INQUIDE
Chemical Engineering and Development
Journal of Science and Engineering
Vol. 08 / Nº 01
e – ISSN: 3028-8533
ISSN – L: 3028-8533
Chemical Engineering and 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. 39
Thermo-hydraulic design of a shell and tube heat exchanger for acrylic acid
cooling.
Diseño térmico-hidráulico de un intercambiador de calor de tubo y coraza para el enfriamiento de
ácido acrílico.
Amaury Pérez Sánchez
1
*; Laura Thalía Álvarez Lores
2
; Laura de la Caridad Arias Águila
3
; Lizthalía Jiménez Guerra
4
Received: 03/06/2025 – Accepted: 29/08/2025 – Published: 01/01/2026
Research
Articles
X
Review
Articles
Essay
Articles
* Corresponding
author.
This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA
4.0) license. Authors retain the rights to their articles and are free to share, copy, distribute, perform, and publicly communicate
the work, provided that proper attribution is given, the use is non-commercial, and any derivative works are licensed under the
same terms.
Abstract.
Shell and tube heat exchangers (STHE) in their various manifestations are undoubtedly the most widely and commonly used heat transfer equipment in the chemical
processing industries. The objective of the present work is to design, from the thermo-hydraulic point of view, a 1-2 STHE to cool 50,000 kg/h of an acrylic acid
stream from 97 to 40 ºC using water as coolant at an inlet temperature of 25 ºC. The proposed STHE will present a heat transfer area of 284.29 m
2
, an overall heat
transfer coefficient of 364.26 W/m
2
.K, a number of tubes of 702, a bundle diameter of 975.62 mm, and a shell diameter of 1,047.62 mm. The selected type of STHE
is split-ring floating head, the heat load has a value of 1,733.59 kW, it will be required 20.74 kg/s (74,664 kg/h) of cooling water to carry out the heat transfer service,
while the values of the pressure drop of both the water (402.54 Pa) and the acrylic acid (2,479.27 Pa) are below the maximum allowable limits set by the heat
exchange process, which are 1,000 Pa and 3,000 Pa for the water and acrylic acid, respectively. The designed STHE will has a purchase cost of USD $ 101,209.
Keywords.
Design; Shell and Tube Heat Exchanger; Area; Pressure Drop, Purchase Cost.
Resumen.
Los intercambiadores de calor de tubo y coraza (ICTC) en sus varias manifestaciones son indudablemente los equipos de transferencia de calor más ampliamente y
comúnmente usados en las industrias de procesamiento químico. El objetivo del presente trabajo es diseñar, desde el punto de vista térmico-hidráulico, un ICTC 1-
2 para enfriar 50 000 kg/h de una corriente de ácido acrílico desde 97 hasta 40 ºC usando agua como refrigerante a una temperatura de entrada de 25 ºC. El ICTC
propuesto presentará un área de transferencia de calor de 284,29 m2, un coeficiente global de transferencia de calor de 364,26 W/m2.K, un número de tubos 702,
un diámetro del haz de 975,62 mm, y un diámetro de la coraza de 1 047,62 mm. El tipo de ICTC seleccionado es de cabezal flotante de anillo hendido, la carga de
calor tiene un valor de 1 733,59, se requerirán 20,74 kg/s (74 664 kg/h) de agua de enfriamiento para llevar a cabo el servicio de transferencia de calor, mientras que
los valores de la caída de presión de tanto el agua (402,54 Pa) como el ácido acrílico (2 479,27 Pa) están por debajo de los límites máximos permisibles fijados por
el proceso de intercambio de calor, los cuales son 1 000 Pa y 3 000 Pa para el agua y el ácido acrílico, respectivamente. El ICTC diseñado tendrá un costo de
adquisición de USD $ 101 209.
Palabras clave.
Diseño; Intercambiador de Calor de Tubo y Coraza; Área; Caída de Presión; Costo de Adquisición.
1.- Introduction
Heat transfer is the field that focuses basically on the rate
heat is exchanged between hot and cold objects, referred to
as the source and the receiver, respectively. The devices
used to facilitate this heat transfer are known as heat
exchangers [1].
Heat exchangers function on the concept of transferring
thermal energy between a fluid at a higher temperature and
one at a lower temperature. They work by enabling the hot
fluid to come into contact with the cooler fluid either
directly or indirectly. This mechanism allows for heat to
transfer from the hotter fluid to the cooler one, leading to a
reduction in the temperature of the first fluid and a rise in
the temperature of the second fluid. The direction of heat
transfer is determined by whether heating or cooling is
required for the particular system [2].´
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; laura.alvarez@reduc.edu.cu; https://orcid.org/0009-0007-2643-018X, Camagüey; Cuba.
3
University of Camagüey; Faculty of Applied Sciences; aguilaariaslaura@gmail.com; https://orcid.org/0000-0002-6494-9747, Camagüey; Cuba.
4
University of Camagüey; Faculty of Applied Sciences; lizthalia.jimenez@reduc.edu.cu; https://orcid.org/0000-0002-2471-7263
The transfer of heat primarily occurs through conduction
and convection. Heat exchangers are typically categorized
based on the number of fluids involved, the characteristics
of the surface elements, design aspects, fluid flow patterns,
and their heat transfer techniques [3].
Among the various categories of heat exchangers, shell and
tube heat exchangers (STHEs) are reasonably simple to
assemble and offer a wide range of applications for both
gases and liquids across extensive temperature and pressure
levels [3].
In STHE, two fluids with varying temperatures flow
through the system. One fluid travels inside the tubes
(known as the tube side) while the other circulates around
the tubes within the shell (referred to as the shell side).
