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The effect of the angle of perforation on perforated inserts in a pipe flow
for heat transfer analysis
Simul Acherjee, Ujjwal Kumar Deb, Md. Moniruzzaman Bhuyan
PII:
DOI:
Reference:
S0378-4754(19)30304-0
https://doi.org/10.1016/j.matcom.2019.10.003
MATCOM 4874
To appear in:
Mathematics and Computers in Simulation
Received date : 31 January 2019
Revised date : 8 August 2019
Accepted date : 8 October 2019
Please cite this article as: S. Acherjee, U.K. Deb and M.M. Bhuyan, The effect of the angle of
perforation on perforated inserts in a pipe flow for heat transfer analysis, Mathematics and
Computers in Simulation (2019), doi: https://doi.org/10.1016/j.matcom.2019.10.003.
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Published by Elsevier B.V. All rights reserved.
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The effect of the Angle of perforation on Perforated
Inserts in a Pipe flow for Heat transfer analysis
Simul Acherjee1, Ujjwal Kumar Deb1* Md. Moniruzzaman Bhuyan1
1Department of Mathematics, Chittagong University of Engineering & Technology, Chittagong 4349,
BANGLADESH
acherjeesimul@gamil.com ; ukdebmath@cuet.ac.bd ; mmbhuyan87@southern.edu.bd
Abstract
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A numerical simulation study of heat transfer analysis is considered with perforated insert using
a different angle of perforation in a circular pipe. In our simulation, we have used 0°, 5°, 10°,
15°, 16°, 17°, 20°, 30°, 40°, 50°, 60°, 65°, 68° and 70 ° the angle of perforation respectively in a
perforated axial insert considering the non-isothermal laminar flow. The inserts are used as
perpendicular with the fluid flow inside a pipe. A uniform heat-flux around the circular tube is
assumed for our simulations. The temperature and pressure distribution are measured for a
different angle of perforations. The relation between heat transfer rate and wall temperature is
observed and found that the heat transfer rate increases inversely with the wall temperature. The
effect of Nusselt number and friction factor are the diagnosis for all including angles and
Reynolds numbers. The Thermal Performance Evaluation Criterion (PEC) also analyzed in this
study.
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Keywords: Heat transfer, perforated inserts, perforation angle, non-isothermal flow, CFD,
Simulation.
1. Introduction
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A heat transfer device exchange heat between fluid to fluid or fluids and solid to fluid with a
variety of temperatures. The properties of fluids, types of inserts, kind of materials, fluid flow
behavior, etc. influence the heat transfer enhancement. So the heat exchanger with high
efficiency is an essential part of the automobiles, the refrigeration and air condition, process
industries, petrochemical industries, chemical reactor power plants, etc. In this regard,
researchers need to develop the system with the satisfactory size and cost of the insert by using
several types of techniques and methods. In 2018, J. P. Meyer and S. M. Abolarin investigated
heat transfer and pressure drop with twisted tape inserts and a square-edge inlet for the
transitional flow in a circular tube and noticed that Colburn j-factor varies with twisted ratios.
They also added that the transition overdue for the supreme heat flux and friction factor play a
reciprocal role with the heat flux when the Reynolds number and twisted ratio remain constant
[1]. Peng Lie and his co-rechargers studied both the experimental and numerical studies with
multiple conical strips inserts a tube for the laminar flow and denoted that the number of conical
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strips, central angle and the decreasing pitch is proportional to the heat transfer rate and flow
resistance. They also added that the increases of slant angle initially increase and then decrease
the heat transfer rate and flow resistance [2]. L. M. Tam and A. J. Ghajar studied transitional
heat transfer in plain horizontal pipes with different inlets and recommended a flow regime map
for the boundary between mixed and forced convection [3]. The performance of short-length
twisted tape and regular spaced twisted tapes do superior to the full-length twisted tapes in
square and rectangular ducts were initiated by S.V. Patil and P.V. Vijay Babu [4].The
comparison of the louvered fin with round tube heat exchanger and the wave fin with round tube
heat exchanger investigated experimentally by A. K. Okbaz et al. In this study they established
that the louvered fin with round tube heat exchanger shown the significant enhancement for the
thermal and hydraulic performance compare to the wave fin with round tube heat exchanger [5].
