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Chemical Engineering & Development
Journal of Science and Engineering
Vol. 08 / Nº 01
e – ISSN: 3028-8533
ISSN – L: 3028-8533
Chemical Engineering & Development
University of Guayaquil | Faculty of Chemical Engineering
Guayaquil – Ecuador
https://revistas.ug.edu.ec/index.php/iqd
Email: inquide@ug.edu.ec
francisco.duquea@ug.edu.ec
Pag. 88
Thermo-hydraulic design of an unfinned and finned double pipe heat
exchanger for milk cooling. Part 1 - Unfinned heat exchanger.
Diseño térmico-hidráulico de un intercambiador de calor de doble tubo sin y con aletas para el
enfriamiento de leche. Parte 1 – Intercambiador de calor sin aletas.
Amaury Pérez Sánchez
1
*; Laura de la Caridad Arias Águila
2
; Heily Victoria González
3
; María Isabel La Rosa Veliz
4
; Zamira María Sarduy Rodríguez
5
&
Lizthalía Jiménez Guerra
6
Received: 06/06/2025 – Accepted: 29/10/2025 – Published: 01/01/2026
Research
Articles
X
Review
Articles
Essay Articles
* Corresponding
author.
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 (CC BY-
NC-SA 4.0) international license. Authors retain the rights to their articles and may share, copy, distribute,
perform, and publicly communicate the work, provided that the authorship is acknowledged, not used for
commercial purposes, and the same license is maintained in derivative works.
Abstract.
Double-pipe heat exchangers (DPHEs) have acquired significance in recent years as a result of their simple construction, compactness, ease of maintenance and
cleaning, and relatively low operating/capital costs, with widespread use in heat transfer services involving sensible heating or cooling of process fluids. This paper
aims to design a DPHE from the thermo-hydraulic point of view, to determine its suitability and applicability to cool down a stream of liquid cow’s milk using
chilled water as coolant. Several design parameters were calculated such as total number of hairpins (21), heat transfer surface area (12.92 m
2
), cleanliness factor
(0.752) and percent over surface (32.96%), which can be considered as satisfactory. Also, it is required a mass flowrate of chilled water of 9.32 kg/s, classified as
high. The designed DPHE cannot be applied satisfactorily in the requested heat transfer service because the pressure drop (9,481,246 Pa) of the tube-side fluid
(chilled water) is quite higher than the maximum allowable limit set by the process (85,000 Pa), which also increases the required pumping power for this fluid to
an important value (110.5 kW). The designed DPHE will cost around USD $ 45,600 based on May 2025.
Keywords.
Unfinned double pipe heat exchanger; thermal design; number of hairpins; pressure drop; pumping power; purchased cost.
Resumen.
Los intercambiadores de calor de doble tubo (ICDT) han adquirido importancia en años recientes como resultado de su construcción simple, compactación, facilidad
de mantenimiento y limpieza, y costos capitales/operación relativamente bajos, con uso extendido en servicios de transferencia de calor que involucren
calentamiento y enfriamiento sensible de fluido de proceso. Este artículo tiene como objetivo diseñar un ICDT desde el punto de vista térmico-hidráulico, para
determinar su idoneidad y aplicabilidad para enfriar una corriente de leche de vaca liquida usando agua fría como agente de enfriamiento. Varios parámetros de
diseño fueron calculados tales como el número total de horquillas (21), área superficial de transferencia de calor (12,92 m
2
), factor de limpieza (0,752) y porcentaje
de sobre superficie (32,96%), los cuales pueden considerarse satisfactorios. También, se requiere un caudal másico de agua fría de 9,32 kg/s, clasificado como
elevado. El ICDT diseñado no puede aplicarse satisfactoriamente en el servicio de transferencia de calor demandado debido a que la caída de presión (9 481 246
Pa) del fluido del lado del tubo (agua de enfriamiento) es muy superior que el limite permisible máximo fijado por el proceso (85 000 Pa), lo cual también
incrementa la potencia de bombeo requerida para este fluido hacia un valor importante (110,5 kW). El IDCT diseñado costara alrededor de USD $ 45 600 basado
en Mayo del 2025.
Palabras clave.
Intercambiador de calor de doble tubo; diseño térmico; número de horquillas; caída de presión; costo de adquisición.
1. Introduction
Heat exchangers are apparatuses designed to facilitate the
transfer of heat between two or more fluids with changing
temperatures [1]. In recent decades, the significance of heat
exchangers has grown substantially due to their roles in
energy efficiency, recovery, and transformation, as well as
the integration of alternative energy sources [2].
The thermal energy that passes through a heat exchanger can
be either sensible heat or latent heat from the flowing fluids.
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; aguilaariaslaura@gmail.com; https://orcid.org/0000-0002-6494-9747, Camagüey;
Cuba.
3
Faculty of Applied Sciences; University of Camagüey; heily.victoria@reduc.edu.cu; https://orcid.org/0009-0007-9319-6506, Camagüey,
Cuba.
4
University of Camagüey; Faculty of Applied Sciences; maria.rosa@reduc.edu.cu; https://orcid.org/0000-0002-9517-6118, Camagüey; Cuba.
5
University of Camagüey; Faculty of Applied Sciences; zamira.sarduy@reduc.edu.cu; https://orcid.org/0000-0003-1428-3809, Camagüey;
Cuba.
6
University of Camagüey; Faculty of Applied Sciences; lizthalia.jimenez@reduc.edu.cu; https://orcid.org/0000-0002-2471-7263 , Camagüey;
Cuba.
The fluid supplying the thermal energy is known as the hot
fluid, whereas the fluid that absorbs thermal energy is
referred as the cold fluid. Within a heat exchanger, the
temperature of the hot fluid is expected to decrease, while
the cold fluid’s temperature will rise. The primary function
of a heat exchanger is to either increase or lower the
temperature of the target fluid [3].