Thermal energy is exchanged between the fluids via the
walls of the tubes, moving from the tube side to the shell
side or vice versa. These fluids can be in liquid or gas state,
INQUIDE
Chemical Engineering and Development
Journal of Science and Engineering
Vol. 08 / Nº 01
e – ISSN: 3028-8533
ISSN – L: 3028-8533
Chemical Engineering and 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. 40
whether on the shell side or the tube side. To facilitate
effective heat transfer, a considerable heat transfer area is
required, leading to the utilization of numerous tubes.
STHEs can be specially designed while considering factors
such as functionality, ease of maintenance, adaptability, and
safety, resulting in a highly durable heat exchanger that
encourages its extensive application across various sectors.
It is projected that over 35-40% of heat exchangers used in
contemporary engineering sectors are of the shell and tube
type, thanks to their reliable structural design, easy
maintenance, and potential for upgrades. For optimal heat
transfer efficiency, shell and tube heat exchangers should
aim for a minimal pressure drop, elevated mass flow
velocity on the shell side, a high heat transfer coefficient,
and minimal to negligible fouling, among other essential
features [3].
STHEs facilitate the exchange of large quantities of heat
efficiently and cost-effectively, offering a low-cost tube
surface while minimizing the area needed on the floor, the
volume of liquid, and the overall weight, while they are
available in diverse sizes and lengths [4].
These heat exchangers are prevalent across various sectors,
such as power generation facilities where they act as
condensers, and in chemical and petrochemical sectors for
preheating or cooling functions [5]. They are also employed
in refrigeration, climate control, and the food production
industry, among others [3]. Common uses often include the
heating or cooling of relevant fluid streams and the
condensation or evaporation of fluid mixtures. Furthermore,
certain applications aim to recover or reject heat or carry out
sterilization, pasteurization, fractionation, distillation,
concentration, crystallization, or thermal adjustment of
process fluids [6].
The thermo-hydraulic design of a shell and tube heat
exchanger generally involves calculating the heat transfer
surface area, amount of heat transferred, overall heat
transfer efficiency, tube quantity, tube dimensions,
arrangement, number of passes for the shell and tube, type
of heat exchanger (like fixed tube sheets or removable tube
bundles), tube spacing, quantity and specifications of
baffles, as well as pressure drops on both the shell and tube
sides, among other factors [4].
Numerous investigations have been documented involving
the design of a STHE. In this context, [5] introduced a
detailed design approach for STHE influenced by the
analysis of flexibility indices. This approach aims to
mitigate challenges like possible design inefficiencies or
inadequate functioning of entire process systems. This
research incorporates a genetic algorithm with stringent
constraints for optimizing the design of the STHE.
Furthermore, [4] provided insights into the calculations
required for designing heat exchangers of the shell and tube
variety, outlining a methodical process for determining
designs, intending to serve as a standardized guide for
performing these calculations systematically for STHE
design. Similarly, [7] focused on designing an STHE
intended for applications related to nanofibril cellulose
production, adhering to the TEMA standards, and executed
parameter calculations manually through the Microsoft
Excel program. Likewise, [8] designed a shell and tube heat
exchanger for Diesel Locomotives employing the Bell
Delaware technique to derive various dimensions, including
shell, tubes, and baffles. Subsequently, a thermal analysis
was executed using COMSOL, applying various thermal
loads while adjusting the number of baffles. Additionally,
[2] highlighted the design and evaluation of shell and tube
heat exchangers by examining different materials and their
heat transfer capabilities from surfaces, while also studying
baffle spacing and its influence on heat transfer through
Computational Fluid Dynamics (CFD) analysis. The
findings were contrasted with theoretical models. The
design and simulation of the heat exchanger was completed
using PTC Creo Parametric and ANSYS Fluent for CFD
analysis, considering materials such as copper, aluminum,
and steel.
In [9], a counter-current shell and tube heat exchanger
constructed for a nitric acid manufacturing facility was
presented, where the design was conducted with the target
processing capacity of 100 tons of nitric acid per day. This
project employed two distinct methodologies, Kern's
approach and Bell's approach, during the design process. It
was determined that Bell's approach provided more precise
results, as the overall heat transfer coefficient derived from
this method closely matched the predicted value.
Additionally, the design included auxiliary components of
the heat exchanger such as flanges, gaskets, bolts, supports,
and saddles. In another study [10], researchers designed and
assessed the effectiveness of a shell and tube heat exchanger
utilizing both Kern's approach and Ansys software,
employing CFD to analyze the temperature and flow rate
within the tubes and shell, reaching the conclusion that the
heat transfer along the tube length varies.
In [11], a straightforward method for designing a shell and
tube heat exchanger for applications in the beverage and
process industries was described; this design process
addressed both thermal and structural aspects. The thermal
design aspect involved calculating the necessary effective
surface area (which refers to the number of tubes) and
determining the logarithmic mean temperature difference,
while the mechanical design involved designing the shell to
withstand both internal and external pressures, along with
the design of tubes, baffles, gaskets, etc. The design process
adhered to the ASME/TEMA standards.
In [12], a shell-and-tube heat exchanger featuring a single
shell pass along with two tube passes was developed to
function as a water heater, utilizing sulfur water as the
heating agent. The construction materials chosen for the
heat exchanger included stainless steel 304 for the shells and
copper for the tubes. Likewise, in [13], a design and rating
approach for STHEs equipped with helical baffles was
INQUIDE
Chemical Engineering and Development
Journal of Science and Engineering
Vol. 08 / Nº 01
e – ISSN: 3028-8533
ISSN – L: 3028-8533
Chemical Engineering and 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. 41
introduced, which was based from existing public sources
and the prevalent Bell-Delaware technique for STHEs
utilizing segmental baffles. This method replaced various
curve-type factors from the literature with mathematical
formulas to simplify engineering design, thereby detailing
the calculation process for the proposed approach. Finally,
[14] explores into the fundamental principles of thermal
design for STHEs, discussing elements such as the
components of STHEs; their classification based on
construction and operation; necessary data for thermal
design; tube-side design; shell-side design, incorporating
tube arrangement, baffling, pressure drop on the shell side;
and the mean temperature difference. It emphasizes the use
of essential equations related to heat transfer and pressure
loss on both the tube side and shell side for the optimal
design of the STHE.
