Heat transfer engineering an international journal, tập 32, số 1, 2011

Heat Transfer Engineering, 32(1):1–13, 2011
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457632.2010.505127

Heat Transfer Fouling: 50 Years
After the Kern and Seaton Model
¨
HANS MULLER-STEINHAGEN
Technische Universit¨at Dresden, Dresden, Germany

Fouling of heat exchangers is a chronic problem in processing industries. In addition to the appropriate selection of
operating conditions and exchanger geometry, there are numerous chemical and mechanical methods to mitigate fouling
and to remove deposits from the heat transfer surfaces. However, all methods to reduce fouling require some understanding
of the mechanisms of the deposition process and of the structure and adhesion of deposits on the heat transfer surfaces.
Almost exactly 50 years ago, D. Q. Kern and his co-author, R. E. Seaton, published a paper attempting to describe the
growth of fouling deposits in terms of an unsteady-state heat and mass balance for the heat transfer surface. More or less
at the same time, the TEMA fouling resistances were published based on operational and anecdotal evidence of fouling for
a range of heat exchanger applications. These two approaches have since formed the basis for most heat transfer fouling
models and heat exchanger designs. Increased costs of energy, raw materials, and production downtime have contributed
to the growing interest in heat transfer fouling. More recently, environmental legislation has put additional pressure on
fouling-related CO2 emissions and disposal of cleaning chemicals. Despite these efforts, fouling of heat exchangers is still
far from been understood in its whole complexity. The present paper documents the 2009 D. Q. Kern Award Lecture in
which some selected aspects of fouling research to date have been presented and areas have been identified where significant
research and development activities are still required.

INTRODUCTION

confronted with fouling problems, as found in a detailed study
for New Zealand [2].

To date, the formation of deposits on heat transfer surfaces is the least understood problem in the design of heat
exchangers. Well-proven codes and correlations are now available for standard heat exchanger design, and computational
fluid dynamics simulation can be performed for complex
single-phase flow conditions. However, all these sophisticated
calculations are offset by the current practice of using constant,
crudely estimated, experience- or imagination-based fouling
resistances or safety margins. Even worse is the situation
for the prediction of pressure drop. While more heat exchangers
are taken out of operation due to excessive, fouling-related
increase in flow restriction [5], there is virtually no information
about the potential effects of deposits on pressure drop.
Considering the fact that heat exchangers are the workhorse
of most chemical, petrochemical, food processing, and power
generating processes, this situation is most unsatisfactory.
The costs of heat exchanger fouling due to oversizing of
equipment, maintenance, fluid treatment, additional hardware,
additional fuel consumption, and loss of production have been
estimated as about 0.25% of the gross domestic product (GDP)
of industrialized countries in several studies from the 1980s and
early 1990s [2–4]. Even today, where “a billion dollars” seems

In most industrial processes, heat-exchanging fluids contain
certain amounts of dissolved or suspended material or provide
conditions favorable for the growth of biological organisms.
Design and operation of heat exchangers are still to a major
extent determined by the process-related formation of deposits
on the heat transfer surfaces, i.e., fouling. A typical example of a
fouled heat exchanger is shown in Figure 1 for the water side of
a gas cooler. Since the thermal conductivity of such deposits is
low, their resistance to heat transfer may well exceed that of the

process fluids, resulting in significantly reduced heat exchanger
performance [1]. As a result, substantial safety margins in the
design, pretreatment of hot/cold fluids, and regular cleaning of
equipment are usually required.
Several surveys [2–4] have reported that more than 90% of industrial heat exchangers suffer from fouling problems and must
be designed with some allowance for the resulting reduction in
thermal and hydraulic performance. This is also indicated in Figure 2, which shows the percentage of operating heat exchangers

Address correspondence to Dr. Hans M¨uller-Steinhagen, Technische Universit¨at Dresden, 01062, Dresden, Germany. E-mail:

1


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H. MULLER-STEINHAGEN

so-called fouling resistances in the calculation of the overall
heat transfer coefficient U.
1
=
U

Figure 1 Fouled heat exchanger. Courtesy of Hong Kong Towngas.

to become a common order of magnitude in terms of public
expenditure or debts, the costs due to fouling are an excessive
burden on industry and economy.
For a long time, fouling was treated as an incomprehensible

and unavoidable curse of any heat exchanger operation. Empirical knowledge was developed with respect to the beneficial
aspects of additives and operating conditions, but no systematic
approaches have been developed to understand the mechanisms
of fouling and to affect these mechanisms in a beneficial way.
Typical examples for this were the addition of potatoes or sawdust to the boiler feedwater to mitigate fouling in early steam
generators.
The present paper documents the 2009 D. Q. Kern Award
Lecture in which some selected aspects of fouling research to
date have been presented and areas have been identified where
significant research and development activities are still required.
It has deliberately been focused on fouling during heat transfer
to single-phase, liquid fluids, as this represents the majority
of investigations to date, and in order to limit the paper to an
acceptable number of pages.

STANDARD DESIGN PROCEDURE FOR FOULING
The possibility of deposition on heat transfer surfaces is generally considered in the design of heat exchangers by using

1
+ Rf,1
α1

A2
1
+ Rwall +
+ Rf,2
A1
α2

(1)

In Eq. (1), α, A, and Rf are the heat transfer coefficients, the
heat transfer areas, and the fouling resistances, respectively, for
the two heat-exchanging fluids; Rwall is the thermal resistance
of the separating wall. It is obvious that the frequently used
expression “fouling factor” is incorrect, as the effect of fouling is
to create an additional thermal resistance. The fouling resistance
reduces the overall heat transfer coefficient U, and hence leads
to the reduction of the heat duty of an existing heat exchanger
or to additional surface requirements in the design of new heat
exchangers. The results of this procedure are heat exchangers
with excess heat transfer surface that may (or may not) allow
plant operation for an acceptable period of time.
In the early 1950s the first compilation of fouling resistances was published in the Standards of the Tubular Exchangers
Manufacturers Association (TEMA), based on operational and
anecdotal evidence of fouling for a range of heat exchanger applications. Even though additional proprietary data are available
within specialist companies, the TEMA values still form the basis for the design of most heat exchangers, worldwide.
However, there are several problems with respect to the uncritical use of the TEMA fouling resistances, such as:
1.
2.
3.
4.

Their origin and operating conditions are not known.
The majority of values are for flow of water or hydrocarbons.
They apply for shell and tube heat exchangers only.
They do not provide any information on the effect on the
deposition rate of operating parameters such as flow velocity,
fluid temperature, heat flux, and fluid composition.
5. They do not indicate after which operating time the given

fouling resistances are reached.
6. They do not provide for time-dependent management of fouling resistance.
In 1990 Chenoweth and co-workers [6] critically reviewed
the original TEMA fouling resistances. However, only minor
modifications have been included in the later editions of the
TEMA Standards, mainly due to the lack of suitable industrial
data.

THE KERN AND SEATON MODEL

Figure 2 Fouling problems in various heat exchanger types [2].

heat transfer engineering

While several attempts were made before the 1950s to correlate the fouling-related reduction of heat transfer, none of these
equations was based on first principles. The decisive change with
respect to the analysis of fouling came with the model developed
by D. Q. Kern and his co-author R. E. Seaton. Almost exactly
50 years ago, they published a paper attempting to describe the
growth of fouling deposits in terms of an unsteady-state heat and
mass balance for the heat transfer surface [7]. Together with the
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H. MULLER-STEINHAGEN

3

Figure 5 Predicted fouling resistance as a function of time and the parameter

b in Eq. (5), according to the Kern and Seaton model [8].

layer:

Figure 3 Typical fouling resistance versus time curves.

˙ r = K2 τw S
m
TEMA fouling resistances, this approach formed for the next
20 years the basis for most heat transfer fouling models and
practical heat exchanger designs.
Having observed that fouling in industrial heat exchangers
often followed a decreasing or even asymptotic trend, as depicted in Figure 3, Kern and Seaton suggested modeling the
fouling processes as a balance between opposing transport processes to and from the heat transfer surface, namely, deposition
and removal [7], as shown in Figure 4.
Therefore, the accumulation of the deposited mass of fouling
material with time was written as
dRf
dm
˙d−m
˙r =
=m
ρd λd
dt
dt

(2)

assuming that the thermal conductivity λd and the density ρd
of the deposit remain constant with time and deposit thickness.

The deposition rate was modeled with a simplified mass transfer
correlation as being proportional to the bulk flow velocity and
the foulant concentration:
˙ d = K1 V C
m

(3)

Modeling of the removal of already deposited material due to
shear forces from the bulk flow was significantly more difficult,
and it was assumed that this may be proportional to the wall
shear stress and to the thickness of the deposit, which may be a
measure for the presence of structural weaknesses in the deposit

Figure 4 Deposition and removal of deposit.

heat transfer engineering

(4)

Both modeling approaches have since been frequently criticized, extended, and improved [8], as they are obviously based
on very simplistic assumptions and ignore several mechanisms
that may be responsible for the accumulation of dirt on the heat
transfer surfaces. Nevertheless, depending on the values of constants K1 and K2 in Eqs. (3) and (4), curves (a), (b), and (c) in
Figure 3 can be reproduced.
Combining Eqs. (3) and (4) and integrating with respect to
time leads to Eq. (5):
Rf (t) =

K3 C V

(1 − e−K4 τw t ) = Rf∗ (1 − e−bt )
λd K4 τw

(5)

which includes the so-called asymptotic fouling resistance Rf ∗ ,
a value that will be obtained after some period of operation
if the removal rate becomes equal to the deposition rate, i.e.,
the deposit is not very hard and adherent. While the value of
this asymptotic fouling resistance is approximately inversely
proportional to the flow velocity for turbulent flow, the rate at
which it is approached increases strongly with flow velocity as
shown in Figure 5.

