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Pag. 26
Thermo-hydraulic design of a finned tube double-pipe heat exchanger
for acetone cooling.
Diseño térmico-hidráulico de un intercambiador de calor de doble tubo aleteado para el
enfriamiento de acetona.
Amaury Pérez Sánchez
1
*; Elizabeth Elianne Artigas Cañizares
2
; Laura Thalia Alvarez Lores
3
; Elizabeth Ranero González
4
& Eddy Javier Pérez
Sánchez
5
Received: 21/11/2024 – Accepted: 03/02/2025 – Published: 01/07/2025
Research
Articles
X
Review
Articles
Essay
Articles
* Corresponding author.
Abstract.
Finned tube double-pipe counter-flow heat exchangers are considered very effective, valuable and advantageous in the heat transfer industry. In the
present paper a finned tube double pipe heat exchanger was designed applying a well-known design methodology, in order to cool down 2 kg/s of an
acetone stream from 90 ºC to 30 ºC using chilled water available at 5 ºC. Several important design parameters were determined like the cleanliness factor
and the number of hairpins, as well as the pressure drop and pumping power of both streams, among others. The heat load had a value of 276,030 W,
while a mass flowrate of chilled water of 3.30 kg/s will be needed to cool the acetone stream. Both fluids will flow under turbulent regime inside the heat
exchanger. The value of the cleanliness factor was 0.359, and about three hairpins will be needed. The pressure drop of both fluids are below the maximum
value established by the heat exchange service, while the chilled water and acetone streams will need a pumping power of 3,662 W and 575 W,
respectively.
Keywords.
Double pipe heat exchanger, finned tube, number of hairpins, pressure drop, pumping power.
Resumen.
Los intercambiadores de calor de flujo a de doble tubo aleteados a contracorriente son considerados muy efectivos, valiosos y ventajosos en la industria
de la transferencia de calor. En el presente artículo un intercambiador de calor de doble tubo aleteado fue diseñado aplicando una metodología de diseño
bien conocida, con el fin de enfriar 2 kg/s de una corriente de acetona desde 90 ºC hasta 30 ºC usando agua fría disponible a 5 ºC. Varios parámetros de
diseño importantes fueron determinados tales como el factor de limpieza y el número de horquillas, así como también la caída de presión y potencia de
bombeo de ambas corrientes, entre otros. La carga de calor tuvo un valor de 276 030 W, mientras que se necesitará un caudal másico de agua fría de 3,30
kg/s para enfriar la corriente de acetona. Ambos fluidos fluirán bajo régimen turbulento dentro del intercambiador de calor. El valor del factor de limpieza
fue de 0,359, y se necesitarán alrededor de tres horquillas. La caída de presión de ambos fluidos está por debajo del valor máximo establecido por el
servicio de transferencia de calor, mientras que las corrientes de agua fría y acetona necesitarán una potencia de bombeo de 3 662 W y 575 W,
respectivamente.
Palabras clave.
Intercambiador de calor de doble tubo, tubo aleteado, número de horquillas, caída de presión, potencia de bombeo.
1. Introduction.
With the development of know-how, the significance of
heat transfer engineering has boosted and there is a
permanently need to encounter new design challenges to
increase the performance and efficacy of the heat transfer
field, particularly due to energy saving interests. Usually,
heat exchangers are widely used for this purpose [1].
Heat exchangers are devices operated in numerous
industries for heat transfer among fluids. Of the several
types of heat exchangers that are utilized at industrial scale,
1
University of Camagüey; Faculty of Applied Sciences; amaury.perez84@gmail.com; https://orcid.org/0000-0002-0819-6760,
Camagüey; Cuba.
2
University of Camagüey; Faculty of Applied Sciences; elizabeth.artigas@reduc.edu.cu; https://orcid.org/0009-0003-3416-1355,
Camagüey; Cuba.
3
University of Camagüey; Faculty of Applied Sciences; laura.alvarez@reduc.edu.cu; https://orcid.org/0009-0007-2643-018X,
Camagüey; Cuba.
4
University of Camagüey; Faculty of Applied Sciences; eliza.eddy2202@gmail.com; https://orcid.org/0000-0001-9755-0276,
Camagüey, Cuba.
5
Company of Automotive Services S.A.; Commercial Department; eddyjavierpsanchez@gmail.com; https://orcid.org/0000-0003-
4481-1262, Ciego de Ávila, Cuba.
possibly the two most significant are the double pipe and
the shell and tube. Despite the fact that shell and tube heat
exchangers generally provide greater surface area for heat
transfer with a more compact design, greater ease of
cleaning, and less probability of leakage, the double pipe
heat exchanger (DPHE) still finds use in practice today [2].
One of the heat exchangers that have attracted the attention
of researchers and engineers is the DPHE due to simplicity,
effectiveness and wide range of usages [3].
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Pag. 27
A DPHE is a distinctive type of heat exchanger with two
concentric pipes, one inside the other. There are two
different fluid flows in a DPHE, such that one fluid flows
inside the inner pipe and the other fluid flows in the annulus
region outside of the inner pipe [4]. It involves two
concentric pipes, two connecting tees, a return head, a return
feed, and packing glands that support the inner pipe within
the outer pipe (Figure 1). Each of two fluids −hot and cold−
flow either through the inside of the inner pipe or through
the annulus formed between the outside of the inner pipe
and the inside of the outer pipe [2].
Fig. 1. Double pipe heat exchanger.
Source: [2].