Several books [1] [15]-[18] describe useful calculation
methodologies to design STHE form the thermal and
hydraulic point of view, which are modern adaptations or
versions of the classic Kern’s method, as well as describing
the Bell-Delaware method.
In certain chemical plant is desired to cool down 50,000
kg/h of a stream of acrylic acid produced at the bottom of a
distillation column prior to be stored, and for that a shell and
tube heat exchanger was proposed. In this context, the aim
of this study is to design a STHE to cool this acrylic acid
stream from 97 ºC to 40 ºC using cooling water at an inlet
temperature of 25 ºC. To design the STHE the calculation
methodology reported in [17], which is based on Kern’s
approach, was applied due to its simplicity and innovative
features. This methodology allows calculating several
design parameters for the STHE such as heat exchange area,
number of tubes, shell diameter, overall heat transfer
coefficient, as well as the pressure drop of both streams.
Also, the purchase cost of the designed STHE will be
calculated and updated to 2024 year.
2.- Materials and methods.
2.1. Problem statement
It’s required to cool down 50,000 kg/h of an acrylic acid
stream coming from the bottom of distillation column from
97 ºC to 40 ºC using cooling water at an inlet temperature
of 25 ºC. For this heat transfer service a horizontal shell and
tube heat exchanger is proposed working as a cooler. The
outlet temperature of the cooling water must not exceed 45
ºC for safety issues, while the pressure drop of the acrylic
acid and cooling water streams should not exceed 5,000 Pa
and 1,000 Pa respectively. The heat exchanger must operate
under countercurrent arrangement and will be of 1-2 type,
i.e. with one shell pass and two tube passes. To design the
proposed 1-2 shell and tube heat exchanger the
methodology reported by [17] will be used, which is based
on Kern’s approach. Also, the purchase cost of the heat
exchanger will be calculated by using the correlation
published in [17], which depends on the calculated heat
exchange area.
2.2. Design methodology.
The calculation methodology applied to design the shell and
tube heat exchanger from the thermo-hydraulic point of
view is shown below.
Preliminary design
Step 1. Definition the initial data available for the two
streams:
Table 1 shows the initial data available for the two streams.
Table 1. Initial data available for the two streams.
Parameter
Units
Cold
fluid
Hot fluid
Mass flowrate
kg/h
Inlet temperature
ºC
Outlet temperature
ºC
Maximum permissible
pressure drop
Pa
Fouling factor
W/m
2
.ºC
Source: Own elaboration.
Step 2. Average temperature of both streams:
• Cold fluid (
):
(1)
• Hot fluid (
):
(2)
Step 3. Physical properties of both fluids at the average
temperature:
Table 2 presents the physical properties that must be defined
for both fluids at the average temperature calculated in the
previous step.
Table 2. Physical properties to be defined for both fluids.
Property
Units
Cold
fluid
Hot
fluid
Density
kg/m
3
Viscosity
Pa.s
Heat capacity
kJ/kg.ºC
Thermal conductivity
W/m.K
Source: Own elaboration.
Step 4. Heat load ():
• For the hot fluid:
(3)
Where the unit of is kW.
Step 5. Required mass flowrate of the cold fluid (cooling
water) (
):
(4)
INQUIDE
Chemical Engineering and Development
Journal of Science and Engineering
Vol. 08 / Nº 01
e – ISSN: 3028-8533
ISSN – L: 3028-8533
Chemical Engineering and 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. 42
Where is given in kW and
is given in kJ/kg.K.
Step 6. Assumption of the overall heat transfer coefficient
(
).
Step 7. Log mean temperature difference ():
• For a countercurrent arrangement:
(5)
Step 8. Factor R:
(6)
Step 9. Factor S:
(7)
Step 10. Temperature correction factor (
):
• For a 1 shell: 2 tube pass heat exchanger:
(8)
Step 11. True temperature difference ():
(9)
Step 12. Provisional heat transfer area (
):
(10)
Where is given in kW.
Step 13. Select the following data for the tubes:
• Nominal diameter.
• Material.
• Length (
).
Step 14. Area of one tube (
):
(11)
Where
and
are given in m.
Step 15. Number of tubes (
):
(12)
Step 16. Tube arrangement:
Triangular or square pitch.
Step 17. Selection of the constants
and
depending on
the tube arrangement (triangular or square) and the number
of tube passes.
Step 18. Bundle diameter (
):
(13)
Where
is given in mm.
Step 19. Select the type of shell and tube heat exchanger:
• Pull-through floating head.
• Split-ring floating head.
• Outside packed head.
• Fixed and U-tube.
Step 20. Shell-bundle clearance (
) in mm.
Step 21. Shell diameter (
):
(14)
Where
and
are given in mm.
Step 22. Fluids allocation inside the heat exchanger.
Tube side coefficient
Step 23. Tube cross-sectional area (
):
(15)
Where
is given in m.
Step 24. Number of tubes per pass (
):
(16)
Where
– number of tube-side passes = 2.
Step 25. Total flow area (
):
(17)
Step 26. Mass velocity of the tube-side fluid (
):
(18)
Where
is given in kg/s.
Step 27. Linear velocity of the tube-side fluid (
):
(19)
Step 28. Reynolds number of the tube-side fluid (
):
(20)
Step 29. Prandtl number of the tube-side fluid (
):
(21)
Where
is given in kJ/kg.K.