Heat exchangers are commonly utilized across various
sectors including energy production facilities, chemical
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Chemical Engineering & Development
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e – ISSN: 3028-8533
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Guayaquil – Ecuador
https://revistas.ug.edu.ec/index.php/iqd
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Pag. 89
manufacturing, biotechnology, the food sector,
environmental engineering, and the recovery of waste heat,
among others. The most basic type of modern heat
exchangers is the double pipe heat exchanger [4], which is
also referred to as a hairpin heat exchanger [1].
The DPHE was developed in the late 1940s, and research
conducted since that time has largely supported its
effectiveness for achieving significant developments. This
type of heat exchanger facilitates the transfer of thermal
energy principally between hot and cold liquids, usually
within concentric piping arranged in various arrangements,
initially set up in parallel and later adapted to counterflow
designs [5].
A DPHE heat exchanger is made up of a one or more tubes
arranged concentrically within a larger diameter pipe,
featuring fittings designed to direct the flow from one section
to another. In this type of heat exchanger, one fluid circulates
inside the inner pipe (tube-side), while another fluid moves
through the surrounding annular area (annulus). The inner
tube is connected via U-shaped bends that are contained in a
return-bed housing [1].
A DPHE can be configured in different series and parallel
setups [1] to fulfill the needs for pressure drop, heat transfer,
and logarithmic mean temperature difference (LMTD) [6].
This type of heat exchanger is utilized for applications
involving low flow rates, a wide range of temperatures [7],
and high pressure services due to the narrower pipe sizes [1],
and is suitable for continuous operations that require low to
medium heat duties [8], specifically for processes needing
sensible heating or cooling in fluids, where compact small
heat transfer surfaces of up to 50 m
2
are necessary [1].
It finds extensive application in typical industries such as
food production, chemicals, biotechnology, and gas and oil
processes [9], which often require heating or cooling of
process fluids, while it is also widely employed in research
facilities related to energy engineering [10].
As noted in [7], the DPHE is crucial for tasks like reheating,
pasteurization, heating and preheating. Its affordability in
terms of design and maintenance makes it a preferred choice,
especially for small-scale industries.
As stated in [6], DPHE is a cost-effective option for closed
loop cooling systems where a sufficient supply of
appropriate water is accessible at an affordable rate to fulfill
the thermal needs.
These heat exchangers are suitable for processes where one
of the streams is either a gas or a thick liquid, or when the
volume is limited under high fouling situations. This is due
to their simple cleaning and maintenance processes. They
can serve as a substitute for shell-and-tube heat exchangers
when operating as a true counter-flow heat exchanger.
DPHEs feature an outer pipe ranging from 50 to 400 mm of
internal diameter, and have a standard length of 1.5 to 12.0
m per hairpin. The inner tube's outer diameter can vary from
19 mm to 100 mm. A significant drawback is their bulkiness
and high cost per unit of heat transfer surface area [1].
An advantage of the DPHE lies in its affordability in terms
of design and maintenance, characterized by a basic
configuration that is easy to install, clean, maintain, and
adapt, which significantly extends its lifespan and
functionality [10].
Peccini et al., [11] suggested that when a stream includes
suspended particles, DPHE might be a preferable option
since they can incorporate a larger diameter inner tube to
prevent blockages. Additionally, this heat exchanger type
offers versatility because of its modular design, enabling
easier adaptations to modifications in processes. The same
authors noted that the longitudinal flow within a DPHE
eliminates stagnant zones, which are likely to accumulate
deposits in shell and tube exchangers.
It is essential to thermally design heat exchangers in a way
that enhances heat transfer while maintaining the pressure
drop of the fluids within acceptable limits. A frequent
challenge faced by industries is efficiently extracting heat
from a utility stream coming out of a specific process and
using that energy to heat another process stream.
One way to maximize heat extraction might involve
augmenting the heat transfer area or increasing the coolant
flow rate; however, both strategies can lead to increased
pumping costs, making it unwise to increase these
parameters without considering pressure drops. The
conventional approach to designing heat exchangers requires
careful assessment of all design factors through a detailed
process of trial and error, accounting for all potential
variations [12].
In [7] it is indicated that engineers encounter significant
difficulties while designing an effective heat exchanger. This
challenge arises not just from the need to accurately evaluate
long-term efficiency and related financial costs, but also
from the crucial necessity of thoroughly examining aspects
such as heat transfer, pressure drop, and overall
effectiveness, which require intensive effort.
According to [13], optimization in the design of heat
exchangers is a subject that has been widely explored in
existing literature. Most research that has addressed this
issue utilized closed-form analytical methods to represent the
operational characteristics of the systems, including
techniques like the LMTD and effectiveness (ε-NTU)
approaches. Such analytical methods rely on the assumption
of consistent physical property values and heat transfer
coefficients, which can lead to significant inconsistencies in
various design scenarios.
In the design of a DPHE, the majority of academic sources
[14,15,16] typically incorporate a broader collection of
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Chemical Engineering & Development
Journal of Science and Engineering
Vol. 08 / Nº 01
e – ISSN: 3028-8533
ISSN – L: 3028-8533
Chemical Engineering & Development
University of Guayaquil | Faculty of Chemical Engineering
Guayaquil – Ecuador
https://revistas.ug.edu.ec/index.php/iqd
Email: inquide@ug.edu.ec
francisco.duquea@ug.edu.ec
Pag. 90
design elements, such as physical dimensions, fluid
distributions, and configurations involving multiple units.
They often rely on a conventional process of
experimentation and validation; in this method. The design
elements are determined initially, and subsequently, the
number of required hairpins for that setup is computed. If the
heat exchanger obtained is considered unsuitable—due to
reasons like the allowable pressure drop for the specified
flow rates falling outside predetermined limits or the streams
velocity are not within the required limits—a modification in
the design is suggested, and calculations are reconsidered.