THE DEVELOPING YEARS OF FOULING RESEARCH
While the Kern and Seaton model was a significant step forward and provided a physically meaningful description of the
effects of velocity on deposition and removal, and an equation
to model the increase of fouling resistance with time, it nevertheless included two parameters that had to be fitted to the actual
fouling problem (i.e., required real operational data). No information was available on how these two parameters may depend
on the materials of fouling and their concentration, the structure
of the deposit, and operating conditions such as surface temperature and flow conditions. Furthermore, the Kern and Seaton
model has obvious deficiencies in that it does not include the
chemical reactions that are the basis of most fouling processes
such as scale formation, crude oil fouling, or food fouling.
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H. MULLER-STEINHAGEN

It was, therefore, not surprising that little use was made of the
Kern and Seaton model in terms of actual heat exchanger design.
The majority of heat exchangers continued to be designed using
the TEMA or proprietary fouling resistances for tubular heat
exchangers. For compact heat exchangers, the use of the TEMA
values would lead to excessive overdesign, making them ineffective and uneconomic. Compact heat exchangers are hence
generally designed with 15–25% excess surface, to accommodate the fouling-related drop in heat transfer capacity [1].
Frequently, design engineers try to compensate for their lack
of accurate physical properties of the heat-exchanging fluids or
the limited reliability of correlations for the clean heat transfer
coefficients (for example, for multiphase and/or multicomponent applications) by arbitrarily increasing the fouling resistance or by multiplying the calculated overall heat transfer coefficients with a “safety factor,” which also increases the fouling
resistance. It has been reported [4] that the practice of specifying fouling resistances increases the heat transfer surface calculated for clean conditions by 20–300%. These findings have
been confirmed by a study from Heat Transfer Research, Inc.
(HTRI), plotting the fouling-related excess area of 2000 recently
designed heat exchangers (see Figure 6).
In addition to increased equipment cost, oversizing of heat
exchangers may even accelerate the rate of deposit formation if
it results in low flow velocities or high surface temperatures.
This unsatisfactory procedure would probably have continued if Taborek et al. [9] had not reminded the heat transfer
community in 1972 that fouling is the major unresolved problem. This important paper triggered a range of investigations,
most notably the systematic investigations on cooling water
fouling by HTRI together with J. Knudsen from Oregon State
University, by N. Epstein and A. P. Watkinson at the University
of British Columbia, by T. R. Bott at Birmingham University,
and by M. Bohnet at the University of Braunschweig. In this
work, typical fouling processes such as scale formation, particulate deposition, and the growth of biological matter have
been investigated using synthetic model fluids under controlled
conditions. Significant differences have been found with respect

Figure 6 Impact of fouling resistance on the design of 2000 shell-and-tube
heat exchangers. Courtesy of HTRI.

heat transfer engineering

Figure 7 Effect of (a) flow velocity and(b) surface temperature on coolingwater fouling.

to the effect of the main operational parameters flow velocity
and surface temperature on the fouling behavior of the different
types of fouling, as exemplified in Figure 7.
In 1985 Epstein summarized findings to-date in his famous 5
× 5 matrix [10], which has been adopted to plot Figure 8. Here,
for the first time, the different mechanisms of fouling and the
different steps in the net deposition process have been brought
together and analyzed. This has led to a much more systematic
and focused approach to the investigation and mitigation of heat
transfer fouling, for both practical and fundamental problems.
For example, fouling is now generally modeled as a consecutive process made up from transport, reaction/attachment, and
removal. The transport rate is determined according to Eq. (6)

Figure 8 Epstein’s 5 × 5 matrix: perceived level of understanding (increasing
from 0 to 5) versus fouling mechanism and type of fouling [10].

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with the mass transfer coefficient β obtained from the appropriate Sh-Re-Sc relationships:
˙ t = β(cb − cs )
m

(6)

The subsequent attachment or reaction rate is obtained from
Eq. (7), with the reaction rate constant kR and the reaction
order n:
˙ a = kR (cs − c∗ )n
m
−E

kR = Ke RTS

(7)
(8)

For a second-order reaction such as the formation of CaSO4
and assuming that the reaction rate must be equal to the transport
rate, Bohnet and co-workers derived Eq. (9) [11]:
⎡
⎤
2
1
β
β
β
1
˙ d = β⎣

+(cb −c∗ )−
(cb − c∗ )⎦
m
+
2 kR
4 kR
kR
(9)
which subsequently has been applied in many investigations
[e.g., 12, 13].
Research and development efforts during these years have
shed considerable light into the most common fouling mechanisms, such as crystallization, particulate, biological, corrosion,
and chemical reaction fouling. Numerous models for fouling
during convective heat transfer have been derived based on these
approaches, to correlate available data.
It is not the aim of this paper to summarize in detail the vast
area of heat transfer fouling research, or to provide a historical
treatise of it. The latter has already been done in a laudable
way for the period up to 1990 by Somerscales [14]. Significant
progress has been made in this period of time by following
several approaches in parallel, such as:
• Detailed investigation of fouling mechanisms, increasingly
also for gas-side fouling and for fouling during boiling.
• Empirical development of mechanical and chemical on-line
fouling mitigation techniques, such as sponge ball systems,
wire brush systems, and chemical additives [15].
• Development of advanced mechanical and chemical cleaning
systems and procedures for heat exchangers [15].
• Development of heat exchanger types with reduced fouling
rates, for example, the fluidized bed heat exchanger [16].

• Development of guidelines for heat exchanger design, e.g., by
HTRI.
It is, however, noteworthy that most of the investigations
published during this period have been obtained for ideal (or
“model”) fluids, and not many research results, and hardly any
of the numerous deposition models, have found their way into
practical heat exchanger design and operation.
heat transfer engineering

5

FOULING BECOMES AN INTERNATIONALLY
ACCEPTED RESEARCH TOPIC
Following up on the increasing academic interest in heat
exchanger fouling, the first conferences targeted specifically
at this topic were organized in Guildford (1979) [17], Troy
(1981) [18], and Alvor (1987) [19]. These pioneering meetings
contributed much to the formation of a “fouling research
community” with significant coherence and interaction.
Consequently, United Engineering Foundation Conferences
(now Engineering Conferences International) decided to
initiate a series of international meetings on fundamental and
technological aspects of heat exchanger fouling. Seven highly
successful meetings have been held in San Luis Obispo, CA
(United States, 1994), Castelvecchio Pascoli (Italy, 1997),
Banff (Canada, 1999), Davos (Switzerland, 2001) [20], Santa
Fe, NM (United States, 2003), Kloster Irsee (Germany, 2005),
and Tomar (Portugal, 2007). These conferences attracted an
increasing number of participants from industry, research organizations, and universities. Papers presented at each of these
conferences have been published in the respective conference

proceedings and probably provide the most comprehensive
overview of the state of the art of this complex subject. The full
proceedings of the 2003–2007 meetings can be downloaded
from />For organizational reasons, the ECI fouling conference series
was continued from 2009 onward as the EUROTHERM Seminar Series, starting with the 2009 conference in Schladming
(Austria). Proceedings of and information about this conference can be found at .
The next conference in this series will be held in Crete (Greece,
June 2011); see the website just given.
For engineers working in the area of food processing, an excellent series of bi-annual conferences at Cambridge University
(England), organized by Wilson, Fryer, and Hastings, provides
current developments in fouling and cleaning in that industry.
FOULING RESEARCH REACHES MATURITY
Increasing costs of energy, raw materials, and production
downtime have contributed to the growing interest in heat transfer fouling. More recently, environmental legislation has put
additional pressure on fouling-related CO2 emissions and disposal of cleaning chemicals [21].
For immediate benefits, fouling task forces including
representatives from major international process engineering
companies, heat exchanger design and construction companies,
and suppliers of chemical and mechanical fouling mitigation
measures have been established by ESDU and HTRI to compile
best practice guides for heat exchanger design and operation.
To date, very detailed reports have been prepared for crude oil
[22], seawater [23], and freshwater [24].
Based on almost 50 years of experience, HTRI has developed
a design methodology that yields smaller, more cost-effective
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H. MULLER-STEINHAGEN

6

shell-and-tube heat exchangers with extended run times between
cleanings [1, 25]. While this methodology has, so far, only been
validated for crude oil processing, its rigorous approach can be
taken as an example for other fluids and heat exchangers types.
Using this methodology, only a small design margin may be
added to the design to address design uncertainties. Rarely is
this margin in excess of 30%.
These experience-based approaches are extremely useful for
appropriate design and operational mitigation of standard fouling problems. However, they cannot be extrapolated to individual fouling problems or lead to a general solution for the reduction or even elimination of fouling. For this, more fundamental
research and development are required. Some of these efforts
are described in the following. It is obvious that the general
approach to improved understanding of deposition mechanisms
has been moving from macro-scale to micro-scale to molecular
level, and that advanced computational tools are increasingly
finding their way into fouling analyses.

Whole Plant Modeling
Heat exchangers are rarely stand-alone units unaffected by
upstream and downstream processes. Hence, the conditions
leading to and resulting from fouling are the result of complex interactions within a range of equipment, including, e.g.,
heat exchangers, settling tanks, reactors, mixers, and evaporators. In many bulk material processes, addition of chemicals to
mitigate fouling is not possible due to product requirements, and
significant changes to the existing hardware cannot be afforded.
However, it may still be possible to reduce the formation of
deposits or improve the economy of the process, if appropriate
operating conditions and/or operating schedules are selected.
This requires understanding of both the local fouling conditions and the overall plant operation. Ideally the optimization

processes should include the following steps:
1. Analysis of plant operating data.
2. Analysis of deposits and of foulant solubility behavior.
3. Laboratory experiments to determine the effect of operating conditions (concentration. flow velocity, bulk and heat
transfer surface temperature).
4. Laboratory experiments to determine possible fouling mitigation methods (e.g., seeding, turbulence promoters, fluidized bed).
5. Modeling of fouling process.
6. Limited number of plant measurements on a slipstream to
confirm the validity of the laboratory data and of the fouling
model for actual plant operating conditions.
7. Heat exchanger model to predict local and overall temperatures and fouling rates.
8. Comparison of heat exchanger model with plant operating
data.
9. Overall plant model with/without fouling related deterioration of heat transfer.
heat transfer engineering

10. Use of model to determine optimum operating conditions/procedures and to investigate the effects of plant modifications to maximize throughput or minimize operating
costs. This model can also be used for model-based process
control and environmental impact studies.
An effective approach to provide the information required
for optimizing plant operation and plant layout requires a combination of fundamental and industrial studies. It is unlikely that
all the information just specified can be collected, due to financial and/or time constraints. The important criterion is, however,
that some plant verification for the developed fouling/operating
model is available. This general approach has been applied successfully in several comprehensive studies:
•
•
•
•

Kraft black liquor in the pulp and paper industry [26, 27].

Bayer liquor in bauxite refineries [28, 29].
Phosphoric acid plants for fertilizer production [30, 31].
Sulfuric acid recovery plant in a titanium oxide extraction
process [32].
• Crude oil preheat train [33, 34].
In the processes just listed, heat exchangers generally suffer
from severe fouling problems, leading to significant limitation
in plant operation and high additional costs. The investigations
have been performed in close collaboration with industry and
resulted in significant gain in knowledge and industrial benefits. Results of these investigations have been implemented into
design and operation of the investigated plants, or are further
investigated in pilot-plant studies. Actual and potential future
savings are in the order of many millions of dollars, providing a
significant payback on the investments for the detailed studies.
A typical example is shown in Figure 9, indicating the predicted
extension of operating time of a sulfuric acid concentration unit
if operated at higher temperatures and with variable flow velocity [32]. The dashed line shows the original operation with
a constant acid flow velocity of 2.5 m/s and increasing heating
steam temperature to overcome the effects of fouling. The solid
line shows the suggested operation with constant maximum
steam temperature of 200◦ C and variable flow velocity from
1 m/s to 2.5 m/s. With the second option, the run time could be
increased from 150 hours to 275 hours, with only minor plant
modifications.
Neural Networks
Despite increased attention during the past decades, correlations recommended for heat exchanger fouling can only be
applied to a limited number of idealized deposition processes,
while they lead to massive uncertainties and inaccuracies for
industrial fluids. These drawbacks may be the result of:
• Nonlinearity of the fouling process.