Step 30. Ratio
, where both
and
are given in m.
Step 31. Tube-side heat-transfer factor (
), depending on
the ratio
and Reynolds number.
INQUIDE
Chemical Engineering and Development
Journal of Science and Engineering
Vol. 08 / Nº 01
e – ISSN: 3028-8533
ISSN – L: 3028-8533
Chemical Engineering and 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. 43
Step 32. Tube-side heat-transfer coefficient (
):
(22)
Where
is given in m.
For water flowing in pipes, the following correlation could
be used:
(23)
Where:
– Average temperature of water (ºC).
– Water velocity (m/s).
– Tube inside diameter (mm).
Shell-side coefficient:
Step 33. Baffle spacing (
):
(24)
Where = 0.2 – 0.5 [17] and
is given in mm.
Step 34. Tube pitch (
):
(25)
Where
is given in m.
Step 35. Cross-flow area of the shell-side fluid (
):
(26)
Where all the parameters are given in m.
Step 36. Mass velocity of the shell-side fluid (
):
(27)
Where
and
are given in kg/h and m
2
, respectively.
Step 37. Shell-side equivalent diameter (hydraulic
diameter) (
):
• Square pitch:
(28)
• Triangular pitch:
(29)
Where
and
are given in m.
Step 38. Reynolds number of the shell-side fluid (
):
(30)
Step 39. Prandtl number of the shell-side fluid (
):
(31)
Where
is given in kJ/kg.K.
Step 40. Selection of the baffle cut (%).
Step 41. Shell-side heat-transfer factor (
), depending on
the baffle cut and Reynolds number.
Step 42. Shell-side heat-transfer coefficient (
):
(32)
Where
is given in m.
Overall heat transfer coefficient calculated
Step 43. Thermal conductivity of the tube material (
).
Step 44. Overall heat transfer coefficient calculated (
):
(33)
Pressure drop
Step 45. Friction factor for the tube-side fluid (
).
Step 46. Pressure drop of the tube-side fluid (
):
(34)
Where = 0.25 for laminar flow (
< 2,100) and = 0.14
for turbulent flow (
> 2,100), while
and
are given
in m,
and
are given in kg/m
3
and m/s, respectively.
Step 47. Friction factor of the shell-side fluid (
).
Step 48. Linear velocity of the shell-side fluid (
):
(35)
Step 49. Pressure drop of the shell-side fluid (
):
(36)
Where
,
,
and
are given in m.
Purchase cost of the heat exchanger
To calculate the purchase cost of the proposed heat
exchanger, the following correlation was used [17]:
(37)
Where:
= 24,000
= 46.
= 1.2
– Heat exchanger area, which must be in the range of 10
– 1,000 m
2
.
The purchase cost calculated by eq. (37) for the designed
heat exchanger is referred to January 2007. To update the
purchase cost of the shell and tube heat exchanger to May
2024, the following correlation was used:
INQUIDE
Chemical Engineering and Development
Journal of Science and Engineering
Vol. 08 / Nº 01
e – ISSN: 3028-8533
ISSN – L: 3028-8533
Chemical Engineering and 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. 44
(38)
Where:
– Cost of the shell and tube heat exchanger in
May 2024.
– Cost of the shell and tube heat exchanger in
January 2007, calculated by eq. (37).
- Chemical Engineering Index in May
2024 = 800.0 [19].
- Chemical Engineering Index in January
2007 = 509.7 [17].
3.- Analysis and Interpretation of Results.
3.1. Preliminary design.
Shown below are each step implemented in the
methodology to design the shell and tube heat exchanger for
acrylic acid cooling.
Step 1. Definition of the initial data available for the two
streams:
Table 3 shows the initial data available for the two
streams.
Table 3. Initial data available for the two streams.
Parameter
Units
Cooling
water
Acrylic
acid
Mass flowrate
kg/h
-
50,000
Inlet temperature
ºC
25
97
Outlet temperature
ºC
45
40
Maximum allowable
pressure drop
Pa
1,000
5,000
Fouling factor
W/m
2
.ºC
1,000
3,000
Source: Own elaboration.
Step 2. Average temperature of both streams:
• Cold fluid (
):
(1)
• Hot fluid (
):
(2)
Step 3. Physical properties of both fluids at the average
temperature:
According to [20], both fluids present the physical
properties displayed in Table 4 at the average temperatures
calculated in the previous step.
Table 4. Physical properties defined for both fluids.
Property
Units
Cooling
water
Acrylic
acid
Density
kg/m
3
994.033
995.54
Viscosity
Pa.s
0.000719
0.0005696
Heat capacity
kJ/kg.ºC
4.179
2.1897
Thermal conductivity
W/m.K
0.6233
0.1449
Source: Own elaboration.
Step 4. Heat load ():
Using the initial data for the hot fluid:
(3)
Step 5. Required mass flowrate of the cold fluid (cooling
water) (
):
(4)
Step 6. Assumption of the overall heat transfer coefficient
(
).
Taking into account the range reported by [17] for coolers
that use water to cool organic solvents, it was assumed a
value for the overall heat transfer coefficient (
) of 300
W/m
2
.K.
Step 7. Log mean temperature difference ():
• For a countercurrent arrangement:
(5)
Step 8. Factor R:
(6)
Step 9. Factor S:
(7)
Step 10. Temperature correction factor (
):
• For a 1 shell: 2 tube pass heat exchanger:
(8)
Step 11. True temperature difference ():
(9)
Step 12. Provisional heat transfer area (
):
(10)
INQUIDE
Chemical Engineering and Development
Journal of Science and Engineering
Vol. 08 / Nº 01
e – ISSN: 3028-8533
ISSN – L: 3028-8533
Chemical Engineering and 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. 45
Step 13. Selection of the following data for the tubes:
• Nominal diameter: ¾ in, 40ST. Thus, according
to [20]:
Outside diameter (
) = 0.0267 m.