Another performance of louvered strip insert, Indri Yaningsih, and Agung Tri Wijayanta
recommended that the decreasing of pitch length increased the Nusselt number, friction factor,
and heat transfer coefficient ratio [6].In a review on passive heat transfer for tube exchangers, S.
Liu and M. Sakr noticed the twisted tape inserts carried out better for laminar flow while ribs,
conical nozzle and conical ring act more effective for turbulent flow [7]. S.Tabatabaeikia et al.
suggested that the backward flow gives better perfection for the louvered strip insert than the
forward one and they also noted that the jagged twisted tape insert provides superior Nusselt the
number and thermal-hydraulic performance compare to other twisted tape inserts, such as classic
twisted tape, butterfly insert, notched twisted tape and perforated twisted tape, in their review of
different types of inserts [8]. Pengxiao Li et al. proposed for the high Reynolds number the slant
angle with 3.3 pitch ratio perform the best among other slant angle and pitch ratio in a numerical
and experimental approach with drainage inserts in a circular tube [9].The efficiency
investigation of Delta Winglet Twisted (DWT) tape inserts give a better efficiency then S-DWT
inserts was prescribed by S. Eimasa-ard et al [10]. For the rectangular cut twisted insert arranged
circular pipe. Bodius Salam et al. scrutinize the effect of Nusselt number and recommended that
the Reynolds number is proportional to heat transfer competence [11].
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In a numerical analysis with the rectangular box inserts in a circular pipe, the heat transfer rate is
proportional with the distance among the inserts was recommend by S. Hossan et al. while M. M.
Bhuyan et al. also noted the same for U-loop circular pipe [12, 13]. For the laminar flow with
full length twisted tape insert-fitted tube Suvanjan et al. run through a CFD exploration of
different geometric parameters to translate the flow behavior [14]. The V-cut twisted tape inserts
with twist ratio (y = 2.93) and cut depth (w = 0.5cm) enhanced 107% heat with less friction
factor than the other V-cut and regular twisted tape inserts were approved by Sami D. Salman et
al. in their numerical study for the laminar flow of V-cut twisted tape insert fitted circular
tube[15]. A CFD study for different types of twisted insert carried by M. M. Bhuyan et al. in
which they prescribed the full length twisted insert behaves better than a short length twisted
inserts [16].
An investigation of Zigzag-Winglet perforated-tape (ZW-PT) insert fitted tube was carried by S.
Suwannapan et al. and noted that the pitch ratio (PR=1.0) gives the better thermal efficiency
factor (TEF) with the blockage ratio (BR=0.15) at the lowest Reynolds number [17].
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J.U.Ahamed et al. inspect experimental study with the perforated twisted insert fitted tube and
their outcome indicates the supreme amount of heat enhanced for Rp = 4.6%, where M. M. K.
Bhuiya et al. recommended the Rp = 4.5% provides superior presentation than plain tube [18, 19,
20]. For the X-shaped longitudinal perforated inserted. Mizanuzzaman et al. noticed that the
porosities of 15.85% give a higher efficiency than the other porosities of 5.7% and 10.15% [21].
M. M. K. Bhuiya et al. examined for perforated strip insert tube and they suggested that the
porosities of 4.4% the enhanced maximum amount of heat [22]. For the axial perforated inserts
fitted U-loop pipe S. Acherjee et al. detected that the porosity of 4.42% enhanced the best
amount of heat [23].