This methodology relies heavily on the designer’s expertise
and does not ensure optimal results. Choices available to
designers for new tests are various; they might modify
lengths, diameters of pipes, arrangements of hairpins, and
other characteristics to achieve a decrease in pressure drop
or enhance the heat transfer coefficient. Professionals rely on
their intuitive judgments to ultimately develop a viable heat
exchanger, which is the primary objective of the design
approach [11].
Numerous investigations are reported where a DPHE was
designed utilizing different methodologies and tools. In this
regard, a comprehensive theoretical and practical study was
conducted in [6] where simulations were executed to
evaluate the design and functionality of a DPHE. This
performance assessment was carried out using
computational fluid dynamics (CFD), while the overall
effectiveness was also calculated.
Likewise, [9] conducted numerical analysis on how the ratio
of pipe diameters and the ratio of diameter to length
influence the performance of heat exchangers in a DPHE,
utilizing CFD software to model the scenarios with
incompressible air. They statistically identified and
optimized the factors that lead to the maximum heat transfer
under constant flow conditions based on the findings. The
researchers noted that their results will aid in future
investigations into the design of heat exchangers with
optimal dimensions for length and diameter.
Additionally, [13] discussed the use of an integer linear
programming (ILP) formulation for designing DPHE. The
model used for the heat exchanger relied on discretizing
conservation equations; consequently, the physical
properties were assessed locally, incorporating their
temperature dependence into the model. The numerical
findings demonstrated the effectiveness of this proposed
method, revealing that analytical methods might either
underestimate or overestimate the necessary size of a heat
exchanger.
In a similar manner, [8] executed an extensive design and
assembly of a laboratory-type DPHE suitable for both
parallel and counterflow arrangements. The heat exchanger
developed in this research was constructed from galvanized
steel for both its tube and shell, while the performance
metrics (such as LMTD, heat transfer rate, effectiveness, and
overall heat transfer coefficient) were collected and
compared across the two configurations utilized.
In [1], several DPHEs were thermally designed in order to be
utilized as oil coolers in naval ships, while the designed
DPHE were evaluated with each other regarding the quantity
of hairpins, the pressure drop, and the power required for
pumping. This assessment incorporated the Nusselt numbers
suggested by various researchers across four different design
categories: clean finned, fouled finned, clean unfinned, and
fouled unfinned.
Similarly, in [10] the effectiveness of existing theoretical
approaches for designing a DPHE with narrow tube spacing
and low fluid velocities was assessed, corresponding to
laminar flow characteristics of the heat transfer fluid within
the annulus. This research scrutinized the reasons behind
discrepancies when comparing theoretical findings with
experimental data, offering suggestions for the proper design
of DPHE.
Likewise, in [17] a DPHE was conceptualized, built, and
incorporated into an operating biomass gasification facility
to capture heat from the syngas released by the gasifier,
which has an exit temperature near 350 ºC.
In [11], the optimization of a DPHE using mathematical
methods was explored, focusing on minimizing the
exchanger area while accounting for the thermo-fluid
dynamic conditions to apply the appropriate transport
correlations, alongside design constraints like maximum
pressure drops and minimum excess area.
This research introduced two mixed-integer nonlinear
programming strategies, expanding the range of design
variables compared to previous studies. These variables
included the distribution of fluid streams (either within the
inner tube or the annulus), the diameters of both tubes, tube
length, the quantity of parallel branches, the number of units
arranged in series and parallel within each branch, as well as
the number of hairpins in each unit, which affect how the
hairpins are configured.
In [12], the most effective design of a DPHE was expressed
as a single-variable geometric programming challenge.
Solving this issue provides the optimal dimensions for the
inner and outer pipe diameters and the utility flowrate
necessary for a DPHE of a specified length, given a
predetermined flowrate for the process stream and a defined
temperature difference from inlet to outlet.
In [18], a DPHE was designed to investigate the heat transfer
process occurring between two fluids (water/water) through
a solid separator. It was developed with a counterflow setup,
utilizing the LMTD analysis method.
In [19], a method combining gray relational analysis (GRA)
with artificial neural networks (ANNs) and genetic
algorithms (GAs) was utilized to assess the importance of
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Chemical Engineering & Development
Journal of Science and Engineering
Vol. 08 / Nº 01
e – ISSN: 3028-8533
ISSN – L: 3028-8533
Chemical Engineering & Development
University of Guayaquil | Faculty of Chemical Engineering
Guayaquil – Ecuador
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Pag. 91
parameters such as effectiveness, thermal resistance, and
overall heat transfer coefficient, to rank these parameters in
a specific sequence. The integrated methodology introduced
in this research has the potential to enhance problem-solving
abilities and offer insightful knowledge to improve heat
exchanger performance across different industries.
In [20] the calculation of thermal design parameters of a
DPHE was outlined to ensure effective heating and
sterilization of an organic fluid stream used in the seed-skin
separation process for various vegetables.
Lastly, [21] explored both analytical and numerical methods
in designing a DPHE. The analysis included the
consideration of sensible heat transfer, and the heat
exchanger was customized to fit the real operating conditions
of a chemical facility. This research employed an analytical
model using the effectiveness-number of transfer units (ɛ-
NTU) method alongside the LMTD approach in the design
of the DPHE, with performance charts created during the
design phase for the specified heat exchanger.
In a Cuban dairy processing plant it’s required to cold down
a liquid cow’s milk stream using chilled water, and for that
two DPHEs have been proposed, the first one unfinned and
the second with longitudinal fins in the inner tube (finned).
In this context, the present paper is the first part of a two-part
project, where an unfinned DPHE is designed in order to
know if this heat exchanger is suitable to implement in this
heat transfer service through the calculation of several design
parameters such as the total number of hairpins, the
cleanliness factor, the percent over surface, the pressure drop
and the pumping power of both liquid streams, among others.
