temperature and pressure.
• Depending on the temperature excess, the bubbles may collapse on the
surface, may expand and detach from the surface to be dissipated in the
body of the liquid, or at sufficiently high temperatures may rise to the
surface of the liquid before being dissipated.
• bubbles are not always in thermodynamic equilibrium with the surrounding
liquid (i.e., the vapor inside the bubble is not necessarily at the same
temperature as the liquid)

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 Transition Boiling (between Points
C and D)

• When DTexcess is increased past point C,

the heat flux decreases.
• This is because a large fraction of the
heater surface is covered by a vapor film,
which acts as an insulation.
• In the transition boiling
regime, both nucleate and
film boiling partially occur.
• Operation in the transition
boiling regime, which is
also called the unstable
film boiling regime, is
avoided in practice.
• For water, transition boiling
occurs over the excess
temperature range from
about 30°C to about
120°C. 11
 Film Boiling (beyond Point D)
• Beyond point D the heater
surface is completely
covered by a continuous
stable vapor film.
• Point D, where the heat flux
reaches a minimum is
called the Leidenfrost
point.
• The presence of a vapor
film between the heater
surface and the liquid is
responsible for the low heat
transfer rates in the film
boiling region.
• The heat transfer rate
increases with increasing
excess temperature due to
radiation to the liquid.

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 Burnout Phenomenon

• A typical boiling process does

not follow the boiling curve
beyond point C.
• When the power applied to the
heated surface exceeded the
value at point C even slightly,
the surface temperature
increased suddenly to point E.
• When the power is reduced
gradually starting from point E
the cooling curve follows Fig.
10–8 with a sudden drop in
excess temperature when point
D is reached.

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Any attempt to increase the heat
flux beyond qmax will cause the
operation point on the boiling
curve to jump suddenly from
point C to point E.
However, surface temperature
that corresponds to point E is
beyond the melting point of most
heater materials, and burnout
occurs.
Therefore, point C on the boiling
curve is also called the burnout
point, and the heat flux at this
point the burnout heat flux.
Most boiling heat transfer
equipment in practice operate
slightly below qmax to avoid any
disastrous burnout.
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 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.

Nucleate Boiling
• No general theoretical relations for heat
transfer in the nucleate boiling regime is
available.
• Experimental based correlations are
used.
• The rate of heat transfer strongly
depends on the nature of nucleation
and the type and the condition of the
heated surface.

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• For nucleate boiling a widely used correlation
proposed in 1952 by Rohsenow:

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17
 Peak Heat Flux

The peak heat flux for nucleate pool boiling developed by Zuber

• The maximum (or critical) heat flux (CHF) in nucleate pool boiling:

• The CHF is independent of the fluid–heating surface combination, as well as the

viscosity, thermal conductivity, and the specific heat of the liquid.
• The CHF increases with pressure up to about one-third of the critical pressure,
and then starts to decrease and becomes zero at the critical pressure.
• The CHF is proportional to hfg, and large maximum heat fluxes can be obtained
using fluids with a large enthalpy of vaporization, such as water.

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 Minimum Heat Flux
• Minimum heat flux, which occurs at
the Leidenfrost point, is of practical
interest since it represents the lower
limit for the heat flux in the film
boiling regime.
• Zuber derived the following
expression for the minimum heat flux
for a large horizontal plate

• This relation above can be in error by

50% or more.

Transition
boiling
regime
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 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.

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 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.

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• 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.
• The use of finned surfaces is also known to
enhance nucleate boiling heat transfer and
the maximum heat flux.
• Boiling heat transfer can also be enhanced by
other techniques such as mechanical
agitation and surface vibration.
• These techniques are not practical, however,
because of the complications involved.

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 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.
• It exhibits the combined effects of convection
and pool boiling.
• External flow boiling over a plate or cylinder is
similar to pool boiling, but the added motion
increases both the nucleate boiling heat flux
and the maximum heat flux considerably.
• The higher the velocity, the higher the
nucleate boiling heat flux and the critical heat
flux.
• Internal flow boiling, commonly referred to as
two-phase flow, is much more complicated in
nature because there is no free surface for the
vapor to escape, and thus both the liquid and
the vapor are forced to flow together.

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• The two-phase flow in a tube
exhibits different flow boiling
regimes, depending on the
relative amounts of the liquid
and the vapor phases.
• Note that the tube contains a
liquid before the bubbly flow
regime and a vapor after the
mist-flow regime.
• Heat transfer in those two
cases can be determined using
the appropriate relations for
single-phase convection heat
transfer.

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• 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.
• Mist flow
– Liquid droplets in vapor phase
• Vapor single-phase flow
– The liquid phase is completely
evaporated and vapor is superheated.

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CONDENSATION HEAT TRANSFER
Condensation occurs when the temperature of a vapor is reduced below
its saturation temperature.
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.
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FILM CONDENSATION
• Liquid film starts forming at the top of
the plate and flows downward under
the influence of gravity.
• d 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
Tsat at the interface and decreases
gradually to Ts at the wall.

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Heat transfer in
condensation depends
on whether the
condensate flow is
laminar or turbulent.
The criterion for the
flow regime is provided
by the Reynolds
number.

