numerical investigation of laminar heat ......dean number of 590 and particle concentration of 3.0%...
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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 9, Issue 13, December 2018, pp. 1216–1243, Article ID: IJMET_09_13_125
Available online at http://iaeme.com/Home/issue/IJMET?Volume=9&Issue=13
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication Scopus Indexed
NUMERICAL INVESTIGATION OF LAMINAR
HEAT TRANSFER AND PRESSURE DROP IN
NANOFLUID FLOW IN COILED HELICAL
DUCT
Nabil Jamil Yasin
Engineering Technical College-Baghdad, Middle Technical University,
Baghdad, Iraq
Kadhum Audaa Jehhef
Department of Power Mechanics, Institute of Technology,
Middle Technical University, Baghdad, Iraq,
ABSTRACT
Heat transfer enhancement in horizontal annuli using variable nanoparticles
concentrations of Al2O3-water nanofluid is investigated. A numerical simulation on
pressure drop and heat transfer of vertical rectangular helical coiled duct by utilizing
nanofluid as the test fluid is presented. The nanofluid suspensions is water-Al2O3 with
volume of fraction of 0.5, 1, 2 and 3 % vol. was examined in this study. Steady state
laminar flow of a single phase nanofluid in helical duct was solved by the
computational fluid dynamics (CFD) approach presented by finite volume method. In
this study, the nanofluid thermo-physical properties are formulated as functions of
nanoparticle volumetric fraction. The heat transfer and flow behavior performance of
these nanofluid suspensions were studied as a function of various parameter such as
rectangular tubes aspect ratio, radius of coil, number of turns, Reynolds number and
Dean number. The results indicate that the heat transfer performance improves
significantly when using volume fraction up to 0.5 % vol. Also, the pressure drop
increases with increasing the duct aspect ratio and coil radius ratio but it decreases
with increasing pitch ratio of the coiled duct. Moreover, there is a significant
enhancement in the Nusselt number when increasing the duct aspect ratio and coil
radius ratio as well as with increasing the Reynolds and Dean number for water and
nanofluid. Finally, the improvement in Nusselt number was obtained by (68 %) at
Dean number of 590 and particle concentration of 3.0% vol., but, the minimum
enhancement in the Nusselt number was obtained by (31 %) at Dean number of 65
and particle concentration of 0.5 % vol.
Key words: Nanofluids, Coiled Duct, Dean Number, Helical Tubes.
Numerical Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in Coiled
Helical Duct
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Cite this Article: Nabil Jamil Yasin and Kadhum Audaa Jehhef, Numerical
Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in
Coiled Helical Duct, International Journal of Mechanical Engineering and
Technology 9(13), 2018, pp. 1216–1243.
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1. INTRODUCTION
The helical coiled tube have several application in engineering system such as nuclear reactor,
power generation plant, heat recovery system, food industry and refrigeration. Due to the high
heat transfer coefficient and compact structure, the heat exchangers of helical coil type are
widely used [1]. In order to prevent the overheating of equipments such as transportation and
other electronic devices, a heat transfer fluid or a coolant is used. However, water or ethylene
glycol of conventional heat transfer fluid basically has low thermal properties. Thus, many
researches used high thermal conductivity small particles in the conventional heat transfer
fluid, in order to obtain high thermal properties nanofluids to enhance the thermal properties
of the heat exchange systems. It has been widely reported in literature that heat transfer rates
in helical coils are higher as compared to a straight tube. [2], used laminar flow of Al2O3 and
CuO-water was flowed in coiled square tubes, e.g., in-plane spiral, conical spiral, and helical
spiral. The results indicated that using volume fraction nanoparticles up to 1% will enhance
the overall performance of heat transfer. Moreover, CuO nanofluid performed fewer
enhancements in heat transfer performance than Al2O3 nanofluid that flowed in coiled tubes.
Also, the in-plane spiral tubes give better performance than other coiled tubes for nanofluids.