• The character of the fouling process, which is unsteady-state
with potentially high fluctuation.
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H. MULLER-STEINHAGEN
204

202

2.5

200

2.0

st

T [°C]

v [m/s]

*

198

1.5

11

11

additional operation time with the
new process control configuration

-ln (Rf), experiment

Velocity
Steam Temperature

12

12

-ln (Rf), experiment

3.0

7

10
9
8

*
7

196
Q=22000 W

8
7

5
5

6

7

8

9

10

-ln (R*f), prediction
1.0

9

6

6
5

10

11

12

5

6

7

8

9

10

11

12

-ln (R*f), prediction

Figure 11 Measured versus fitted asymptotic fouling resistances, using a
mechanistic model (left, mean average error 38%) and a neural network (right,
mean average error 15%).

194

0.5
0

25

50

75

100

125

150

175

200

225

250

275

Time [h]

date:

Figure 9 Operational time before shut-down for cleaning of a sulfuric acid
evaporator, operating either with constant flow velocity (dotted line) or constant
steam temperature (solid line).

• The large number of variables and different mechanisms.
• The lack of rigorous understanding of the underlying mechanisms.
• The inherent inadequacy of conventional regression methods
to correlate experimental data with an ill-distributed parameter variation.
The use of artificial neural networks is a pragmatic alternative
to address many industrial fouling problems with significantly
better accuracy than conventional parametric regression models.
This can be done by using neural networks as an interpolation
tool within a range of experimental results (black-box approach)
[35], or as a hybrid approach where the neural network is used in
combination with prior knowledge (PK) of the process [36, 37],
as shown in Figure 10. This “prior knowledge” may, for example, be the experience that the fouling rate generally increases
with surface temperature and/or decreases with flow velocity.
The results of the second method are found to be more reliable
than those provided by the first method.
The following promising results have been found in the very
limited number of investigations that have been published to

• Experimental data could be correlated significantly better with
a suitable neural network than with the models recommended
by the original authors. This is clearly demonstrated in
Figure 11 for cooling water fouling data.
• Satisfactory capability of the network for those areas (i.e.,
induction period and high surface temperature) where not
enough information about the underlying phenomena and/or
insufficient experimental data are available.
• The reliability of the resulting networks was confirmed when
they were applied to those data that had not been used before.
• Once converged, the resulting network is a simple and small
program that even inexperienced users can apply or that can

be embedded into any heat exchanger design software.
Despite these promising results, several questions still remain
unanswered, which will have to be addressed if such techniques
are to be pursued for industrial applications:
• Validation for process fluids where the number of input variables is large, and with poorer understanding of the basic
phenomena which govern the fouling process. A typical example for this could be crude oil fouling.
• Application to cases where the dominant mechanisms change
with operating conditions and/or time. One such example is
crystallization fouling, which is diffusion-controlled at very
low velocities and reaction-controlled at higher velocities.
• The predictability of the network may severely deteriorate if
data bases are ill-distributed and much weight of the data is
concentrated only in specific domains.
• Poor extrapolation of the resulting network beyond the range
of learning data.
• Inclusion of discrete variables such as heat exchanger geometries into neural network modeling.

CFD Modeling

Figure 10 Hybrid neural network (PK = prior knowledge).

heat transfer engineering

Fouling in industrial heat exchangers is strongly dependent
on local concentrations, temperatures, and shear rates. This is
exemplified in Figure 12, which shows the inlet zone of a gas
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Figure 12 Negative effect of excessive inlet baffle spacing on deposit formation.

cooler with cooling water flowing on the shell side. Very severe
deposit formation was found in the area between the last baffle and the tube sheet; further away, fouling was significantly
less. Looking at the pictures on the left side of Figure 12, one
recognizes the large spacing between tube sheet and first baffle, as compared to the subsequent baffle–baffle spacing. The
large gap leads to a significant reduction in flow velocity and to
significant flow maldistribution, both reducing local shear rates
and increasing local wall temperatures, even to the extent that
undesirable local nucleate boiling may have occurred, which
significantly increases the deposition rate [38]. It is obvious
that the relatively simple analytical models developed for heat
exchanger design and fouling do not provide the required information about local conditions. However, numerical simulation
of flow and temperature distribution using commercial computational fluid dynamics (CFD) software has now reached a
quality where it is possible to identify critical areas in industrial
heat exchangers in terms of hot spots or low velocity zones. Detailed modeling of shell-side flow of large shell-and-tube heat
exchangers has been performed, including leakage streams between baffles, tubes, and shell [39]. This is an area of work with
tremendous potential, not only for shell-and-tube heat exchangers, but also for compact heat exchanger types [40].
First attempts have been undertaken to model the local growth
of deposits in addition to the local temperatures and shear rates
[41]. The inclusion of additional mass transfer mechanisms and
heat transfer engineering

reaction kinetics increases the computational effort enormously,
but this will be resolved with the advent of increasingly powerful
microprocessors. More importantly, such modeling approaches

depend on the quality of models for the local deposit formation,
which are still under investigation.

Heat Transfer Surface–Deposit Interaction
Numerous methods have been developed to remove depositforming constituents from heat exchanging fluids, to increase
their solubility in these fluids, or to clean heat transfer surfaces
once they have fouled. While the first are highly specific to the
composition/chemistry of the fluids, the last of these only deals
with a problem after it has occurred. From a technical point of
view, it would be much more desirable if heat transfer surfaces
could be developed on which deposits do not stick at all. In
general, maximum adhesion occurs in interacting systems that
undergo a maximum decrease in surface energy, and poorest
fouling adhesion should occur on materials that have low surface energies. Surface coatings with organic polymers such as
polytetrafluoroethylene (PTFE) and Saekaphen have a very low
surface energy, but they are mainly used to avoid corrosion as
the coatings themselves provide a significant additional resistance to heat transfer. While the durability of the coatings increases with thickness, this has the inverse effect on heat transfer.
vol. 32 no. 1 2011


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H. MULLER-STEINHAGEN

Therefore, the coating thickness should be kept as thin as possible. These conditions can be met with modern surface-coating
techniques such as ion beam implantation, magnetron sputtering, and autocatalytic Ni–P–PTFE coatings.
However, results obtained with a wide range of surface coatings have been contradictory [42], indicating increased or decreased deposit formation on surfaces with low surface energy,
as compared with standard stainless steel. Hence, there is a lack
of understanding of the principal interacting forces between
depositing material and metallic substrate. Since the effect of
gravitational forces on deposition is usually negligible, these

forces consist of a Lifshitz–van der Waals (LW) interaction
component, electrostatic double-layer component (EL), Lewis
acid–base component (AB), and Brownian motion component
(Br). Equations to predict these interactions energies may be
found in [43]. The total interaction energy ETOT between a
deposit and a metal surface can be written as the sum of the
respective interaction terms:
E TOT =

E LW +

E EL +

E AB +

E Br

(10)

It has been suggested, e.g., by Visser [44] that the balance
between all possible interactions between a deposit and a metal
surface determines whether a system will foul or not; i.e., adhesion/fouling will take place when ETOT is negative.
However, experimental evidence has shown that under certain conditions some systems may foul, even though the total interaction energy E132 TOT between deposit (1) and metal surface
(2) in fluid (3) is positive—for example, if the initial E132 TOT
is positive (i.e., repulsive), but the substantial cohesive energy
E131 TOT between the foulant particles leads to coagulation into
larger particles. It is also not necessarily correct that the system
will foul if the total interaction energy E132 TOT is negative. For
example, if the cohesive energy E131 TOT exactly equals the adsorption energy E132 TOT, the energy characteristics of the heat
transfer surface will be the same as that of the foulant particles.

This means that the colloidal particles in the wall-near boundary
layer may not attach to the surface or coagulate to each other,
but remain suspended in the solution in some sort of dynamic
equilibrium. Therefore, the cohesive energy E131 TOT will have
to be taken into account in the investigation of fouling behavior,
and particularly during the fouling induction period. Based on
these findings, the following criterion to determine whether a
system will foul or not has been suggested in [45]:
T OT
E 131
−

T OT
E 131
−

T OT
> 0,
E 132

T OT
E 132
=0

fouling possible either,
immediately or later
(11)

no or minimal fouling (12)

If the Lifshitz–van der Waals forces are dominant, the surface
free energy γs,min at which fouling is minimal can be calculated
from:
√

γ S,min = (1/2)

γ1L W +

γ3L W

(13)

heat transfer engineering

9

Figure 13 Surface free energy versus asymptotic fouling resistance for various
surface materials. Experimental data from F¨orster et al. [46] .

with γ1L W and γ3L W being the surface free energies of deposit
and the liquid, which can be determined by standard measurements. For the deposition of CaSO4 from aqueous solutions, the
free surface energies of crystalline CaSO4 and of water are γ1L W
= 35.5 mN/m and γ3L W = 21.8 mN/m. According to Eq. (12),
a heat transfer surface with a surface free energy γ2L W = γs,min
= 28 mN/m should have minimum fouling. This is confirmed
by comparison with the experimental data by F¨orster et al. [46]
shown in Figure 13. The location of the fouling minimum coincides with the experimental findings for the DLC-F sputtered
surface, for which also a surface free energy of 28 mN/m was
measured.

Similar agreement between predicted minimum fouling surfaces and measurements has also been found for deposition of
milk and microbes. While the findings just described are promising, they are nevertheless only a first step forward. There is
experimental evidence that other effects, such as surface roughness, aging, and temperature, will also have significant effects
on deposition rate and asymptotic fouling resistance.
Molecular Modeling
While the modeling of surface–deposit interaction may provide some information about the sticking propensity of various
deposits on various surfaces, it still depends on the measurement
of lumped parameters taking into account several molecular effects happening on the interface between surface and deposit.
The weakness of this approach is evidenced by the poor correlation of surface energy and fouling rate or fouling delay time, as
reported in [42]. Here it was found that stainless-steel surfaces
implanted with hydrogen ions suffered considerably more from
fouling than the original steel surfaces, which in turn fouled
significantly faster than stainless-steel surfaces implanted with
fluorine ions. In both cases, the surface energies of the implanted surfaces as well as their polar components are almost
identical. This phenomenon has been analyzed by Rizzo et al.
[47], who found that the induction period of the nucleation process of CaSO4 crystallization fouling could not be correlated
with results from surface energy measurements. Instead, a linear relation between the slope of the ln(induction period) versus
ln–2(supersaturation ratio) plots and the electronegativity of the
implanted ions was observed, as shown in Figure 14.
This empirical result sheds some light on the contradictory results reported in [42]; it nevertheless does not allow
vol. 32 no. 1 2011


10

¨
H. MULLER-STEINHAGEN

Figure 15 Predicted formation of titania and silica deposits on a rutile substrate
[49].