Likewise, the purchase cost of the unfinned DPHE was also
calculated. In the second paper, a finned DPHE is designed
where the key design parameters previously mentioned are
also computed, while the results will be compared and
evaluated with respect to those calculated for the unfinned
DPHE of the present study, in order to select the most
suitable, economical and applicable DPHE from the thermo-
hydraulic point of view to carry out this heat transfer service.
2. Materials and methods.
2.1. Problem statement.
It is required to cool down 4,320 kg/h of a liquid cow’s milk
stream from 60 ºC to 10 ºC by means of chilled water
available at 2 ºC, where the outlet temperature of the chilled
water stream must not exceed 8 ºC. The following data are
available for the tube and the annulus:
• Nominal diameter annulus: 2 in.
• Nominal diameter inner tube: 1 in.
• Length of tube: 3 m.
• Number of tubes inside the annulus: 1.
• Tube material: Carbon steel.
• Thermal conductivity of the tube material: 52
W/m.K.
Design an unfinned double pipe heat exchanger using the
methodology reported by [15], where several thermo-
hydraulic and design parameters should be calculated such
as the heat transfer surface area, the total number of hairpins,
the cleanliness factor, the percent over surface, the pressure
drop and the pumping power of both liquid streams. It’s
required that the pressure drop for both the tube-side and
annulus fluid don’t exceed 85,000 Pa. Lastly; calculate the
purchased equipment cost of the designed DPHE and update
it to 2025.
2.2. Design methodology.
Percent over surface
Step 1. Definition of the initial parameters for the streams:
Table 1 presents the initial parameters that must be defined
for both fluid streams
Table 1. Initial parameters to be defined for both streams.
Parameter
Hot
fluid
Cold
fluid
Units
Mass flowrate
kg/h
Inlet temperature
ºC
Outlet temperature
ºC
Maximum allowable
pressure drop
Pa
Fouling factor
m
2
.K/W
Source: Own elaboration.
Step 2. Definition of the geometric dimensions for the
hairpins:
Table 2 shows the geometric dimensions to be defined for
the hairpins.
Table 2. Geometric dimensions to be defined for the hairpins.
Parameter
Symbol
Units
Tube length
m
Internal diameter annulus
m
Internal diameter inner tube
m
External diameter inner tube
m
Thermal conductivity metallic
material of the inner pipe
W/m.K
Source: Own elaboration.
Step 3. Definition of the flow arrangement inside the double-
pipe heat exchanger:
• Counterflow.
• Parallel.
Step 4. Allocation of fluids inside the double-pipe heat
exchanger
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e – ISSN: 3028-8533
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Chemical Engineering & Development
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Pag. 92
Step 5. Consider insulation of the double-pipe heat
exchanger against heat losses.
Step 6. Average temperature of both fluids:
• Hot fluid ():
(1.1)
• Cold fluid (
):
(1.2)
Step 7. Physical parameters of both fluids at the average
temperature:
Table 3 displays the physical properties that must be defined
for both fluids at the average temperature calculated in the
previous step.
Table 3. Physical parameters to be defined for both fluids.
Parameter
Hot
fluid
Cold
fluid
Units
Density
kg/m
3
Viscosity
Pa.s
Heat capacity
kJ/kg.K
Thermal conductivity
W/m.K
Source: Own elaboration.
Step 8. Heat load ():
• Using the data for the hot fluid:
(1.3)
• Using the data for the cold fluid:
(1.4)
Where both
and
are given in kg/h.
Step 9. Mass flowrate of one stream:
• Mass flowrate of the hot fluid:
(1.5)
• Mass flowrate of the cold fluid:
(1.6)
Step 10. Tube wall temperature (
):
(1.7)
Step 11. Viscosity of both fluids at the tube wall temperature:
Hot fluid (
) [Pa.s].
Cold fluid (
) [Pa.s].
Step 12. Net free flow area of the inner tube (
):
(1.8)
Step 13. Velocity of the tube-side fluid (
):
(1.9)
Where
is given in kg/s.
Step 14. Reynolds number of the tube-side fluid (
):
(1.10)
Step 15. Prandtl number of the tube-side fluid (
):
(1.11)
Where
is given in J/kg.K.
Step 16. Nusselt number for the tube-side fluid (
):
• Laminar flow (
< 2,300)
(1.12)
Valid for smooth tubes for the following conditions:
0.48 <
< 16,700
0.0044 <
< 9.75
2
• Turbulent flow (2,300 <
< 10
4
) [Gnielinski’s
correlation]:
(1.13)
Where
is the Fanning friction factor for the tube-side fluid
and is calculated using the following correlation:
(1.14)
• Turbulent flow (10
4
<
< 5 x 10
6
) [Prandtl’s
correlation]:
(1.15)
Valid for
> 0.5.
Where:
(1.14)
Step 17. Heat transfer coefficient for the tube-side fluid (
):
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Pag. 93
(1.16)
Step 18. Net free flow area of the annulus (
):
(1.17)
Step 19. Velocity of the annulus fluid (
):
(1.18)
Step 20. Hydraulic diameter (
):
(1.19)
Step 21. Reynolds number of the annulus fluid (
):
(1.20)
Step 22. Prandtl number of the annulus fluid (
):
(1.21)
Where
is given in J/kg.K.
Step 23. Nusselt number for the annulus fluid (
):
• Laminar flow (
< 2,300)
(1.22)
Valid for smooth tubes for the following conditions:
0.48 <
< 16,700
0.0044 <
< 9.75
2
• Turbulent flow (2,300 <
< 10
4
) [Gnielinski’s
correlation]:
(1.23)
Where
is the Fanning friction factor for the annulus fluid
and is calculated using the following correlation:
(1.24)
• Turbulent flow (10
4
<
< 5 x 10
6
) [Prandtl’s
correlation]:
(1.25)
Valid for
> 0.5.
