Heat transfer engineering an international journal, tập 31, số 1, 2010 1 2

Heat Transfer Engineering, 31(1):1–2, 2010
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903263176

editorial

The New 3rd Edition of the ALPEMA
Plate-Fin Heat Exchanger Standards
JOHN R. THOME
Laboratory of Heat and Mass Transfer, Ecole Polytechnique F´ed´erale de Lausanne, Lausanne, Switzerland

As the Chairman of ALPEMA (Aluminum Plate-Fin Heat
Exchanger Manufacturers’ Association) since May 2008, I wish
to announce the new third edition of the ALPEMA Standards
for the construction of brazed aluminum plate-fin heat exchangers. The development of the new third edition of the
ALPEMA Standards has involved a significant effort by the
former chairman of ALPEMA, David Butterworth, the current secretariat (Simon Pugh of IHS, London), and the five
ALPEMA member companies [Chart Energy and Chemicals
Inc. (USA), Fives Cryo (France), Kobe Steel, Ltd. (Japan),
Linde AG (Germany), and Sumitomo Precision Products Co.,
Ltd. (Japan)]. I wish to acknowledge their many contributions to
help me update and extend this industrial standard for the safe
construction and operation of brazed aluminum plate-fin heat
exchangers.
In brief, brazed aluminum plate-fin exchangers are the most
effective and energy-efficient heat exchangers for handling a
wide range of services, noted particularly for their compactness
and low weight. This class of heat exchangers nearly always provides the lowest capital, installation, and operating cost whenever the application is within the operating range of these units,
in particular over a wide range of cryogenic and non-cryogenic

applications. Where it is feasible to use a brazed aluminum platefin heat exchanger, it is usually the most cost-effective solution,
often by a significant margin. These units enjoy a very large
heat transfer surface area per unit volume of heat exchanger.
They provide a total surface area of 1000 to 1500 m2 /m3 of vol-

ume; this compares very well with the approximate range of 40
to 70 m2 /m3 for shell-and-tube units. Plate-fin heat exchangers
with surface area per unit volume of 2000 m2 /m3 are sometimes
employed in the process industry!
Plate-fin heat exchangers find applications in aircraft, automobiles, rail transport, offshore platforms, etc. However, the
main applications are in the industrial gas processing, natural
gas processing, LNG (liquefied natural gas) facilities, refining
of petrochemicals, and refrigeration services. Their ability to
carry multiple streams, occasionally up to 12 or more (as opposed to typically only two streams in a shell-and-tube heat
exchanger), allows process integration all in one unit. The very
large surface area per unit volume is particularly advantageous
when operating at low temperature differences between the
hot and cold streams. Such applications are typically found in
cryogenic systems and hydrocarbon dewpoint control systems
where temperature difference is linked to compressor power
consumption.
The first edition of the ALPEMA Standards was published
in 1994, and it was extremely successful and popular. The second edition was published in 2000. New industrial developments and applications, experience with using the ALPEMA
Standards, and feedback from users have indicated that the
time was right for a third edition. The new third edition is
expected to appear early in 2010. The most significant additions and amendments that have been made are summarized
here:

Address correspondence to Prof. John Thome, Laboratory of Heat and Mass
Transfer, EPFL-STI-IGM-LTCM, Mail 9, CH-1015 Lausanne, Switzerland.

E-mail:

1. A new Chapter 9 has been added to cover cold boxes and
block-in-shell heat exchangers.

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J. R. THORNE

2. Many figures have been redrawn to make them easier to
understand.
3. Photographs of the most common types of fin geometries
have been added.
4. Information has been provided on two-phase distributors
with diagrams.
5. Guidance on flange design and transition joints is
included.
6. Guidance on acceptable mercury levels is given.
7. Allowable nozzle loadings have been updated.
8. Many small changes have been made to improve
clarity.
The new third edition can be purchased and downloaded
from the following website: />standards/petrochemical-standards.ht

heat transfer engineering

John R. Thome has been professor of heat and mass

transfer at the Swiss Federal Institute of Technology in Lausanne (EPFL), Switzerland, since 1998,
where his primary interests of research are two-phase
flow and heat transfer, covering both macro-scale and
micro-scale heat transfer and enhanced heat transfer.
He directs the Laboratory of Heat and Mass Transfer
(LTCM) at the EPFL with a research staff of about
18–20 and is also director of the Doctoral School
in Energy. He received his Ph.D. at Oxford University, England, in 1978. He is the author of four books: Enhanced Boiling Heat
Transfer (1990), Convective Boiling and Condensation, third edition (1994),
Wolverine Engineering Databook III (2004), and Nucleate Boiling on MicroStructured Surfaces (2008). He received the ASME Heat Transfer Division’s
Best Paper Award in 1998 for a three-part paper on two-phase flow and flow
boiling heat transfer published in the Journal of Heat Transfer. He has received
the J&E Hall Gold Medal from the UK Institute of Refrigeration in February,
2008 for his extensive research contributions on refrigeration heat transfer. Since
2008, he has been chairman of ALPEMA (the plate-fin heat exchanger manufacturers association). He has published widely on the fundamental aspects of
micro-scale two-phase flow and heat transfer. He is an associate editor of Heat
Transfer Engineering.

vol. 31 no. 1 2010


Heat Transfer Engineering, 31(1):3–16, 2010
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903263200

Single-Phase Flow in Meso-Channel
Compact Heat Exchangers for Air
Conditioning Applications
AMIR JOKAR,1 STEVEN J. ECKELS,2 and MOHAMMAD H. HOSNI2

1
2

School of Engineering and Computer Science, Washington State University–Vancouver, Vancouver, Washington, USA
Mechanical and Nuclear Engineering Department, Kansas State University, Manhattan, Kansas, USA

Experimental study of the single-phase heat transfer and fluid flow in meso-channels, i.e., between micro-channels and minichannels, has received continued interest in recent years. The studies have resulted in empirical correlations for various
geometries ranging from simple circular pipes to complicated enhanced noncircular channels. However, it is still unclear
whether the correlations developed for conventional macro-channels are directly applicable for use in micro-/mini-channels,
i.e., hydraulic diameter less than 3 mm, with heat exchanger applications. A few researchers have agreed that similar results
may be obtained for the laminar flow regime regardless of the channel size, but no general agreement has been reached for
the transitional and turbulent flow regimes yet. In this study, different meso-channel air–liquid compact heat exchangers
were evaluated and the experimental results were compared with published empirical correlations. A modified Wilson plot
technique was applied to obtain the heat transfer coefficients, and the Fanning equation was used to calculate the pressure
drop friction factors. The uncertainty estimates for the measured and calculated parameters were also calculated. The results
of this study showed that the well-established heat transfer and pressure drop correlations for the macro-channels are not
directly applicable for use in the compact heat exchangers with meso-channels.

INTRODUCTION

adequately predict the single-phase heat transfer and pressure
drop in multiport circular and rectangular mini-channels with
hydraulic diameter ranging from 0.96 to 2.13 mm. However,
they mentioned their findings were in contrast to the results
and conclusions that Wang and Peng [4] obtained in a similar study. Steinke and Kandlikar [5, 6] recently made extensive
reviews of single-phase heat transfer and pressure drop in microchannels. They generated a database from the available literature and compared the results obtained by different researchers
in order to answer this fundamental question of whether the classical macro-scale theories can be applied to micro- and minichannels. Subsequently, they concluded these theories are in
good agreement with smaller channel size provided all the flow
factors, such as development of flow, efficiency of fins, and
experimental uncertainties, are accurately taken into consideration. We believe more applied research on micro- and minichannel heat transfer and fluid flow with different industry applications can further clarify the answers to this question, and may

result in a set of general correlations for each scale and regime.
The co-authors previously obtained heat transfer and pressure
drop for different type of air–liquid meso-channel compact heat
exchangers and published the results in conference proceedings

There have been many experimental studies conducted on
single-phase fluid flow within compact heat exchangers with
micro- and mini-channels, and new findings have been reported
for different applications. However, the researchers offer differing opinion on the role of channel size, as classified by Kandlikar
and Grande [1], in correlating heat transfer and pressure drop,
especially at the transitional and turbulent regimes. This issue
becomes more complicated when the heat exchanger channel
geometries are compact and enhanced, such as in automotive
compact heat exchangers, as described by Webb and Kim [2].
Some researchers reported the possibility of significant differences between the macro- and micro-scale theories and correlations, while others believe the differences are not significant
and that the same correlations can provide results that are generally in good agreement. For example, Webb and Zhang [3] found
the existing correlations for conventional macro-channels can
Address correspondence to Dr. Amir Jokar, School of Engineering and
Computer Science, Washington State University Vancouver, 14204 NE Salmon
Creek Ave, Vancouver, WA 98686, USA. E-mail:

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A. JOKAR ET AL.

[7–9]. The objective of this article is to review the previous
results and offer a conclusion on the single-phase flow in mesochannel compact heat exchangers of this sort.

The air–liquid heat exchangers under study were analyzed
on both air and water sides. A 50% glycol–water mixture was
pumped into the enhanced circular and noncircular channels of
these heat exchangers while, on the other side, air was pushed
through the fin passages with louvered surfaces. The goal was
to obtain semi-empirical heat transfer correlations for the flow
of the glycol–water mixture in the meso-channels and the flow
of air through the louvered fin surfaces. For this purpose, a
modified version of the Wilson plot technique presented by
Briggs and Young [10] was applied to find the single-phase heat
transfer correlations. The glycol–water pressure drop was also
analyzed and the Fanning equation was used to calculate the
friction factor.
The compact heat exchangers in this study were operated
as components of a refrigeration system. They were in turn installed within the secondary fluid loops connected to the main
refrigeration loop of a custom automotive air conditioning system. The main refrigeration loop included a compressor, condenser, evaporator, and expansion valve. The secondary fluid
system included two loops that exchanged energy with the main
refrigeration loop. In air conditioning (AC) mode, one of these
loops was formed between the evaporator and the cooler-core
compact heat exchanger to absorb thermal energy from the passenger cabin and transfer it to the evaporator during summer
conditions. The other loop was formed between the condenser
and the radiator of compact heat exchanger to transfer thermal
energy from the condenser to the surroundings. In heat pump
(HP) mode, the two secondary loops were switched using a fourway valve, so that one loop was formed between the condenser
and the heat-core compact heat exchanger, and the other loop
between the evaporator and radiator. By changing the glycol–
water mixture flow rates through the secondary fluid loops and
controlling the temperatures, the required energy was transferred to/from the compact heat exchangers. The experimental
data were used to calculate the heat transfer rate and pressure
drop of the heat exchangers.