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The literature as mentioned above indicates that the perforated type inserts represent better
performance than the plain type inserts. However, there is no literature found where an
investigation has done related to the effect of angle of perforation. For this reason, we assume
that this type of investigation helps us to understand the better performance of the heat transfer
rate. A non-isothermal laminar flow is chosen for the physics while water as acting fluid in the
simulation. The simulation is conducted to study the influence of the angle of perforation on heat
transfer rate and fluid flow performance. And the results are compared with perforated inserts
tube and plane tube. This is guided to compute the effect of angle on performance and evaluate
the heat transfer augmentation and pressure drop.
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2. Governing Equations
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To describe the heat transfer characteristics for the different angle oriented perforated insert in a
circular pipe a numerical model is being formed. A generalization of energy equation and flow
equation is useful to compute the numerical model. These the following equations are needed to
explain the heat transfer phenomena in our simulation [24]:

u
t
( 2.1)
+  (  u ) = 0
The rate of change of density at a fixed point in the fluid is expressed by equation (2.1).
u
t
(
=   [− pI +   u + (  u )
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
T
) − 23  (   u ) I ] + F
( 2.2 )
Equation of momentum defines by equation (2.2) which interprets the rate of change of
momentum at per unit volume of the fluid. The left hand side of this equation represents the
convective acceleration of the fluid particle.
T
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C p
t
+  C p u   T =   ( k  T ) +Q+Q vh +W p
( 2.3 )
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The heat transfer phenomena of fluid for unsteady condition represents by equation (2.3).
Re =
 uD

( 2.4 )
Equation (2.4) denotes the Reynolds number which expresses the ratio of the inertial force and
the viscosity.

d2
Rp = 4
,
L W
where L is the length, W is the width of the insert and ‘‘d” is the diameter of the pore.
( 2.5 )
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The heat transfer coefficient (h) was evaluated by
h=
q
Q=
where
is the constant heat flux,
A
Q
Tw − Tb
( 2.6 )
,
( 2.7 )
,
is the surface area of the tube, T w is the average wall
temperature and Tb is the bulk temperature of the fluid.
Tb =
Tout + Tin
2
,
where Tin and Tout are the inlet and outlet average temperature. The Nusselt number (
calculated by
Nu =
hD
k
( 2.8 )
) is
( 2.9 )
.
p
( 2.10 )
,
( 2.11)
2
 L  v 

 
 D  2 
Nu
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f =
f
Where D is the inside diameter of the tube and k is the thermal conductivity of water at the initial
temperature. Then the friction factor (f) and thermal performance factor (  ) expressed as
follows:
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=
 f 


 fo 
1
3
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where  is the ratio between the heat transfer ratio and the friction ratio. Where Nu o and f o are
the Nusselt number and friction factor for the 0° angle oriented tube.
3. Boundary Conditions
For the wall u = 0 indicates the no slip condition while u = u o represents the inlet velocity in the
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velocity field for 0.014 ms-1 and 0.021 ms-1 with an initial temperature T = To = 293.15 K . The
outlet with zero normal stress is generated by the following equation.
(
[− pI +   u + (  u )
T
) − 23  (   u ) I ]n =-f n
o
( 3.1)
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The heat flux 32087w/m2 is taken as constant in our simulation.
4. Computational domain and Mesh generation
The computational domain with the dimension of 3435.62mm × 70 mm × 5 mm in a tubular
copper pipe is taken for our simulation. The dimension of rectangular copper inserts both are
1600mm×70mm×2mm fitted perpendicular with the fluid flow inside the tube. Where 20mm is
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the axial distance and 16mm is the transverse distance between two adjacent pores. The domain
and the angle of perforation 0°,5°,10°,15°,16°,17°,20°,30°,40°,50°, 60°,65°, 68°, and 70°
respectively for the porosities of Rp ꞊ 4.5% represents in Fig 4.1.0° is measured from
perpendicular with the insert and then other angles were counted downward from this line.
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Fig. 4.1: (a) The computational domain, (b) inserts with 0°, (c) inserts with 65°, (d) the angle of perforation 0°, 5°,
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10°, 15°, 16°, 17°, 20°, 30°, 40°, 50°, 60°, 65°, 68° and70 ° respectively.