DPHE have been utilized in the chemical processing
industry for over 100 years. The first patent on this unit
appeared in 1923 [2]. They are applied in several industrial
processes and research areas; for example in waste heat
recovery, for heating/cooling in chemical processes, as well
as in the food industry to pasteurize/preheat liquid products
(juices, mashes, jelly, etc.).
The DPHE is particularly convenient because it can be
connected in any pipe-fitting shop from standard parts and
offers an economical heat-transfer surface. The flow
arrangement in this heat exchanger could be countercurrent
or parallel (co-current). In countercurrent arrangement, the
fluid in the pipe flows in a direction reverse to the fluid in
the annulus. In parallel arrangement, the two fluids flow in
the same direction. The variations of fluid temperature
within the heat exchanger depend on whether the flow is
parallel or countercurrent [2].
The main application of the DPHE is for sensible heating or
cooling of process fluids where small heat transfer areas (up
to 50 m
2
) are necessary. This heat exchanger is also very
appropriate for handling fluids with high pressure, because
of the smaller diameter of the pipes. The major disadvantage
is that they are bulky and expensive per unit of heat transfer
surface area [5].
Although this unit is not extensively employed in industry
(the heat transfer area is small relative to other heat
exchangers), it serves as an excellent starting point from an
academic and/or training perspective [2].
According to [6], if the stream contains solids in suspension,
DPHEs may also be a better alternative, because they can
be built with an inner tube with larger diameter to avoid
plugging. Smaller diameters of the outer tube in DPHEs are
effective for high-pressure applications, because it involves
a smaller wall thickness. In addition, DPHEs may be easily
cleaned, and the longitudinal flow avoids the existence of
stagnation regions, which in shell and tube exchangers may
cause fouling and corrosion. DPHEs have also the
advantage of robustness due to its modular structure, which
permits an easier adaptation to process adjustments.
Growing need to develop and improve the effectiveness of
heat exchangers has led to a broad range of investigations
for increasing heat transfer rate along with decreasing the
size and cost of the industrial apparatus accordingly [3]. The
enhancement of heat transfer has become an important
factor in achieving these goals and has captured the interest
of many researchers [7].
Enhancement of heat transfer in heat exchangers can be
accomplished through two techniques [7]:
1. Increasing the convection coefficient. The convection
coefficient may be improved by increasing turbulence,
creating secondary flow, and inducing swirl flow. One or
more of these mechanisms may be accomplished using coil-
spring wire, ribs, indentation, spiral flutes transverse-ribbed
tubes, helically ribbed tubes, wire-coil insert, twisted-tape
insert, ribbed or ribbed grooved walls. Also, the convective
heat transfer coefficient may be enhanced using fluids that
experience a phase transition or by using
electrohydrodynamic enhancement tools and employing
mist flow.
2. Expanding the heat transfer area by employing
longitudinal fins, wire-on-tube heat exchangers.
Other techniques apply both effects. Examples of these
techniques are spiral fins or ribs and offset strip fins.
According to [4] the performance of heat exchangers can be
enhanced by adopting appropriate procedures. These
procedures comprise the implementation of extended
surfaces, surface vibration, rough surfaces, and coiled tubes.
Other authors [7] numerically investigated the effect of
inserting porous substrates at both sides of the wall that
separates the cold and hot working fluids on the
performance of a conventional concentric tube heat
exchanger.
Thermal systems are currently amongst the most dynamic
technical systems. Numerous methods have been explored
and tested in order to increase heat transfer in these systems
and accomplish a high level of thermal performance. By
exploiting a number of surface-enhancement-based
approaches, the heat transfer rate of conventional heat
exchangers may be improved. This development in heat
transfer rate results from the conditions provided by the use
of enhanced surfaces. These conditions prevent the
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Pag. 28
formation of the boundary layer, improve the turbulence
level, increase the heat transfer area, and generate swirling
and/or secondary flows. Enhanced heat transfer surfaces
have several objectives for their use, being the most
important to reduce the size of heat exchangers, which could
lead to a decrease in their costs. In addition, they reduce the
pumping power that is needed for specific thermal exchange
processes, and improve the heat transfer coefficient. In turn,
this increases the effectiveness and efficiency of thermal
processes and results in operating cost savings [8].
Recently, several researchers have investigated ways to
enhance heat transfer using the passive way in double-pipe
heat exchangers (DPHE), such as using twisted strips,
extended surfaces or fins, wired coils, and other turbulence-
generating tools [9].
The use of solid fins to boost the heat transfer rates between
two different fluids in tubular heat exchangers is one of the
most successful and extensively applied approaches. Finned
tubes are one of the most commonly used ways of passively
enhancing the heat transfer in circular tube. They are
applied to decrease the size of a heat exchanger required for
a specified heat duty, or to increase heat transfer rate of an
existing heat exchanger design. An internally finned tube
can substantially increase the surface area, and can
significantly augment the heat transfer rate. Finned tubes
perform differently depending on whether the flow is
laminar or turbulent. For both laminar and turbulent flow
regimes, the finned tubes exhibit significantly higher heat
transfer coefficients when contrasted with the
corresponding smooth tubes. The performance of finned
pipe is mainly determined by the type of flow, fin efficiency
(which determines the average heat transfer coefficient) and
the friction factor, which is responsible for
pressure/pumping loss [10].