The heat transfer enhancement is higher at high Reynolds number due to increase the heat
transfer coefficient. The maximum pressure drop was obtained with higher volume
concentration [3]. [4] studied the nanofluid heat transfer in helically coiled tubes at constant
heat flux. The higher heat transfer enhancement was given by helical tube with large
curvature ratio. The maximum enhancement in the heat transfer can be obtained in shell and
helical tube heat exchanger when nanofluid used as reported by [5]. However, the increase of
nanoparticles volume concentration leads to Nusselt number increase and the reduction of the
entropy generation due to heat transfer effect as reported by [6] who used the entropy
generation analyses to study heat transfer of nanofluid flow in heat exchanger of helical coiled
tube. The results of 2% vol. CuO-water nanofluid, it showed that the rate of heat transfer was
14 % greater than the pure water, but this improvement will decrease because the higher
viscosity due to the higher particle concentration. Also, [7] investigated the thermal and
hydraulic performance of aqueous Multi-wall carbon nanotubes (MWCNT) in double helical
coil heat exchanger. The enhancement of the heat transfer was come from the thermal
conductivity by MWCNT and due to the centrifugal force in the helical tube caused by
secondary flow intensity. [8] investigated the thermal performance of the hybrid nanofluid
used in coiled heat exchanger. Their results indicated that the increase in Nusselt number is
accompanied by increasing concentration of nanoparticle. Also, the pressure drop increased as
the concentration of particle and Reynolds number increased. Moreover, [9] studied the flow
characteristics and heat transfer in helical duct plate heat exchanger using in a series
arrangement in counter flow of water as the test fluid. Their results showed that the aspect
(width-to-height) ratio and pitch ratio variation has effect on heat transfer rate enhancement
and pressure drop reduction. Also, [10] indicated that the Nusselt number increased with
increase the Dean number, due to formation of stronger secondary flow, thinning boundary
layer and increasing fluid thermal conductivity. However, the pressure drop was increased
with increasing the Dean number as well as particle concentration. [11] studied the
enhancement of heat transfer by using CuO-water mixture that flows in the heat exchanger of
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type helical coil at laminar flow regime. Their results showed that the enhancement in the heat
transfer coefficient was increased with increasing the CuO nanoparticles in base fluid. [12]
investigated the enhancement of the heat transfer by using Fe2O3, Al2O3 and CuO non-
Newtonian nanofluids that flows in a shell and helical coil heat exchanger. They used non-
Newtonian nanofluids with the concentration range of 0.2–1.0 wt % in aqueous
carboxymethyl cellulose (CMC) base fluid. They showed that the Nusselt number increased
with increasing volume fraction, Dean number (coil-side water flow rate), shell side fluid
temperature and stirrer speeds. Also, the better heat transfer nanofluid was CuO/CMC-based
nanofluid as compared with the other two kinds of fluid.
The heat transfer enhancement by PANI (polyaniline) water based nanofluid in heat
exchanger with vertical helically coiled tube was investigated experimentally by [13]. They
found that the heat transfer coefficient increased with an increase in the volume fraction in
nanoparticles and Reynolds number.
As a result, this work introduced various configurations of the special type of helical
coiled duct in order to enhance the heat transfer rate by using Al2O3-water nanofluid with
various volume fractions. In this study, three dimensional computational domain was solved
by simulation model of heat transfer and nanfluid flow in the in a vertical rectangular helical
duct with different duct cross section aspect ratio, different helical pitch, different coil radios
and various inlet Reynolds number and Dean number.
2. PROBLEM FORMULATION
2.1. Mathematical Modeling
The Computational Fluid Dynamics (CFD) applied using ANSYS-Fluent V.16.2 software
based on finite volume method to study the flow and heat transfer characteristics in vertical
rectangular helical duct. In the finite volume method, the flow domain discretized into a finite
set of control volumes called mesh or cells as a computational domain, and then the governing
convection equations, momentum and energy applied on each cell.
2.2. Physical Model
The computational domain and physical problem of the vertical coiled helical duct is shown
in Figure. 1. The computational domain consists of the inlet section with various inlets
Reynolds number and Dean number and at constant inlet temperature.
Figure 1 Physical model problem geometrey and dimenssions of the present study.