Figure 14 Slope of nucleation curves versus electronegativity Eea for stainlesssteel surfaces implanted with fluorine, oxygen, hydrogen, and neon ions [47].

extrapolation to other surfaces and fouling fluids. Therefore,
molecular modeling has been applied by Puhakka and coworkers [48–50] in order to obtain explanations for interaction
mechanisms (chemical or physical nature of bonding) between
heat transfer surfaces and deposits. In particular, there has been
investigation of whether there is any physicochemical explanation at molecular level for the effects of surface material (e.g.,
stainless steel), surface oxidation, or surface coating (such as
SiOx, TiCN, DLC) on inorganic fouling. For this, the total electronic energy and the electronic energy density distribution were
solved to define the energetically stable structures for chemical
compounds and reaction intermediates.
Investigations by Puhakka et al. [48–50] indicated that molecular modeling is capable of distinguishing different fouling
mechanisms on heat transfer surfaces and to estimate the significance of the chemical effects of the process fluid on the
uppermost layer structure of the heat transfer surface, which is
responsible for the initial period of fouling. Water can adsorb
onto solid surfaces as a molecule, or it can dissociate forming
partially or fully hydroxylated surfaces. The existence of hydroxyl groups on the surfaces has an effect on the initial stage
of deposition formation. When the surface hydroxyl groups
exist, fouling can take place via condensation reactions with
species containing hydroxyl groups. On surfaces without hydroxyl groups, fouling takes place preferably via adsorption of
ions. Following the modeling of water adsorption, the subsequent adsorption of calcium (Ca2+) and carbonate (CO3 2−) ions
onto surfaces and the formation mechanism of CaCO3 deposits
were determined. Fouling was found to happen via hydrogen
carbonate intermediates, and the final deposit structure varied
for the different surface materials. As an example, the formation
of deposits from pure Ti(OH)4 and Ti(OH)4 /Si(OH)4 solutions
on TiO2 (rutile) surfaces has been simulated, as shown in Figure
15 [49].
Unquestionably, molecular modeling is a powerful tool that

will make a significant contribution to the improved understanding of deposit formation and fouling mitigation. This may
include the adsorption of antifoulants on clean heat transfer
surfaces, and the effects of surface modifications and of trace
heat transfer engineering

additives to the fluids. However, this fundamental approach to
the understanding of deposit formation is still in its infancy and
is associated with many assumptions and a significant computational effort. It is, nevertheless, an excellent example for the
pathway that fouling research has to follow in order to develop
from “art” to “science.”

CONCLUSIONS
Fifty years after Kern’s pioneering work, fouling is still the
major problem in the design and operation of industrial heat exchangers. This may lead to the conclusion that fouling research
activities to date have not been particularly successful—which
is not at all correct. The increased awareness of fouling and the
improved qualitative understanding of the effects of flow velocity, surface temperature, and surface topography on fouling
rates already have had a major impact on the way heat exchanger
design is approached and on the way existing exchangers are
operated.
Numerous chemical additives have been developed that, in
many cases, can reduce the deposition rates of selected fouling
problems considerably. However, these chemicals add to the
plant operating costs, and their application may be restricted
by environmental legislation or by product specifications. The
strategic long-term goal must therefore be to avoid fouling altogether by appropriate design of heat exchangers and selection
of suitable plant operating parameters.
Several designs of self-cleaning heat exchangers have been
introduced into the market with considerable success, e.g., a
sponge ball system for power plant condensers, wire brush

systems for medium-size cooling-water applications, and the
fluidized-bed heat exchanger for severely fouling process liquids. The application of these concepts may, with appropriate
modifications, be extended to other fouling problems and operating conditions.
In the near to medium term, tangible progress in the mitigation of heat exchanger fouling can only be achieved by close
cooperation between industry and research institutions, because
improved understanding of the process of deposit formation
will always be a prerequisite. However, this progress will come
with a substantial price tag. It requires considerable initial
vol. 32 no. 1 2011


¨
H. MULLER-STEINHAGEN

investment for appropriately sized and well-instrumented
equipment, as well as a longer term funding strategy, which
extends beyond that of typical doctoral programs. Companies
need to assess the true costs caused by their fouling problems
and initiate research projects for better design of the next
generation of heat exchangers or for improved plant operation.
Rather than spending time and efforts on uncoordinated
research and development, a number of relatively generic
high-priority fouling problems (e.g., crude-oil fouling, coolingwater fouling, milk fouling, etc.) may be identified, which
will then be investigated by (virtual?) research centers with
industrial input. Startup funds should be provided by industry
with matching contributions from governmental programs.
There must also be a willingness from all involved partners
to share know-how and benefits to a significantly larger extent
than is common practice today. Encouraging examples for
such an approach are several projects funded by the European

Commission, the HTRI Crude Oil Fouling Task Force, and the
ESDU Best Practice Data Items on crude-oil fouling, seawater
fouling, and cooling-water fouling, which have been produced
with substantial contributions from industrial working parties.
These application-oriented attempts must be accompanied
and extended by increased fundamental research related to the
mechanisms of deposit formation and adhesion. As has been
demonstrated in the preceding discussion, innovative scientific
and computational approaches have a significant potential. The
interactive forces between deposits and surfaces are not at all
well understood, even though they are the key to understanding
the initiation of deposit adhesion. The application of fundamental models such as the DLVO theory or molecular dynamics
modeling may already provide useful information about the relationship between surface characteristics and deposition rates
for simple aqueous systems, but cannot yet deliver conclusive
recommendations for most industrial fouling problems. Ultimately, nanotechnology may allow the development of nonfouling surfaces, as amply demonstrated by nature with the leaves
of flowers or the scales of fish.
Despite all efforts to reduce the formation of deposit on heat
transfer surfaces, we will never be able to avoid it altogether
and in all applications. Cleaning of heat exchangers will still be
required, even though—hopefully—in less frequent intervals.
There is still a significant potential to improve the efficiency of
existing cleaning processes and to develop new cleaning concepts. The mechanisms of cleaning are even less understood
than deposit formation itself, even though significant practical
experience is available.

m
m˙
n
Q
q

R
Rf
Rf ∗
Rwall
s
t
T
v
U

A
b
c
E
kR
K

heat transfer surface area, m2
lumped parameter in Eq. (5)
concentration of depositing reacting material, kg/m3
activation energy, J/mol
Reaction rate constant, m4/kg-s
constant
heat transfer engineering

mass, kg
rate of mass deposited, kg/m2-s
order of reaction
heat flow rate, W
heat flux, W/m2

universal gas constant, 8.314 J/(mol-K)
fouling resistance, m2-K/W
asymptotic fouling resistance, m2-K/W
thermal resistance of wall separating heat exchanging
fluids, m2-K/W
deposit thickness, m
time, s
temperature, K
flow velocity, m/s
overall heat transfer coefficient, W/m2-K

Greek Symbols
α
β
γ
λ
ρ
τw

film heat transfer coefficient, W/m2-K
mass transfer coefficient, m/s
interfacial energy, J/m2
thermal conductivity, W/m-K
density, kg/m3
wall shear stress, N/m2

Subscripts
1, 2
a
b

d
ea
min
s
st
t
r

fluid 1, fluid 2
attachment
bulk
deposit, delay
electronegativity
minimum
surface/interface
steam
transport
removal

Superscripts
AB
Br
EL
LW
TOT
∗

NOMENCLATURE

11

Lewis acid–base
Brownian motion
electrical double layer
Lifshitz–van der Waals
total
at saturation

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Heat Transfer to Kraft Pulp Black Liquor Part I: Experimental Results, APPITA Journal, vol. 48, no. 1, pp. 45–50,
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DSP Formation in the Bayer Process—Measurements on a
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[29] Duncan, A., Silica Scaling in Bauxite Refineries, Ph.D.
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[32] M¨uller-Steinhagen, H., and Lancefield, D., Deposit
Formation in the Evaporator of a Sulphuric Acid
Recovery Plant for TiO2 Pigment Production, ECI
Symposium Series, vol. RP2, 2005, http://services.
bepress.com/eci/heatexchanger2005/12

[33] Yeap, B. L., Wilson, D. I., Polley, G. T., and Pugh, S. J.,
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(in press).

¨
Hans Muller-Steinhagen
is the Rector of the Technical University of Dresden, Germany. Previously, he
has been Director of the Institute of Technical Thermodynamics of the German Aerospace Centre (DLR)
and of the Institute of Thermodynamics and Thermal
Engineering of the University of Stuttgart. His research work covers a wide range of topics related to
heat and mass transfer, multiphase flow, fuel cells,
solar technologies and process thermodynamics. He
is the author of more than 600 articles and has received numerous international awards, including the 2009 AIChE D.Q. Award.
Professor M¨uller-Steinhagen is a fellow of the Royal Academy of Engineering,
past-President of EUROTHERM, member of the Executive Boards of EUREC
and ICHMT, of the Innovation Council of the State of Baden-W¨urttemberg,
and associate editor of Heat Transfer Engineering. He is also chairman of the
Advisory Board of the Desertec Industrial Initiative.

vol. 32 no. 1 2011


Heat Transfer Engineering, 32(1):14–19, 2011
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457631003732805

Heat Transfer Enhancement of
Square-Pitch Shell-and-Tube Spray
Evaporator Using Interior Spray
Nozzles
TONG-BOU CHANG, JUN-CHENG LI, and CHIH-CHANG LIANG
Department of Mechanical Engineering, Southern Taiwan University, Tainan, Taiwan

This study proposes a new nozzle/heater arrangement for enhancing the heat transfer coefficient of a square-pitch shell-andtube spray evaporator. In the proposed approach, the nozzle tubes are positioned within the tube bundle in such a way that the
surface of each heater tube is sprayed simultaneously by four cooling sprays. As a result, the dry-out phenomenon on the lower
surface of the heater tubes is prevented. The experimental results reveal that the shell-side heat transfer coefficient obtained
using the proposed spray technique is significantly higher than that achieved in a conventional flooded-type evaporator.
Moreover, it is shown that the heat transfer performance increases as the saturation temperature decreases and the spray
film flow rate increases.

INTRODUCTION

the liquid film on the solid heated surface, and therefore allowed
the vapor bubbles to be more easily released.
In a refrigeration cycle, an expansion process is required to
reduce the refrigerant pressure to a level at which evaporation
can take place. In practice, the resulting pressure drop can be
used to drive a liquid spray. However, even though spray evaporation is known to have a high heat transfer performance, it is
seldom used in compact heat exchangers with tube bundles since
the conventional sprays (i.e., overhead sprays) used in such systems generally fail to reach the lower tubes in the bundle (Figure
1). Moeykens and Pate [4] performed overhead spray evaporation tests on a horizontal plain tube using R134-a as the coolant.
The results showed that when the tube had a high surface heat
flux, a dry-out phenomenon occurred on the lower surface, and
thus the heat transfer performance of the spray evaporator mode

was lower than that of the pool boiling mode. In an attempt to
resolve this problem, Moeykens and co-workers [5, 6] and Chyu
and co-workers [7–9] investigated the effects of many different
spray parameters (e.g., the nozzle height, the nozzle orifice diameter, the spray mass flow rate, and the spray angle) on the heat
transfer performance of overhead shell-and-tube spray evaporator systems with triangular-pitch or square-pitch tube bundles.
The experimental results showed that the heat transfer performance obtained in the uppermost row of tubes was significantly
higher than that obtained in any of the other rows within the
bundle. Ribatski and Jacobi [10] presented a comprehensive

Spray evaporation systems, in which cooling liquid droplets
are sprayed directly onto the heated surface, are widely applied
in the winery and poultry industries. Compared to conventional
flooded-type evaporators, spray evaporators improve the heat
transfer performance and reduce the chiller refrigerant inventory
by around 20–90%, depending on the system design.
Spray cooling heat transfer was first examined experimentally by Hodgson and Sutherland [1] in 1968. In their experiments, the temperature of the heated surface was higher than
the Leidenfrost temperature, and thus film boiling conditions
were observed. The findings of Hodgson and Sutherland [1]
prompted many other researchers to investigate the complex
mechanisms associated with spray heat transfer. For example,
Choi and Yao [2] investigated the heat transfer mechanisms of
horizontal impacting sprays and found that film boiling heat
transfer is controlled primarily by the liquid mass flux. Pais
et al. [3] conducted a series of spray cooling tests and showed
that the impact of the refrigerant droplets caused a breakup of
This study was supported by the National Science Council of Taiwan (NSC
96–2221–E–218–034).
Address correspondence to Professor Tong-Bou Chang, Department of Mechanical Engineering, Southern Taiwan University, 1, Nan-Tai Street, YungKang
City, Tainan County, Taiwan. E-mail:

14


T.-B. CHANG ET AL.