The use of a finned tube to increase heat transmission is
becoming more important in a growing number of industrial
applications; thus, the finned tube has been the subject of
several studies [8]. In this context, [9] investigated the
convection heat transfer in a countercurrent double-tube
heat exchanger with a curved rectangular fin and
rectangular fin in a turbulent flow using water-Al
2
O
3
and
water-TiO
2
nanofluids. Also, in [11] the enhancement of the
thermal performance of the phase change material in a
double-tube heat exchanger using new grid annular fins was
investigated. In this study, the grid annular fins, which
consisted of straight and circular strip components, were
located on the inner tube. In another study, [8] carried out a
numerical investigation of heat transfer enhancement in a
double pipe heat exchanger embedded with an extended
surface on the inner tube’s outer surface with the addition
of Alumina nanofluid and by using computational fluid
dynamics (CFD) simulation. This investigation was carried
out at Reynolds numbers ranging from 250 to 2,500 with an
inner diameter of 20.4 mm. while the effect of the inner
pipe’s U fins’ geometry on pressure drop, temperature
distribution, and thermal performance was also scrutinized.
Moreover, [12] carried out the numerical examination of
heat transfer enhancement in individual annular serrated
fins double tube heat exchanger, concluding that the
maximum value of Nusselt number and maximal skin
friction coefficient was found in 14 serrated fins. Besides,
[4] studied the characteristics of convective heat transfer in
the annular region of a finned DPHE with an innovative
diamond-shaped fin design. The diamond-shaped fins are
longitudinally increased on the outer surface of the inner
pipe of the DPHE. The arrangement of the diamond-finned
annulus was verified by the numerous values of the
geometrical parameters, such as the radii ratio, fins number,
fin-height, and fin thickness. The effects of these variables
on various performance parameters, such as the product of
the Reynolds number and friction factor, Nusselt number,
and j-factor, were computed. The type of fin evaluated in
this study was considered for the first time in the design of
DPHEs. In [10] a simple semi-empirical-numerical
methodology to evaluate heat transfer and pressure drop
characteristics in a finned tube heat exchanger with internal
and/or external fins was described, which can be applied in
a wide range of operating conditions of practical
importance. In [3] the thermo hydraulic performance of a
proposed design of an air-to-water double pipe heat
exchanger with helical fins on the annulus gas side was
numerically studied. Three-dimensional CFD simulations
were implemented, using the FLUENT software with the
aim of examine the gas side fluid flow, turbulence, heat
transfer, and power consumption for different arrangements
of the heat exchanger. Moreover, [13] carried out various
experiments to investigate and compare the heat transfer in
a DPHE for counter flow arrangement with and without
usage of longitudinal triangular fins. Triangular fins with
dimensions of 9 mm base, 8 mm height and 2 mm thickness
were applied in this study. Other authors [6] investigated the
design optimization of a DPHE using mathematical
programming. The heat exchanger area is decreased and the
thermo-fluid dynamic settings are considered for the
application of the right transport equations, together with
design conditions, such as maximum pressure drops and
minimum excess area. The modular structure of this heat
exchanger type and the allocation of the streams (inside the
inner tube or in the annulus) are also considered. Two
mixed-integer nonlinear programming (MINLP)
approaches were also purported. Likewise, [14] aimed to
develop new designs of DPHE to improve the
heating/cooling processes at the lowest possible pumping
power. Consequently, the thermal performance analysis of
three configurations of DPHE was implemented. The
studied arrangements were circular wavy DPHE, plain oval
DPHE and an oval wavy DPHE. In addition, the
conventional DPHE was utilized as a reference heat
exchanger, and a validated CFD approach was executed to
perform this study. In [15], the helical fins effect in the
performance of a water-air DPHE was examined
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Pag. 29
experimentally. The performance in terms of average heat
transfer rate, heat transfer coefficient and effectiveness of
heat exchanger in plain inner pipe (without helical fin) was
assessed and contrasted with a heat exchanger having
helical fins installed over inner pipe. In [1], the analysis of
fully developed laminar convective heat transfer in an
innovated design of a finned DPHE with longitudinal fins
of variable thickness of the tip subjected to the constant heat
transfer rate boundary conditions was investigated. In this
study, the overall performance of the proposed DPHE was
examined by taking into account the friction factor, the
Nusselt number and the j-factor. Finally, [16] aimed at
comparison of heat transfer characteristics using different
fin profiles for a DPHE under various operating conditions
to evolve with the best possible configuration. The selected
configurations in this study were rectangular, triangular and
concave parabolic. Base width, height and number of fins
were held identical to be specifically compared. Numerical
simulation was completed using commercial CFD software.
Several particular heat transfer parameters like temperature
deviation, heat transfer rate, heat transfer coefficient and fin
effectiveness for the models mentioned above were
compared and shown.
The addition of porous material as an alternative method to
improve heat exchange in these thermal equipment seems to
be promising. In this sense, [17] investigated the heat
transfer enhancement when porous fins are attached at the
inner cylinder of a DPHE. This arrangement is selected in
order to augment the heat transfer surface area between the
fins and the cold fluid to be heated. The influence of several
parameters such as Darcy number, the height and spacing of
fins and the thermal conductivity ratio on the hydrodynamic
and thermal fields were also investigated.
Liquid acetone is produced in a chemical processing plant,
and it’s desired to cool down this liquid acetone stream from
90 ºC to 30 ºC, using chilled water available at 5 ºC. To
accomplish this heat exchange operation, a finned tube
double pipe heat exchanger has been proposed due to space
availability and limited budget. Thus, the present paper
aimed to design a finned tube DPHE both from the thermal
and hydraulic points of view, using the methodology and
correlations reported in [5] and [18], where several
important design parameters were determined such as the
cleanliness factor and the total number of hairpins, as well
as the pressure drop and pumping power of both streams.