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The outlet fluid section was considered with fixed atmospheric pressure boundary condition
of zero pressure outlet. Also, the constant uniform heat flux q'' in W/m2 is applied on the wall
of the helical duct. In the present study, the square and rectangular cross sections of the
helical coiled duct with different coiled duct cross section aspect ratio, different helical pitch,
different coil radios, all these design and configuration parameters was listed in Table.1.
Table 1 Different design parameters employed in this study.
Parameter Symbol Units Values
Width b mm 10
Length a mm 10, 20, 30 and 40
Duct Aspect Ratio (a/b) - 0.25, 0.3, 0.5 and 1
Pitch p mm 40, 32, 26 and 21
Pitch Ratio (p/b) - 0.25, 0.31, 0.38 and 0.47
Coil Radius R mm 10, 20, 30 and 40
Radios ratio (R/b) - 1, 2, 3 and 4
Number of Turns n - 10, 12, 14 and 16
Reynolds Number Re - 160-1500
Dean Number De - 65-650
Volume Fraction ф % 0.1-3.0
2.3. Assumption
When the nanofluid flows through the helical coiled duct test section, it extracted the heat
from the heat sources of the applied heat flux on the duct wall. Thus, the following
assumptions are applied in this work:
• A three-dimensional computational domain;
• The thermal conductivity walls does not change with temperature;
• Laminar, single phase, steady-state and fully-developed fluid flow;
• Incompressible and Newtonian nanofluid;
• Thermal equilibrium state for fluid phase and the nanoparticles;
• The slip velocity between the solid and the fluid phases is ignored because the nanoparticles
are so small in sizes, so.
2.4. Governing Equations
In this study, the heat transfer and fluid flow are described by the 3D steady-state governing
equations such as continuity, momentum, and energy equations with constant thermo-physical
properties [14].
The equation of continuity is:
∂
∂xi
ρui = 0 (1)
The equation of momentum is:
∂
∂xj
ρuiuj =∂P
∂xi
+∂
∂xj
[μ∂ui
∂xj
+∂ui
∂xi
−2
3δij +
∂ui
∂xj
] (2)
The equation of energy given by:
∂
∂xi
ρuiT =∂
∂xj
Γ∂T
∂xj
(3)
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Where the thermal diffusivity Γ is molecular given by:
Γ =μ
Pr (4)
2.5. The Key Parameters of Flow and Heat Transfer
The inlet nanofluids flows with uniform constant average velocity of (Uav), thus the inlet
Reynolds number can be defined as:
Re =ρUavD
μ (5)
In coil tubes, to determine the flow is laminar or turbulrnt, the critical Reynolds number
may be determined using the correlation by using [15]
Recr = 2300 [1 + 8.6Dh
R
0.45
] (6)
And Prandtl number given by:
Pr =μCp
k (7)
Similar to Reynolds number for flow in pipes, Dean number is used to characterize the
flow in a helical pipe. The Dean number (De) is defined as:
De = ReDh
2R
0.5
(8)
Where Dh is the hydraulic diameter and given by.
Dh =4P
Ac
The numerical heat transfer coefficients of the nanofluid and water and Dean number are
computed from the following equations.
Heat flux in the test section is determined as follows:
q′′ =mwCpwTin−Tout
As
(9)
Also, the heat transfer coefficient of the base fluid and nanofluid can be calculated as
follows:
h =q′′
Tw−Tf
(10)
Also, the Nusselt number can be defined as [16]:
Nu =hDh
k (11)
2.6. Pressure Drop and Friction Factor
The Poiseuille equation is used for laminar flow regime (Re < 2300), is given by:
f =64
Re (12)
For coiled tubes, the friction factor involves the pressure drop across the working length
of coil and the friction factor given by:
f = [∆P
0.5ρUav2] δ4/nπ (13)
Where the pressure drop was computed from the numerical results as:
∆P = Pin − Pout
Thus, it can be determined the fluid pumping power (Pp) as:
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Pp = ∆PV (14)
2.7. Boundary Conditions
Based on the previous assumptions, the assigned boundary conditions as plotted in Figure.2
are the following:
(a) At the inlet boundary:
ux = uin , uy = 0 , T = Tin , k = kin , ε = εin
(b) At the heated wall boundary of the coiled helical duct:
ux = uy = 0 , −k∂T
∂y= q′′
(e) At the outlet boundary:
∂ux
∂x=
∂uy
∂x= 0,
∂T
∂x= 0,
∂k
∂x= 0,
∂ε
∂x= 0
Figure 2 Boundary conditions of the computational domain used in the present analysis.