In this article, the experimental test facilities are first described, followed by the geometry and size of the compact heat
exchangers. The calculation method and data analysis to determine heat transfer and pressure drop correlations from the
measured data are then explained. The resulting single-phase
correlations are finally presented, discussed, and compared with
the relevant previous studies.

EXPERIMENTAL TEST FACILITY
The air conditioning system under study consisted of a main
refrigeration loop using R-134a as the working fluid and two
secondary fluid loops using a 50% glycol–water mixture as the
secondary cooling/heating fluid. Figure 1 shows a schematic
heat transfer engineering

Figure 1 Schematic of the test facility.

diagram of the test facility, and the following subsections give
a brief description of the system components.

Secondary Fluid Loops
Secondary glycol–water mixture loops were designed to exchange energy with the evaporator and condenser. The temperatures at the inlet/outlet ports of each device were measured
using 0.2 m long type-K thermocouples probes. The thermocouple probes were inserted a minimum of 0.1 m into the flow
longitudinally and fixed in the center of the 0.02 m inner diameter tubes such that the bulk temperature could be measured.
The pressure drop of the glycol–water mixture passing through
the compact heat exchangers was measured by differential pressure transducers installed between the inlet and outlet ports. The
glycol–water mixture flow rates in each loop were measured by
a turbine-type flow meter.

Conditioned Air
Two environmental chambers were used in this study. In
each chamber, the air temperature and humidity were controlled

using conditioned air from external heating/cooling and humidifying/dehumidifying systems. In one of the environmental
chambers, conditioned air was circulating through either the
cooler-core (AC mode) or heater-core (HP mode) compact heat
exchanger to simulate cabin conditions. In the other chamber,
either hot (AC mode) or cold (HP mode) air was circulating
through the radiator compact heat exchanger to simulate ambient conditions. Two ducts were designed and built for metering
air flow through the compact heat exchangers. The heat exchangers were installed in the middle of the air ducts during
each test. Induction fans installed at the ducts’ entrance were
used to push air through the heat exchanger, while calibrated
ASME standard nozzles were used to measure the air flow rate.
The mean inlet and outlet air temperatures were measured using
several type-K thermocouples distributed on imaginary vertical
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A. JOKAR ET AL.

5

THE COMPACT HEAT EXCHANGERS
Five different meso-channel compact heat exchangers, as
parts of the secondary fluid system, were tested and analyzed
in this study. Theses heat exchangers, which were used as the
cooler-core, heater-core, or radiator of the automotive air conditioning system, are described next.

Cooler-Core

Figure 2 Thermocouples installation on the front and back of the mesochannel compact heat exchangers.

plains both in the front and back of the heat exchangers, as

typically shown in Figure 2. A chilled-mirror dew-point sensor
measured the dew-point temperature at the ducts’ inlets. The
wet bulb temperature was calculated from psychrometrics using
the measured dry bulb and dew-point temperatures.

Refrigeration Loop
The refrigeration loop included an evaporator, a condenser, a
compressor, and an expansion valve. Thermocouples and pressure transducers were installed at the inlet and outlet ports of
all components for temperature and pressure measurements. A
Coriolis-effect flow meter was used to measure the refrigerant
mass flow rate, which was controlled by varying the compressor
speed using a frequency-controlled AC motor. The refrigerant
charge was varied for each test condition to control the subcooled and superheated temperatures at the condenser and evaporator exits, respectively. These temperatures were controlled at
about 5◦ C for a stable system operation.

This heat exchanger is installed in cars to cool the cabin
in warm conditions (AC mode). Three compact heat exchangers, which were manufactured in different sizes and internal
flow-passage configurations, were tested as cooler-cores in this
study. Air flowed over the fin passages and the glycol–water mixture passed through the rectangular meso-channels, as shown in
Figure 3.
The glycol–water rectangular channels had small enhancements (bumps) on the top and bottom surfaces. These enhancements contacted each other in the middle of channels creating two-dimensional flow passages. The geometry and size of
the glycol–water flow rectangular channels and their internal
enhancements are presented in Figure 4. This figure showed
that the glycol–water was flowing, perpendicular to the page,
through cavities separated by these enhancements. The enhancements created a pattern, as shown in Figure 4, and this pattern
was repeated along the length of rectangular tube.
On the air side, the three meso-channel compact heat exchangers had louvered thin-plate fins, as described by Kays and
London [11]. The interconnecting thin-plate fins were sandwiched between the two parallel rectangular glycol–water channels, as shown in Figure 3. The louvers on the thin-plate fin surfaces were used to promote turbulence and reduce the boundary

Test Procedure

A range of test conditions was used to obtain adequate data
for analyzing the performance of the heat exchangers. All the
system variables such as temperatures, pressures, and flow rates
were recorded every 10 s as raw data. Once the fluctuations
in glycol–water mean temperature within the heat exchangers
became stable (within ±1◦ C), the system was considered to be
at a steady-state condition. The data collection then began and
continued for at least 10 min for each test condition. The timeaveraged data were then used to analyze the heat exchangers’
performance.
heat transfer engineering

Figure 3 Cutaways of the three meso-channel compact heat exchangers used
as the cooler-core.

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A. JOKAR ET AL.

Figure 5 Geometry and size of the louvered thin-plate fins in the three mesochannel compact heat exchangers used as the cooler-core.

The flow of glycol–water mixture within the heater-core was
analyzed in the same way as the circular tubes. For the air
side, an analysis similar to the air flow across a compact heat
exchanger with continuous parallel fins was applied.
Figure 4 Geometry and size of the glycol–water flow channels in the three
meso-channel compact heat exchangers used as the cooler-core.

Radiator
layer thickness of the air flowing across the compact heat exchangers. The geometry and size of these thin-plate fins are
presented in Figure 5.

Heater-Core
This heat exchanger is installed in cars to warm the cabin in
cold conditions (HP mode). The heater-core used in this study
was a finned-tube cross-flow compact heat exchanger, which
was run in heat pump mode to heat the passenger cabin. A
cutaway of this heat exchanger is shown in Figure 6.
Air flowed through the finned passages, while the mixture of
glycol–water passed through the circular tubes. Figure 6 showed
the cross-sectional area of the circular tubes through which the
glycol–water mixture flowed. This figure also showed the helical springs that were inserted into the circular tubes to promote
turbulent flow and increase heat transfer. This finned-tube compact heat exchanger included eight circular tubes (two-passes)
with continuous fins, as described by Kays and London [11].
The fin surfaces were parallel continuous thin plates with 16
holes through which 16 circular tubes were inserted and fitted
to the plates tightly, as shown in Figure 6. The parallel continuous thin plates were not simply flat plates. In fact, part of the fin
surfaces between the circular tubes was sliced vertically along
the air flow passages creating louvers. These louvers between
the fin surfaces promote the flow turbulence even at low air
flow rates. The geometry and size of the circular tubes with the
helical-spring inserts and the fin surfaces is shown in Figure 7.
heat transfer engineering

This heat exchanger is installed in cars to exchange thermal energy between the air conditioning system and ambient
in either warm (AC mode) or cold (HP mode) conditions. The
radiator in this study was a cross-flow compact heat exchangers
in which the glycol–water mixture flowed through its rectangular enhanced meso-channels, and on the other side, air flowed

through the fin passages with louvered surfaces, as shown in
Figure 8.

Figure 6 A cutaway of the meso-channel compact heat exchanger used as
the heater-core.

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A. JOKAR ET AL.

7

Figure 7 Geometry and size of the glycol–water flow channels and the louvered thin-plate fins in the meso-channel compact heat exchanger used as the
heater-core.

The rectangular meso-channels had small enhancements, i.e.,
bumps, which were raised from the bottom and top surfaces to
promote flow transition from laminar to turbulent and to increase
the heat transfer effectiveness, as shown in Figure 9.
The interconnecting thin-plate fins were sandwiched between
two neighboring meso-channels, as shown in Figure 8. These
fins were not simply flat plates, and in fact, the fin surfaces
were louvered along the flow passes. These louvers promoted
turbulence and reduced the boundary layer thickness of the air
flowing through the radiator. The geometry and size of the louvered thin-plate fins on the radiator are shown in Figure 9.

Figure 9 Geometry and size of the glycol–water flow channels and the louvered thin-plate fins in the meso-channel compact heat exchanger used as the
radiator.

DATA REDUCTION AND CALCULATION METHOD
A multi-channel data acquisition system allowed continuous
data collection and monitoring of the experimental test facility.
Heat transfer and pressure drop correlations within the mesochannel compact heat exchangers were obtained from extensive
data sets gathered from multiple experimental test runs. This
section reviews in detail the equations used for the heat exchanger analysis.