2. Materials and methods.
2.1. Problem definition.
It’s required to cool 2 kg/s of an acetone stream from 90 ºC
to 30 ºC using chilled water at 5 ºC. The chilled water outlet
temperature must not be higher than 25 ºC. The following
initial parameters are available (Figure 2):
• Length of hairpin (
): 4.2 m.
• Nominal diameter of annulus: 2 in.
• Nominal diameter of inner tube: ¾ in.
• Fin height (
): 0.0125 m
• Fin thickness (): 0.9 mm.
• Number of fins per tube (
): 28.
• Material: Carbon steel.
• Thermal conductivity of carbon steel (
): 52 W/m.K
[5].
• Number of tubes inside the annulus (
): 1.
Fig. 2. Cross section of a longitudinally finned inner tube
heat exchanger and nomenclature of the initial
parameters.
Source: [5].
According to [5] the fouling factors for acetone and water
are 0.000352 and 0.000176 m
2
.K/W respectively. It’s
preferred that both streams flow under countercurrent
arrangement in the designed heat exchanger, while the
pressure drop of the acetone and chilled water must not
exceed 200,000 Pa and 900,000 Pa, respectively. Calculate
the surface area and the number of hairpins of the heat
exchanger, as well as the pressure drops and pumping power
for both streams.
2.2. Number of hairpins.
Step 1. Definition of the initial parameters.
Step 2. Diameters of both the inner tube and annulus.
Step 3. Average temperature of both fluids:
• Hot fluid:
(1)
• Cold fluid:
(2)
Step 4. Physical properties of both fluids at the average
temperature of the previous step.
Table 1 shows the physical properties that must be defined
for both fluids at the average temperature calculated in the
previous step.
Table 1. Physical properties of both fluids
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Pag. 30
Physical
property
Acetone
Chilled
water
Units
Density
h
c
kg/m
3
Viscosity
h
c
Pa.s
Thermal
conductivity
h
k
c
k
W/m.K
Heat capacity
h
Cp
c
Cp
J/kg.K
Source: Own elaboration.
Step 5. Heat load ():
(3)
Step 6. Mass flowrate of chilled water (
):
(4)
Step 7. Location of the fluids inside the heat exchanger.
Step 8. Net cross-sectional area in the annulus with
longitudinal finned tubes (
):
(5)
Step 9. Total wetted perimeter of the annulus with
longitudinally finned inner tubes (
):
(6)
Step 10. Hydraulic diameter (
):
(7)
Step 11. Heat transfer perimeter of the annulus for heat
transfer (
):
(8)
Step 12. Equivalent diameter for heat transfer (
):
(9)
Step 13. Velocity of the tube side fluid (
):
(10)
Step 14. Reynolds number of the tube side fluid (
):
(11)
Step 15. Prandtl number of the tube side fluid (
):
(12)
Step 16. Nusselt number of the tube side fluid (
t
Nu
):
• Laminar regime (
< 2,300):
Temperature of the tube wall (
):
(13)
Viscosity of the tube side fluid (
) and water (
) at
.
Nusselt number of the tube side fluid under laminar flow:
(14)
• Transition regime (2,300
10,000):
h
t
Cp
t
∙ρ
t
∙u
t
=0.116∙
Re
t
0.66
-125
Re
t
∙ 1+
d
i
L
t
0.66
∙Pr
t
-0.66
∙
μ
t
μ
w
0.14
(15
)
• Turbulent regime (10,000 <
< 5,000,000):
Friction factor (
t
f
):
(16)
Nusselt number (
t
Nu
):
(17)
Step 17. Convective heat transfer coefficient of the tube side
fluid (
t
h
):
(18)
Step 18. Velocity of the annulus fluid (
a
u
):
(19)
Step 19. Reynolds number of the annulus fluid (
a
Re
):
(20)
Step 20. Prandtl number of the annulus fluid (
a
Pr
):
(21)
Step 21. Nusselt number of the annulus fluid (
a
Nu
):
• Laminar regime (
< 2,300):
Viscosity of the annulus fluid (
) at
.
Nusselt number of the annulus fluid:
(22)
• Transition regime (2,300
10,000):
h
t
Cp
a
∙ρ
a
∙u
a
=0.116∙
Re
a
0.66
-125
Re
a
∙ 1+
D
h
L
t
0.66
∙Pr
a
-0.66
∙
μ
a
μ
w
0.14
(23
)
• Turbulent regime (10,000 <
< 5,000,000):
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Friction factor (
):
(24)
Nusselt number (
a
Nu
):
(25)
Step 22. Convective heat transfer coefficient of the annulus
fluid (
):
(26)
Step 23. Finned heat transfer area (
):
(27)
Step 24. Unfinned heat transfer area (
):
(28)
Step 25. Total area of hairpin (
):
(29)
Step 26. Factor :
(30)
Step 27. Fin efficiency (
):
(31)
Step 28. Overall surface efficiency (
):
(32)
Step 29. Area of the inner tube (
):
(33)
Step 30. Overall heat transfer coefficient under fouled
conditions (
):
(34
)
Step 31. Overall heat transfer coefficient under clean
conditions (
):
(35)
Step 32. Cleanliness factor (
CF
):
(36)
Step 33. Log-mean temperature difference () (for
countercurrent flow):
(37)
Step 34. Total heat transfer surface area without fouling
(
):
(38)
Step 35. Total heat transfer surface area with fouling (
):
(39)
Step 36. Number of hairpins (
):
(40)
2.3. Pressure drop.
Step 37. Friction factor of the tube side fluid (
):
• Laminar regime (
< 2,300):
(41)
Friction factor of the tube side fluid under laminar flow:
(42)
• Turbulent regime (4,000 <
< 5,000,000):
(43)
Step 38. Pressure drop of the tube side fluid (
):
(44)
Step 39. Friction factor of the annulus fluid (
):
• Laminar regime (
< 2,300):
(45)
Friction factor of the annulus fluid under laminar flow:
(46)
• Turbulent regime (4,000 <
< 5,000,000):
(47)
Step 40. Pressure drop of the annulus fluid (
):
(48)
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Pag. 32
2.4. Pumping power.
Step 41. Pumping power required for the tube side fluid
(
):
(49)
Where
is the pump efficiency = 0.80 - 0.85 [5].