Where:
(1.24)
Step 24. Equivalent diameter for heat transfer (
):
(1.26)
Step 25. Heat transfer coefficient for the annulus fluid (
):
(1.27)
Step 26. Fouled overall heat transfer coefficient based on the
outside area of the inner tube (
):
(1.28)
Step 27. Log-mean temperature difference ():
• For parallel flow:
(1.29)
• For counterflow:
(1.30)
Step 28. Heat transfer surface area (
):
(1.31)
Where is given in kW.
Step 29. Heat transfer area per hairpin (
):
(1.32)
Step 30. Number of hairpins (
):
(1.33)
Step 31. Clean overall heat transfer coefficient based on the
outside heat transfer area (
):
(1.34)
Step 32. Cleanliness factor ():
(1.35)
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Pag. 94
Step 33. Total fouling (
):
(1.36)
Step 34. Percent over surface ():
(1.37)
Pressure drop and pumping power
Step 35. Frictional pressure drop of the tube-side fluid (
):
(1.38)
Where for laminar flow (
< 2,300):
(1.39)
Correction of the Fanning friction factor for laminar flow
(
):
(1.40)
Where m = - 0.58 for heating and - 0.50 for cooling under
laminar flow.
Step 36. Pumping power for the tube-side fluid (
):
(1.41)
Where
is given in kg/s and
is the isentropic efficiency
of the pump.
Step 37. Frictional pressure drop of the annulus fluid (
):
(1.42)
Where for laminar flow (
< 2,300):
(1.43)
Correction of the Fanning friction factor for laminar flow
(
):
(1.44)
Where m = - 0.58 for heating and - 0.50 for cooling under
laminar flow.
Step 38. Pumping power for the annulus fluid (
):
(1.45)
Where
is given in kg/s and
is the isentropic efficiency
of the pump.
Purchased equipment cost
According to [22], the purchased equipment cost for a DPHE
is calculated using the following correlation:
(1.46)
Where:
•
- Purchased equipment cost of the DPHE
referred to January 2007 (USD $).
•
- Heat transfer surface area of the DPHE,
calculated in Step 28 (m
2
).
Later on, this purchased equipment cost calculated by
equation (1.46) is updated to March 2025 using the Chemical
Engineering Plant Cost Index corresponding to March 2025
and by applying the following equation:
(1.47)
Where:
•
- Purchased equipment cost of the DPHE
referred to May 2025 (USD $).
•
- Purchased equipment cost of the DPHE
based to January 2007 (USD $).
•
- Chemical Engineering Plant Cost
Index referred to May 2025 = 806.8 [23].
•
- Chemical Engineering Plant Cost
Index referred to January 2007 = 509.7 [22].
3. Analysis and Interpretation of Results.
3.1. Percent over surface.
Step 1. Definition of the initial parameters for the streams:
The following table (Table 4) presents the values of the
initial parameters to be defined for both streams.
Table 4. Values of the initial parameters to be defined for
both streams.
Parameter
Hot fluid
(Milk)
Cold fluid
(Water)
Units
Symb
ol
Value
Symb
ol
Value
Mass
flowrate
4,320
-
kg/h
Inlet
temperatur
e
60
2
ºC
Outlet
temperatur
e
10
8
ºC
Maximum
allowable
pressure
drop
85,00
0
85,000
Pa
INQUIDE
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Pag. 95
Fouling
factor
0.000
1
0.00017
6
m
2
.K/
W
Source: Own elaboration.
Taken from [14].
Taken from [15].
Step 2. Definition of the geometric dimensions for the
hairpins:
Table 5 shows the values of the geometric dimensions to be
defined for the hairpins.
Table 5. Values of the geometric dimensions to be defined
for the hairpins.
Parameter
Symbol
Value
Units
Length
3
m
Internal diameter annulus
0.05250
m
Internal diameter inner
tube
0.02664
m
External diameter inner
tube
0.03340
m
Thermal conductivity
metallic material of the
inner pipe
52
W/m.K
Source: Own elaboration.
According to [15].
Step 3. Definition of the flow arrangement inside the double-
pipe heat exchanger:
The fluids will flow under counterflow arrangement inside
the DPHE.
Step 4. Allocation of fluids inside the double-pipe heat
exchanger.
As suggested by [14] and [22], the hot fluid (milk) will be
located in the annulus, while the cold fluid (water) will be
located in the inner pipe.
Step 5. Consider insulation of the double-pipe heat
exchanger against heat losses.
The heat exchanger will be thermally insulated to avoid
excessive heat losses.
Step 6. Average temperature of both streams:
• Hot fluid (milk) ():
(1.1)
• Cold fluid (water) (
):
(1.2)
Step 7. Physical parameters of both fluids at the average
temperature:
According to [24,25,26], both the milk and the water have
the physical parameters presented in Table 6 at the average
temperature calculated in the previous step.
Table 6. Values of the physical parameters for the milk and
the water.
Parameter
Hot fluid (Milk)
Cold fluid
(Water)
Units
Symb
ol
Value
Symb
ol
Value
Density
1,013.
2
999.9
7
kg/m
3
Viscosity
0.001
06
0.001
52
Pa.s
Heat
capacity
3.919
4.205
kJ/kg.
K
Thermal
conductiv
ity
0.580
0.571
W/m.
K
Source: Own elaboration.
Step 8. Heat load ():
• Using the data for the hot fluid (milk):
(1.3)
Where
is given in kg/h.
Step 9. Mass flowrate of one stream:
• Mass flowrate of the cold fluid (water):
(1.6)
Step 10. Tube wall temperature (
):
(1.7)
Step 11. Viscosity of both fluids at the tube wall temperature:
According to [25,26], both the milk and the water present the
following values of the viscosity at
= 20 ºC.