15
Condenser
T

Nozzle
P

Pressure
gage

3
R

T
R

P

Relief
valve

heater
m

T

RTD

m

Flow
meter

S

Side
glass

T

P

T
P

Test section

Chiller

2
T
4

m

Bypass valve

P

Cooling water

R

T
1

S

Pump

Strainer

Storage
tank

Figure 2 Schematic illustration of experimental system.

Conventional Breaks

EXPERIMENTAL APPARATUS

Figure 1 Sketch of liquid film distribution in square-pitch tube bundle with
overhead sprays.

review of the experimental parameters affecting the heat transfer performance of spray and falling-film evaporation in tube

bundles. Chang and Chiou [11] performed overhead spray cooling tests on a tube bundle and found that a dry-out phenomenon
occurred on the lower tubes. In order to eliminate the dry-out
phenomenon in triangular-pitch tube bundles, Chang and coworkers [12, 13] attached liquid collectors to the underside of
each tube in the bundle. The collectors were designed in such a
way as to collect the liquid film flowing over the surface of the
tubes and to guide the overfill liquid such that it impacted a tube
located in the row below. The experimental results showed that
the heat transfer performance of the enhanced spray evaporator
system was superior to that of a pool boiling system under both
low and high heat flux conditions.
However, the liquid collectors proposed in [12] and [13]
are ineffective in square-pitch shell-and-tube spray evaporators
since the liquid film distribution differs from that in triangularpitch tube bundles. In a recent study, Chang et al. [14] showed
that the dry-out problem can be prevented in compact triangularpitch shell-and-tube evaporators by introducing liquid sprays
within the bundle interior. In the present study, the same concept
is applied to resolve the dry-out problem in square-pitch shelland-tube spray evaporators. The experimental results show that
the deployment of nozzle sprays within the evaporator system
results in a significantly improved heat transfer performance
compared to that obtained in a conventional pool boiling system.
heat transfer engineering

An experimental system was constructed to enable the shellside heat transfer coefficients of the tube bundle to be evaluated
in either a spray evaporation mode or a pool boiling mode. As
shown in Figure 2, the experimental system included a refrigerant flow loop, a test section containing an array of heater
tubes and spray nozzles, a cooling water flow loop to cool the
condenser, a storage tank, and a data acquisition system.
The refrigerant flow loop had the form of a closed-type circulation system and was designed in such a way as to ensure
that the liquid refrigerant entered the test section at the desired
flow rate and temperature. During the experiments, the film flow
rate of the sprays within the bundle was controlled by regulating

the differential pressure across the spray nozzles using a bypass
valve installed on the outlet side of the refrigerant pump. The
evaporated vapor refrigerant exiting the test section was fed to
a condenser, and the resulting liquid then flowed past an RTD
temperature meter and returned to the storage tank. Meanwhile,
the non-evaporated liquid refrigerant exited the test section via
an outlet pipe fitted to its lower surface and was returned to the
storage tank via a flow meter and a bypass valve. The experimental tests were conducted using R141-b refrigerant as the
working fluid. R141-b is an HCFC refrigerant and has a boiling
temperature of just 32◦ C under atmospheric pressure. As a result, the test system could be maintained at a low pressure and
was therefore safer from an experimental point of view.
Figure 3 presents a schematic illustration of the heater and
nozzle tube arrangement in the square-pitch tube bundle considered in the present study. As shown, each nozzle tube is located
in the center of an imaginary square formed by four neighboring heater tubes. The nozzle tubes are designed to spray four
sprays at angles of 45◦ to the horizontal and vertical axes of the
tube. Thus, as shown in Figure 4, each heater tube in the bundle
is sprayed simultaneously by four neighboring nozzles. As a
vol. 32 no. 1 2011


16

T.-B. CHANG ET AL.

Figure 3 Schematic illustration of proposed heater and nozzle tube arrangement in square-pitch tube bundle.

result, the heater surfaces receive sufficient refrigerant liquid to
prevent the dry-out phenomenon. The four holes in each nozzle
have the form of full-cone circular hydraulic nozzles and have
an orifice diameter of 1 mm and a cone angle of 90◦ . Note that

due to budget constraints, the tube bundle installed within the
test section comprised just four heater tubes and nine nozzle
tubes (Figure 5).
The test section had the form of a cylindrical stainless-steel
vessel with a length of 40 cm, an internal diameter of 30 cm, and
a thickness of 0.5 cm. The heat source within the test section
was provided by four resistor-type copper heater tubes, fastened
at one end of the vertical side plates of the test section. Each
heater tube had a diameter of 19.05 mm (3/4 in) and was capable
of generating a maximum heat flux of 220 kW/m2. In order to
prevent axial conductivity heat losses, the outer copper surface
of each tube was fabricated with a thickness of just 0.5 mm
and the unheated section was filled with silica. Four thermocouples were embedded in the surface of each heater tube through
within drilled ports, filled with lead–tin solder. Importantly, the
port diameter was kept to a minimum in order to ensure that
the temperature of the solder bead closely matched that of the
wall. The thermocouple wires were then run through the space
between the outer surface of the cartridge heater and the in-

Figure 5 Schematic illustration of tube bundle used in present experimental
tests.

ner surface of the copper tube (see inset in Figure 5). In order
to maintain the cartridge heater in a centerline position within
the tube, the space between the outside of the cartridge heater
and the inside of the copper tube was filled with a mixture of
magnesium dioxide powder and highly conductive grease.
During the experiments, the thermocouple signals, the RTD
output signal, the spray film flow rate, and the surface heat
flux were monitored continuously by the data acquisition system. Having waited for approximately 30 min for the system

to reach steady-state conditions (as indicated by a variation in
the saturation temperature of less than 0.1◦ C/min), each data
point of interest was obtained by averaging a minimum of 20
data-acquisition scans. Note that in the tests, the input power
was immediately turned off if any of the heater temperature
measurements suddenly increased (indicating the occurrence of
dry-out) in order to protect the measurement instrumentation.

EXPERIMENTAL DATA REDUCTION
In the tests, the film flow rate of the refrigerant was varied
in the range 0.09–0.12 kg/ms, while the heat flux was varied
from 104 W/m2 to more than 105 W/m2. Finally, the saturation
temperature was set to 20◦ C, 24◦ C, or 28◦ C, respectively.
The mean shell-side heat transfer coefficient, h, was determined in accordance with Newton’s cooling law, i.e.,
h=

Figure 4 Schematic illustration of proposed internal spray method.

heat transfer engineering

q
¯
Tw − Tsat

(1)

where q is the wall heat flux (W/m2), T¯w is the average wall
temperature (◦ C), and Tsat is the saturation temperature (◦ C).
Note that in computing the mean shell-side heat transfer
coefficient, the average wall temperature was taken as the

vol. 32 no. 1 2011


T.-B. CHANG ET AL.

arithmetic mean of the 16 thermocouple readings, i.e.,
T A,1 +T A,2 +T A,3 +T A,4 +TB,1 +TB,2 +TB,3 +TB,4
+TC,1 +TC,2 +TC,3 +TC,4 +TD,1 +TD,2 +TD,3 +TD,4

4

o

16

: 20 C

(2)

o

: 24 C

where subscripts A, B, C, and D denote the heater tubes positioned in the four locations shown in Figure 5, while subscripts
1, 2, 3, and 4 denote the four thermocouple positions on the top,
sides, and lower surface of each heater tube, respectively.
To ensure the accuracy of the measured data, each measuring device was calibrated prior to use. Following calibration, the
accuracies of the temperature sensors (RTD and TC), power meter, and flow meter were found to be ±0.2◦ C, ±0.1%, and ±0.1
kg/ms, respectively. Based upon these calibration results, and
applying the propagation-of-error method presented in [15], the

experimental uncertainty in the average shell-side heat transfer
coefficient was found to be of the order of ±6%.

2.5x104

h(W/m2-k)

Tw =

3.0x10

17

o

: 28 C

2.0x104

1.5x104

1.0x10

4

m=0.12 kg/ms

5.0x103

2.0x104

RESULTS AND DISCUSSION

4.0x10

4

6.0x104

8.0x10

4

1.0x105

1.2x10

5

q"(W/m )
2

Figure 6 illustrates the variation of the overall heat transfer
coefficient (HTC) of the tube bundle with the surface heat flux
as a function of the saturation temperature (i.e., 20◦ C, 24◦ C,
˙ = 0.06
and 28◦ C) and a constant spray film flow rate of m
kg/ms. The pool boiling data obtained by immersing all four
heater tubes in the refrigerant and specifying a saturation temperature of 20◦ C are also plotted for comparison purposes. The
results confirm that the proposed interior spray cooling method

achieves a better heat transfer performance than the pool boiling
mode at a saturation temperature of 20◦ C. It is also observed
that for a constant value of the wall heat flux, the HTC decreases
with an increasing saturation temperature. From inspection, the
3.0x10

4

o

: Spray at 20 C
o

: Spray at 24 C
2.5x104

o

: Spray at 28 C
o

: Pool booling at 20 C

h(W/m2-k)

2.0x104

1.5x104

1.0x10

4

5.0x103

0.0x10

0

2.0x104

4.0x10

4

6.0x104

8.0x10

4

1.0x105

1.2x10

5

q"(W/m )
2

Figure 6 Variation of heat transfer performance with surface heat flux as a
˙ = 0.06
function of saturation temperature for constant spray film flow rate of m
kg/ms. Note that pool boiling data are also presented for comparison purposes.

heat transfer engineering

Figure 7 Variation of heat transfer performance with surface heat flux as a
˙ = 0.12
function of saturation temperature for constant spray film flow rate of m
kg/ms.