2.8. Thermophysical Properties of Nanofluids
Introducing the Nanofluid volume fraction (ф), the thermophysical properties of the
Nanofluid, namely the density and heat capacity, have been calculated from Nanoparticle and
the pure fluid properties at the ambient temperature as follows. The nanofluids thermo-
physical properties used in the present study are formulated for mixture of the pure water and
Al2O3 nanoparticles only is used, these properties are listed in Table. 2.
Table 2 The thermophysical properties of water and nanoparticle at T=298 K.
Thermo-physical properties Water Al2O3
Density, ρ (kg/m3) 998.2 3970
Specific heat Cp (J/Kg K) 4182 765
Thermal conductivity, k (W/m K) 0.6 40
Dynamic viscosity, µ (Ns/m3) 0.001003 0
In this work, to model the nanofluids flow in a vertical helical duct, the single-phase
model is considered, thus the thermal–physical properties equations are used as following.
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Density:
Equation used to compute the effective density for a classical two-phase mixture given by
[17]:
ρnf = ∅ρp + 1 − ∅ ρf (15)
Specific heat:
Calculation of the effective specific heat of nanofluid is straight forward. It can be based on
the physical principle of the mixture. The specific heat is calculated for a classical two-phase
mixture as follow [18]:
Cpnf
= ∅ ρpCp
p+ 1− ∅ ρfCp
f
ρnf
(16)
Thermal expansion:
Equation of the effective thermal expansion at the reference temperature (Tin) for a classical
two-phase mixture given by [19]:
βnf = ∅ ρpβp+ 1− ∅ ρfβf
ρnf
(17)
Dynamic viscosity:
The effective viscosity is calculated with the Einstein equation [20] which is applicable to
spherical particles in volume fractions of less than 5.0 vol.% and is defined as follows [21]:
μnf = μf
1−∅2.5 (18)
Thermal conductivity:
For particle–fluid mixtures, numerous theoretical studies have been conducted dating back to
the classical work of [22]. For the two component entity of spherical-particle suspension, the
determined by Maxwell-Garnett’s (MG model) given by:
knf = [kp+2kf−2∅kf−kp
kp+2kf+∅kf−kp
] kf (19)
Maxwell’s formula shows that the effective thermal conductivity of nanofluids relies on
the thermal conductivity of the spherical particle, the base fluid and the volume fraction of the
solid particles.
2.9. Numerical Solution
The Finite Volume Method (FVM) is used to solve and discretize the physical governing
equations along the computational domain of the helical coiled duct with specific boundary
conditions. To couple the pressure-velocity system, SIMPLE algorithm was utilized. The
second order upwind scheme is selected for the convective terms in order to achieve a more
precise numerical solution. The appropriate convergence criteria are obtained. The
convergence criteria for the continuity, momentum, and energy equations are 10-6, 10-6, and
10-8, respectively. It is assumed that the inlet fluid flow is laminar. The governing equations
are iteratively solved until the set residuals are obtained.
2.10. Mesh Generation
To perform the simulation of the present compositional channel of the helical rectangular duct
domain on a computer as presented in Figure.3, the PDEs need to be discretized, resulting in a
finite number of points in space. In the present study the ANSYS-Fluent-v.16.2 meshing
software starts with advanced SOLIDWORKS 2016 x64 Edition reading, after drawing all the
geometrical details, and generates the mesh of annular channel in the Design Modular. The
meshing procedure start with face mesh and continue to the whole volume using volume mesh
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to have the whole 3D model of annular channel of the double pipe heat exchanger for further
simulation.