Heat Transfer Calculation Method

Figure 8 A cutaway of the meso-channel compact heat exchanger used as
the radiator.

heat transfer engineering

A set of experiments was performed to analyze the thermohydrodynamic performance of each heat exchanger. The Wilson
plot technique was then applied to find the heat transfer correlations for both the glycol–water mixture and air. The first step
vol. 31 no. 1 2010


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A. JOKAR ET AL.

was to calculate the overall heat transfer coefficient for each
data point. The experimental data and measured dimensions of
the heat exchangers were used to obtain the overall heat transfer
coefficient based on the glycol–water side. This coefficient was
calculated from the following heat transfer equations:
Q˙ g = Ug Ag TLM F

(1)

˙ g,tot CP,g (Tg,out – Tg,in )
Q˙ g = m

(2)

(3)

where the log-mean temperature difference was defined as:
TLM =

T1 − T2
Ln( T1 / T2 )

T1 = Ta,out – Tg,in
T2 = Ta,in – Tg,out

(4)

The fin surfaces on the compact heat exchangers were effective in transferring heat between glycol–water mixture and
air. This effect was taken into account by adding the fin thermal efficiency to the energy balance equation. The fin thermal
efficiency, presented in Incropera and DeWitt [12], is shown as:
ηfin =

˙ fin
˙ fin
Q
Q
=

˙ max
hAfin (Ta – Tb )
Q

(5)

where “b” denotes the fin base. This equation implies the maximum heat transfer rate is attainable only if the entire fin surface
is at the base temperature, which is generally not the case. The
fin efficiencies for different fin geometries have been presented
graphically in many references as a function of the heat transfer
coefficient. One simple case is the straight fin with a uniform
cross-sectional area. As shown in Incropera and DeWitt [12],
the fin efficiency in this case is analytically calculated as
ηfin =

tanh(mL)
mL

(6)

where L is the fin length and parameter “m” is defined as
m2 =

hP
kfin Ac

(7)

Since the fin plates on the compact heat exchangers in this
study had a uniform cross-sectional area, Eq. (6) was applied to

approximate the fin efficiency.
The fin overall surface efficiency to characterize an array of
fins, as presented in Incropera and DeWitt [12], is defined as:
ηo =

˙ tot
˙ tot
Q
Q
Afin
=1−
=
(1 − ηfin )
˙
hAtot (Ta − Tb )
Atot
Qmax

Atot = Afin + Ab

(8)

heat transfer engineering

(9)

Applying an energy balance between the glycol–water mixture and air for the compact heat exchangers yielded:
hg Ag,tot (Twall – Tg ) = ηo ha Aa,tot (Ta – Twall )

where F is a correction factor for multipass cross-flow heat

exchangers. This factor was empirically estimated using the
inlet/outlet temperatures of fluids passing through the heat exchanger, as described in Incropera and DeWitt [12]. The correction factor was estimated as 0.9 for most conditions in this study.
Combining Eqs. (1) and (2), the overall heat transfer coefficient
was calculated as:
˙ g,tot CP,g (Tg,out – Tg,in ) / Ag TLM F
Ug = m

where the subscript “tot” denotes the total exposed area of the
finned and un-finned surfaces. The total area was calculated by:

(10)

Knowing the overall heat transfer coefficient and overall fin
surface efficiency, the modified Wilson plot technique, introduced by Briggs and Young [10], was applied to find a heat
transfer correlation for both sides of the heat exchangers. Assuming the areas on both sides of the channel are not the same,
and neglecting the wall thermal resistance due to the small wall
thickness and high thermal conductivity of the wall’s material,
the overall heat transfer coefficient was calculated as:
1
1
1
=
+
Ug Ag
hg A g
h a A a ηo

(11)

The heat transfer coefficient in this study was assumed to

be in the form of the Dittus-Boelter equation, as described in
Incropera and DeWitt [12], and presented as:
h=C

kfluid
Dh

Rep Prn = Ch

(12)

Equation (11) is then rearranged as:
hg
1 h g Ag 1
1
+
=
U
Cg
Ca h a Aa ηo

(13)

It should be noted that the Dittus–Boelter equation is valid for
a single-phase fluid with the Prandtl number greater than 0.7;
however, that correlation was not exactly used in this study.
Equation (12) was applied to both glycol–water and air flows in
the heat exchangers knowing the Prandtl numbers of air and the
glycol–water mixture were greater than 0.7. The parameters of
the Wilson plot technique were then defined as:

⎧
1
1
⎪
⎪
⎨b = C ,m = C
g
a
(14)
Y = b + mX
⎪
h
h
g
g Ag 1
⎪
⎩Y =
,X =
U
h a Aa ηo
To obtain more accurate results, all the thermophysical properties were calculated as a function of temperature. The properties for the glycol–water mixture were obtained from the
ASHRAE Handbook of Fundamentals [13].
It was necessary to evaluate the heat exchangers’ fin characteristics to complete the Wilson plot technique. Based on the
heat exchanger geometries presented in previous section, the
characteristics of the fin surfaces of the five meso-channel compact heat exchangers are summarized in Table 1.
In order to apply the Wilson plot technique, Eq. (14), it was
necessary to calculate the hydraulic diameter on both glycol–
water and air sides. The hydraulic diameter on the glycol–water
side was calculated based on the flow cross-sectional area and
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A. JOKAR ET AL.

9

Table 1 Measured and calculated parameters for the five meso-channel compact heat exchangers
Parameter
Fin pitch (number of fin plates/m)
Hydraulic diameter (air side), Dh (m)
Fin thickness, t (m)
Frontal area, Afr (m2 )
Minimum free-flow area, Amin (m2 )
σ = Amin /Afr
Area of single fin plate, Asingle−fin
(m2 )
Total fins area, Afin,tot (m2 )
Total unfinned area (pipe base), Ab,tot
(m2 )
Total heat transfer area (air side),
Aa,tot (m2 )
Total glycol–water heat transfer area
(based on the internal wall
projected area), Ag,tot (m2 )
Aa,tot /Afin,tot
Aa,tot /Ag,tot

Cooler-core (42 mm)

Cooler-core (58 mm)

Cooler-core (78 mm)

Heater-core

Radiator

620
2.27E-3
0.08E-3
5.17E-2
3.68E-2
0.712
2.62E-4

540
2.67E-3
0.10E-3
5.28E-2
3.89E-2
0.736
4.35E-4

540
2.81E-3
0.10E-3
5.79E-2
4.29E-2
0.741
6.86E-4

1100
1.45E-3
0.10E-3
3.88E-2
2.01E-2
0.519
5.61E-3

860
3.62E-3
0.10E-3
1.96E-1
1.57E-1
0.802
2.47E-2

0.959
0.403

1.218
0.462

1.805
0.587

1.544
0.095

3.715

0.805

1.362

1.680

2.392

1.638

4.520

0.424

0.488

0.620

0.094

0.848

1.420
3.211

1.379
3.746

1.325
3.857

1.061
17.4

1.217
5.330

wetted perimeter. The hydraulic diameter on the air side was
calculated from the following equation, as defined by Kays and
London [11]:
AC
Dh
=4
L
A

(15)

where Ac is the minimum cross-sectional area of the air flow
(i.e., Amin in Table 1), and A is the total heat transfer area on the
air side (i.e., Aa,tot in Table 1). In Eq. (15), “L” is an equivalent
flow length measured from the leading edge of the first channel
to the leading edge of the second channel.
The Reynolds number in Eq. (12) was defined as a function
of mass flux:
ReD =

GDh
µ

(16)

The mass flux of the glycol–water mixture was calculated
based on the measured flow rate and the minimum free-flow
area of the meso-channels. The mass flux of the air flowing
through the compact heat exchangers was also calculated based
on the measured air flow rate and the minimum free-flow area
of the fin plates, as presented in Table 1.
The parameters X and Y used in the Wilson plot technique
were calculated for each single experiment. These data points
were then curve-fitted linearly using the least-squares method.
The slope and intercept of the fitted line would thus be the inverse
of coefficients Ca and Cg , respectively, as presented in Eq. (14).
The heat transfer coefficients of the glycol–water mixture (hg )
and air (ha ) were then obtained by Eq. (12).
For the air side, the new value of “ha ” was used to recalculate the parameter “m” in Eq. (7). The fin efficiency and overall
surface efficiency were then calculated from Eqs. (6) and (8),
respectively, based on the calculated parameter “m.” These calculations created a trial–error loop between “m” and ha in the
Wilson plot technique. The procedure was repeated until the
heat transfer engineering

difference between the new and old value of ha became less
than 0.1%.

Friction Factor Calculation Method
The frictional pressure drop for the glycol–water mixture
within the meso-channel compact heat exchangers was calculated by subtracting the pressure drop across the inlet/outlet
manifolds and gravitational pressure drop from the total pressure drop:
Pf =

Ptot −

Pgr −

Pman

(17)

The pressure drop from the inlet port to the outlet port was
measured by a differential pressure transducer. The gravitational
pressure drop was considered to be zero for this analysis since
the inlet and outlet ports were at the same height. The inlet/outlet
manifolds pressure drop was approximated as a function of the
inlet head velocity as:
Pman = K

ρu2m
2

(18)
in

where K is obtained empirically. This constant was approximated as 1.5 for the compact heat exchangers in this study, as
described by Shah and Wanniarachchi [14]. It was found that
the frictional pressure drop was the largest component of the
total pressure drop, being over 90% of the total pressure drop
for the glycol–water mixture in the meso-channel compact heat
exchangers.
The Fanning friction factor for the glycol–water flow was
then defined as:

Cf,g =
vol. 31 no. 1 2010

f
=
4

Pf

Dh ρm
L 2G2

(19)
g


10

A. JOKAR ET AL.
Table 2 Uncertainty estimates for the measured and calculated parameters of the five meso-channel compact heat exchangers
Test Range
Parameter

Uncertainty

Cooler-core
(42 mm)

Cooler-core
(58 mm)

Cooler-core
(78 mm)

Heater-core

Radiator

Average temperature, glycol–water mixture (◦ C)
Average temperature, air (◦ C)
Pressure difference, glycol–water mixture (kPa)
Air volumetric flow rate (m3 /s) × 10−2
Glycol–water volumetric flow rate (m3 /s) × 10−4
Glycol–water Fanning friction factor
Y (Wilson plot parameter)
Nusselt number, glycol–water mixture

±0.2◦ C
±0.2◦ C
±274 Pa
±2%
±1%
±7%
±6%
±6%

2–17
18–35
5–26
4.601–17.35

1.346–3.710
0.61–1.0
28–96
20–44

2–16
20–26
3–18
4.851–17.74
1.301–3.690
0.33–0.56
49–128
9–19

1–17
16–30
4–15
4.837–17.21
1.350–4.031
0.72–1.1
41–136
10–25

(–5)–45
(–10)–26
5–39
2.742–13.84
1.415–3.966
0.24–0.48
10–46

70–230

31–64
19–52
2.5–7
14.85–79.38
1.365–4.104
0.07–0.19
18–80
10–22

For each individual test point, the frictional pressure drop
and the Fanning friction factor were calculated. An appropriate
correlation was then developed for the Fanning friction factor
based on the experimental data, as shown in the Results section.