• Hot fluid (milk) (
) [Pa.s] = 0.00205 Pa.s
• Cold fluid (
) [Pa.s] = 0.00100 Pa.s
Step 12. Net free flow area of the inner tube (
):
(1.8)
Because the cold fluid (water) will flow in the inner tube, and
the hot fluid (milk) will flow in the annulus, the following
new nomenclature presented in Table 7 will be applied for
the flowrates, physical parameters and fouling factors of both
streams.
Table 7. New nomenclature to be applied for both streams.
Hot fluid (milk)
Cold fluid (water)
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Pag. 96
Paramet
er
Former
nomencl
ature
New
nomencl
ature
Former
nomencl
ature
New
nomencl
ature
Flowrat
e
Density
Viscosit
y
Heat
capacity
Thermal
conducti
vity
Fouling
factor
Source: Own elaboration.
Table 8 displays the values of the parameters included in
steps 13-25.
Table 8. Values of the parameters included in steps 13-25.
Step
Parameter
Symbol
Value
Units
13
Velocity of the
tube-side fluid
(water)
16.64
m/s
14
Reynolds
number of the
tube-side fluid
(water)
291,629
-
15
Prandtl number
of the tube-side
fluid (water)
11.19
-
16
Fanning
friction factor
for the tube-
side fluid
(water)
0.00362
-
Nusselt
number for the
tube-side fluid
(water)
1
1,237.84
-
17
Heat transfer
coefficient for
the tube-side
fluid (water)
26,531.78
W/m
2
.K
18
Net free flow
area of the
annulus
0.00129
m
2
19
Velocity of the
annulus fluid
(milk)
0.92
m/s
20
Hydraulic
diameter
0.0191
m
21
Reynolds
number of the
annulus fluid
(milk)
16,796
-
22
Prandtl number
of the annulus
fluid (milk)
7.16
-
23
Fanning
friction factor
for the annulus
fluid (milk)
0.00684
-
Nusselt
number for the
annulus fluid
(milk)
2
99.49
-
24
Equivalent
diameter for
heat transfer
0.0491
m
25
Heat transfer
coefficient for
the annulus
fluid (milk)
1,175.24
W/m
2
.K
Source: Own elaboration.
1
Since 10
4
<
< 5 x 10
6
, the tube-side fluid (water) flows
under turbulent regime, thus Prandtl’s correlation (equation
1.15) was used to calculate the Nusselt number for this fluid.
This equation is also valid to use because
= 11.19 > 0.5.
2
Since 10
4
<
< 5 x 10
6
, the annulus side fluid (milk)
flows under turbulent regime, thus Prandtl’s correlation
(equation 1.25) will be used to calculate the Nusselt number
for this fluid. This equation is also valid to use because
= 7.16 > 0.5.
Table 9 reveals the values of the parameters included in steps
26-34.
Table 9. Values of the parameters included in steps 26.-34.
Step
Parameter
Symbol
Value
Units
26
Fouled overall
heat transfer
coefficient
based on the
outside area of
the inner tube
774.31
W/m
2
.K
27
Log-mean
temperature
difference
1
23.51
ºC
28
Heat transfer
surface area
12.92
m
2
29
Heat transfer
area per hairpin
0.629
m
2
INQUIDE
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Pag. 97
30
Number of
hairpins
21
-
31
Clean overall
heat transfer
coefficient
based on the
outside heat
transfer area
1,030.11
W/m
2
.K
32
Cleanliness
factor
0.752
-
33
Total fouling
0.00032
m
2
.K/W
34
Percent over
surface
32.96
%
Source: Own elaboration.
1
For counterflow arrangement.
3.2. Pressure drop and pumping power.
Table 10 presents the values of the parameters included in
steps 35-38.
Table 10. Values of the parameters included in steps 35-38.
Step
Parameter
Symbol
Value
Units
35
Frictional
pressure drop of
the tube-side
fluid (water)
9,481,246
Pa
36
Pumping power
for the tube-side
fluid (water)
1
110.5
kW
37
Frictional
pressure drop of
the annulus fluid
(milk)
77,392
Pa
38
Pumping power
for the annulus
fluid (milk)
1
114.58
W
Source: Own elaboration.
1
A value of 0.80 was selected for the isentropic efficiency of
the pump [15].
3.3. Purchased equipment cost
Using equation (1.46) and for a value of the heat transfer
surface area of 12.92 m
2
, the purchased equipment cost of
the designed DPHE, based on January 2007, is:
(1.46)
Accordingly, the purchased cost of the designed DPHE,
referred to May 2025, is:
(1.47)
4. Discussion
The heat load had a relatively high value of 235.14 kW,
while it is needed a mass flowrate of 9.32 kg/s for the chilled
water, which can be considered high. This is because the low
value required for the outlet temperature of the chilled water
stream (8 ºC) which reduced the cold fluid temperature
difference (
=
= 6 ºC), whereas the somewhat
high value of the liquid milk flowrate (4,320 kg/h or 1.2 kg/s)
and the relatively high temperature difference of the milk
stream (
=
= 50 ºC) both also influence in the
relatively high value of the heat load, which in turn effects
on the high value obtained for the mass flowrate of chilled
water, as shown by equation (1.6). In [15] the value of the
heat load was 87.1 kW for a water-to-water DPHE.
The value of the velocity of the tube-side fluid (chilled water)
is high (16.64 m/s), which is due to the high value obtained
for the chilled water mass flowrate. This value of chilled
water velocity is 18 times higher than the calculated value of
the velocity (0.92 m/s) for the annulus fluid (milk), and is
well above the recommended range reported by [22] for the
velocity of water in tubular heat exchangers (1.5-2.5 m/s).