HTC obtained at a saturation temperature of 20◦ C is 15% higher
than that obtained at 24◦ C, which is in turn 28% higher than that
obtained at 28◦ C. The higher value of the HTC at a lower saturation temperature suggests that the liquid distribution on the
heated surface improves (i.e., the size of the dry region reduces)
as the saturation temperature reduces and therefore results in a
better heat transfer performance.
Figure 7 illustrates the variation of the mean shell-side HTC
with the wall heat flux for the same saturation temperatures
as those considered in Figure 6, but a higher spray film flow
˙ = 0.12 kg/ms. As in Figure 6, it is observed that
rate of m
the mean shell-side HTC reduces with an increasing saturation
temperature. However, comparing the two figures, it is evident
that for a given saturation temperature and wall heat flux, the
shell-side HTC increases with an increasing spray film flow rate.
This result can be attributed to the fact that a greater film flow rate
increases the force with which the droplets impact the liquid film
on the heated surface and therefore prevents the liquid film from

developing a thermal insulation layer. In addition, the greater
film flow rate improves the distribution of the liquid film on the
heater tubes, and therefore reduces the size of the dry regions.
Figure 8 illustrates the effect of the spray film flow rate on
the mean shell-side HTC for a constant saturation temperature
of 20◦ C. It is observed that for all values of the surface heat
flux, the HTC reduces with a reducing film flow rate. From
inspection, it is found that for low values of the heat flux (i.e.,
q = 2×104 W/m2 ), the HTC obtained at a spray film flow rate
of 0.12 kg/ms is 12% higher than that obtained at a film flow rate
of 0.09 kg/ms, which in turn is 29% higher than that obtained
at a film flow rate of 0.06 kg/ms. However, for higher values of
the heat flux, i.e., q > 105 W/m2, the HTC obtained for a spray
vol. 32 no. 1 2011


18

T.-B. CHANG ET AL.
3.0x10

4

3.0x10

: 0.12 kg/ms
: 0.09 kg/ms
: 0.06 kg/ms

2.0x104

1.5x104

1.0x10

4

2.0x104

1.5x104

1.0x10

Tsat=20 oC

5.0x103

2.0x104

4.0x10

4

: 0.12 kg/ms
: 0.09 kg/ms
: 0.06 kg/ms

2.5x104

h(W/m2-k)

h(W/m2-k)

2.5x104

4

6.0x104

8.0x10

4

1.0x105

1.2x10

4

Tsat=28 oC

5.0x103

2.0x104

5

q"(W/m2)
Figure 8 Variation of heat transfer performance with surface heat flux as a
function of spray film flow rate for constant saturation temperature of Tsat =

20◦ C.

4.0x10

4

6.0x104

8.0x10

4

1.0x10 5

1.2x10

5

q"(W/m )
2

Figure 9 Variation of heat transfer performance with surface heat flux as a
function of spray film flow rate for constant saturation temperature of Tsat =
28◦ C.

CONCLUSIONS
film flow rate of 0.12 kg/ms is 35% higher than that obtained at
a film flow rate of 0.09 kg/ms, which in turn is 48% higher than
that obtained at 0.06 kg/ms. In other words, the efficacy of a
higher film flow rate in enhancing the heat transfer performance

increases with an increasing surface heat flux. Ribatski and
Thome [16] conducted an experimental investigation into the
onset of the local dry-out phenomenon in evaporating falling
films on horizontal plain tubes, and showed that the onset of
dry-out was determined principally by the heat flux and the film
flow rate. They also reported that for a constant heat flux, an
increasing film flow rate was found to induce an increase in the
heat transfer coefficient.
Figure 9 shows the effect of the spray film flow rate on
the mean shell-side HTC for a constant saturation temperature
of 28◦ C. As in Figure 8, it can be seen that the efficacy of
a higher spray film flow rate in enhancing the heat transfer
performance increases with an increasing surface heat flux. For
low values of the heat flux (i.e., q = 2 × 104 W/m2 ), the HTC
obtained at a spray film flow rate of 0.12 kg/ms is 4% higher
than that obtained at 0.09 kg/ms, while that obtained at 0.09
kg/ms is 16% higher than that obtained at 0.06 kg/ms. However,
for higher surface heat fluxes, i.e., q > 105 W/m2, the HTC
obtained at a spray film flow rate of 0.12 kg/ms is 28% higher
than that obtained at 0.09 kg/ms, which in turn is 41% higher
than that obtained at 0.06 kg/ms. Significantly, these percentage
improvements are smaller than those observed in Figure 8 for
the lower saturation temperature of 20◦ C. Thus, it is inferred
that a better liquid distribution is attained at a lower saturation
temperature.
heat transfer engineering

This study has presented an interior spray method for enhancing the heat transfer performance of a compact square-pitch
shell-and-tube spray evaporator. In the proposed approach, each
heater tube is sprayed simultaneously by four separate nozzles

in order to prevent the dry-out phenomenon. The experimental results have shown that the mean shell-side heat transfer
coefficient (HTC) obtained using the proposed technique is significantly higher than that obtained in a conventional flooded
type evaporator over a wide range of surface heat fluxes and
refrigerant film flow rates. In addition, it has been shown that
a better liquid distribution on the tube surface reduces the dry
regions at lower saturation temperature then the shell-side HTC
is correspondingly improved. In addition, it has been suggested
that a better liquid distribution is achieved on the tube surface at
lower saturation temperatures, which reduces the size of the dry
region and therefore prompts a corresponding improvement in
the shell-side HTC. Moreover, the results have shown that the efficacy of a higher spray film flow rate in enhancing the heat transfer performance increases with an increasing surface heat flux.
NOMENCLATURE
h
HTC
•
m
q
T
Tsat
Tw

heat transfer coefficient (W/m2-K)
heat transfer coefficient
spray film flow rate (kg/ms)
wall heat flux (W/m2)
temperature (◦ C)
saturation temperature (◦ C)
average wall temperature (◦ C)

vol. 32 no. 1 2011

T.-B. CHANG ET AL.

REFERENCES
[1] Hodgson, J. W., and Sutherland, J. E., Heat Transfer from a
Spray Cooled Isothermal Cylinder, Industrial & Engineering Chemistry, Fundamentals, vol. 7, pp. 567–571, 1968.
[2] Choi, K. J., and Yao, S. C., Mechanisms of Film Boiling Heat Transfer of Normally Impacting Spray, International Journal of Heat and Mass Transfer, vol. 30, no. 2,
pp. 311–318, 1987.
[3] Pais, M. R., Chow, L. C., and Mahefkey, E. T., Surface
Roughness and Its Effects on Heat Transfer Mechanism in
Spray Cooling, ASME Journal of Heat Transfer, vol. 114,
pp. 211–219, 1992.
[4] Moeykens, S. A., and Pate, M. B., Spray Evaporation Heat
Transfer of R-134a on Plain Tubes, ASHRAE Transactions,
vol. 100, pp. 173–184, 1994.
[5] Moeykens, S. A., Newton, B. J., and Pate, M. B., Effects of
Surface Enhancement, Film-Feed Supply Rate, and Bundle Geometry on Spray Evaporation Heat Transfer Performance, ASHRAE Transactions, vol. 101, pp. 408–419,
1995.
[6] Moeykens, S. A., and Pate, M. B., The Effects of Nozzle
Height and Orifice Size on Spray Evaporation Heat Transfer Performance for a Low-Finned, Triangular-Pitch Tube
Bundle with R-134a, ASHRAE Transactions, vol. 101,
pp. 420–433, 1995.
[7] Chyu, M. C., Zeng, X., and Ayub, Z. H., Nozzle-Sprayed
Flow Rate Distribution on a Horizontal Tube Bundle,
ASHRAE Transactions, vol. 101, pp. 443–453, 1995.
[8] Zeng, X., Chyu, M. C., and Ayub, Z. H., Performance
of Nozzle-Sprayed Ammonia Evaporator With SquarePitch Plain-Tube Bundle, ASHRAE Transactions, vol. 103,
pp. 68–81, 1997.
[9] Zeng, X., Chyu, M. C., and Ayub, Experimental on Ammonia Spray Evaporator With Triangular-Pitch Plain-Tube

Bundle, Part 1: Tube Bundle Effect, International Journal
of Heat and Mass Transfer, vol. 44, pp. 2229–2310, 2001.
[10] Ribatski, G., and Jacobi, A. M., Falling-Film Evaporation
on Horizontal Tubes—A Critical Review, International
Journal of Refrigeration, vol. 28, no. 5, pp. 635–653, 2005.
[11] Chang, T. B., and Chiou, J. S., Spray Evaporation Heat
Transfer of R-141b on a Horizontal Tube Bundles, International Journal of Heat and Mass Transfer, vol. 42,
pp. 1467–1478, 1999.

heat transfer engineering

19

[12] Chang, T. B., and Chiou, J. S., Heat Transfer Enhancement
in a Spray Evaporator, Journal of Enhanced Heat Transfer,
vol. 12, no. 1, pp. 85–100, 2005.
[13] Chang, T. B., Effects of Nozzle Configurations on a Shelland-Tube Spray Evaporator With Liquid Catcher, Applied
Thermal Engineering, vol. 26, no. 8, pp. 814–823, 2006.
[14] Chang, T. B., Lu, C. C., and Li, J. C., Enhancing the Heat
Transfer Performance of Triangular-Pitch Shell-and-Tube
Evaporators Using an Interior Spray Technique, Applied
Thermal Engineering, vol. 29, pp. 2527–2533, 2009.
[15] Holman, J. P., Experimental Methods for Engineers, 6th
ed., McGraw-Hill, New York, pp. 49–56, 1994.
[16] Ribatski, G., and Thome, J. R., Experimental Study on the
Onset of Local Dryout in an Evaporating Falling Film on
Horizontal Plain Tube, Experimental Thermal and Fluid
Science, vol. 31, issue 6, May 2007.
Tong-Bou Chang is a professor in the Department
of Mechanical Engineering, Southern Taiwan University, Tainan, Taiwan. He received his Ph.D. degree at National Cheng Kung University, Taiwan,

in 1997. His research interests include heat transfer
with phase change, energy-system optimization, heat
and mass transfer in porous medium, enhancement of
heat transfer, and high-performance heat exchangers.
He has co-authored more than 40 papers in archival
journals and conference proceedings.He is currently
working on two-phase heat transfer using nanofluids.

Jun-Cheng Li was a graduate student in the Department of Mechanical Engineering, Southern Taiwan
University, Taiwan. His research interests include
spray heat transfer, enhancement of heat transfer, and
high-performance heat exchangers. He is currently
working at a heat transfer company as an engineer.