taken for each of them. These data were then used to develop
heat transfer correlation and the Fanning friction factor for each
separately, as discussed next.
Heat Transfer Correlations

The Measurement Uncertainty
The uncertainty estimates for the measured parameters were
obtained from the relevant manufacturer’s literature and through
calibration, as summarized in Table 2. An uncertainty analysis
method, introduced by Coleman and Steele [15], was then applied to estimate the overall uncertainties for the Nusselt number
and Fanning friction factor. The last three uncertainty estimates
in Table 2 were the most important quantities. The uncertainties
of Nusselt numbers in this table were estimated by applying the
propagation of uncertainty estimates in the parameter Y of the

Wilson plot technique. As presented in Eq. (14), the intercept
and slope of the X–Y plot were equal to the inverse of leading coefficient “C” in the heat transfer correlation given by Eq.
(12). Thus, the uncertainty estimate for the Nusselt correlations
might be approximated by the corresponding uncertainties of
the parameter Y.
RESULTS AND DISCUSSION
The five different meso-channel compact heat exchangers
were installed in the system, and the experimental data were

The Wilson plot procedure, as discussed in the previous section, was applied to each data set to determine the heat transfer
correlation for each heat exchanger. Table 3 summarizes the
coefficients of these correlations based on the general form of
Eq. (12).
The Prantdl number exponent “n” is estimated as 0.3 for
cooling and 0.4 for heating, based on the Dittus–Boelter equation introduced in Eq. (12). The optimized Reynolds number
exponent “p” gave the minimum deviation in the Wilson plot.
It should be noted that in the conventional Wilson plot method,
the constant coefficients for the heat transfer correlations on
both sides (Cg and Ca ) are obtained for the specific geometries of a heat exchanger, while the Reynolds exponents (pg
and pa ) are assumed known (e.g., 0.8 in fully turbulent flow as
in Dittus–Boelter correlation). However, in the modified Wilson
plot method, introduced by Briggs and Young [10], the Reynolds
exponent, along with the constant coefficients, is optimized and
obtained through a trail-and-error calculation process. The optimized Reynolds components for the specific geometries of each
heat exchanger in this study are presented in Table 3.
If one compares the correlations just discussed with the ones
for smooth macro-channels, the proposed correlations provide

Table 3 Heat transfer correlations for the five meso-channel compact heat exchangers
Coefficients of Nu equation:

Nu = CRep Prn a

Cooler-core
(42 mm)

Cooler-core
(58 mm)

Cooler-core
(78 mm)

Heater-core

Radiator

Cglycol−water
pglycol−water
hglycol−water (W/m2 -K)
Cair
pair
hair (W/m2 -K)
Average deviationb (%)

0.120
0.78
2909–6346
1.673
0.5
226–440
12

0.036
0.78
956–2138
0.578
0.65
160–375
3

0.048
0.78
983–2266
0.744
0.60
145–312
15

0.177
0.75
1412–2946
0.268
0.65
88–266
6.5

0.138
0.70
3470–12199
0.438
0.65

102–288
5

an

is equal to 0.3 for cooling and 0.4 for heating the fluid.
between experiment and correlation = | Experiment—Correlation| /Experiment.

b Deviation

heat transfer engineering

vol. 31 no. 1 2010


A. JOKAR ET AL.

11

Figure 10 The Wilson plot X and Y parameters for the five meso-channel
compact heat exchangers.

higher heat transfer rates under the same flow conditions. This
difference could be explained by (1) the surface enhancements
on both glycol–water and air sides, and (2) the scale of channels. On the glycol–water side, the flow cross-sectional areas
in rectangular meso-channels had enhancements (bumps) on
the top and bottom surfaces. On the other side, air passed
through the heat exchangers’ openings, which were small rectangular channels with louvers on the sides. These corrugations
made the flow turbulent and enhanced the heat transfer rate.
Figure 10 shows the results for the parameters X and Y in

the Wilson plot technique for the meso-channel compact heat
exchangers.
Figure 10 shows satisfactory agreement between the experimental results and the proposed correlations. The deviation between the experimental and predicted Y value versus Reynolds
numbers of glycol–water mixture and air are shown in Figure
11 for the five meso-channel compact heat exchangers.
Figure 11 shows that the deviations of parameter Y in Wilson plot method were randomly distributed (not correlated) with
Reynolds number around zero for both the glycol–water and air
flows. The average deviation between experiment and correlation in Wilson plot for the five heat exchangers under study was
from 3 to 15%, as presented in Table 3, while the uncertainty on
the heat transfer was 6%, as presented in Table 2.
These are air–liquid heat exchangers that were tested under
real operating conditions for an automotive air conditioning
system. The temperature and flow rate of both air and liquid
sides were controlled to meet the desired summer and winter
conditions. During the testing of the cooler-cores for summer
conditions, there were a few test points at which condensation
took place, although the amount of condensation was estimated
and taken into account. This two-phase flow on the air side could
be a source of some of the larger deviations in Figure 11, and may
affect the energy balance on the air side but not on the liquid
side. It is important to note that the energy balance on the liquid
side was used to calculate the overall heat transfer coefficient
in Wilson plot. The measurement on the liquid side, which was
highly accurate, was the base of calculations for the heat transfer
and pressure drop in meso-channels of heat exchangers.
heat transfer engineering

Figure 11 Deviation of Y parameter from the curve-fitted line in Wilson plot
for the five meso-channel compact heat exchangers.

The correlations obtained for the glycol–water mixture in
this study were qualitatively compared to other correlations for
laminar and turbulent flows in macro-channels, as shown in
Figure 12. Kays and Crawford [16] showed that the Nusselt
number for the laminar flow inside a smooth rectangular channel
is constant. For an aspect ratio greater than 8, such as parallel
plates, the correlation is obtained from the following equations:
L
W

≥ 8.0
channel

NuH = 8.235 (heat flux constant)
NuT = 7.540 (temperature constant)

(20)

Two correlations for the turbulent flow inside circular tubes
were also plotted in Figure 12. One was the Dittus–Boelter
correlation, which is valid for fully turbulent region. The other
correlation was by Gnielinski for smaller Reynolds numbers,
presented in Incropera and DeWitt [12], which is given by:
NuD =

(f/8)(ReD − 1000) Pr
1 + 12.7(f/8)1/2 (Pr2/3 −1)

vol. 31 no. 1 2010

0.5 < Pr < 2000
2300 < ReD < 5 × 106
(21)


12

A. JOKAR ET AL.

Figure 12 Comparison of the single-phase heat transfer correlations for the
five meso-channel compact heat exchangers with other relevant correlations.

where the friction factor is given by:
f = 4Cf =

1
[0.79lnReD − 1.64]2

(22)

It should be noted that the last two correlations are basically
used for the flow inside a smooth circular tube. However, as long
as the Prandtl number is greater than 0.5, these correlations can
be applied accurately for noncircular cross sections, provided
that the tube diameter is replaced by the hydraulic diameter
defined by Eq. (15); see Kays and Crawford [16].
The differences among the correlations shown in Figure 12
might be explained by the difference in geometric patterns of
the flow passages and the size of channels. However, it was
hard to compare closely the channels with different geometries

and enhancement configurations. For example, Figure 12 shows
the higher Nu numbers belonged in turn to 42 mm, 78 mm,
and 58 mm cooler cores, although the numbers for 78 mm and
58 mm are close. These results are consistent with Figure 10 for
the Wilson plot, with Eq. (14) for the overall heat transfer coefficient and with Table 3 for the correlations. Looking carefully at
the enhancements inside the cooler cores in Figure 4, it appears
the higher number of enhancements belonged in turn to 58 mm,
78 mm, and 42 mm. It looks like these enhancements might add
more turbulence to the flow but at the same time decreased the
direct surface heat transfer area between the liquid inside and
air outside.
It should also be noted that in this study, the overall heat
transfer coefficient on the glycol–water side, as in Eq. (1), was
calculated based on the internal wall projected area of the chanheat transfer engineering

nels, as presented in Table 1. In case of the heater-core, however,
the helical-spring inserts could have greater effect on the internal heat transfer surface enhancement. This might explain the
relatively higher values of heater-core Nusselt number in Figure
12, compared to other rectangular meso-channels.
It is clear from Figure 12 that the Nusselt numbers of the flow
inside the meso-channels of the compact heat exchangers are
not constant but increasing with Reynolds number, although the
Reynolds numbers are less than the nominal critical Reynolds
number (2300) for the entire testing range. In fact, the slopes of
the curve-fitted lines for all the meso-channels are quite similar
to those of the Dittus–Boelter and Gnielinski correlations for
fully turbulent flow.
This mismatch indicates that the flow regimes inside the
meso-channels could not be laminar but probably are in a transition from laminar to turbulent. The laminar theory was originally implemented to the obtained experimental data, which
resulted in much higher errors. After carefully analyzing the

heat exchangers and their complicated internal geometries, it
was realized that the flow might not be laminar (Reynolds exponent equal to zero), as anticipated, but might be near turbulent.
A modified Wilson plot method was thus implemented to account for the Reynolds exponents larger than zero. The results
were much more promising and the errors dropped significantly.
The Reynolds exponents were optimized in order to obtain the
minimum possible error through the experimental data. As can
been seen from Table 3, all these exponents were found to be
less than 0.8, which can belong to transition flow. The theory of
critical Reynolds number 2300, known as the border of laminar
flow, is quite well established for simple geometries, such as the
smooth circular tubes. However, it is believed this theory cannot
necessarily be true for confined complex micro-channels, such
as the three-dimensional meso-channels of this study. It was preferred in this study to rely on the experimental data, which were
collected under operating conditions of a real thermal system,
rather than referring to the theories that are applicable to other
configurations.
Furthermore, the entrance-length effects were assumed quite
small and negligible for the channel configuration and arrangement in this study. As seen in Figures 3 through 9, the parallel
meso-channels of the cooler-cores and radiator are not simply smooth and straight channels. The enhanced plate surfaces
of these heat exchangers, once brazed together, make small
and two-/three-dimensional confined spaces that are distributed
along the channels. These patterns, as shown in Figures 4 and
9, are much more complex than assuming parallel and straight
channels. These surface enhancements are also intended to promote turbulence and to reduce the boundary layer thickness
along the flow.
The results of the work by Olsson and Sunden [17] were also
reviewed and included in Figure 12 for comparison. They studied heat transfer through single rectangular tubes that were used
in automotive radiators. The results were somewhat comparable with the results of this study, and interestingly their Nusselt
number did not stay constant even at the Reynolds numbers less
vol. 31 no. 1 2010

