Advanced Heat and Mass Transfer
SS 22
Credits to Prof. Specht (OvGU)
Jun.-Prof. Alba Diéguez Alonso
L 3: Vaporization and Condensation

Vaporization and Condensation
Quelle: Wärme- und Stoffübertragung in der Thermoprozesstechnik, Eckehard Specht, Vulkan-Verlag GmbH, 2014.
If the aggregate state of a substance (or a mixture) changes from the liquid to the vapour phase, or viceversa, i.e.,
evaporation or condensation occurs, special behaviors happen in the heat transfer.
When the necessary heat is applied to a heating surface so that the surface temperature is higher than the boiling
temperature of the adjacent liquid, this liquid evaporates. In evaporation and condensation, the latent heat associated
with the phase change is important.
The transition from the liquid to the vapour phase state by boiling is assisted by heat transfer from a solid surface to
the liquid; conversely, condensation to the liquid state results in heat transfer from the liquid to the solid surface.
Since these processes involve fluid movement, evaporation and condensation are classified as forms of convective
heat transfer.
In fact, evaporation or condensation can achieve large heat transfer rates with small temperature differences. In
addition to the latent heat, two other parameters are important for characterising the processes, namely the surface
tension at the liquid-vapour interface and the difference in density between the two phases. This difference induces a
buoyancy force proportional to 𝒈 " 𝝆𝒍 − 𝝆𝒗 . Due to the combined effects of latent heat and buoyancy-driven flow, the
heat transfer coefficients and rates of evaporation or condensation are generally much larger than those characteristic
of convective heat transfer without phase change.
In many technical applications characterised by high heat flows, evaporation or condensation occurs, e.g. in a closed
electrical circuit.
Quelle: Fundamentals of Heat and Mass Transfer, Incropera, DeWitt, Bergamn, Lavine, John Wiley & Sons, 2007

Vaporization
Quelle: Wärme- und Stoffübertragung in der Thermoprozesstechnik, Eckehard Specht, Vulkan-Verlag GmbH, 2014.
𝑻𝒘 − 𝑻𝒃𝒐𝒊 Difference between heating surface and boiling temperature
Convection
When vaporization occurs at a solid-liquid interface, being the equilibrium vapor pressure of the substance greater
or equal to the environment pressure (temperature higher or equal to boiling temperature of the substance), it is
called boiling
Example of vessel boiling (water, 1 atm)
The heating surface temperature is only slightly above the boiling temperature of the liquid.
𝑇! − 𝑇"#$ < ~5 °𝐶
Nucleate boiling
Quelle: Fundamentals of Heat and Mass Transfer, Incropera, DeWitt, Bergamn, Lavine, John Wiley & Sons, 2007
~5 °𝐶 < 𝑇! − 𝑇"#$ < ~30 °𝐶
There are 2 different regimes in this area. First, isolated bubbles form at the nucleation
sites and separate from the surface. This separation leads to considerable fluid mixing at
the surface and increases the heat flux. In this regime, most of the heat exchange occurs
by direct transfer from the surface to the fluid in motion at the surface, rather than by
vapour bubbles rising from the surface.
As the temperature difference increases, more nucleation sites become active and the
increased bubble formation leads to bubble interference and coalescence. The vapour
escapes in the form of jets or columns that subsequently coalesce into vapour slugs.
At some point, the tightly packed bubbles inhibit the movement of the liquid near the
surface. At this point, 𝛼 begins to decrease. However, the heat flux increases until point B
("burn-out point"). At point B, the maximum heat flux is reached (critical heat flux). At
higher temperature differences, the increase in temperature difference is compensated by
the decrease in 𝛼.
Boiling diagram