Fig. 4.2: Meshing of the domain.
Fig 4.2 displayed the massing of the domain where the finer mesh is considered to increase
acquiesce of the result. Since our domain is large so we used MSI B85-PC-MATE motherboard
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with 16GB DDR3 ram based computer to compute the results. Around the insert and pore, the
mesh elements were crowded.
5. Results and discussion
This study leads to understanding the heat transfer phenomena for the effect of angle oriented
perforated inserts fitted tube with the simulated results. In our simulation, we oriented different
angle of perforation 0°, 5°, 10°, 15°, 16°, 17°, 20°, 30°, 40°, 50°, 60°, 65°, 68° and 70°
respectively with the porosities of 4.5% for the Reynolds number 1100, 1400 and 1700. We
ignored the thickness of the copper pipe and for the water domain by considering a constant heat
flux neighboring to the surfaces of the domain. The convection of heat over the solid is
neglected. The simulation studies are done by the COMSOL Multiphysics software.
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(a) 0° Perforated inserts tube
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5.1 Temperature Performance Evaluation
(b) 65° perforated inserts tube
Fig. 5.1: Surface temperature of the fluid for 0° and 65° angle oriented perforated inserts tube
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It is known that the perforated inserts fitted tube enhanced more heat than the plane tube [22-23].
A Tube fitted with angle oriented axial perforated inserts plays a better role in case of heat
transfer than the general axial perforated inserts, which is presented by Fig. 5.1. The fluid
particles move rapidly in an axial perforated inserts tube since the perforation of 0° does not
make enough obstacles with the streamline for the fluid particle so there is the streamline unable
to create more curves. On the other hand, the streamline for the fluid particle in angle oriented
axial perforated inserts tube create a curve easily so the temperature is increased.
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5.2 Wall temperature and Heat transfer rate relation
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Fig. 5.2: The comparison of wall temperature and heat transfer rate for the different angle of perforation
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Fig 5.2 describes the contrast of heat transfer rate and wall temperature for the Reynolds number
1100. In this study, we notify that wall temperature varies inversely with the heat transfer rate.
This is because when the fluid particles get enough facility to mix and transfer heat to the core
particles of the tube then the surface temperature decrease with the increase of heat transfer rate
otherwise it acts reversely.
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5.3 Nusselt number Performance Evaluation and Streamline analysis.
Fig. 5.3: Nusselt number variation with Reynolds number for the different angle of perforation
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The relationship between the Nusselt number and the Reynolds number is depicted in Fig. 5.3
for 0° and other angles. We observed that the Nusselt number varies with the Reynolds number
and increased for all angles of perforated inserts with the increasing of the Reynolds number.
The highest Nusselt number is found for the angle of perforation 65°in all Reynolds
numbers. From our simulation, It is observed a sharp drop of Nusselt number around 65-70
degree. The reason behind this the fluid particle might move rapidly at 68 degree and 70 degrees
compared to 65 degrees. So, fluid particles do not get more time to transfer heat to the core
particles of the tube, which increase the surface temperature and decrease the heat transfer rate.
(b)
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(a)
(c)
Fig. 5.4: Streamline phenomena of the fluid for (a) 65°, (b) 68° and (c) 70° angle oriented perforated inserts tube.
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The performance of the streamline phenomena for 65°, 68°, and 70° angle oriented perforated
inserts tube is shown in Fig 5.4. From these results, we observed that such kind of illustration
shows an amount of highly heated fluid particles near to the wall and a huge amount of lower
heated particle at the core for 68° and 70° angle oriented perforated inserts tube.
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5.4 Friction Factor Performance Evaluation
Fig. 5.5 Friction factor variation with Reynolds number for the different angle of perforation
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In Fig 5.5, we observed that the friction factor is decreased with the increasing of the Reynolds
number. The friction factor varies with the variation of angle. The friction factor rises at the
angle of 30° to50° and then it showed a downward trend till to 60°.