Inside diameter (
) = 0.0209 m.
• Material: Stainless steel (18/8).
• Length (
) = 4.83 m.
Step 14. Area of one tube (
):
(11)
Step 15. Number of tubes (
):
(12)
Step 16. Tube arrangement:
The triangular pitch was selected in order to give higher heat
transfer rates, even at the expense of higher pressure drops
[17], because the pressure drop is not an important
parameter to consider in this heat transfer service according
to the supervisors of the industry where this STHE will be
installed. However, the pressure drop will be calculated for
both fluid streams in this design methodology, and the
values obtained will be compared to the maximum
allowable limits set by the process.
Step 17. Selection of the constants
and
:
According to [17], for a triangular tube arrangement and a
number of tube passes (
) of 2, the values of these
constants are:
•
= 0.249.
•
= 2.207.
Step 18. Bundle diameter (
):
(13)
Step 19. Select the type of shell and tube heat exchanger:
The selected type of shell and tube heat exchanger is split-
ring floating head for efficiency and ease of cleaning [17].
Step 20. Shell-bundle clearance (
):
As referred by [17], the shell-bundle clearance for a value
of the bundle diameter (
) of 975.62 mm and a split-ring
floating head type, is 72 mm.
Step 21. Shell diameter (
):
(14)
Step 22. Fluids allocation inside the heat exchanger.
Taking into account suggestions reported by [17], the cold
fluid (cooling water) will be located on the tube side, while
the hot fluid (acrylic acid) will be located on the shell side.
3.2. Tube side coefficient.
Due to the allocation of the cold fluid on the tubes and the
hot fluid on the shell, the nomenclature of some parameters
will be corrected to agree with the nomenclature of the
equations that will be used hereafter.
Table 5 indicates the initial and corrected nomenclature of
the parameters employed in the upcoming equations.
Table 5. Original and corrected nomenclature of the parameters used in the
upcoming equations.
Parameter
Original
nomenclature
Corrected
nomenclature
Units
Hot fluid flowrate
kg/h
Cold fluid
flowrate
kg/h
Hot fluid density
kg/m
3
Cold fluid density
kg/m
3
Hot fluid viscosity
Pa.s
Cold fluid
viscosity
Pa.s
Hot fluid heat
capacity
kJ/kg.K
Cold fluid heat
capacity
kJ/kg.K
Hot fluid thermal
conductivity
W/m.K
Cold fluid thermal
conductivity
W/m.K
Source: Own elaboration.
Table 6 depicts the results of the parameters calculated in
the steps 23 to 32, in order to determine the tube-side heat-
transfer coefficient.
Table 6. Results of the parameters calculated in steps 23-32.
Step
Parameter
Symbol
Value
Units
23
Tube cross-sectional
area
0.00034
m
2
24
Number of tubes per
pass
351
-
25
Total flow area
0.1193
m
2
26
Mass velocity of the
tube-side fluid
173.85
kg/s.m
2
27
Linear velocity of the
tube-side fluid
0.175
m/s
28
Reynolds number of the
tube-side fluid
5,056.57
-
29
Prandtl number of the
tube-side fluid
4.82
-
INQUIDE
Chemical Engineering and Development
Journal of Science and Engineering
Vol. 08 / Nº 01
e – ISSN: 3028-8533
ISSN – L: 3028-8533
Chemical Engineering and 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. 46
30
Ratio
-
231.10
-
31
Tube-side heat-transfer
factor
1
0.0041
-
32
Tube-side heat-transfer
coefficient
2
1,162.11
W/m
2
.K
1
For a value for
and
of 5056.57 and 231.10, respectively.
2
Equation (23) was employed to calculate this parameters since water flows
in the pipes.
Source: Own elaboration.
3.3. Shell-side coefficient.
Table 7 presents the results of the parameters calculated in
steps 33-42, to determine the shell-side heat transfer
coefficient.
Table 7. Results of the parameters calculated in steps 33-42.
Step
Parameter
Symbol
Value
Units
33
Baffle spacing
1
209.52
mm
34
Tube pitch
0.0334
m
35
Cross-flow area of the
shell-side fluid
0.0440
m
2
36
Mass velocity of the
shell-side fluid
315.65
kg/s.m
2
37
Shell-side equivalent
diameter
2
0.0191
m
38
Reynolds number of
the shell-side fluid
10,584.47
-
39
Prandtl number of the
shell-side fluid
8.61
-
40
Selection of the baffle
cut
-
25%
-
41
Shell-side heat-
transfer factor
0.0058
-
42
Shell-side heat-
transfer coefficient
3
947.66
W/m
2
.K
1
A value of 0.2 was selected for to calculate the baffle spacing.
2
Equation (29) was employed to calculate the shell side equivalent
diameter due to the selection of the triangular pitch arrangement.
3
The viscosity correction term
was not considered because
both fluids have low viscosity [17].
Source: Own elaboration.
3.4. Overall heat transfer coefficient calculated.
Step 43. Thermal conductivity of the tube material (
).
Because the material selected for the tubes is stainless steel
18/8, the thermal conductivity of this material is 16 W/m.K
[17].
Step 44. Overall heat transfer coefficient calculated (
):
(33)
3.5. Pressure drop
Step 45. Friction factor for the tube-side fluid (
).
According to [17], for a Reynolds number of the tube-side
fluid (cooling water) of 5,056.57, the friction factor (
) has
a value of 0.0058.
Step 46. Pressure drop of the tube-side fluid (
):
(34)
Where
as suggested by [17] because
water is not considered a highly viscous fluid.
Step 47. Friction factor of the shell-side fluid (
).