A. JOKAR ET AL.

13

Table 4 Pressure drop correlations for the five meso-channel compact heat exchangers
Coefficients of Cf equation:
Cf = CRen
Cglycol−water
nglycol−water
Ptotal−glycol−water (kPa)
Average deviationa (%)
a Deviation

Cooler-core
(42 mm)

Cooler-core
(58 mm)

Cooler-core
(78 mm)

Heater-core

Radiator

5.779
–0.4

5–26
3

6.970
–0.5
3–17
4

1.693
–0.1
4–15
8

1.654
–0.2
2–7
13

17.18
–0.8
5–39
21

between experiment and correlation = | Experiment – Correlation| /Experiment.

than 2300. This also proves that the flow might not necessarily
be laminar but could be in transition. The slight difference between the results of this study and those of Olsson and Sunden
[17] could be due to the difference in the channel configurations, geometry, enhancement size, and flow conditions. Plus,
the experimental data in this study were taken for the integrated
heat exchanger and not a single tube, as they did. The results

of this study might be interesting and useful to those who are
looking at the heat exchanger as an integrated thermal system,
but probably not to those who are focusing on single channels
or single fin arrays.
In summary, it was concluded that the flow inside such mesochannel compact heat exchangers was near turbulent even at very
low Reynolds numbers. Because of this and due to the surface
enhancements inside the meso-channels, the heat transfer rate in
these heat exchangers was increased compared to conventional
smooth pipe heat exchangers. Extensive analyses of enhanced
surfaces have been presented by Webb [18].
It should be noted that the experimental results presented in
this article focus mainly on the liquid single-phase flow inside
the enhanced meso-channels of the compact heat exchangers.
The air pressure drop was not measured, and there was less attention/accuracy on the air-side heat transfer. However, overall
heat transfer correlations for the air side were approximated using the results of Wilson plot method, as presented in Table 3.
Looking carefully at Figures 3 through 9 and Table 1, one can
find that the fin configuration and geometries for the compact
heat exchangers were not identical. Also, the flow conditions
for testing these heat exchangers were slightly different, as presented in Figure 10 and Table 2. As a result, correlations with
different Reynolds exponent and constant coefficients on the air
side were expected and obtained for these heat exchangers.

The first term describes the effect of turbulent flow and the
second is the contribution from laminar flow. In fact, the more
turbulent the flow is, the less dependent the Fanning friction
factor is on the Reynolds number. Ultimately, it was found that
a simpler form of the correlation provided the best fit to the
data. The pressure drop correlations for the five meso-channel
compact heat exchangers are summarized in Table 4.
A comparison of the correlations with the experimental data

and some other correlations is shown in Figure 13. The friction
coefficient for the laminar flow shown in Figure 13 was found
from:
Cf =

C
Re

(24)

where C is 16 for the case of circular tube. For the rectangular
channels, Kays and Crawford [16] evaluated and plotted the
constant C for different aspect ratio. The constant C for the
cooler-cores with 42, 58, and 78 mm was found to be 21.8, 22.0,
and 22.4, respectively, and for the radiator 22.3.
The fully turbulent flow inside the rectangular channels could
be estimated by the correlations for circular tubes using the

Pressure Drop Correlations
The measured pressure drop for the glycol–water mixture in
each compact heat exchanger was used to determine the corresponding Fanning friction factor for each test point. A correlation was then fitted to the experimental data using the general
form, introduced by Shah and Wanniarachchi [14], as shown
here:
C2
(23)
Cf = C1 +
Re
heat transfer engineering

Figure 13 Comparison of the single-phase pressure drop correlations for the

five meso-channel compact heat exchangers with other relevant correlations.

vol. 31 no. 1 2010


14

A. JOKAR ET AL.

hydraulic diameter. Kays and Crawford [16] argued that the effects of corners on the flow pattern in the noncircular channels in
the turbulent region are negligible. They presented a correlation
for the smooth circular tube in the fully turbulent region as:
Cf
= 0.023Re−0.2
(25)
2
It is important to point out that this correlation is used for
Reynolds numbers greater than 20,000. No specific correlation
has been reported for the transition region in the rectangular
channels. The roughness of the tube walls can affect the friction
coefficient. Kays and Crawford [16] presented the following
correlation for flows inside pipes in the fully rough region:
Cf
D
= 2.46ln
2
ks

+ 3.22

−2

(26)

The parameter ks is the wall roughness, which was set at 1
mm to form an upper level in the Cf versus Re plot, as shown in
Figure 13.
Figure 13 shows that the slope of the fitted line for current
study was more similar to the turbulent region than the laminar
region. This conclusion could be confirmed by looking at the
proposed correlations listed in Table 4, since the exponents of
the inverse Reynolds numbers were not unity (as in laminar
flow). Therefore, the glycol–water flows in the meso-channels
of the compact heat exchangers with the interior enhancements
were near turbulent even at low Reynolds number.
The results of the work by Olsson and Sunden [17] were
also reviewed and included in Figure 13 for comparison. They
studied pressure drop through single rectangular tubes that were
used in automotive radiators. Their Fanning friction factors
were above the laminar flow region, and the data did not follow
the trend/slope of the laminar flow, but looked more like the
turbulent flow. These results were consistent with the results of
this study.

SUMMARY AND CONCLUSIONS
Single-phase heat transfer and fluid flow of five meso-channel
compact heat exchangers, with different interior channel configurations and sizes, were reviewed and analyzed in this article.
Fifty percent glycol–water mixture was pumped through the enhanced meso-channels which had either circular or rectangular
cross section. On the other side, cold or hot air was pushed over
the channels, which included louvered thin plate fins.

One unique feature of this study is that the measurements of
actual heat exchangers with various dimensions were detailed
under realistic operating conditions. These heat exchangers were
components of the secondary fluid loop of an automotive air
conditioning system that were investigated experimentally. The
refrigeration system and its two secondary fluid loops were
operated at different conditions in both air-conditioning and
heat-pump modes. The experimental data included temperatures, pressures, and flow rates that were collected at steadyheat transfer engineering

state conditions. The previously obtained correlations for the
heat transfer and pressure drop of the glycol–water mixture and
air flowing through these meso-channel compact heat exchangers were reviewed, compared, and discussed.
Investigating these correlations, one can conclude that the
conventional macro-scale correlations through the circular or
noncircular channels do not perfectly match the experimental
results obtained for the meso-channel compact heat exchangers
under study. It was observed that even at low Reynolds numbers
(less than 1000), the Nusselt number of the glycol–water flow
within these meso-channels does not stay constant, as it does
in macro-channels, but increases with Reynolds number. This
difference can probably be explained by combinations of two
effects: (1) the surface enhancements on the channel walls, and
(2) the transition from macro scale to micro-/mini-scale channels. On the glycol–water side of the compact heat exchangers,
the enhancements inside the meso-channels promoted turbulent
flow and increased heat transfer in comparison with the smooth
channels.
There is still a long way to go to fully understand the fluid
flow and heat transfer within the micro-/mini-scale channels,
especially at the transition and turbulent flow regimes, yet the
results of this study may be used along the way for improving

the compact heat exchanger design.

NOMENCLATURE
A
b
C
Cp
Cf
D
f
F
G
h
h
H
k
ks
K
L
m
˙
m
Nu
P
Pr
˙
Q
Re
t
T

u
U

heat transfer area or cross-sectional area (m2 )
intercept in Wilson plot
constant
specific heat capacity (J/kg-K)
Fanning friction factor
diameter (m)
Moody friction coefficient
correction factor
mass flux (kg/m2 -s)
heat transfer coefficient (W/m2 -K)
modified heat transfer coefficient (W/m2 -K)
height (m)
thermal conductivity (W/m-K)
wall roughness
pressure loss coefficient
length (m)
parameter in fin efficiency or slope in Wilson plot
mass flow rate (kg/s)
Nusselt number
perimeter (m)
Prandtl number
heat transfer rate (W)
Reynolds number
thickness (m)
temperature (K)
single passage velocity (m/s)
overall heat transfer coefficient (W/m2 .K)

vol. 31 no. 1 2010


A. JOKAR ET AL.

W
X
Y

width (m)
Wilson parameter in x direction
Wilson parameter in y direction

Greek Symbols
P
T
η
µ
ρ
σ
θ

pressure difference (Pa)
temperature difference (K)
fin efficiency
dynamic viscosity (Pa-s)
density (kg/m3 )
surface area ratio
louvers angle (degrees)

Subscripts
a
b
c
f
fin
fr
g
gr
h
in
l
LM
m
man
max
min
o
out
port
tot
wall

air
fin base
cross-sectional area
friction
heat exchanger fins
frontal area
glycol–water mixture

gravity
hydraulic
inlet
louvers
logarithmic mean (temperature difference)
mean value
manifold
maximum
minimum
overall
outlet
inlet/outlet ports
total
channel’s wall

Superscripts
n
p

Prandtl number exponent
Reynolds number exponent

REFERENCES
[1] Kandlikar, S. G., and Grande, W. J., Evolution of Microchannel
Flow Passages—Thermohydraulic Performance and Fabrication
Technology, Heat Transfer Engineering, vol. 24, no. 1, pp. 3–17,
2003.