Step 42. Pumping power required for the annulus fluid (
):
(50)
3. Results.
The values of the main design parameters calculated for the
proposed finned tube double-pipe heat exchanger are shown
hereafter, which include the calculated number of hairpins,
as well as the pressure drop and pumping power for both
streams.
3.1. Number of hairpins.
Step 1. Definition of the initial parameters:
Table 2 shows the initial parameters which are required to
design the double-pipe heat exchanger.
Table 2. Initial parameters available.
Parameters
Symbol
Value
Units
Mass flowrate of
acetone
2.00
kg/s
Inlet temperature of
acetone
90
ºC
Outlet temperature
of acetone
30
ºC
Inlet temperature of
water
5
ºC
Outlet temperature
of water
25
ºC
Fouling factor of
acetone
0.000352
m
2
.K/W
Fouling factor of
water
0.000176
m
2
.K/W
Maximum pressure
drop for acetone
200,000
Pa
Maximum pressure
drop for water
900,000
Pa
Source: Own elaboration.
Step 2. Diameters of both the inner tube and annulus.
Presented next are the values of the inner and outer
diameters for an inner tube with a nominal diameter of ¾
Schedule 40, and also the outer diameter for an annulus with
a nominal diameter 2 Schedule 40, as reported by [19].
• Inner diameter of tube (
) = 0.02093 m.
• Outer diameter of tube (
) = 0.02667 m.
• Inner diameter of annulus (
) = 0.0525 m.
Step 3. Average temperature of both fluids:
• Acetone:
(1)
• Water:
(2)
Step 4. Physical properties of both fluids at the average
temperature of the previous step.
Table 3 displays the values of the physical properties for
both fluids, which were determined according to data
reported in [19].
Table 3. Physical properties of both fluids.
Physical
property
Acetone
Chilled
water
Units
Density
745.20
999.10
kg/m
3
Viscosity
0.000229
0.00114
Pa.s
Thermal
conductivity
0.146
0.589
W/m.K
Heat capacity
2,300.25
4,188.47
J/kg.K
Source: Own elaboration.
Step 5. Heat load (
Q
):
(3)
Step 6. Mass flowrate of chilled water (
c
m
):
(4)
Step 7. Location of the fluids inside the heat exchanger:
According to suggestions stated by [2] and [20], the cold
fluid (water) will be located inside of the inner tube, while
the hot fluid (acetone) will flow on the annulus. Thus, the
Table 4 presents the former and new symbols that will
present the initial parameters for both fluids, taking into
account the selected location of fluids. That is the subscripts
h
and
c
will be replaced by
a
and
t
, respectively, for all
the initial parameters and physical properties of both fluids.
Table 4. Former and new symbols of the initial parameters
for both fluids.
Parameter
Former
symbol
New
symbol
Units
Mass flowrate of
acetone
kg/s
Mass flowrate of
water
kg/s
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Pag. 33
Density of acetone
kg/m
3
Density of water
kg/m
3
Viscosity of acetone
Pa.s
Viscosity of water
Pa.s
Thermal
conductivity of
acetone
W/m.K
Thermal
conductivity of
water
W/m.K
Heat capacity of
acetone
J/kg.K
Heat capacity of
water
J/kg.K
Fouling factors of
acetone
m
2
.K/W
Fouling factors of
water
m
2
.K/W
Source: Own elaboration.
Table 5 exhibits the results of the parameters determined in
steps 8 to 17.
Table 5. Results of the parameters determined in steps 8 –
17.
Ste
p
Parameter
Symbo
l
Value
Unit
s
Equa
t.
8
Net cross-
sectional area in
the annulus with
longitudinal
finned tubes
0.0012
9
m
2
(5)
9
Total wetted
perimeter of the
annulus with
longitudinally
finned inner
tubes
0.949
m
(6)
10
Hydraulic
diameter
0.0054
m
(7)
11
Heat transfer
perimeter of the
annulus for heat
transfer
0.784
m
(8)
12
Equivalent
diameter for heat
transfer
0.0066
m
(9)
13
Velocity of the
water
9.60
m/s
(10)
14
Reynolds
number of the
water
1
176,09
4
-
(11)
15
Prandtl number
of the water
8.10
-
(12)
16
Friction factor
0.0040
-
(16)
Nusselt number
of the water
1,017.
61
-
(17)
17
Convective heat
transfer
coefficient of the
water
28,637
W/m
2
.K
(18)
1
Since
10,000 the tube-side fluid flows under
turbulent regime, thus equations (16) and (17) will be used
to determine the Nusselt number.
Source: Own elaboration.
Table 6 exhibits the results of the parameters calculated in
steps 18 to 22.
Table 6. Results of the parameters determined in steps 18 –
22.
Ste
p
Parameter
Symb
ol
Value
Units
Equ
at.