The Reynolds number of the tube-side fluid (chilled water)
was 291,629, which is 17.4 times higher than the Reynolds
number (16,796) of the annulus fluid (milk). This high value
obtained for the Reynolds number of the chilled water stream
occurs essentially because the high value of the velocity
obtained for this fluid. This result agrees with the unfinned
water-to-water DPHE designed in [15], where the value of
the Reynolds number of the tube-side fluid (159,343) is
higher than the Reynolds number of the annulus fluid
(15,201).
In case of the Prandtl number, the value of this parameter for
the chilled water (11.19) was 1.56 times higher than the
Prandtl number for the milk (7.16). This is fundamentally
because the highest value of the heat capacity (4,205 J/kg.K)
and the viscosity (0.00152 Pa.s) obtained for the water as
compared to the values of these parameters for the milk,
which were 3,919 J/kg for the heat capacity and 0.00106 Pa.s
for the viscosity.
In [1] the Prandtl number of the tube-side fluid (sea water) at
a temperature of 25 ºC, in order to cool down a stream of
engine oil in a DPHE, was 6.29, with a value for the specific
heat capacity and viscosity of 4,004 J/kg.K and 0.000964
Pa.s, respectively. Likewise, in [15] the Prandtl number of
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Pag. 98
cold water at 27.5 ºC, in order to be heated by hot water in a
DPHE, was 5.77, with a value for the specific heat capacity
and viscosity of 4,179 J/kg.K and 0.000841 Pa.s,
respectively.
Regarding the Nusselt number, the tube-side fluid (chilled
water) had a value of 1,237.84 for this parameter, which was
12.44 times higher than the value of the Nusselt number
(99.49) for the annulus fluid (milk). Considering that the
same equation (Prandtl’s correlation) was employed to
calculate the Nusselt number for both streams, the highest
value obtained of this parameter for the chilled water is due
to the higher values that the chilled water stream presents for
the Reynolds and Prandtl numbers, as compared to the lower
values of these parameters for the milk stream. These results
agree with those reported by [1], where the Nusselt number
of the tube-side fluid (sea water) ranged from 422.0330 -
634.7506, which were higher than the Nusselt number
(34.692) of the annulus fluid (engine oil).
Similarly, they also agree with the results reported by [15]
where the Nusselt number (375.3) for the tube-side fluid (hot
water) is higher than the Nusselt number (89.0) of the
annulus fluid (cold fluid). It is worth to mention that all these
authors also employed the Prandtl’s correlation applied in
our study to calculate the Nusselt number for both streams.
The heat transfer coefficient (26,531.78 W/m
2
.K) for the
water (tube-side fluid) was 22.57 times higher than the value
of the heat transfer coefficient (1,175.24 W/m
2
.K) for the
milk (annulus fluid). This result is directly influenced by the
higher value of the Nusselt number that the chilled water
presents with respect to the value of the Nusselt number for
the milk.
These findings coincide with the reported by [1], where the
values of the heat transfer coefficients for the tube-side fluid
(sea water) ranged between 12,885 – 19,379 W/m
2
.K and
were higher than the value of the heat transfer coefficient
(64.549 W/m
2
.K) for the annulus fluid (engine oil). In the
same way, our results are similar with those reported by [15]
where the heat transfer coefficient (4,911 W/m
2
.K) of the
tube-side fluid (hot water) is 3.65 times higher than the heat
transfer coefficient for the annulus (1,345 W/m
2
.K).
The value of the pressure drop of the tube side fluid (chilled
water) is quite high (9,481,246 Pa), and is well above the
maximum allowable limit set by the heat transfer system
(85,000 Pa). This occurs fundamentally because the high
value of the velocity obtained for this fluid (16.64 m/s) and
the relatively high number of hairpins (21). This high value
of the pressure drop for the chilled water influences on the
significant value of the pumping power obtained for this
fluid (110.5 kW). On the other hand, the calculated pressure
drop for the annulus fluid (milk, 77,392 Pa) is below the
maximum allowable set by the system, thus requiring a
pumping power of 114.58 W.
As noted in [15], when a significant volume of fluid moves
through the tube or the annulus of a DPHE, the pressure drop
can exceed the acceptable levels due to high flow velocities,
which applies to our research. In these situations, it is
advisable to divide the mass flow into several parallel
streams, while the lower mass flow rate side can be placed in
a series configuration. Consequently, the system will be
organized in a parallel-series layout.
Similarly, [14] points out that an increase in fluid velocity
results in greater pressure drops, and if the heat exchanger
must be integrated into an existing process, the designer
should comply with the maximum permissible pressure drop
for both streams. This reference also notes that if the
calculated pressure drop is too high, it will be necessary to
enlarge the flow area, either by increasing the diameter of the
tubes or by adding more parallel branches. Conversely, if the
determined pressure drop is smaller than allowable, reducing
the flow area could be an option. In either scenario, the
design process needs to be restarted.
This author further emphasizes that a smaller flow area for
both fluids (and subsequently, a reduced tube diameter) leads
to increased velocity and heat transfer coefficients, but it also
causes greater pressure drops. He recommends, as an initial
step, to choose the tube diameter based on fluid velocities,
suggesting speeds of 1-2 m/s for liquids with low viscosity,
and also proposing that upon the final length is known, the
pressure drop for each fluid can be computed, which may
demand adjustments to the chosen pipe diameters.
In [15] the pressure drop of the tube-side fluid is 460.1 Pa,
thus requiring a pumping power of 0.84 W, while the
pressure drop of the annulus fluid is 2,876.4 Pa, therefore
needing a pumping power of 5.0 W. In [1], the pressure drop
and the pumping power of the tube-side fluid (sea water) for
the unfinned clean DPHE design type are 9,376.4 kPa and
27.468 kW, respectively, while the values of these
parameters for the unfinned fouled DPHE design type are
9,597 kPa and 28.114 kW, respectively. This reference also
reports that the pressure drop and pumping power for the
annulus fluid (engine oil) for the unfinned clean DPHE
design type are 42.237 MPa and 298.193 kW, respectively,
while the values of these parameters for the unfinned fouled
DPHE design type are 43.231 MPa and 305.211 kW,
respectively.