Figure 3 Meshed computational domain
2.11. Grid Independent Test
Before conducting the simulation, the computational domain presented in above is tested for
grid independence test for better result accuracy as well as time effectiveness. In the present
paper, four different mesh size models were modeled using Design Modular and only one
suitable mesh will be selected for simulation model. The model with very fines mesh size will
be taken as reference for the other models. To make sure that the results are due to the
boundary conditions and physics used, not the mesh resolution, mesh independence should be
studied in CFD. The standard method to test for grid independence is to increase the
resolution and repeat the simulation. If the results do not change appreciably, the original grid
is probably adequate. Computations have carried out for four selected node sizes (i.e., 73801,
124608, 240058 and 589277). Table 3 presented grid independence summary of the test
results. The results showed that the nodes given ad 240058 and 589277 produce almost
identical results with a percentage error of 0.02%. Thus, a computational domain with nodes
of 240058 was chosen to increase the computational accuracy and to reduce the computations
time.
Table 3 Grid independent test
Mesh Type Number of Nodes Average Nusselt number of
heated wall
Difference with previous
coarse mesh (%)
Course 73801 6.91 -
Medium 124608 7.33 5.82
Fine 240058 7.51 2.39
Very Fine 589277 7.54 0.39
2.12. Model results validation
To ensure the reliability of the numerical simulation code used in this study, in the laminar
range flow, the numerical results of friction factor were compared with the correlation
proposed by [23] for the water flows in a helical coiled duct, as follows:
f = 2.552Re−0.15 Dh
2Rh
0.51
(20)
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The present results of the numerical simulation are gave a good agreement with the
correlation of [23], within maximum deviation 5.6% as shown in Figure. 4. Therefore, the
numerical methods adopted in this study for pressure drop predictions were judged to be
reliable. Also, the heat transfer coefficients for the present numerical data were compared
with the [2] numerical results for laminar flow in coil ducts as plotted in Figure.5.
Figure.4 Comparison of friction factor coefficient between present simulation and numerical data
given by [23] for water.
Figure.5 The present results of heat transfer coefficient as compared with the data given by [2] for
water flow.
3. RESULTS AND DISCUSSION
3.1. Pressure Drop and Friction Factor
The effect of duct dimensions on the pressure drop can be showed clearly an in Figure. 6 a
and b, that present the pressure drop of water for duct with aspect ratio of 1 and 0.25
0
0.005
0.01
0.015
0.02
0.025
0 2 4 6
Friction
factor, f
Re
Guo, et al., (2001)
Present Numerical Work
(water)
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6
Heat Transfer
Coefficient,
W/m.K
Re
Sasmito, et al. [5]
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respectively. The pressure drop results indicated that as the aspect ratio of coiled duct
decreases, the pressure drop across the water flow duct decreases for all pitch ratios.
a) Ar=1
b) Ar=0.25
Figure.6 Comparison of pressure drop between two aspect ratio numerical data for water.
3.2. Effect of Geometry (Aspect Ratio)
In this section, the effect of cross-sectional of the duct geometry was considered; due to it has
significant effects on the performance of heat transfer. In this study, it was used four different
square cross section tubes geometries according to the aspect ratio of the duct such as 0.25,
0.3, 0.5 and 1 by increasing the width of the duct and remained at constant height with water
as the base working fluid. To investigate the flow patterns inside the helical ducts, it can be
noted that the convective heat transfer is directly affected by the flow behavior inside the
helical coiled ducts. From the previous literature studies, showed that the in the case of using
helical coiled ducts the presence of centrifugal force due to curvature that can generate
significant radial pressure gradients in flow core region. However, the axial velocity and the
centrifugal force will approach zero. Therefore, a secondary flow should develop along the
outer wall in order to balance the momentum transport. As showed in Figure7a for square
duct (Ar=1), the secondary flow with higher velocities is generated along the outer wall of the
helical duct, and the secondary flows appear as one-pair. But when decreasing the aspect ratio
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of the duct to 0.5, 0.3 and 0.25, the secondary flow with higher velocities began to stretch
along the width of the duct and become more and more until to reach the inner wall of the
duct, due to increasing the flow area of the duct. The high velocities secondary flow with is
affected on the heat transfer rate inside the helical duct. Figure 8 presents the temperature
contours over the cross sections of various duct aspect ratios. In general, the temperatures
separated in two heated zone in the upper and lower region of the duct. But when decreasing
the aspect ratio in coiled duct, it was showed that the deference in temperature becomes
stronger between the two regions, and it appeared cold regions in the upper and lower
temperatures. A mixed region in the middle of the duct was become as separator between the
two cold regions. The temperature of the upper region increased with decreasing the duct
aspect ratio. This phenomenon indicates that the coiled ducts have higher rate of heat transfer
with low aspect ratio when compared to that of high aspect ratio or square ducts that caused
by the secondary flows. Also, the results of this study concluded that there is a higher
intensity of secondary flow in the case of using rectangular coiled ducts, and this lead to
increase the rate of the heat transfer.