According to [17], for a Reynolds number of the shell-side
fluid (acrylic acid) of 10,584.47 and a baffle cut of 25%, the
friction factor (
) has a value of 0.0049.
Step 48. Linear velocity of the shell-side fluid (
):
(35)
Step 49. Pressure drop of the shell-side fluid (
):
(36)
3.6. Purchase cost of the heat exchanger.
For a value of the heat exchange area of 207.47 m
2
, the
purchase cost of the designed shell and tube heat exchanger
is:
(37)
Since the purchase cost calculated by equation (37) is for
January 2007, the purchase cost of this equipment referred
to May 2024 is:
INQUIDE
Chemical Engineering and Development
Journal of Science and Engineering
Vol. 08 / Nº 01
e – ISSN: 3028-8533
ISSN – L: 3028-8533
Chemical Engineering and 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. 47
(38)
4.- Discussion
A shell and tube heat exchanger with one shell pass and two
tube passes was designed to cool a stream of acrylic acid,
originated at the bottom of a distillation column, from 97 to
40 ºC by means of cooling water at an inlet temperature of
25 ºC, and using the design methodology reported by [17],
which is based on Kern’s approach. The cooling water was
allocated to flow inside the tubes, while the acrylic acid was
assigned to flow on the shell.
The calculated value of the heat load for this heat exchanger
service was 1,733.59 kW, while it will be required a
flowrate of 20.74 kg/s (74,664 kg/h) for the selected heat
transfer agent (cooling water). The log mean temperature
difference had a value of 29.76 ºC, while the values of the
temperature correction factor and the true temperature
difference were 0.683 and 20.326 ºC, respectively.
The mass velocity and linear velocity of the cooling water
were 173.85 kg/s.m
2
and 0.175 m/s, respectively, while the
calculated Reynolds number for this fluid was 5,056.57,
thus indicating that the cooling water will flow under the
transition regime. The calculated heat transfer coefficient of
the tube-side fluid was 1,162.11 W/m
2
.K.
The values of the mass velocity and linear velocity of the
acrylic acid were 315.65 kg/s.m
2
and 0.317 m/s,
respectively. The calculated Reynolds number for the
acrylic acid was 10,584.47, thus stating that this fluid will
flow under turbulent regime in the designed heat exchanger.
The calculated shell-side heat transfer coefficient was
947.66 W/m
2
.K.
The heat transfer coefficient of the tube-side fluid is about
1.23 times higher than the shell-side heat transfer
coefficient, which agrees with the results of the shell and
tube heat exchanger designed in [17], where the heat
transfer coefficient of the tube-side fluid (brackish water) is
3,852 W/m
2
.K, while the heat transfer coefficient for the
shell-side fluid (methanol) is 2,740 W/m
2
.K (i.e. about 1.40
times higher).
The calculated pressure drop of the tube-side fluid, i.e.
cooling water (402.54 Pa) is about 6.16 times lower than the
pressure drop of the shell-side fluid, i.e. acrylic water
(2,479.27 Pa). This result agrees with the results of the
pressure drop calculated during the design of a shell and
tube heat exchanger in [17], where the value of the pressure
drop (7.2 kPa) of the brackish water used as a coolant (tube-
side fluid) is lower than the value of the pressure drop (272
kPa) of the shell-side fluid (methanol). The values of the
calculated pressure drop in the present study for both fluids
are below the maximum allowable limits set by the heat
exchange service.
A calculated value of the overall heat transfer coefficient of
364.26 W/m
2
.K was obtained, which is above the assumed
value (300 W/m
2
.K) in step 6, thus indicating that the design
has adequate area for the duty required [17].
Accordingly, the designed shell and tube heat exchanger in
this study will present the following design data:
• Type: Split-ring floating head.
• Heat transfer area (): 284.29 m
2
.
• Number of tubes (): 702.
• Bundle diameter (
): 975.62 mm.
• Shell diameter (
): 1,047.62 mm.
The shell and tube heat exchanger designed in [17] in order
to cool 100,000 kg/h of a methanol stream by means of
brackish water, has the following design parameters:
• Type: Split-ring floating head.
• Heat transfer area (): 278 m
2
.
• Number of tubes (): 918.
• Bundle diameter (
): 826 mm.
• Shell diameter (
): 894 mm.
In [9] a shell and tube heat exchanger was designed to cool
0.827 kg/s of nitric oxide stream from 150 ºC to 50 ºC, using
water at a supply temperature of 35 ºC. The parameters of
the shell and tube heat exchanger designed in this study are
shown below:
• Heat transfer area (): 8.98 m
2
.
• Number of tubes (): 60.
• Bundle diameter (
): 240.049 mm.
• Shell diameter (
): 251.049 mm.
• Overall heat transfer coefficient (): 405.62
W/m
2
.K.
• Shell side pressure drop: 82.93 kPa.
In this study, the nitric oxide was allocated on the shell-side,
while the cooling water was allocated on the tubes.
However, the value of tube side heat transfer coefficient
(1,059.197 W/m
2
.K) is 1.51 times lower than the value of
the shell-side heat transfer coefficient (1,601.63 W/m
2
.K),
which differs with the results of our study.
Other authors [7] carried out the design of a shell and tube
heat exchanger for nanofibril cellulose production
applications. The results of the performance parameters
obtained during the design of this STHE are shown below:
• Heat transfer rate (): 167,720 W.
• Area of heat transfer (): 16.87 m
2
.
• Number of tubes (
): 53.
• Bundle shell (
): 1.85 m.
• Convection heat transfer coefficient in the tube
(
): 135.34 W/m
2
.K.
• Convection heat transfer coefficient in shell (
):
0.5934 W/m
2
.K.