Lastly, the designed DPHE will cost around USD $ 45,600
referred to May 2025.
5. Conclusions.
In this paper, an unfinned double-pipe heat exchanger was
designed from the thermo-hydraulic point of view, to carry
out the cooling of a liquid cow’s milk stream using chilled
water as coolant.
The hot fluid (milk) was located in the annulus, while the
cold fluid (chilled water) was located in the inner tube.
INQUIDE
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Pag. 99
Several design; geometrical and operating parameters were
calculated for the DPHE such as the heat transfer surface area
(12.92 m
2
), total number of hairpins (21), cleanliness factor
(0.752) and percent over surface (32.96%), which can be
considered as acceptable and adequate. A high value of the
required mass flowrate of chilled water was obtained,
amounting 9.32 kg/s.
Likewise, the pressure drop of the tube-side fluid is quite
high (9,481,246 Pa) and surpasses the maximum allowable
pressure drop set by the heat exchange process for both
streams (85,000 Pa), whereas the pressure drop of the
annulus fluid (77,392 Pa) is below this maximum allowable
limit. The high value obtained for the pressure drop of the
tube-side fluid increases the required pumping power for this
fluid to a significant value (110.5 kW), while the required
value of the pumping power for the annulus fluid is 114.58
W. It’s concluded that the DPHE designed in this study
cannot be successfully implemented in this heat exchange
system because of the high values of pressure drop and
pumping power obtained for the tube-side fluid (chilled
water). The designed DPHE will cost around USD $ 45,600
based on May 2025. It’s recommended to increase the
diameter of both pipes and redesign the unfinned DPHE to
decrease the pressure drop of the tube-side fluid to a value
below the minimum allowable limit set by the heat transfer
system for this parameter.
6.- Author Contributions (Contributor Roles
Taxonomy (CRediT))
1. Formal Conceptualization: Amaury Pérez Sánchez.
2. Data curation: Laura de la Caridad Arias Aguila, Heily
Victoria González, Zamira María Sarduy Rodríguez.
3. Formal analysis: Amaury Pérez Sánchez, María Isabel
La Rosa Veliz, Lizthalía Jiménez Guerra.
4. Acquisition of funds: Not applicable.
5. Research: Amaury Pérez Sánchez, Laura de la Caridad
Arias Aguila, Heily Victoria González, María Isabel La
Rosa Veliz
6. Methodology: Amaury Pérez Sánchez, Laura de la
Caridad Arias Aguila, Lizthalía Jiménez Guerra.
7. Project management: Not applicable.
8. Resources: Not applicable.
9. Software: Not applicable.
10. Supervision: Amaury Pérez Sánchez, Laura de la
Caridad Arias Aguila.
11. Validation: Amaury Pérez Sánchez, Laura de la Caridad
Arias Aguila, Heily Victoria González, Zamira María
Sarduy Rodríguez.
12. Display: Not applicable.
13. Wording - original draft: Heily Victoria González,
María Isabel La Rosa Veliz, Zamira María Sarduy
Rodríguez, Lizthalía Jiménez Guerra.
14. Writing - revision and editing: Amaury Pérez Sánchez,
Laura de la Caridad Arias Aguila.
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Journal of Science and Engineering
Vol. 08 / Nº 01
e – ISSN: 3028-8533
ISSN – L: 3028-8533
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Guayaquil – Ecuador
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Pag. 100
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Nomenclature.
Heat transfer surface area
m
2
Net free flow area of the annulus
m
2
Net free flow area of the inner
tube
m
2
Heat transfer surface area
m
2
Heat capacity
kJ/kg.K
Cleanliness factor
-
External diameter inner tube
m
Internal diameter inner tube
m
Equivalent diameter for heat
transfer
m
Hydraulic diameter
m
Internal diameter annulus
m
Fanning friction factor
-
Corrected Fanning friction
factor
-
Heat transfer coefficient
W/m
2
.K
Thermal conductivity
W/m.K
Thermal conductivity metallic
material of the inner pipe
W/m.K
Tube length
m
Mass flowrate
kg/h
Factor
-
Number of hairpins
-
Nusselt number
-
Percent over surface
%
Pumping power
kW or W
Prandtl number
-
Frictional pressure drop
Pa
Maximum allowable pressure
drop
Pa
Heat load
kW
Fouling factor
m
2
.K/W
Reynolds number
-
Total fouling
m
2
.K/W
Temperature cold fluid
ºC
Average temperature cold fluid
ºC
Temperature hot fluid
ºC
Tube wall temperature
ºC
Average temperature hot fluid
ºC
Log-mean temperature
difference
ºC
Clean overall heat transfer
coefficient
W/m
2
.K
Fouled overall heat transfer
coefficient
W/m
2
.K
Velocity
m/s
INQUIDE
Chemical Engineering & Development
Journal of Science and Engineering
Vol. 08 / Nº 01
e – ISSN: 3028-8533
ISSN – L: 3028-8533
Chemical Engineering & Development
University of Guayaquil | Faculty of Chemical Engineering
Guayaquil – Ecuador
https://revistas.ug.edu.ec/index.php/iqd
Email: inquide@ug.edu.ec
francisco.duquea@ug.edu.ec
Pag. 101
Greek symbols
Density
kg/m
3
Viscosity
Pa.s
Viscosity of the fluid at the tube
wall temperature
Pa.s
Isentropic efficiency of the pump
-
Subscripts
1
Inlet
2
Outlet
Annulus fluid
Cold fluid
Hot fluid
Tube side fluid