a) Ar=1
b) Ar=0.5
c) Ar=0.3
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d) Ar=0.25
Figure.7 Velocity profiles of water flow in rectangular helical spiral vertical duct at Lc = 500 mm,
Rh=40 mm and n=10.
a) Ar=1
b) Ar=0.5
c) Ar=0.3
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d) Ar=0.25
Figure. 8 Temperatures profiles of water flow in rectangular helical spiral vertical duct at Lc = 500
mm, Rh=40 mm and n=10.
3.3. Effect of Radius of coil
As indicated before, the duct with rectangular cross sectional area have significant heat
transfer area as compared with square duct, thus in this study it is benefits to discuss the
parameters that can effects on the velocity field and heat transfer rate in the rectangular coiled
ducts, one of these parameters is radios coil as presented Figures 9 and 10 respectively. The
Figure showed that the core of the maximum velocities was transferred from the lower corner
to upper corner along the inner wall as decreasing the radios coil ratio. The effect of radios
coil ratio on the temperatures distribution was presented in Figure10. The hot plume was
increased in the middle of the duct began from the inner duct, and the temperatures of the
upper zone of the duct increased with increasing the ratio of the radios coil for the case of
water as working fluid. Also, the cold layers transferred from upper to lower region when
increasing this ratio.
a) R/b=1
b) R/b=2
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c) R/b=3
d) R/b=4
Figure. 9: Velocity profiles of water flow in rectangular helical spiral vertical duct at Lc = 500 mm,
Ar=0.25 mm and n=10.
a) R/b=1
b) R/b=2
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c) R/b=3
d) R/b=4
Figure. 10: Temperatures profiles of water flow in rectangular helical spiral vertical duct at Lc = 500
mm, Ar=0.25 mm and n=10.
3.5. Effect of Number of Turns
Increasing the number of coil turns will cause to lead lo create a small maximum velocity near
the outer wall as showed in Figure 11 the results indicated that the maximum velocity of the
secondary flow was reduced when increasing the number of coil turns of the rectangular duct
when used the water and at Lc = 500 mm, Ar=0.25 mm and Rh=40 mm. In addition to the
upper and lower longitude cold zones in the coiled duct, there is a small cold zone was
appeared near the outer wall when increased the number of turns from 14 to 16 as presented
in Figure 12. Also, the increasing the coil turns lead to increasing the temperatures of the
upper zone of the duct.
a) n=10
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b) n=12
c) n=14
d) n=16
Figure. 11: Velocity profiles of water flow in rectangular helical spiral vertical duct at Lc = 500 mm,
Ar=0.25 mm and Rh=40 mm.
a) n=10
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b) n=12
c) n=14
d) n=14
Figure 12: Temperatures profiles of water flow in rectangular helical spiral vertical duct at Lc = 500
mm, Ar=0.25 mm and Rh=40 mm.