heat transfer engineering

15

[2] Webb, R. L., and Kim, N., Advances in Air-Cooled Heat Exchanger Technology, Journal of Enhanced Heat Transfer, vol. 14,
no. 1, pp. 1–26, 2007.
[3] Webb, R. L., and Zhang, M., Heat Transfer and Friction in
Small Diameter Channels, Microscale Thermophysical Engineering, vol. 2, no. 3, pp. 189–202, 1998.
[4] Wang, B. X., and Peng, X. F., Experimental Investigation on
Liquid Forced-Convection Heat Transfer Through Microchannels,
International Journal of Heat and Mass Transfer, vol. 37, no.
suppl. 1, pp. 73–82, 1994.
[5] Steinke, M. E., and Kandlikar, S. G., Single-Phase Liquid Friction Factors in Microchannels, International Journal of Thermal
Sciences, vol. 45, no. 11, pp. 1073–1083, 2005.
[6] Steinke, M. E., and Kandlikar, S. G., Single-Phase Liquid Heat
Transfer in Plain and Enhanced Microchannels, Proc. 4th International Conference on Nanochannels, Microchannels and
Minichannels, Ireland, pp. 943–951, 2006.
[7] Jokar, A., Eckels, S. J., and Hosni, M. H., Evaluation of Heat
Transfer and Pressure Drop for the Heater-Core in an Automotive
Heat Pump System, Proc. 2004 ASME International Mechanical Engineering Congress and RD&D Expo, Anaheim, CA, no.
60824, 2004.
[8] Jokar, A., Hosni, M. H., and Eckels, S. J., Correlations for Heat
Transfer and Pressure Drop of Glycol–Water and Air Flows in
Minichannel Heat Exchangers, ASHRAE Transactions, vol. 111,
part 2, no. 4803, 2005.
[9] Jokar, A., Hosni, M. H., and Eckels, S. J., Thermal-Fluid Characteristics of an Automotive Radiator Used as the External Heat
Exchanger in an Auto Air Conditioning System, Proc. 2005 ASME
Heat Transfer Summer Conference, San Francisco, CA, no. 72061,
2005.
[10] Briggs, D. E., and Young, E. H., Modified Wilson Plot Techniques
for Obtaining Heat Transfer Correlations for Shell and Tube Heat
Exchangers, Chemical Engineering Progress Symp., AIChE Heat

Transfer, vol. 65, no. 92, pp. 35–45, 1969.
[11] Kays, W. M., and London, A. L., Compact Heat Exchangers, 3rd
ed., McGraw-Hill, New York, 1984.
[12] Incropera, F. P., and DeWitt, D. P., Fundamentals of Heat
and Mass Transfer, 4th Ed., John Wiley & Sons, New York,
1996.
[13] AHRAE, ASHRAE Handbook of Fundamentals, Chapter 18,
American Society of Heating, Refrigerating and Air-Conditioning
Engineers, Atlanta, GA, 2001.
[14] Shah, R. K., and Wanniarachchi, A. S., Plate Heat Exchanger
Design Theory, Industrial Heat Exchangers, Lecture Series No.
1991-04, J.-M. Bushlin, Von Karman Institute for Fluid Dynamics,
Sint-Genesius-Rode, Belgium, 1992.
[15] Coleman, H. W., and Steele, W. G., Experimentation and Uncertainty Analysis for Engineers, John Wiley & Sons, New York,
1989.
[16] Kays, W. M., and Crawford, M. E., Convective Heat and Mass
Transfer, 2nd Ed., McGraw-Hill Pub., New York, 1980.
[17] Olsson, C. O., and Sunden, B., Heat Transfer and Pressure
Drop Characteristics of Ten Radiator Tubes, International Journal of Heat and Mass Transfer, vol. 39, pp. 3211–3220,
1996.
[18] Webb, R. L., Principles of Enhanced Heat Transfer, John Wiley
& Sons, New York, 1994.

vol. 31 no. 1 2010


16

A. JOKAR ET AL.
Amir Jokar is an assistant professor in the School

of Engineering and Computer Science at Washington State University Vancouver, WA. He received his
Ph.D. in 2004 from Kansas State University, Manhattan, KS. His research area is in thermal/fluid sciences
with more background in micro-/mini-channel heat
transfer and fluid flow, thermal systems design and
simulation, condensation, and evaporation.

Mohammad Hosni is the department head of the
Mechanical and Nuclear Engineering Department at
Kansas State University, Manhattan, KS. He received
his Ph.D. in 1989 from Mississippi State University,
Mississippi State, MS. His area of expertise is thermal
and fluid sciences, and he has extensive experience
in both experimental and computational evaluation of
indoor air distribution. He is a fellow of the ASME
and ASHRAE.

Steven Eckels is a professor in the Mechanical and
Nuclear Engineering Department at Kansas State
University, Manhattan, KS. He received his Ph.D. in
1993 from Iowa State University, Ames, IA. His main
research areas include two-phase flow and heat transfer, enhanced heat transfer, thermal system modeling,
and human thermal comfort. He is currently director
of the Institute for Environmental Research at Kansas
State University.

heat transfer engineering

vol. 31 no. 1 2010

Heat Transfer Engineering, 31(1):17–24, 2010
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630903263242

Exergy Efficiency of Two-Phase Flow
in a Shell and Tube Condenser
YOUSEF HASELI, IBRAHIM DINCER, and GREG F. NATERER
Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, Oshawa, Ontario, Canada

This study deals with a comprehensive efficiency investigation of a TEMA “E” shell and tube condenser through exergy
efficiency as a potential parameter for performance assessment. Exergy analysis of condensation of pure vapor in a mixture of
non-condensing gas in a TEMA “E” shell and tube condenser is presented. This analysis is used to evaluate both local exergy
efficiency of the system (along the condensation path) and for the entire condenser, i.e., overall exergy efficiency. The numerical
results for an industrial condenser with a steam–air mixture and cooling water as working fluids indicate significant effects
of temperature differences between the cooling water and the environment on exergy efficiency. Typical predicted cooling
water and condensation temperature profiles are illustrated and compared with the corresponding local exergy efficiency
profiles, which reveal a direct (inverse) influence of the coolant (condensation) temperature on the exergy efficiency. Further
results provide verification of the newly developed exergy efficiency correlation with a set of experimental data.

INTRODUCTION

systems to evaluate both energy and exergy efficiencies and exergy destruction in an actual system. The comprehensive work
of Fiaschi and Manfrida [5] is another example, in which the
exergy destruction was analyzed at the component level, in a
semi-closed gas turbine combined cycle, in order to identify the
critical plant devices and main sources of irreversible losses.
Utilization of the exergy method in heat exchangers has
also been examined previously. Akpinar [6] studied experimentally the effects on heat transfer, friction factor, and dimensionless exergy loss by mounting helical (spring shaped) wires
of different pitch in the inner pipe of a double-pipe heat exchanger. The effects of process parameters, such as the mass

flow rate and temperature, on the entropy generation and exergy loss were theoretically and experimentally investigated by
Naphon [7] for a horizontal concentric tube heat exchanger.
In past work of San and Jan [8] involving a wet cross-flow
heat exchanger, the effectiveness, exergy recovery factor, and
second-law efficiency of the wet heat exchanger were individually defined and numerically evaluated for various operating conditions. Additionally, the exergy-based thermoeconomic
methodology has been developed in [9] and [10] for optimization
purposes.
Exergy analysis of condensation of steam from a mixture of
air in a TEMA “E” shell and tube condenser has been recently
performed by Haseli et al. [11]. They proposed two correlations
for evaluating the exergy efficiency along the exchanger and
entire condenser. These correlations are linear functions of a dimensionless temperature, defined as the ratio of the difference

Exergy is a measure of the departure of the state of a system
from that of the environment. It can be defined as the maximum
obtainable work from the combined system and its environment.
Unlike energy, exergy is not conserved, since it is destroyed
by irreversibilities. The exergy destruction during a process is
proportionally related to the entropy generation due to these
irreversibilities. Dincer [1] has examined exergy from several
perspectives and introduced the exergy analysis method as a
useful tool for developing more efficient energy-resource use.
Rosen and Dincer [2] studied the effects of variations in deadstate properties on the results of energy and exergy analyses. In
their case study, a coal-fired electrical generating station was
examined to illustrate the actual influences. Although energy
and exergy values are dependent on the intensive properties of
the dead state, it was shown that the main results of energy
and exergy analyses are usually not significantly sensitive to
reasonable variations in these properties.
Utilization of exergy analysis has been widely adopted recently in different applications. For instance, Ozgener et al.

[3, 4] applied the exergy method in geothermal district heating
The authors acknowledge the support provided by the Natural Sciences and
Engineering Research Council of Canada.
Address correspondence to Professor Ibrahim Dincer, Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, Ontario, Canada, L1H 7K. E-mail:


17


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Y. HASELI ET AL.

Figure 1 Plan view of the condenser.

between the coolant and environment temperatures, to the temperature difference between the condensation and environment.
Unlike the past work, this article develops a formulation of
exergy efficiency of condensation of a pure vapor in detail,
considering the influence of the presence of a non-condensing
gas in a TEMA “E” shell and tube condenser. Illustrative examples will provide new information about the effects of the
coolant, condensation, and environment temperatures on the
exergy efficiency. Furthermore, the correlation of the overall exergy efficiency proposed in previous work is validated through
comparisons with a set of experimental data.

Figure 2
flows.