INQUIDE
Chemical Engineering and Development
Journal of Science and Engineering
Vol. 08 / Nº 01
e – ISSN: 3028-8533
ISSN – L: 3028-8533
Chemical Engineering and 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. 48
• Overall heat transfer coefficient actual (
):
0.5932 W/m
2
.K.
• Effectiveness (): 89.21%.
Likewise, in [4] a STHE is designed to cool 1.5 kg/s of an
oil stream from 107 ºC to 27 ºC using 1.72 kg/s of cooling
water with an inlet temperature of 27 ºC. In this study, the
hot fluid is allocated on the shell side while the cold fluid is
located on the tube side, which is similar to the conditions
of our study. Several parameters are calculated in this work,
some of which are presented below:
• Energy transferred (): 129,660 W.
• Heat transfer area (): 3.43 m
2
.
• Number of tubes (
): 26.
• Heat transfer coefficient on the tube side (
):
126.63 W/m
2
.K.
• Heat transfer coefficient on the shell side (
):
182.65 W/m
2
.K.
• Overall heat transfer coefficient assumed (): 800
W/m
2
.K.
• Effectiveness (): 50.01%.
5.- Conclusions.
A shell and tube heat exchanger with on shell pass and two
tube passes was designed from the thermo-hydraulic point
of view, using a well-known design methodology based in
Kern’s approach, in order to cool down 50,000 kg/h of an
acrylic acid stream from 97 ºC to 40 ºC using cooling water
at an inlet temperature of 25 ºC. Several parameters were
determined such as heat load (1,733.59 kW); overall heat
transfer coefficient (364.26 W/m
2
.K); heat transfer area
(284.29 m
2
); number of tubes (702); and shell diameter
(1,047.62 mm). The mass flowrate of cooling water
required to cool this acrylic acid stream is 20.74 kg/s
(74,664 kg/h). The selected shell and tube heat exchanger
type was split-ring floating head, while the pressure drop of
the water (402.54 Pa) and the acrylic acid (2,479.27 Pa) are
lower than the maximum allowable pressure drop set by the
service. The purchase cost of the designed shell and tube
heat exchanger is USD $ 101,209.
6.- Author Contributions (Contributor Roles
Taxonomy (CRediT))
1. Conceptualization: Amaury Pérez Sánchez.
2. Data curation: Laura Thalía Alvarez Lores, Lizthalía
Jiménez Guerra.
3. Formal Analysis: Amaury Pérez Sánchez, Laura Thalía
Alvarez Lores, Laura de la Caridad Arias Aguila.
4. Acquisition of funds: Not applicable.
5. Research: Amaury Pérez Sánchez, Laura Thalía
Alvarez Lores, Laura de la Caridad Arias Águila,
Lizthalía Jiménez Guerra.
6. Methodology: Amaury Pérez Sánchez, Laura de la
Caridad Arias Águila.
7. Project management: Not applicable.
8. Resources: Not applicable.
9. Software: Not applicable.
10. Supervision: Amaury Pérez Sánchez.
11. Validation: Amaury Pérez Sánchez, Laura Thalía
Alvarez Lores.
12. Display: Not applicable.
13. Wording - original draft: Laura Thalía Alvarez Lores,
Laura de la Caridad Arias Águila, Lizthalía Jiménez
Guerra.
14. Writing - revision y editing: Amaury Pérez Sánchez.
7.- Appendix.
Nomenclature.
Constant to use in equation (37)
-
Area of one tube
m
2
Tube cross-sectional area
m
2
Total flow area
m
2
Heat exchanger area to use in
equation (37)
m
2
Provisional heat transfer area
m
2
Cross-flow area of the shell-side
fluid
m
2
Constant to use in equation (37)
-
Heat capacity
kJ/kg.K
Shell-bundle clearance
mm
Shell-side equivalent diameter
(hydraulic diameter)
m
Tube inside diameter
m
Tube outside diameter
m
Bundle diameter
m
Shell diameter
mm
Temperature correction factor
-
Mass velocity
kg/s.m
2
Tube-side heat-transfer coefficient
W/m
2
.K
Shell-side heat-transfer coefficient
W/m
2
.K
Friction factor for the tube-side
fluid
-
Friction factor of the shell-side
fluid
-
Tube-side heat-transfer factor
-
Thermal conductivity
W/m.K
Thermal conductivity of the tube
material
W/m.K
Constant to use in equation (13)
-
Baffle spacing
mm
Tube length
m
Mass flowrate
kg/h
Constant to use in equation (37)
-
Constant to use in equation (13)
-
Number of tube-side passes
-
Number of tubes
-
Number of tubes per pass
-
Tube pitch
m
Prandtl number
-
Pressure drop of the tube-side fluid
Pa
Heat load
kW
INQUIDE
Chemical Engineering and Development
Journal of Science and Engineering
Vol. 08 / Nº 01
e – ISSN: 3028-8533
ISSN – L: 3028-8533
Chemical Engineering and 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. 49
Factor
-
Reynolds number
-
Factor
-
Temperature cold fluid
ºC
Temperature hot fluid
ºC
Average temperature cold fluid
ºC
Average temperature hot fluid
ºC
Log mean temperature difference
ºC
True temperature difference
ºC
Overall heat transfer coefficient
assumed
W/m
2
.K
Overall heat transfer coefficient
calculated
W/m
2
.K
Linear velocity
m/s
Greek symbols
Factor
-
Density
kg/m
3
Viscosity
Pa.s
Subscripts
Inlet
Outlet
Cold fluid
Hot fluid
Shell side fluid
Tube side fluid
8.- References.
[1] M. Flynn, T. Akashige, and L. Theodore, Kern's
Process Heat Transfer, 2nd ed. Beverly, USA:
Scrivener Publishing, 2019.
https://dokumen.pub/kerns-process-heat-transfer-
2nbsped-9781119364177-9781119364832-
9781119363644-1119364175.html
[2] E. J. Fernandes and S. H. Krishanmurthy, "Design and
analysis of shell and tube heat exchanger," Int. J. Simul.