18
Velocity of the
acetone
2.08
m/s
(19)
19
Reynolds number of
the acetone
1
36,550
.6
-
(20)
20
Prandtl number of
the acetone
3.61
-
(21)
21
Friction factor
0.0056
-
(24)
Nusselt number of
the acetone
186.69
-
(25)
22
Convective heat
transfer coefficient
of the acetone
4,127.
6
W/m
2
.
K
(26)
1
Since
10,000 the annulus fluid flows under turbulent
regime, thus equations (24) and (25) will be used to
determine the Nusselt number.
Source: Own elaboration.
Table 7 shows the results of the parameters calculated in
steps 23 to 36.
Table 7. Results of the parameters determined in steps 23 –
36.
Ste
p
Parameter
Symb
ol
Value
Unit
s
Equa
t.
23
Finned heat
transfer area
6.092
m
2
(27)
24
Unfinned heat
transfer area
0.492
m
2
(28)
25
Total area of
hairpin
6.584
m
2
(29)
26
Factor
420
-
(30)
27
Fin efficiency
0.190
-
(31)
28
Overall surface
efficiency
0.250
-
(32)
29
Area of the inner
tube
0.552
m
2
(33)
30
Overall heat
transfer coefficient
(fouled)
182.65
W/m
2
.K
(34)
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Pag. 34
31
Overall heat
transfer coefficient
(clean)
508.39
W/m
2
.K
(35)
32
Cleanliness factor
0.359
-
(36)
33
Log-mean
temperature
difference
41.86
ºC
(37)
34
Total heat transfer
surface area
without fouling
12.97
m
2
(38)
35
Total heat transfer
surface area with
fouling
36.10
m
2
(39)
36
Number of hairpins
2.78
3
-
(40)
Source: Own elaboration.
3.2. Pressure drop.
Since the tube side fluid (water) flows under turbulent
regime (
= 176,094 10,000), the equations (43) and
(44) were used to determine the pressure drop for this fluid.
Accordingly:
Step 37. Friction factor of water (
) for turbulent regime:
(43)
Step 38. Pressure drop of water (
):
(44)
Because the annulus fluid (acetone) flows under turbulent
regime (
= 36,550.6 10,000), the equations (47) and
(48) were used to determine the pressure drop for this fluid.
Therefore:
Step 39. Friction factor of acetone (
) for turbulent regime:
(47)
Step 40. Pressure drop of acetone (
):
(48)
3.3. Pumping power.
Step 41. Pumping power required for the water (
):
(49)
Step 42. Pumping power required for the acetone (
):
(50)
4. Discussion.
The heat load necessary to cool down the acetone stream
was of 276,030 W, while a mass flowrate of chilled water
of 3.30 kg/s is needed by the heat exchange process. The
velocity of chilled water (9.60 m/s) is 4.61 times higher than
the velocity of acetone (2.08 m/s). This is because the higher
value of the chilled water mass flowrate (3.30 kg/s) as
compared to the mass flowrate of acetone (2.0 kg/s), as well
as to the higher value of the parameter net cross-sectional
area in the annulus with longitudinal finned tubes (0.00129
m
2
) used in equation (19), as compared with the value of the
term
(0.00034 m
2
) used in equation (10).
The Reynolds number of the chilled water (176,094) is
about 4.82 times higher than the Reynolds number of
acetone (36,550.6), which is due to the higher value of the
velocity (9.60 m/s) and density (999.10 kg/m
3
) of the chilled
water compared to the values of these parameters for the
acetone (velocity of 2.08 m/s and density of 745.20 kg/m
3
).
Also, the higher value obtained for the inner diameter of the
tube (0.02093 m), as compared to the value of the hydraulic
diameter (0.0054 m), influenced in this result. As stated
above, the fluids will flow under turbulent regime inside the
designed DPHE since the calculated values of the Reynolds
number for both fluids are higher than 10,000.
In case of the Nusselt number, the value of this parameter
for chilled water (1,017.61) is 5.45 times higher than the
Nusselt number of acetone (186.69), which is due to the
higher values obtained of Reynolds (176,094) and Prandtl
(8.10) number for chilled water as compared to the values
of this parameters for acetone (Reynolds number of
36,550.6 and Prandtl number of 3.61).
Regarding the convective heat transfer coefficient, the value
of this parameter for the chilled water (28,637 W/m
2
.K) is
6.94 times higher than the value obtained for the acetone.
This is mainly due to the higher value of the Nusselt number
(1,017.61) and thermal conductivity (0.589 W/m.K)
obtained for chilled water as compared to the values of these
parameters for acetone (Nusselt number of 186.69 and
thermal conductivity of 0.146 W/m.K).
The calculated value of the fin efficiency was 0.190, which
can be considered low. This is primarily due to the high
value obtained for the convective heat transfer coefficient
of acetone (4,127.6 W/m
2
.K), which in turn increases the
value of the factor
m
(equation 30) thus decreasing the fin
efficiency (equation 31). The overall surface efficiency had
a value of 0.250, which can also be considered low. The low
value obtained for the fin efficiency influenced in the low
value of the overall surface efficiency.
The overall heat transfer coefficient under clean conditions
(
) had a value of 508.39 W/m
2
.K, which is 2.78 times
higher than the overall heat transfer coefficient under fouled
conditions (182.65 W/m
2
.K). The calculated value of
agrees with the ranges reported by [5] and [18] for this type
of heat transfer service.
The cleanliness factor had a value of 0.359, which can be
considered low. This is owing to the small value obtained
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Pag. 35
for the overall heat transfer coefficient under fouled
conditions (182.65 W/m
2
.K) and the high value of the clean
surface overall heat transfer coefficient (508.39 W/m
2
.K).