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When the final state is subcooled liquid instead of saturated liquid:
Modified latent heat of vaporization

For vapor that enters the condenser as superheated

vapor at a temperature Tv instead of as saturated vapor:

Rate of heat transfer

This relation is convenient to use to

determine the Reynolds number when the
condensation heat transfer coefficient or the
rate of heat transfer is known.

The properties of the liquid should be

evaluated at the film temperature

The hfg should be evaluated at Tsat

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 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 ─ Laminar (wavy)
– Re > 1800 ─ Turbulent
• The Reynolds number increases in the
flow direction.

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 Heat Transfer Correlations for Film Condensation
1 Vertical Plates
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.

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33
The average heat transfer coefficient for laminar film
condensation over a vertical flat plate of height L is

(10-22)

All properties of the liquid are to be

evaluated at the film temperature.
The hfg and v are to be evaluated
at the saturation temperature Tsat. 34
35
2 Inclined Plates
Equation 10–22 was developed for vertical plates,
but it can also be used for laminar film condensation
on the upper surfaces of plates that are inclined
by an angle  from the vertical, by replacing g in that
equation by g cos, or gsin when  is the angle with
the horizontal.

(10-22)

3 Vertical Tubes

Equation 10–22 for vertical plates can also be

used to calculate the average heat transfer
coefficient for laminar film condensation on the
outer surfaces of vertical tubes provided that the
tube diameter is large relative to the thickness
of the liquid film.
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4 Horizontal Tubes and Spheres
The average heat transfer coefficient for film condensation
on the outer surfaces of a horizontal tube is

For a sphere, replace the

constant 0.729 by 0.815.

The laminar condensation equations presented above match experimental

data very well as long as the film remains smooth and well behaved. In
practice, it has been found that ripples will develop in the film for Reynolds
numbers as low as 30 or 40. When this occurs, the experimental values of h
can be 20 percent higher. McAdams suggested that the 20 percent increase be
adopted for design purposes

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5 Horizontal Tube Banks
The average thickness of the liquid film at the lower tubes is
much larger as a result of condensate falling on top of them
from the tubes directly above.
Therefore, the average heat transfer coefficient at the lower
tubes in such arrangements is smaller.
Assuming the condensate from the tubes above to the ones
below drain smoothly, the average film condensation heat
transfer coefficient for all tubes in a vertical tier can be
expressed as

This relation does not account for the

increase in heat transfer due to the ripple
formation and turbulence caused during
drainage, and thus generally yields
conservative results. 38
Because the film Reynolds number is so important in determining condensation
behavior, it is convenient to express the heat-transfer coefficient directly in terms
of Re.

39
So the heat transfer coeff becomes

For a vertical plate A/PL=1.0,

For a horizontal cylinder A/PL=π

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Effect of Vapor Velocity
In the analysis above we assumed the vapor velocity to be small and
thus the vapor drag exerted on the liquid film to be negligible, which
is usually the case.
However, when the vapor velocity is high, the vapor will “pull” the
liquid at the interface along since the vapor velocity at the interface
must drop to the value of the liquid velocity.
If the vapor flows downward (i.e., in the same direction as the liquid),
this additional force will increase the average velocity of the liquid
and thus decrease the film thickness.
This, in turn, will decrease the thermal resistance of the liquid film
and thus increase heat transfer.
Upward vapor flow has the opposite effects: the vapor exerts a force
on the liquid in the opposite direction to flow, thickens the liquid film,
and thus decreases heat transfer.

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The Presence of Noncondensable Gases in Condensers
Experimental studies show that the presence of
noncondensable gases in the vapor has a
detrimental effect on condensation heat transfer.
Even small amounts of a noncondensable gas in
the vapor cause significant drops in heat transfer
coefficient during condensation.
It is common practice to periodically vent out the
noncondensable gases that accumulate in the
condensers to ensure proper operation.
Heat transfer in the presence of a noncondensable
gas strongly depends on the nature of the vapor
flow and the flow velocity.
A high flow velocity is more likely to remove the
stagnant noncondensable gas from the vicinity of
the surface, and thus improve heat transfer.

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FILM CONDENSATION INSIDE
HORIZONTAL TUBES
Most condensation processes encountered in
refrigeration and air-conditioning applications
involve condensation on the inner surfaces of
horizontal or vertical tubes.
Heat transfer analysis of condensation inside
tubes is complicated by the fact that it is strongly
influenced by the vapor velocity and the rate of
liquid accumulation on the walls of the tubes.
For low vapor velocities:

The Reynolds number of the vapor is to be evaluated

at the tube inlet conditions using the internal tube
diameter as the characteristic length. 43
DROPWISE CONDENSATION
Dropwise condensation, characterized by
countless droplets of varying diameters on the
condensing surface instead of a continuous
liquid film and extremely large heat transfer
coefficients can be achieved with this
mechanism.
The small droplets that form at the nucleation
sites on the surface grow as a result of
continued condensation, coalesce into large
droplets, and slide down when they reach a
certain size, clearing the surface and exposing it
to vapor. There is no liquid film in this case to
resist heat transfer.
As a result, with dropwise condensation, heat
transfer coefficients can be achieved that are
more than 10 times larger than those associated
with film condensation.
The challenge in dropwise condensation is not Dropwise condensation of
to achieve it, but rather, to sustain it for
steam on copper surfaces:
prolonged periods of time.

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