Multidisci. Des. Optim., vol. 13, no. 15, pp. 1-8, 2022.
https://doi.org/10.1051/smdo/2022005
[3] P. Bichkar, O. Dandgaval, P. Dalvi, R. Godase, and T.
Dey, "Study of Shell and Tube Heat Exchanger with the
Effect of Types of Baffles," Procedia Manufacturing,
vol. 20, pp. 195-200, 2018.
https://doi.org/10.1016/j.promfg.2018.02.028
[4] R. Ragadhita and A. B. D. Nandiyanto, "How to
Calculate and Design Shell and Tube-type Heat
Exchanger with a Single Heat Transfer," ASEAN
Journal for Science and Engineering in Materials, vol.
3, no. 1, pp. 21-42, 2024.
https://ejournal.bumipublikasinusantara.id/index.php/a
jsem/article/view/400
[5] L.-Y. Chen, V. S. K. Adi, and R. Laxmidewi, "Shell
and tube heat exchanger flexible design strategy for
process operability," Case Studies in Thermal
Engineering, vol. 37, p. 102163, 2022.
https://doi.org/10.1016/j.csite.2022.102163
[6] D. Bogale, "Design and Development of Shell and
Tube Heat Exchanger for Harar Brewery Company
Pasteurizer Application (Mechanical and Thermal
Design)," American Journal of Engineering Research,
vol. 03, no. 10, pp. 99-109, 2014.
https://www.ajer.org/papers/v3(10)/N0310990109.pdf
[7] H. N. Purnamasari, T. Kurniawan, and A. B. D.
Nandiyanto, "Design of shell and tube type heat
exchanger for nanofibril cellulose production process,"
International Journal of Research and Applied
Technology, vol. 1, no. 2, pp. 318-329, 2021.
https://ojs.unikom.ac.id/index.php/injuratech/article/vi
ew/6410
[8] S. P. Chit, P. K. Ma, and C. C. Khaing, "Thermal
Design of Shell and Tube Heat Exchanger," Iconic
Research and Engineering Journals, vol. 3, no. 1, pp.
313-318, 2019.
https://www.irejournals.com/formatedpaper/1701405.
pdf
[9] S. Kashyap, "Design of a shell and tube heat
exchanger," IJARIIE, vol. 3, no. 4, pp. 536-550, 2017.
https://ijariie.com/FormDetails.aspx?MenuScriptId=1
4928&srsltid=AfmBOorg5c2Z1jtVWTTZnLXZyVP8
vibVhGOjifhzbpeF7esiJJQgjic7
[10] D. Singh and N. D. Pal, "Designing and Performance
Evaluation of a Shell and Tube Heat Exchanger using
Ansys (Computational Fluid Dynamics),"
International Journal of Scientific Engineering and
Applied Science, vol. 2, no. 3, pp. 427-446, 2016.
https://ijseas.com/volume2/v2i3/ijseas20160348.pdf
[11] S. H. Gawande, S. D. Wankhede, R. N. Yerrawar, V. J.
Sonawane, and U. B. Ubarhande, "Design and
Development of Shell & Tube Heat Exchanger for
Beverage," Modern Mechanical Engineering, vol. 2,
pp. 121-125, 2012.
http://dx.doi.org/10.4236/mme.2012.24015
[12] F. H. Napitupulu, T. B. Sitorus, H. V. Sihombing, A.
H. Siburian, and H. Siagian, "Design and fabrication of
shell and tube heat exchanger with one pass shell and
two pass tube as a water heater with hot sulfur water,"
Journal of Physics: Conference Series, vol. 2421, p.
012034, 2023. https://doi.org/10.1088/1742-
6596/2421/1/012034
[13] J.-F. Zhang, Y.-L. He, and W.-Q. Tao, "A Design and
Rating Method for Shell-and-Tube Heat Exchangers
With Helical Baffles," Journal of Heat Transfer, vol.
132, pp. 1-8, 2010. https://doi.org/10.1115/1.4000457
[14] R. Mukherjee, "Effectively Design Shell-and-Tube
Heat Exchangers," Chemical Engineering Progress,
pp. 1-17, 1998. https://www.torr-
engenharia.com.br/wp-
content/uploads/2011/05/exchanger.pdf
[15] S. Kakaç, H. Liu, and A. Pramuanjaroenkij, Heat
Exchangers - Selection, Rating and Thermal Design,
3rd ed. Boca Raton, USA: CRC Press, 2012.
[16] E. Cao, Heat transfer in process engineering. New
York, USA: The McGraw-Hill Companies, Inc., 2010.
https://dokumen.pub/heat-transfer-in-process-
INQUIDE
Chemical Engineering and Development
Journal of Science and Engineering
Vol. 08 / Nº 01
e – ISSN: 3028-8533
ISSN – L: 3028-8533
Chemical Engineering and 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. 50
engineering-1nbsped-0071624082-
9780071624084.html
[17] R. Sinnott and G. Towler, Chemical Engineering
Design, 6th ed. Oxford, UK: Butterworth-Heinemann,
2020.
https://app.knovel.com/kn/resources/kpCEDE0001/toc
[18] R. Mukherjee, Practical Thermal Design of Shell-and-
Tube Heat Exchangers. New York, USA: Begell
House, Inc., 2004.
[19] Chemical Engineering. (2024) Economic Indicators.
Chemical Engineering Magazine. 52.
[20] D. W. Green and M. Z. Southard, Perry's Chemical
Engineers' Handbook, 9th ed. New York, U.S.A.:
McGraw-Hill Education, 2019.