The value of the cleanliness factor calculated in this study
is lower than the value suggested by [5] for typical designs
(0.85). According to [5], the cleanliness factor is a term
developed for the steam power industry that provides an
allowance for fouling and which relates the overall heat
transfer coefficient when the heat exchanger is fouled to
when it is clean. This approach provides a fouling allowance
that varies directly with the clean surface overall heat
transfer coefficient (
), and although the cleanliness factor
results in favorable trends, the designer is still left with the
problem of selecting the appropriate for his application
[5].
The total heat transfer surface area with and without fouling
had values of 36.10 m
2
and 12.97 m
2
respectively; therefore
around 3 hairpins will be needed for the designed finned
tube DPHE (Figure 3). The calculated values of the pressure
drop for the chilled water and acetone were 886,903 Pa and
171,518 Pa, respectively, which are below the maximum
allowable pressure drop values set by the process for both
fluids (900,000 Pa and 200,000 Pa for chilled water and
acetone respectively). It’s worth mentioning that the
pressure drop of chilled water is 5.17 times higher than the
pressure drop of acetone, which is due essentially to the
higher value obtained for the velocity (9.60 m/s) and density
(999.10 kg/m
3
) for chilled water as compared to the values
obtained of these parameters for the acetone (velocity and
density of 2.08 m/s and 745.20 kg/m
3
respectively).
Fig. 3. Schematics of the designed finned tube DPHE
containing the three hairpins and fluids flowing under
countercurrent arrangement.
Source: Own elaboration.
Finally, the pumping power required for the chilled water
(3,662 W) is 6.37 times higher than the pumping power
required for acetone (575 W), which is largely due to the
higher value of pressure drop obtained for the chilled water
stream as compared to the value of pressure drop for
acetone.
In [5], a finned tube DPHE was designed to cool 3 kg/s of a
an engine oil stream from 65 ºC to 55 ºC using sea water
available at 20 ºC, where the sea water (cold fluid) was
located in the inner tube and the engine oil in the annulus.
Among the results obtained, the flow regime in the inner
tube is turbulent and in the annulus is laminar; the fin
efficiency and overall surface efficiency have values of
0.682 and 0.703, respectively; the overall heat transfer
coefficient under fouled and clean conditions are 108.6
W/m
2
.K and 127.6 W/m
2
.K, respectively; the cleanliness
factor is 0.85 and two hairpins will be necessary for this heat
transfer service. Finally, the pressure drop and pumping
power for the sea water are 135 kPa and 237.3 W,
respectively, while the pressure drop and pumping power
for the engine oil (under laminar regime) are 7.5 MPa and
31.8 kW, respectively.
In [2] another finned tube DPHE was designed using the
Kern’s design methodology, where it is desired to cool
8,165 kg/h of 28 ºAPI gas oil from 121 ºC to 93 ºC using
water at 27 ºC as the cooling medium. In this design project,
the hot fluid (gas oil) was located in the annulus, while the
cold fluid (water) was located in the inner tube. The values
for the fin efficiency and the overall surface efficiency are
0.307 and 1.54, respectively; while the clean and the fouled
(design) overall coefficients have values of 1,618.3 W/m
2
.K
and 670 W/m
2
.K, respectively. It is necessary to use four
hairpins and the calculated pressure drops in the annulus and
inner pipe are of 62,604.39 Pa and 10,824.77 Pa,
respectively.
5. Conclusions.
A finned-tube double-pipe heat exchanger was designed
from both the thermal and hydraulic viewpoints using the
methodology and correlations reported in [5] and [18],
where several design parameters were determined such as
cleanliness factor and the number of hairpins, as well as the
pressure drop and pumping power of both streams, among
others. The heat load had a value of 276,030 W, while a
mass flowrate of chilled water of 3.30 kg/s will be needed
to cool the acetone stream. Considering the calculated
values of the Reynolds number for the chilled water
(176,094) and acetone (36,550.6), both streams will flow
under turbulent regime inside the designed DPHE, while the
convective heat transfer coefficients for the chilled water
and acetone were of 28,637 and 4,127.6 W/m
2
.K,
respectively. The overall heat transfer coefficient under
fouled and clean conditions had values of 182.65 and 508.39
W/m
2
.K, respectively, while the cleanliness factor was
0.359. The total heat transfer surface area without and with
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Pag. 36
fouling had values of 12.97 and 36.10 m
2
, respectively. The
designed finned tube DPHE will need three hairpins, and
the pressure drop of both the chilled water (886,903 Pa) and
acetone (171,518 Pa) are below the maximum values
established by the heat exchange process. The chilled water
stream will need a pumping power of 3,662 W, while the
pumping power required by the acetone stream will be of
575 W.
6.- Author Contributions.
1. Conceptualization: Amaury Pérez Sánchez.
2. Data curation: Laura Thalía Alvarez Lores.
3. Formal Analysis: Amaury Pérez Sánchez, Elizabeth
Elianne Artigas Cañizares.
4. Acquisition of funds: Not applicable.
5. Research: Amaury Pérez Sánchez, Elizabeth Elianne
Artigas Cañizares, Laura Thalía Alvarez Lores.
6. Methodology: Amaury Pérez Sánchez.
7. Project management: Not applicable.
8. Resources: Not applicable.
9. Software: Not applicable.
10. Supervision: Amaury Pérez Sánchez.
11. Validation: Amaury Pérez Sánchez.
12. Visualization: Not applicable.
13. Writing – original draft: Elizabeth Elianne Artigas
Cañizares, Laura Thalía Alvarez Lores
14. Writing - revision y editing: Amaury Pérez Sánchez.
7.- Referencias.