Chih-Chang Liang was a graduate student in the
Department of Mechanical Engineering, Southern
Taiwan University, Taiwan. His research interests include spray heat transfer, enhancement of heat transfer, and high-performance heat exchangers. He is currently working at the Ministry of National Defense
as an engineer.

vol. 32 no. 1 2011


Heat Transfer Engineering, 32(1):20–32, 2011
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457631003732821

Transient Turbulent Flow and Heat
Transfer Phenomena in Plate-Fin
Type Cross-Flow Heat Exchanger

ISAK KOTCIOGLU,1 AHMET CANSIZ,2 SINAN CALISKAN,3 and SENOL
BASKAYA4
1

Department of Mechanical Engineering, University of Atat¨urk, Erzurum, Turkey
Department of Electrical-Electronics Engineering, University of Atat¨urk Erzurum, Turkey
3
Department of Mechanical Engineering, University of Hitit, Corum, Turkey
4
Department of Mechanical Engineering, Gazi University, Ankara, Turkey
2

In this article, a transient performance of a plate-fin cross-flow heat exchanger with convergent–divergent longitudinal vortex
generators is investigated. The effect of flow geometry is taken into account to analyze the transient forced convection heat
transfer in a designed heat exchanger. The time-dependent Nusselt number and dissipation energy criterion are experimentally
measured in 4- and 8-kW heater powers for various Reynolds numbers between 42,000 and 60,000 for the hot and cold fluids.
In order to present the quality of the heat exchanger, the general empirical equations of the time-dependent Nusselt number
and friction factor were derived as a function of the Reynolds number corresponding to fin geometry parameters. Following
this, the transient behavior of the heat exchanger according to the change in the inlet and outlet temperatures of the hot and
cold fluids was analyzed. The results showed that the variations of the time-dependent dissipation energy criterion increase
with the increase in the Reynolds number. The appropriate correlations are proposed to predict the heat transfer and friction
characteristics of the transient performance for the presented configuration, which indicates the designed heat exchanger
has good heat conduction.

INTRODUCTION

The cross-flow heat exchanger with convergent–divergent
longitudinal vortex generators (CDLVG) can serve as an effective tool to augment forced convection heat transfer. The
formations of the vortices in these heat exchangers, which are
produced by the winglet elements, have a definite effect on the

local average velocity and temperature field of the fluid. The flow
between the winglets, which have longitudinal velocity components, is important in the heat transfer characteristics, secondary
flow, and boundary-layer distribution of the heat exchangers.
The winglets strongly disturb the boundary-layer structure due
to the influences of the interacting CDLVGs, which are located
at different intervals in the cross-flow channels. In designing
such heat exchangers, it is necessary to analyze the interactions
between the local heat transfer and flow distribution within the
plate fins in cross-flow heat exchangers.
There are number of studies in the literature that improved
the heat exchanger design from various perspectives. The energy dissipation criterion (ie ) was proposed by Sano and Usui
[1] on the basis of correlating the heat transfer coefficient (h).
As an approximate method for the finned-tube cross-flow heat

Unsteady thermal processes are very important in modern
power and dynamic systems, heat exchangers and other engineering applications. Heat exchangers are generally designed to
meet certain performance requirements under steady operating
conditions. There are several heat exchanger types for different
applications, according to their size, weight, shape, and flow
pattern. Based on the flow pattern, one of the important types is
the plate-fin compact heat exchanger. During recent years, the
transient behavior of plate-fin compact heat exchangers with
changes in the inlet temperature or flow rate of fluids has been
widely employed in engineering applications, especially in the
automotive industry, power plants, chemical processes and cryogenics, aerospace industries, combustion, air conditioning and
refrigerant apparatus, and air/gas heating and cooling systems.
This study was supported by Atat¨urk University project BAP-1997/37.
Address correspondence to Dr. Isak Kotcioglu, Department of Mechanical
Engineering, Faculty of Engineering, University of Atat¨urk 25240, Erzurum,
Turkey. E-mail:

20


I. KOTCIOGLU ET AL.

exchangers, Ataer [2] showed the effect of the transient behavior
of the heat exchangers on overall performance. The approaches
and various techniques are developed for the prediction of transient behavior of cross-flow finned-type heat exchangers. These
techniques provide the applicability for other heat exchanger
types. For an extensive review of the transient response of heat
exchangers, Shah et al. [3] presented a transient response analysis including problem formulation related to the inlet temperatures and flow rates. Spiga and Spiga [4] presented the analytical
solutions for the transient temperature distributions of the core
wall and unmixed gases with arbitrary initial and inlet by using
the threefold Laplace transform for cross-flow heat exchangers.
The heat and mass transfer characteristics of heat exchangers
during frost formation process were analyzed numerically by
Seker et al. [5]. The design and thermal selection of heat exchangers have been extensively studied by Kakac and Liu [6].
Dynamic response of the discharge air temperature to changes
in the hot water flow rates has been studied for a commercial
finned serpentine tube water-to-air heat exchanger by Pearson
et al. [7]. Roetzel and Xuan [8] analyzed the dynamic behavior
of cross-flow heat exchangers extensively for different arrangements such as the various combinations of temperature and flow
transients. The transient temperature response of cross-flow heat
exchangers having finite wall capacitance with fluids unmixed
was investigated numerically by Mishra et al. [9]. They have
examined the heat exchanger according to flow rate of hot and
cold fluids. Tandiroglu and Ayhan [10] investigated the effect
of the flow geometry parameters on the transient forced convection heat transfer for turbulent flow in a circular tube with baffle
inserts. Numerical analysis on the flow field and heat transfer

by interaction between a pair of vortices in rectangular channel
flow was reported by Yang et al. [11]. The fundamental studies
of unsteady convective heat transfer processes in many industrial applications and related calculations have been presented
by Kakac and Yener [12]. The flow and heat structures in a platefin heat exchanger were improved by Sohankar [13]. Numerical
and experimental analyses were carried out by Leu et al. [14] to
study the heat transfer and flow in the plate fin and tube heat exchangers with inclined block shape vortex generators mounted
behind the tubes. Biswas et al. [15] studied the flow structure
of an air stream over winglet pair-type vortex generators. They
found that the winglet pair produced a main vortex, a corner
vortex, and an induced vortex, based on the flow structure in
regions between the winglets. Ferrouillat et al. [16] have investigated the potential of using delta and rectangular winglet
pairs as a mixer as well as a chemical reactor. The relationships
between the effectiveness and number of transfer units of the
cross-flow heat exchanger were determined by Kotcioglu et al.
[17]. In another study by Kotcioglu and Caliskan [18], the relationships between the effectiveness and the number of transfer
units of the cross-flow heat exchanger were investigated.
In this study, the unsteady convective heat transfer properties
of a compact heat exchanger with CDLVGs for the case of timedependent temperature changes were presented. The effects of
the CDLVGs for various flow velocities on the cross-flow heat
heat transfer engineering

21

exchanger were investigated experimentally. The correlations
for the heat transfer coefficients and pressure drop ( P) characteristics were obtained as functions of the Reynolds (Re) number
and Prandtl (Pr) number.
The arrangement of winglets can create an original geometry
for a diffuser–nozzle couple that promotes the turbulence levels.
As a consequence, suitable correlations are also proposed to
predict the heat transfer and friction characteristics, which is

a new type designed for the cross-flow heat exchangers. The
configuration of the designed heat exchanger core was formed
and tested for different hot flow inlet conditions.
Further in this study, the dissipation energy criterion, the
time-dependent Nusselt number, pressure drop, and transient
forced convection in the designed heat exchanger were evaluated. The transient performance of the system related to the
effect of flow geometry on transient forced convection heat
transfer for turbulent flow in a cross-flow heat exchanger with
CDLVG was determined.

EXPERIMENTAL APPARATUS AND PROCEDURE
A schematic diagram of the experimental apparatus for the
designed heat exchanger is shown in Figure 1. The apparatus
basically includes a cross-flow compact heat exchanger core, hydrodynamic entrance section, heating section, cold air channel
inlet and outlet, hot air channel inlet and outlet, hot and cold air
blower, air filters, clacks, orifice meters, pressure measurement

Figure 1 Experimental setup: 1 and 2 are hot and cold air blower, 3 and 4
are clacks, 5 and 6 are orifice meters, 7, 8, 15, and 16 are U-manometers, 9 is
the heat exchanger core, 10 and 11 are cold air channel inlet and outlet, 12 and
13 are hot air channel inlet and outlet, 14 is the heating section, 17 is the data
acquisition card, 18 is the computer, and 19–26 are thermocouples.

vol. 32 no. 1 2011


22

I. KOTCIOGLU ET AL.

Figure 2 Geometric features of the matrix with placement of fins: (a) whole
heat exchanger; (b) one of the finned plates.

units, and thermocouples. The experiments are conducted
mainly in the test section of the apparatus, which is manufactured from stainless-steel plates (1.5 mm thick). As shown
in Figure 2, a and b, the heat exchanger is in a cube shape and
its dimensions of the duct are La = 0.2 m (length), Lb = 0.2 m
(height), and Lc = 0.2 m (width). In order to inhibit the heat
loss and obtain a uniform heat flux, the outer surface of the test
section is insulated with a layer of glass wool. In order to obtain
a linear velocity distribution in the channels, wire sieves are
placed between the test section and the outlet of the heaters. For
the flow and heat transfer tests, the surface temperatures, inlet
and outlet temperatures, and the pressure drop across the test
section were measured.
The vortex generator system is configured schematically in
Figure 2b [18]. The apparatus under investigation is based on
the transient analysis and not suitable for fluid visualization.
Thus we only relied on the correlations regarding the system.
This kind of vortex generator system was also discussed previously in various articles, where exact visualization was provided
[19–21].
The form of winglet permutation is shown on the plate of
cross-flow heat exchanger in Figure 2b. For this particular design
of the heat exchanger, the angle of winglet in the flow direction
(inclination angle) for the hot fluid is βh = 30◦ and for the cold
fluid is βc = 60◦ . The trailing edges of the winglets are located
at a distance of x = 0.005 m from the inlet.
As the CDLVGs act as plates in the flowing fluid, each new
edge starts a new boundary layer (which is very thin), and thus
the high heat transfer coefficients can be obtained. While the hot

flow is passing from one direction of the channels, the cold flow
is passing from the other direction. The flow rate of the hot air
flow was controlled by adjusting the clack valve and measured
by pressure probes with an accuracy of ±0.3% of full scale. Experimental results were obtained for different mass flow rates
and different heater powers. In order to measure the pressure
losses the pressure taps are mounted across the orifice plates
located at the inlet and outlet ends of the test section. Similarly,
the measurements of the cold air flow rates were performed via
flow meters with an accuracy of ±0.22% of full scale. In order
to determine the effectiveness of the heat exchanger, the temperatures (T) of the fluid in the test section were measured by
heat transfer engineering

mounting the thermocouples at different locations on the surface
of the test section. Similarly, the velocity of fluid (u) in the test
section was measured continuously with the pressure taps. Temperatures were measured with 0.25-mm-diameter Teflon coated
T-type copper-constantan thermocouples. This procedure provides the measurements being taken at four locations in the same
cross-section. The accuracy of the thermocouples is ±0.15%.
All of the thermocouples and pressure sensors are fully calibrated with a dry-box temperature calibrator with 0.01◦ C precision. The flow properties of the heat exchanger were determined
at average bulk temperature. The effect of thermal radiation for
internal flow is ignored during the experiments due to low temperature differences between the wall and fins. All of the measurements were collected and processed by a personal computer
through the data acquisition card and software.
The experimental apparatus was operated in the blow-out
mode. In order to investigate the heat transfer behavior of the
system under transient conditions the experiments were performed for forced convection turbulent flow in the cross-flow
heat exchanger with winglets under various mass flow rates and
different heater powers. In each run, the hot flow rate and temperatures in the channel inlet and exit were measured. We analyzed
the cross-flow heat exchanger by considering the variation of
the thermal properties of hot flow and cold flow with temperature for heat transfer. The hot and cold flow outlet temperatures,
which vary with time, were measured until a steady-state condition was reached. The pressure drops corresponding to the heat
transfer enhancement due to the winglet-type CDLVGs arrangements in the square channels were obtained by performing the

measurements. Experimental measurements of both heat transfer and pressure drop in the cross-flow heat exchanger for a
transient heat transfer were presented by evaluating the friction
factor (f ).