3.6. Effect of Volume Faction
The main aim of this study is studying the effect of the nanoparticles amount that adding to
the water that used as a base fluid in this study. These nanoparticles affected on the
determining of the performance of the heat transfer. Intuitively, to increase the thermal
conductivity of the nanofluid it was needed to add larger amount of nanoparticles in the base-
fluid; but this leads to increase the fluids friction factor. In this study, it was used four
different volume fraction 0, 0.5, 1, 2, and 3% of Al2O3.
Figure. 13 showed the velocity contours for the rectangular vertical coiled duct for various
volume fractions. Interestingly, the results showed that the velocity distribution has less
affected when using low volume fractions. But when increasing the volume fractions to 0.5%
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vol., the core maximum velocity increased by 1.1 %; whereas, at 3% Al2O3 concentration,
the core maximum velocity increased by 8.2 % due to the secondary flow appears in two-
pairs as compared to that in one-pair at lower nanoparticle concentrations, because the
stronger effect of the nanofluid suspension.
Conversely, the thermal conductivity of the nanofluid has significant effects on the
thermal behavior of the fluids, as showed in Figure.14, due to the small amount of
nanoparticle (0.5%) were added to the water will changes the distributions of the temperature
inside the helical coiled duct. The hot zone in the temperature of the upper of the rectangular
duct was increased from 305 to 307 K when increased the volume fraction from 0% to 0.5 %.
But when using higher amount of nanoparticle concentration such as (2 and 3% vol.), it can
be showed that the temperatures also slightly change, but they also mainly affected by the
nanofluid hydrodynamics and when create the (secondary flows) inside the helical coiled
duct.
a) Water
b) Al2O3 Nanofluid 0.5%
c) Al2O3 Nanofluid 1.0 %
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d) Al2O3 Nanofluid 2.0 %
e) Al2O3 Nanofluid 3.0 %
Figure.13: Velocity profiles of Al2O3 Nanofluid with various volume fraction flows in rectangular
helical spiral vertical duct at Lc = 500 mm, Ar=0.25 mm, Rh=40 mm and n=10.
a) Water
b) Al2O3 Nanofluid 0.5%
Numerical Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in Coiled
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c) Al2O3 Nanofluid 1.0 %
d) Al2O3 Nanofluid 2.0 %
e) Al2O3 Nanofluid 3.0 %
Figure.14: Temperature distribution of Al2O3 Nanofluid with various volume fraction flows in
rectangular helical spiral vertical duct at Lc = 500 mm, Ar=0.25 mm, Rh=40 mm and n=10.
3.7. Pressure drop and Nusselt number
The effect of three parameters of coiled duct includes aspect ratio, coil radius ratio and pitch
coil radius on the pressure drop was plotted in Figure 15. The results showed that the pressure
drop trend is the same for both aspect and coil radius ratios, where the pressures drop
increased with them. But pressure drop will decreasing with Pitch coil radius. Also, in
general the pressure drop increased with increasing Reynolds number. For water flow in
helical duct, the pressure drop increased with increasing the Reynolds number. As plotted in
Figure 15a, the minimum pressure drop was obtained is 561 N·m-2 at Re = 160 with aspect
ratio of0.25. But, the maximum one was obtained is 665 N·m-2 at Re = 1500 with aspect ratio
of 1. So based on these results, it can be noted that as the aspect ratio increases the pressure
drop increases.
Figure.16 presented the effect of aspect ratio, coil radius ratio and pitch coil radius on the
Nusselt number. The result showed that the using ducts with high aspect ratio will become
good choose in order to increasing the heat transfer rate and then increase the Nusselt number.
The Nusselt number by 43% by using duct with aspect ratio of a/b=1 instead of duct of aspect
ratio of a/b=0.25. And it increased by 21% by using duct with aspect ratio of R/b=4 instead of
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duct of radius ratio of R/b=1, but, it decreased by -28% by using duct with Pitch ratio of
p/b=0.25 instead of duct of aspect ratio of p/b=0.47at Re=1500.
The Dean number (De) is varied from 65 to 590 for water, where water is considered as
reference fluid in this study. Variations of pressure drop versus Dean number for various duct
aspect ratios are shown in Figure. 17. It is seen that the increase in Dean number increases the
pressure drop, and it can be noted that when the Dean number is increased, the secondary
flow is intensified.