Quelle: Wärme- und Stoffübertragung in der Thermoprozesstechnik, Eckehard Specht, Vulkan-Verlag GmbH, 2014.
Transition Boiling (Partial Film Boiling)
Quelle: Fundamentals of Heat and Mass Transfer, Incropera, DeWitt, Bergamn, Lavine, John Wiley & Sons, 2007
~30 °𝐶 < 𝑇! − 𝑇"#$ < ~120 °𝐶
In this area, vapour formation is so rapid that a film of vapour begins to
form on the surface. At any point on the surface, conditions can oscillate
between film and nucleate boiling. The proportion of the total surface
area covered by the vapour film increases with increasing temperature
difference. Due to the lower thermal conductivity of the vapour compared
to the liquid, 𝛼 and thus heat flux decreases.
Stabile Filmverdampfung
𝑇! − 𝑇"#$ > ~120 °𝐶
At point L, also called the Leidenfrost point, the heat flux has a minimum. At
this point, the surface is completely covered with a vapour film. The heat
transfer from the surface to the fluid takes place by heat conduction and
radiation through the vapour. As the temperature increases, radiation
through the vapour film becomes more important and the heat flux
increases with increasing temperature difference. 𝛼 remains more or less
constant due to the vapour film.
( )
( ) 0
T
T
d
q
d
B =
D
D
!
( )
( )
( )
( ) ( )
( )
0
T
T
q
0
T
T
d
T
q
d
T
T
d
d
2
B
B
B
B <
D
D
-
=
D
D
÷
ø
ö
ç
è
æ
D
=
D
D
a !
!
Vaporization
When vaporization occurs at a solid-liquid interface, being the equilibrium vapor pressure of the substance greater
or equal to the environment pressure (temperature higher or equal to boiling temperature of the substance), it is
called boiling
𝑻𝒘 − 𝑻𝒃𝒐𝒊 Difference between heating surface and boiling temperature
Example of vessel boiling (water, 1 atm)
Boiling diagram
Stable Film Evaporation
why Difference b/w Q and a
Ans: due to temperature difference

Vaporization
Quelle: Wärme- und Stoffübertragung in der Thermoprozesstechnik, Eckehard Specht, Vulkan-Verlag GmbH, 2014.
It is difficult for nucleus points to form in clean containers with smooth walls.
Especially in glass containers that have been evacuated beforehand, nucleus
points cannot form. In such containers, liquids can be heated far above their
boiling temperature without vaporization.
The vaporization process is dependent on a number of variables, including
liquid and vapour properties, surface properties and process variables.
Therefore, a theoretical description of the heat transfer during vaporizaiton is
very challenging. Consequently, empirical approaches are used.
𝑻𝒘 − 𝑻𝒃𝒐𝒊 Difference between heating surface and boiling temperature
Example of vessel boiling (water, 1 atm)
Boiling diagram
When vaporization occurs at a solid-liquid interface, being the equilibrium vapor pressure of the substance greater
or equal to the environment pressure (temperature higher or equal to boiling temperature of the substance), it is
called boiling

Vaporization – Nusselt function
Quelle: Wärme- und Stoffübertragung in der Thermoprozesstechnik, Eckehard Specht, Vulkan-Verlag GmbH, 2014.
Of the previously explained regions, the nucleate boiling regime is the most interesting from a technical point of view,
as the heat flux is high with low temperature differences due to the high values of the convective heat transfer
coefficient.
The material properties with the index g refer to the vapour,
those with l to the liquid.
o
s Surface tension
y Wetting angle in degrees between vapour bubble and heating wall
VDI Atlas
The Nusselt function is calculated with the diameter of the bubbles db as characteristic length

Vaporization – Vaporization technology
Quelle: Wärme- und Stoffübertragung in der Thermoprozesstechnik, Eckehard Specht, Vulkan-Verlag GmbH, 2014.
Possible operating points of an evaporator (vaporization)

Condensation
Quelle: Wärme- und Stoffübertragung in der Thermoprozesstechnik, Eckehard Specht, Vulkan-Verlag GmbH, 2014.
Condensation occurs when the temperature of a vapour is reduced below its saturation temperature. In industrial
equipment, the process usually occurs when the vapour comes into contact with a cold surface (surface condensation).
The latent energy of the vapour is released (phase change), the heat is transferred to the surface and a condensate
(liquid) is formed.
Other common modes are homogeneous condensation, where the vapour condenses out as droplets in a gas phase
and forms a fog; and direct contact condensation, which occurs when the vapour is brought into contact with a cold
liquid. However, in this lecture we will only consider surface condensation.
Surface condensation can occur in two ways, depending on the nature of the surface. The main form of condensation is
when the liquid film covers the entire cold surface and flows continuously off the surface under the action of gravity.
This is called film condensation and is characteristic of clean, uncontaminated surfaces.
If the surface is coated with a wetting-inhibiting substance, dropwise condensation can occur. The droplets form in
cracks, depressions, and cavities in the surface and can grow and fuse through continued condensation. The heat
transfer coefficient for dropwise condensation is much higher than for film condensation. However, the mechanisms are
not well understood and empirical correlations are used. VDI Atlas.
Quelle: Fundamentals of Heat and Mass Transfer, Incropera, DeWitt, Bergamn, Lavine, John Wiley & Sons, 2007