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an innovative design of a finned double-pipe heat exchanger with
variable fin-tip thickness," Energy Conversion and Management, vol.
98, pp. 69-80, 2015.
http://dx.doi.org/10.1016/j.enconman.2015.03.038
[2] M. Flynn, T. Akashige, and L. Theodore, Kern's Process Heat
Transfer, 2nd ed. Beverly, USA: Scrivener Publishing, 2019.
[3] A. Faisal and S. Jain, "Analysis of a Double Pipe Heat Exchanger
with Straight and Helical Fins," International Journal of Science,
Engineering and Technology, vol. 9, no. 4, pp. 1-6, 2021.
[4] M. Ishaq, A. Ali, M. Amjad, K. S. Syed, and Z. Iqbal, "Diamond-
Shaped Extended Fins for Heat Transfer Enhancement in a Double-
Pipe Heat Exchanger: An Innovative Design," Applied Sciences, vol.
11, p. 5954, 2021. https://doi.org/10.3390/app11135954
[5] S. Kakaç, H. Liu, and A. Pramuanjaroenkij, Heat Exchangers -
Selection, Rating and Thermal Design, 3rd ed. Boca Raton, USA:
Taylor & Francis Group, 2012.
[6] Peccini, J. C. Lemos, A. L. H. Costa, and M. J. Bagajewicz, "Optimal
Design of Double Pipe Heat Exchanger Structures," Industrial &
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https://10.1021/acs.iecr.9b01536
[7] M. K. Alkam and M. A. Al-Nimr, "Improving the performance of
double-pipe heat exchangers by using porous substrates,"
International Journal of Heat and Mass Transfer, vol. 42, pp. 3609-
3618, 1999.
[8] M. F. Hasan, M. Danismaz, and B. M. Majel, "Thermal performance
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surfaces using nanofluid technique as enhancement," Case Studies in
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https://doi.org/10.1016/j.csite.2023.102774
[9] Jalili, N. Aghaee, P. Jalili, and D. D. Ganji, "Novel usage of the
curved rectangular fin on the heat transfer of a double-pipe heat
exchanger with a nanofluid," Case Studies in Thermal Engineering,
vol. 35, p. 102086, 2022. https://doi.org/10.1016/j.csite.2022.102086
[10] G. A. Rao and Y. Levy, "A semi empirical methodology for
performance estimation of a double pipe finned heat exchanger,"
presented at the 9th Biennial ASME Conference on Engineering
Systems Design and Analysis (ESDA08), Haifa, Israel, 2008.
[11] M. Sanchouli, S. Payan, A. Payan, and S. A. Nada, "Investigation of
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Thermal Engineering, vol. 34, p. 101986, 2022.
https://doi.org/10.1016/j.csite.2022.101986
[12] J. Mansour, Z. K. Kadhim, and K. A. Hussein, "CFD study of Heat
Transfer Characteristics for Annular Serrated Finned-Tube Heat
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5, no. 1, pp. 77-87, 2018.
[13] V. Mathanraj, V. L. Krishna, J. L. V. Babu, and S. A. Kumar,
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exchanger employing triangular fins," IOP Conf. Series: Materials
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[14] S. Al-Zahrani, "Heat transfer characteristics of innovative
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[15] S. Sivalakshmi, M. Raja, and G. Gowtham, "Effect of helical fins on
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Nomenclature
Net cross-sectional area in the annulus
with longitudinal finned tubes
m
2
Finned heat transfer area
m
2
Area of the inner tube
m
2
Total heat transfer surface area
without fouling
m
2
Total heat transfer surface area with
fouling
m
2
Total area of hairpin
m
2
Unfinned heat transfer area
m
2
Heat capacity
J/kg.K
Cleanliness factor
-
Inner diameter of tube
m
Outer diameter of tube
m
Equivalent diameter for heat transfer
m
Hydraulic diameter
m
Inner diameter of annulus
m
Friction factor for heat transfer
-
Friction factor for pressure drop
-
Convective heat transfer coefficient
W/m
2
.K
Fin height
m
Thermal conductivity
W/m.K
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Pag. 37
Thermal conductivity of the inner
tube material
W/m.K
Length of hairpin
m
Log-mean temperature difference
ºC
Mas flowrate
kg/s
Factor
-
Number of fins per tube
-
Number of hairpins
-
Number of tubes inside the annulus
-
Nusselt number
-
Pressure drop
Pa
Maximum allowable pressure drop
Pa
Pumping power
W
Heat transfer perimeter of the annulus
for heat transfer
m
Prandtl number
-
Total wetted perimeter of the annulus
with longitudinally finned inner tubes
m
Heat load
W
Fouling factor
m
2
.K/W
Reynolds number
-
Temperature of the cold fluid
ºC
Temperature of the hot fluid
ºC
Tube wall temperature
ºC
Average temperature of the cold fluid
ºC
Average temperature of the hot fluid
ºC
Velocity
m/s
Overall heat transfer coefficient under
clean conditions
W/m
2
.K
Overall heat transfer coefficient under
fouling conditions
W/m
2
.K
Greek symbols
Density
kg/m
3
Viscosity
Pa.s
Fin thickness
m
Fin efficiency
-
Overall surface efficiency
-
Subscripts
1
Inlet
2
Outlet
Cold fluid
Hot fluid
Annulus fluid
Tube side fluid