Control volume of the condenser, illustrating the inlet and outlet

the system was brought to the dead state isentropically. Also, To

refers to the dead state (environment) temperature.
In Eq. (1), the term E˙ d accounts for the time rate of exergy
destruction due to irreversibilities within the control volume.
For an arbitrary control volume of a condenser shown in Figure
1, we have (see Figure 2):
E˙ inlet =

FORMULATION OF EXERGY EFFICIENCY
Exergy (second law) efficiency is formulated herein for condensation of pure vapor in a TEMA “E” shell and tube condenser, taking into consideration the effect of non-condensing
gas leakage. A plan view of this type of condenser is depicted
in Figure 1. The direction of the hot fluid, which enters from
one end of the heat exchanger and flows through the baffles to
the other end of it, is indicated with lined arrows. Condensation
takes place in the shell side, due to contact between the hot fluid
and cold wall of the tubes, through which coolant is flowing.
The steady-state exergy rate balance for a control volume can
be written as [12]:
1−
j

To ˙
˙ cv +
Qj −W
Tj

˙ 1 e1 −
m
1

˙ 2 e2 −E˙ d = 0

m

˙ v1 ev1 + m
˙ g1 eg1 + m
˙ c1 ec,1
˙ 1 e1 = m
m

(1)

E˙ outlet =

˙ 2 e2 = m
˙ v2 ev2 + m
˙ g2 eg2 + m
˙ c2 ec2
m
2

˙ cond econd
+m

˙ v1 ev1 + m
˙ g eg1 + m
˙ c ec1 ) − (m
˙ v2 ev2 + m
˙ g eg2 + m
˙ c ec2
(m
˙ cond econd ) = E˙ d

+m

(5)

With respect to the conservation of vapor mass,
˙ v2 + m
˙ cond
˙ v1 = m
m

˙ j represents the time rate of heat transfer at the location
where Q
˙ cv
on the boundary at the instantaneous temperature of Tj ; W
represents the time rate of energy transfer, by work other than
˙ accounts for the time rate of exergy transfer
flow work; and me
accompanying mass flow and flow work, with subscripts 1 and 2
representing the inlet and outlet, respectively. The specific flow
exergy, e, is evaluated using Eq. (2) as follows:

(4)

˙ g1 = m
˙ g2 = m
˙ g and m
˙ c1 = m
˙ c2 = m
˙ c . Thus, with
where m

˙j = W
˙ cv = 0, Eq. (1) can be written as follows:
Q

2

V2
e = (h − ho ) − To (s − so ) +
+ gz
2

(3)

1

(6)

Equation (5) can be rearranged as follows:
˙ v2 + m
˙ g (eg1 − eg2 ) − m
˙ cond ) ev1 − m
˙ v2 ev2 ] + m
˙ cond econd
[(m
˙ c (ec2 − ec1 ) + E˙ d
=m

(7)

or

(2)

where h and s denote, respectively, enthalpy and entropy of the
system and ho and so are the values of the same properties, if
heat transfer engineering

˙ v2 (ev1 − ev2 ) + m
˙ g (eg1 − eg2 ) + m
˙ cond (ev1 − econd )
m
˙ c (ec2 − ec1 ) + E˙ d
=m
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(8)


Y. HASELI ET AL.

The second law efficiency, i.e., exergy efficiency, can be now
defined as
˙ c (ec2 − ec1 )
m
ηex =
˙ g (eg1 − eg2 ) + m
˙ v2 (ev1 − ev2 ) + m
˙ cond (ev1 − econd )
m
(9)
In other words, ηex is the ratio of the net increase in the flow

exergy of cold fluid (coolant) between the inlet and outlet, to
the net decrease of the flow exergy of hot fluid (binary mixture)
from the inlet to the outlet.
The term e2 − e1 (net change of flow exergy) is evaluated
using Eq. (2) as follows:
e2 − e1 = h2 − h1 − To (s2 − s1 )

(10)

of condensate. As condensation occurs at Tcond ≤ Tv1 , the difference between the inlet enthalpy of vapor at a temperature of
Tv1 and the condensate enthalpy is determined by the sum of
heat transfer from cooling of the vapor from Tv1 to Tcond and
latent heat released at the condensation temperature. It may be
written in the form of the following expression:
hv1 − hcond = cp,v (Tv1 − Tcond ) + hfg|T=Tcond

sv1 − scond =

s2 − s1 = cp ln

T2
T1

(incompressible flow) (13)

where R is the gas constant and P denotes the pressure.
Thus, the flow exergy change in the coolant, vapor, and noncondensable gas in Eq. (9) can be formulated using Eqs. (14)–
(16).
ec2 − ec1 = cp,c (Tc2 − Tc1 ) − To ln

Tc2
Tc1

ev1 − ev2 = cp,v (Tv1 − Tv2 ) − To ln

Tv1
Tv2

(14)

sv + sv|T=Tcond − scond|T=Tcond

= cp,v ln

(11)

Also, depending on whether the flow is incompressible or compressible, the change of entropy between two states of a process
can be described as
P2
T2
− R ln
(compressible flow) (12)
s2 − s1 = cp ln
T1
P1

(18)

Also, entropy of the inlet vapor, sv1 , may be expressed as the
sum of the entropy difference due to the temperature difference

Tv1 − Tcond at constant pressure Pv1 and entropy of saturated
vapor at a temperature of Tcond , sv|T=Tcond . Hence, the entropy
difference in Eq. (17) can be written as

Assuming a constant specific heat, cp , the difference of enthalpy
between two states of a process may be written as
h2 − h1 = cp (T2 − T1 )

19

Tv1
Tcond

+ sfg|T=Tcond

(19)

Substituting Eqs. (18) and (19) into Eq. (17) yields
ev1 − econd = cp,v (Tv1 − Tcond ) + hfg|T=Tcond
− To cp,v ln

Tv1
Tcond

+ sfg|T=Tcond

or
ev1 − econd = cp,v (Tv1 − Tcond ) − To ln
+ hfg|T=Tcond − To sfg|T=Tcond

Tv1
Tcond
(20)

It should be noted that hfg and sfg are dependent on the saturation
temperature. The next section presents numerical results of the
second law efficiency for an industrial scale condenser.

RESULTS AND DISCUSSION
Pv1
+ To Rv ln
Pv2

(15)

eg1 − eg2 = cp,g (Tg1 − Tg2 ) − To ln

+ To Rg ln

Tg1
Tg2

Pg1
Pg2

(16)

In the bulk mixture, it is assumed that the temperature is uniform,
so that vapor and non-condensable gas temperatures are the
same in the inlet and outlet of the control volume, i.e., Tv1 = Tg1

and Tv2 = Tg2 . Also,
ev1 − econd = hv1 − hcond − To (sv1 − scond )

(17)

The preceding method cannot be used to determine the difference between inlet flow exergy of steam and the flow exergy
heat transfer engineering

This section deals with numerical evaluation of the exergy
efficiency, ηex , for a typical counter-current TEMA “E” shell
and tube exchanger of almost standard industrial design. The
condenser has an exchange area of 30 m2 , with 0.438 m diameter
and 2.438 m length. The shell is divided into eight equal spaces
by seven baffles with a cut of 35.5%. The tubes, which are of
19.05 mm OD, 14 SWG, are arranged on a 25.4 = mm triangular
pitch with a characteristic angle of 30◦ [13]. Superheated steam
at 125◦ C and 1 kg/s enters the condenser. Condensation of steam
takes place in baffle spaces when contacting the cold wall of the
tubes, through which cooling water at a mass flow rate of 62.5
kg/s is flowing.
It is convenient to present correlations that predict the evaporation/condensation enthalpy and entropy of water vapor, as
required in Eq. (20). The following correlations are used for
hfg and sfg , based on the ASME International Steam Tables for
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20

Y. HASELI ET AL.

Figure 3 Variation of exergy efficiency along the condensation path at various
environment temperatures.

Industrial Use [14]. They correlate the variables by linear functions of temperature, at which the condensation/evaporation of
water occurs, with less than 0.3% error in the range of 10–70◦ C.
T : [◦ C] (21)

hfg = 2501.6 − 2.3981T

h : [kJ/kg] ,

sfg = 9.0093 − 0.0324T

s : [kJ/kg.K] , T : [◦ C] (22)

Equation (9) can be utilized to evaluate either exergy efficiency along the condensation path (local exergy efficiency) or
for the entire condenser (overall exergy efficiency). In the first
case, one needs to obtain the variation of temperatures (including
the shell side, tube side, and condensate) along the condensation path. For this purpose, the numerical model of Haseli and
Roudaki [13], which uses film theory with heat and mass transfer equations, is utilized to determine the relevant parameters.
By accounting for a diversity of parameters, such as the effects
of heat and mass transfer rates, variations of physical properties with temperature and the effects of exchanger geometry on
performance, the model can accurately predict the temperature
profiles and rate of condensation of steam in the presence of
air along a shell and one-path tube condenser. The previous
exergy methodology is merged with the past model of Haseli
and Roudaki [13] to obtain the variation of exergy efficiency
along the condenser. In order to determine the overall exergy
efficiency of the condenser, one must use the outlet values of
temperatures and mass flow rates, as well as the appropriate

average condensation temperature resulting from the previously
mentioned model.
Figure 3 illustrates the variation of exergy efficiency, ηex ,
along the condensation path at various environment temperatures for a typical process condition. In this figure, a higher
environment temperature at a constant inlet cooling-water temperature results in a lower exergy efficiency along the condenser.
In other words, as the temperature difference between the inlet cooling water and environment, i.e., Tin = Tc,in − To , deheat transfer engineering

Figure 4 Similarity of exergy efficiency curves along the condenser.

creases, then ηex is reduced. It can also be observed from the
figure that ηex decreases from the entrance of the steam–air
mixture to the location after the midpoint in the condenser—a
region around the fifth baffle space. Then it starts to increase
from this point to the outlet of the heat exchanger. It seems
that there is a relation between the condensation heat transfer and the exergy efficiency. Past studies [13, 15] have shown
that from the region where exergy efficiency is a minimum,
the condensation and heat transfer rates diminish significantly.
Beyond this region, the relative role of sensible heat transfer
increases.
Figure 4 depicts the set of curves that correspond to the same
T. It is seen that when T = 0, the exergy graphs decrease
consistently along the exchanger. An important result from Figure 4 is that T has a significant influence on the exergy efficiency, rather than the inlet cooling-water temperature itself.
As T increases, ηex becomes higher. This result agrees with
the definition of exergy. When a system carries more exergy, it
deviates more from the environment. Based on these results, it
can be understood why ηex decreases from the entrance of the
steam–air mixture to around the fifth baffle space, considering
the configuration of the condenser in this study (a counterflow
type). As cooling water flows in the opposite direction of the
steam–air mixture, its temperature increases from the last baffle

space to the first one. An example is shown in Figure 5. At a
given environment temperature, the local T = (Tc − To ) will
increase in the same direction. Except for the region where the
curves of Figure 3 have a positive slope, it seems that the local T plays a dominant role in the variation of ηex . However,
as reported in our previous work [11], in addition to T, the
condensation temperature may influence the exergy efficiency.
Additional explanation about this trend will be given hereafter.
In our recent paper [16], the predictive model exhibits error in
the last baffle spaces (as an example, in Figure 4, with baffle
numbers 6 to 8). This may explain the divergence of curves after
vol. 31 no. 1 2010


Y. HASELI ET AL.

Figure 5

Variation of cooling water temperature along the condensation path.

baffle number 6 in Figure 4. Reference [16] presents the detailed
derivation of an explicit expression for the exergy efficiency.
Figure 6 shows the effects of air mass flow rate on ηex . It
reveals that higher exergy efficiency may result from higher air
leakage. Irreversibility of the process, as characterized by the
entropy generation rate in the condenser, diminishes with air
leakage since this reduces the rate of condensation heat transfer
[17]. Based on the relation between the local T and exergy
efficiency, one expects that the profile of cooling water temperature corresponding to the higher air mass flow rate in Figure 6
is higher. The predicted cooling water temperature and condensation temperature profiles along the condenser are depicted in
Figure 7 for the same air mass flow rates shown in Figure 6.