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Thermal Performance Criterion (PEC)
Fig. 5.6 Thermal performance variation with Reynolds number for the different angle of perforation
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In Fig. 5.6, the Thermal Performance Evaluation Criterion (PEC) is shown which describes the
performance of the device. For the different angle oriented inserts the highest PEC is found for
the perforation angle 65° with the Reynolds number of 1100 and 1400. However, for the
Reynolds number of 1700, the maximum PEC is observed for the 60° perforation. Moreover, the
highest pick is found at the Reynolds number of 1400 with an angle around 65°. At the angle of
perforation 60° and 65°, perforated inserts tube the PEC is found 1.09 to 1.10 and 1.10 to 1.13
times greater than the 0° angle respectively.
6. Conclusion
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A CFD study of heat transfer analysis with perforated insert using the different angle of
perforation in a circular pipe is investigated. The heat transfer phenomena are observed by
simulation studies with a different angle (0°, 5°, 10°, 15°, 16°, 17°, 18°, 20°, 30°, 40°, 50°, 60°,
65°, 68°, and 70 ° ) oriented perforated inserts for a tubular pipe. A constant heat-flux around the
tube is assumed for our simulations. It is found that at the 65° angle oriented perforated inserts
tube, the Nusselt number and thermal Performance Evaluation Criterion tends to be higher than
all other angles considered in our simulation. For the 65°angle oriented perforated inserts, the
Nusselt number is obtained 1.11 to 1.13 times and thermal Performance Evaluation Criterion is
found 1.10 to 1.13 times greater than the 0° angle. The highest Nusselt number is found for the
angle of perforation 65°in all Reynolds numbers. However, afterwards, the Nusselt number
shows a sharp fall around 65° to 70°. It is also observed that the fluid temperature varies
inversely up to saturated level with the gradual increase of high Reynolds number for all angles
of perforated inserts.
Acknowledgment
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The authors gratefully acknowledge the technical supports to the Centre of Excellence in
Mathematics (CEM), Mahidol University, Bangkok-10400, Thailand and the Simulation Lab,
Department of Mathematics, Chittagong University of Engineering and Technology (CUET),
Chittagong – 4349.
References
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exchangers”, Renewable and Sustainable Energy Reviews”, 2013.
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Enhancement by Using Different Types of Inserts”, Advances in Mechanical Engineering,
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13. M. M. Bhuyan, U. K. Deb, M. Shahriar, S. Acherjee, “Simulation of heat transfer in a tubular
U-loop pipe using the rectangular inserts and without insert”, AIP Conference Proceedings
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transfer enhancement in low Reynolds number of a circular pipe with full length twisted tape
insert”, Proceedings of 12th IRF International Conference, 2014, India.
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Highlights of Review
A numerical simulation study of heat transfer analysis is considered with perforated insert
using different angle of perforation in a circular pipe. In our simulation, we have used 0°, 5°,
10°, 15°, 16°, 17°, 18°, 20°, 30°, 40°, 50°, 60°, 65°, 68° and 70 ° angle of perforation
respectively in a perforated axial insert considering the non-isothermal laminar flow.
•
To describe the heat transfer characteristics for the different angle oriented perforated insert
in a circular pipe a numerical model is being formed. A generalization of energy equation
and flow equation is useful to compute the numerical model.
•
It is found that at the 65° angle oriented perforated inserts tube, the Nusselt number and
thermal Performance Evaluation Criterion tends to be higher than all other angles
considered in our simulation.
•
For the 65°angle oriented perforated inserts the Nusselt number is obtained 1.11 to 1.13
times and thermal Performance Evaluation Criterion is found 1.10 to 1.13 times greater than
the 0° angle.
•
The highest Nusselt number is found for the angle of perforation 65°in all Reynolds
numbers. However, afterwards the Nusselt number shows a sharp fall around 65° to 70°. It
is also observed that the fluid temperature varies inversely up to saturated level with the
gradual increase of high Reynolds number for all angles of perforated inserts.
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•