Quelle: Wärme- und Stoffübertragung in der Thermoprozesstechnik, Eckehard Specht, Vulkan-Verlag GmbH, 2014.
The velocity and thickness of the condensed film are very small. Therefore, convective
heat transfer between the film and the wall can be neglected compared to conductive heat
transfer perpendicular to the wall.
Assumptions (Nusselt analysis):
1. Laminar flow and constant properties are assumed for the liquid film.
2. It is assumed that the vapour is a pure substance and has a uniform temperature equal to Tboi.
Since there is no temperature gradient in the vapour, heat transfer in the liquid-vapour interface can
only occur by condensation at the interface and not by conduction in the vapour.
3. The shear stress at the liquid-vapour interface is assumed to be negligible. With this assumption
and from the previous assumption of uniform vapour temperature, there is no need to consider
vapour velocity or thermal boundary layers.
4. Momentum and energy transfer by advection in the condensate film are assumed to be negligible.
This assumption is reasonable because of the low velocities associated with the film. It follows that
heat transfer through the film occurs only by conduction only, in which case the temperature
distribution of the fluid is linear.
Condensation – Film Condensation
Quelle: Fundamentals of Heat and Mass Transfer, Incropera, DeWitt, Bergamn, Lavine, John Wiley & Sons, 2007

Quelle: Wärme- und Stoffübertragung in der Thermoprozesstechnik, Eckehard Specht, Vulkan-Verlag GmbH, 2014.
In steady state conditions, the heat flux
transferred through the film is equal to the enthalpy
of vaporization released by the growth of the
condensation film
( ) 0
0
y
w =
=
( ) 0
y
y =
d
=
t ( ) 0
y
y
w
=
d
=
¶
¶ ( ) ú
û
ù
ê
ë
é
×
-
×
d
×
n
= 2
y
2
1
y
x
g
w
Condensation – Film Condensation
The velocity and thickness of the condensed film are very small. Therefore, convective
heat transfer between the film and the wall can be neglected compared to conductive heat
transfer perpendicular to the wall.
The flow velocity is determined from the
momentum conservation equation. Due to the low
velocities, it can be assumed that the gravitational
force and the viscous forces are in equilibrium
Friction negligible in the
interface liquid-vapour due to
low vapour velocities

Quelle: Wärme- und Stoffübertragung in der Thermoprozesstechnik, Eckehard Specht, Vulkan-Verlag GmbH, 2014.
( ) ( )
( )
ò
d
×
×
r
=
x
0
dy
y
,
x
w
x
m
!
( ) ú
û
ù
ê
ë
é
×
-
×
d
×
n
= 2
y
2
1
y
x
g
w
( ) ( )
x
g
3
1
x
m 3
d
×
n
×
r
×
=
!
𝑑
𝑑𝑥
( ) ( )
x
g
3
1
x
m 3
d
×
n
×
r
×
=
!
( ) ( ) h
x
dx
m
d
x
q D
×
=
!
! ( ) ( ) ( )
w
si
3
T
T
h
x
dx
d
x
g
-
×
l
=
D
×
d
×
d
×
n
×
r ( ) 0
0
x =
=
d
Condensation – Film Condensation

Quelle: Wärme- und Stoffübertragung in der Thermoprozesstechnik, Eckehard Specht, Vulkan-Verlag GmbH, 2014.
( )
x
x
d
l
=
a Local convective heat transfer coefficient
ò ×
a
×
=
a
L
0
x dx
L
1 Averaged heat transfer coefficient
Newton‘s approach, for more general
description
The average convective heat transfer
coefficient is therefore one third greater
than the local one (at location x = L).
Condensation – Film Condensation
Charestictic length is thickness of film
Equations are important for exam

Quelle: Wärme- und Stoffübertragung in der Thermoprozesstechnik, Eckehard Specht, Vulkan-Verlag GmbH, 2014.
n
d
×
=
w
Re
d
×
r
=
m
w
!
( ) ( )
x
g
3
1
x
m 3
d
×
n
×
r
×
=
!
3
/
1
Re
3
3
4
Nu -
×
×
=
3
/
1
2
g
Nu ÷
÷
ø
ö
ç
ç
è
æ n
×
l
a
=
Laminar flow
Turbulen flow
The heat transfer is thereby
increased by about 15% to 50%
15
,
1
f » to 1,5
Waviness of the film
Condensation – Film Condensation
Important