As seen in Figure 7, since the temperature profiles of cooling
water are approximately the same in the first few baffle spaces,

Figure 6 Effect of air mass flow rate on exergy efficiency along the condensation path and predicted outlet steam mass flow rates.

heat transfer engineering

21

Figure 7 Predicted cooling-water and condensation temperatures along the
condensation path at three different air mass flow rates.

the local T is the same (environment temperature is 10◦ C in
Figure 6) in this region for all cases. On the other hand, a significant difference between the condensation temperature profiles
occurs, as a higher air mass flow rate results in a lower condensation temperature in the first baffle spaces. Thus, comparing
curves of Figures 6 and 7, it may be implied that the condensation temperature may have an inverse impact on the exergy
efficiency, while other process parameters remain nearly constant. A comparison of the temperature and ηex profiles in the
last baffle space in Figures 6 and 7, respectively, shows that the
condensation temperature may inversely influence the exergy
efficiency, since the cooling-water temperature has the same
profile for all cases in this region, so T is constant. The predicted outlet steam mass flow rates are also given in Figure 6.
Air is a non-condensable component that provides resistance to
heat and mass transfer processes. Increasing the air mass flow
rate leads to a lower heat transfer rate and condensation rate.
Further discussion may be found elsewhere (such as [15]). In
order to explain the trend of curves in Figure 3, as long as all
steam has not condensed, ηex decreases along the condensation
path. When condensation of steam finishes (usually by the last
baffle space), ηex will increase.
Dependence of the overall exergy efficiency of the condenser,

ηex,overall , on the environment temperature at different inlet cooling water temperatures is illustrated in Figure 8. At a fixed external environment temperature, a higher inlet cooling water
temperature leads to a higher overall exergy efficiency. Since
the cooling water carries more exergy at the higher inlet temperature (and therefore a higher mean temperature of cooling
water), the irreversibility within the system will diminish. In
addition, in order to establish a specific ηex,overall at different environment conditions, it is required to change the inlet cooling
water temperature. A similarity between the illustrated curves
can be observed in Figure 8. A common trend that agrees with
previous results is that ηex,overall increases when the difference
vol. 31 no. 1 2010


22

Y. HASELI ET AL.
Table 1 Inlet and outlet measured performance parameters
Quantity

Inlet
(◦ C)

Vapor temperature
Steam mass flow rate (kg/s)
Cooling water temperature (◦ C)
Cooling water mass flow rate (kg/s)
Pressure (kPa)

Outlet

62.94
58.48

0.345
0.0392
47.63
51.57
43.45
22.9

Note. Source: Ref. [18].

Figure 8 Dependence of the overall condenser exergy efficiency on environment temperatures at various inlet cooling-water temperatures.

between the inlet cooling-water temperature and environment
temperature increases.
In a previous study [11], the following correlation was developed to predict the overall exergy efficiency of a heat exchanger,
where condensation of steam takes place in the presence of air:
ηex,overall = 0.9677θ + 0.1939 (R2 = 0.994)

(23)

where θ is defined as:
θ=

Tc,in − To
Tcond − To

(24)

For further validation purposes, predictions of the proposed
correlation described in Eq. (23) are compared with past experimental data of Webb et al. [18], which were taken from

Figure 9 Illustration of the experimental configuration of Webb et al. [18].

heat transfer engineering

a similar industrial-scale exchanger. Webb and his coworkers
measured an extensive set of experimental data of condensation
of steam and steam–air mixtures at atmospheric and reduced
pressures in TEMA “E” shell and “J” shell condensers. The
experiments consist of a condenser, an after condenser, cooling water circuit, vacuum pump, and plant instrumentation. The
experimental setup is illustrated in Figure 9. Steam was generated by a boiler at a rate of up to 1 MW and the system was
usually operated under partial vacuum, maintained by a liquid
ring pump. Cooling water was circulated in a pump-around with
controlled addition to give the desired temperature. Calibrated
thermocouples were used to measure the coolant and vapor inlet
and outlet temperatures. The condensate flow rate was measured
by direct collection in each half of the condenser and the cooling
water flow rate by an orifice plate. A typical reported set of measured performance parameters of a TEMA “E” shell condenser
is given in Table 1.
Comparisons of Eq. (23) with experimental data (based on
Table 1) are illustrated in Figure 10 at various ambient temperatures (represented by the numbers beside the points) in the
range of 10–45◦ C. From this figure, it is apparent that Eq. (23)
overpredicts the second law efficiency of the exchanger within
an offset of –15%. This overprediction is even lower at cooler
ambient temperatures. Close agreement between this correlation
and experimental data over a range of temperatures in Figure 10

Figure 10 Comparison of proposed correlation, Eq. (23), with measured data
of Webb et al. [18].

vol. 31 no. 1 2010

Y. HASELI ET AL.

provides useful validation of the predictive model and resulting
correlation in Eq. (23).

CONCLUSIONS
The exergy efficiency has been formulated for condensation
of a binary mixture with one non-condensable component in
a TEMA “E” shell and tube condenser. The exergy efficiency
model may be expressed as a function of the inlet and outlet
temperatures and mass flow rates of both streams across the
boundary of a control volume, as well as the condensation temperature. Numerical results are obtained through a combination
of the exergy formulation with a recent calculation method for
an industrial-scale countercurrent condenser, where condensation of steam occurs in the presence of air with cooling water
as a coolant. The results show that the temperature difference
between the cooling water and environment has a considerable
influence on the exergy efficiency, whereas the condensation
temperature has an inverse effect on the exergy efficiency. In
addition, when the inlet cooling water temperature is greater
than the environment temperature, the exergy efficiency decreases along the heat exchanger, as long as condensation of
steam occurs. However, when condensation of steam almost
finishes, it tends to increase. The correlation of overall exergy
efficiency of the condenser proposed in previous work was also
verified through a comparison of the model results with a set of
experimental data.

NOMENCLATURE
cp

e
E˙ d
E˙ inlet
E˙ outlet
g
h
hfg
ho
˙
m
˙ air
m
P
˙j
Q
R
R2
s
sfg
so
sv|T=Tcond

specific heat, kJ/kg-K
flow exergy, kJ/kg
exergy destruction rate, kW
inlet exergy rate, kW
outlet exergy rate, kW
gravitational acceleration, m/s2
enthalpy, kJ/kg
condensation latent heat, kJ/kg

enthalpy at reference environment (dead state),
kJ/kg
mass flow rate, kg/s
air mass flow rate, kg/s
pressure, kP
heat transfer rate at the location j on the boundary,
kW
gas constant, kJ/kg-K
correlation coefficient
entropy, kJ/kg. K
latent entropy, kJ/kg. K
entropy at reference environment (dead state),
kJ/kg-K
entropy of saturated vapor at a temperature of Tcond ,
kJ/kg-K
heat transfer engineering

T
Tc,in
Tj
To
V
˙ cv
W
z

23

temperature, K
cooling water temperature at condenser inlet, ◦ C

instantaneous temperature, K
dead state/environment temperature, K
velocity, m/s
energy transfer rate by work, kW
elevation, m

Greek Symbols
sv
T
Tin

θ
ηex
ηex,overall

entropy difference due to temperature difference,
kJ/kg-K
difference between a given cooling water temperature and environment temperature, ◦ C
difference between cooling water temperature at
the inlet of control volume and environment temperature, ◦ C
dimensionless temperature, Eq. (23)
exergy efficiency
overall exergy efficiency

Subscripts
1
2
c
cond
g

o
v

inlet conditions
outlet conditions
coolant
condensate
non-condensable gas
reference environment (dead state)
vapor

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heat transfer engineering

Yousef Haseli received his master’s degree in mechanical engineering from the University of Ontario,
Institute of Technology, Ontario, Canada (received
the Governor General’s Gold Medal). He received
his B.Sc. degree in mechanical engineering, thermal power plant option (first class honors), from the
Power and Water University of Technology, Tehran,
Iran. His research interests are mathematical modeling of condensation of steam–air mixture, second law
analysis of energy systems, thermodynamic modeling of integrated gas turbine SOFC power plants, and transport phenomena in
fluidized beds. He has published more than 20 articles in journals and conference
proceedings.
Ibrahim Dincer is a full professor in the Faculty
of Engineering and Applied Science at University of
Ontario, Institute of Technology, Ontario, Canada.
Renowned for his pioneering works, he has authored
and co-authored several books and book chapters,
over 450 refereed journal and conference papers, and
numerous technical reports. He has chaired many national and international conferences, symposia, workshops, and technical meetings. He has delivered over
100 plenary, keynote, and invited lectures. He is an

active member of various international scientific organizations and societies,
and serves as editor-in-chief, associate editor, regional editor, and editorial
board member on various prestigious international journals. He is a recipient
of several research, teaching, and service awards, including the Premier’s research excellence award in 2004. He has made innovative contributions to the
understanding and development of sustainable energy technologies and their
implementation.
Greg Naterer is a Tier 1 Canada Research Chair in
Advanced Energy Systems and a professor of mechanical engineering at the University of Ontario Institute of Technology. He is an associate dean in the
Faculty of Engineering and Applied Science. He received his Ph.D. in mechanical engineering from the
University of Waterloo in 1995. His research interests
involve design of energy systems, hydrogen technologies, and heat transfer, with over 210 journal and conference publications in these fields. He has authored
a book entitled Heat Transfer in Single and Multiphase Systems (CRC Press,
2003), as well as another book in 2008 entitled Entropy Based Design of Fluids
Engineering Systems. He is a fellow of the Canadian Society for Mechanical
Engineering and an associate fellow of the American Institute of Aeronautics
and Astronautics.

vol. 31 no. 1 2010