DATA REDUCTION
In order to obtain accurate results, the data collection during
the experiments was carefully monitored. The detailed geometrical configuration of the cross-flow heat exchanger is given in
Figure 2b, whereas the properties and the characteristics of this
setup is tabulated in Table 1. Considering Figure 2b, the total
number of channels (N) of the plate-fin heat exchanger with
winglet-type CDLVGs is given by
N=

L − bc + 2tw
bc + bh + 2tw

(1)

where bh and bc are the winglet-type fin height for each channel
of hot and cold fluids (bh = bc = 0.01 m), respectively, L is the
channel dimension (L = La = Lc = Lb = 0.2 m), and tw is the
plate and fin thickness. According to the definition given in Eq.
(1) the number of channels is calculated as 9 for each of the
hot and cold fluid flows separately, which indicates a total of 18
channels. The frontal areas both in the hot (Afr,h = L a L b ) and
cold (Afr,c = L c L b ) fluid sides in the heat exchanger are given as
vol. 32 no. 1 2011


I. KOTCIOGLU ET AL.

Table 1 Geometrical characteristics of the heat exchanger
Channel dimensions
Total number of channels
Length of each winglet (Figure
2b)
Height of each winglet and
channels
Number of rectangular winglets
Distance interval of winglets
(Figure 2b)
Span of winglet (Figure 2b)
Thickness of plate-fin winglets
(Figure 2b)
The angle of winglet in the flow
direction of hot fluid
The angle of winglet in the flow
direction of cold fluid
Fin efficiency

La × Lb × Lc 0.20 × 0.20 × 0.20 m
N
18
l
0.010 m
bh = bc

0.010 m

Nw
g

64
0.010 m

e
tw

c+g
0.0015 m

βh

30◦

βc

60◦

ηf

0.74

0.04 m2. Similarly, the heat transfer volumes between the plates
on the hot fluid and cold fluid sides are given as Vp,h = N L a L b bh
and Vp,c = N L c L b bc , respectively. These relations give the heat
transfer volume as 0.0034 m3 for both of the fluid sides. The
heat transfer areas for hot and cold fluids are given as Ah =
βcomp Vp,h and Ac = βcomp Vp,c , respectively, where βcomp is the
compact rate. By taking the compact rate as βcomp = 302 m2/m3,
these relations give Ah = Ac = 1.0268 m2. The minimum freeflow areas for hot and cold fluids calculated from the definition

of the hydraulic diameter are given as Ao,h = Dh Ah /(4L b )
and Ao,c = Dc Ac /(4L c ). The channel hydraulic diameter is
given as Dc = Dh = 4bh L 2(bh + L), which has the same
value of 0.0163 m for the hot and the cold air sides. By using
this hydraulic diameter value, the minimum free flow areas is
obtained as Ao,h = Ao,c = 0.021 m2. Note that these calculations
are performed by considering the plate and fin thickness (tw ).
In order to determine the time-dependent fluid dissipation
energy criterion (ie ), the experimental investigation of the transient turbulent flow in a cross-flow heat exchanger based on
the geometric properties is required. The heat transfer coefficients (h) can be compared and correlated with the dissipation
energy criterion and the unit mass of the fluid. At the different
turbulence levels, the contribution due to mean velocity to the
dissipation energy criterion is very small. This is due to the fact
that the majority of the contribution is due to the fluctuating velocity components relating to different length scales structures.
The energy dissipation rate per unit mass of the fluid (ε), on
the other hand, is a time-averaged quantity and it is from the
fluctuations only.
In this study, in order to investigate the time-dependent Nusselt number (Nu) and the dissipation energy criterion for a crossflow heat exchanger, the calculation methodology is developed
in terms of the fundamental correlations taken from the literature [1]. In this heat exchanger, the investigation is also related
to the changes in the outlet temperatures for various mass flow
rates and different heater powers. The heat transfer coefficients
are correlated by means of energy dissipation rate per unit mass
heat transfer engineering

23

of fluid in a heat exchanger. Then, a simple dissipation energy
criterion is used to compare heat transfer coefficients at a constant value of ε. Using Fanning’s friction factor, the value of ε
in fully developed turbulent flow is expressed by [10]
ε=

2 f u3
( P)u
=
ρL
L

(2a)

where L is the channel length, u is the average velocity of the
fluid in the channel, ρ is the density of the fluid. For convenience
the pressure drop ( P) and the friction factor is related as P
= 2f ρu2. Eq. (2a), which is related to the Reynolds number, can
be written in dimensionless form as
εL 4
= 2 f (Re)3
v3

(2b)

where ν is the kinematic viscosity of the fluid and the term in
the left-hand side of Eq. (2b) is dimensionless and represents
the flow conditions by means of energy dissipation criterion,
which in turn corresponds to the Reynolds number. Similarly,
the term (v 3 /ε)1/4 in Eq. (2b) is defined as Kolmogorov length
scale (η).
The friction factor and heat transfer coefficient for augmentation technique are represented by f a and ha , respectively. In
addition, for a smooth channel the friction factor and heat transfer coefficient are represented by f s and hs , respectively. For
the same Reynolds number in the plate-fin cross-flow heat exchanger with winglet-type CDLVGs, the ratios of the friction
factors ( f ) and heat transfer coefficients ( h ) can be expressed

as follows, respectively:
f

fa
εa
=
fs
εs

(3)

ha
Nua
=
hs
Nus

(4)

=

and
h

=

The energy dissipation rates per unit mass for the augmentation technique (εa ) and smooth channel (εs ) are calculated for
the Reynolds number. As a criterion of the heat transfer augmentation, the ratio of the heat transfer coefficients with and
without a heat transfer promoter at the same value of ε in constant pumping power is considered. The heat transfer coefficient
of a smooth channel at εa is given for turbulent flow by [10]

ht = hs

0.27
f

(5)

where ht and hs are the heat transfer coefficients for turbulent
flow and for a smooth channel, respectively. The time-dependent
dissipation energy criterion (ie ) from Eqs. (3) and (4) by using
the corresponding terms of f εs and h h s for turbulent flow,
respectively, is given as
ie =
vol. 32 no. 1 2011

f
0.27
h

(6)


24

I. KOTCIOGLU ET AL.

Using the ratio of the dissipation energy criterion together
with friction factor and the Reynolds number, the Nusselt number correlation equation of heat transfer with arbitrary shape of
the cross-flow heat exchanger may be explained from Eq. (2a)
for transient turbulent flow as

Nua = 0.22i e [2 f (Re)3 ]0.27 (Pr)0.4

where T w is the surface temperature of the heat exchanger core,
T m is the average bulk temperature, and A is the total heat transfer surface area. For all calculations, the values of the thermophysical properties of the hot and cold air are obtained at the
average bulk mean temperature, which is Tm = (Tin + Tout )/2,
where T in corresponds to inlet and T out corresponds to outlet temperatures. The Nusselt number for the test section in
cross-flow heat exchanger with winglet-type CDLVGs by heat
convection can be expressed in terms of heat transfer coefficient
(h), the hydraulic diameter (Dh ), and thermal conductivity (k)
as
h Dh
(12)
Nu =
k
The Nusselt number based on the projected area will reflect
the effect of the variation in the surface area as well as that
of the disturbances in the flow due to fins on the heat transfer.
However, the Nusselt number based on the total area will reflect
only the effect of the flow disturbances. The total area is equal
to the sum of the projected area and surface area contribution
from the pin fin.
The friction factors (f ) in terms of the winglet inclination
angle (β) variation of the correlation is given as [17]

(7)

The Prandtl number in the preceding equation is given as
Pr = Cp µ k, where Cp is the specific heat, µ is the dynamic
viscosity, and k is thermal conductivity of the fluid. The Prandtl
number is an important parameter affecting the heat transfer of

plate fins inserted on plates in the channel. Since air is used as
working fluid, its Prandtl number in the considered temperature
range remains almost constant. Note that the time-dependent
variables are Re and Pr numbers throughout the derivation. The
density and the viscosity of the fluid change with temperature
and the pressure for these nondimensional numbers.
Experimental measurements of both heat transfer and pressure drop in the cross-flow heat exchanger for a transient flow
condition are presented to describe the effects of the flow conditions and geometry parameters. Thus, the friction factor is given
as
1 dP
Dh
(8)
f =−
0.5u 2 ρ d x

f = C0 (Re)−m (tan β)n

where C0 is the friction coefficient for the square channel configuration. The empirical correlations of the convergent–divergent
longitudinal vortex generators and the proposed time-dependent
friction factor correlation model are obtained from Eq. (13). The
values of the correlation coefficients C0 , m and n belonging to
the friction factor are presented in Table 2. As the winglet inclination angle is increased, the strength of the longitudinal vortex
is intensified.
In a previous study [17], the time averaged Nusselt number
for a square channel with winglet type CDLVG was expressed
as

where d P/d x is the pressure gradient and Dh is the hydraulic
diameter of the channel. In cross-flow compact heat exchangers the heat transfer results are correlated in terms of the
Reynolds number, flow conditions, and geometry parameters.

The Reynolds number is defined in terms of the mass velocity
(G), the hydraulic diameter, and the dynamic viscosity as
Re =

G Dh
µ

(9)

As shown schematically in Figure 2a, both surfaces have
a rectangular fin cross-section in the flow direction with
convergent–divergent longitudinal vortex generators. Based on
˙ of the air flow in channel the mass velocity
the mass flow rate (m)
is given as
G=

m˙
Af

Nu = a(Re)b (Pr)c (L a /bh )d (w/g)e (tan β)f

(10)

Q conv
A (Tw − Tm )

(11)

Table 2 Parameters of the empirical relationships of the friction factor given in Eq. (13)

Cases
8 kW hot air
4 kW hot air
8 kW cold air
4 kW cold air

(14)

where Pr = 0.71, (La /bh ) is the test section geometry ratio, (w/g)
is the plate length of winglet to distance interval of winglets
ratio, and a, b, c, d, e, and f are the correlation coefficients. The
proposed time-dependent Nusselt number correlation model in
the range of 35,000 < Re < 60,000 in a CDLVG given in this
study is obtained from Eq. (14).
Empirical correlations are obtained for the time averaged
Nusselt number as a function of steady-state condition Nusselt
number and Reynolds number for all of the flow conditions. The

where Af is the flow area for the hot and cold air channels. The
heat transfer coefficient (h) is calculated from the convective
heat transfer rate (Qconv ) as
h=

(13)

C0

m

n

R2

χ2

RMSE

0.216
0.194
0.241
0.367

0.130
0.110
0.150
0.227

1.644
1.827
1.392
1.171

0.992
0.985
0.951
0.999

4.10e − 3
3.02e − 5
4.72e − 4

2.63e − 6

1.212
2.023
2.678
1.040

heat transfer engineering

vol. 32 no. 1 2011