And the effect of Dean number on heat transfer rate and on the Nusselt number for water
is predicted in Figure. 18. It can be showed that Nusselt number significantly increases with
increase the Dean number with similar trend. In laminar regime due to the curvature of the
tubes centrifugal force is generated. This centrifugal force developed secondary flow. Due to
effect of secondary flow there is higher heat transfer coefficient and high Nusselt number. The
heat transfer enhancement is more in vertical position due to rapid developments of secondary
flow.
The pressure drop was observed to be increase with increase particle concentration as well
as Dean number as shown in Figure 19 due to the increased density and viscosity at higher
particle nanoparticles concentration. Also, the results indicated that the Nusselt number to be
increase with increasing the particle concentrations as well as Dean number as shown in
Figure 20. The results concluded that the nanoparticles concentration will lead to increase the
maximum Nusselt number enhancement in by (68 %) was obtained at Dean number of 590
and particle concentration of 3.0%but, the minimum enhancement in Nusselt number by (31
%) was obtained at Dean number of 65 and particle concentration of 0.5%. The Nusselt
number increasing with increasing the Dean number due to as the secondary flow formation
increased and this lead to increase the boundary layer thinning. The decreasing thermal
boundary thickness and increasing nanofluid conductivity are the main reason for
enchantment the coefficients of the nanofluids heat transfer in coiled duct when a nanofluid is
passing through the coiled tube.
a) Aspect ratio
500
520
540
560
580
600
620
640
660
680
700
0.2 0.4 0.6 0.8 1 1.2
Pressure
Drop, ΔP, pa
Aspect Ratio, (a/b)
Re=160
Re=500
Re=1000
Re=1500
Numerical Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in Coiled
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b) Radius ratio
c) Pitch ratio
Figure. 15 Pressure drop of the water pitch coil radius ratio with various Reynolds numbers.
a) Aspect ratio
500
550
600
650
700
0.2 1.2 2.2 3.2 4.2 5.2
Pressure
Drop, ΔP,
pa
Coil Radius Ratio, (R/b)
Re=160
Re=500
Re=1000
Re=1500
500
550
600
650
700
750
800
850
0.2 0.3 0.4 0.5 0.6
Pressure
Drop, ΔP,
pa
Pitch Ratio, (P/b)
Re=160
Re=500
Re=1000
Re=1500
0
5
10
15
20
25
0.2 0.4 0.6 0.8 1 1.2
Nusselt
Number,
Nu
Aspect Ratio, (a/b)
Re=160
Re=500
Re=1000
Re=1500
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b) Coil radius ratio
c) Pitch coil radius
Figure. 16: Nusselt number of the water against coil radius ratio with various Reynolds numbers.
Figure. 17: Pressure drop of the water against Dean number ratio with various aspect ratio.
0
2
4
6
8
10
12
14
16
0.2 1.2 2.2 3.2 4.2 5.2
Nusselt
Number,
Nu
Coil Radius Ratio, (R/b)
Re=160
Re=500
Re=1000
Re=1500
0
5
10
15
20
0.2 0.3 0.4 0.5 0.6
Nusselt
Number,
Nu
Pitch Ratio, (P/b)
Re=160
Re=500
Re=1000
Re=1500
500
520
540
560
580
600
620
640
660
680
700
0 100 200 300 400 500 600 700 800
Pressure
Drop, ΔP,
pa
Dean Number, De
Ar=1
Ar=0.5
Ar=0.3
Ar=0.25
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Figure. 18: Nusselt number of the water against Dean number ratio with various aspect ratio.
Figure. 19: Pressure drop of the water against Dean number ratio with various nanoparticle volume fractions.
Figure. 20: Nusselt number of the water against Dean number ratio with various nanoparticle volume fractions.
0
5
10
15
20
25
30
0 100 200 300 400 500 600 700 800
Nusselt
Number, Nu
Dean Number, De
Ar=1
Ar=0.5
500
520
540
560
580
600
620
640
50 100 150 200 250 300 350 400 450 500 550 600 650 700 750
Pressure
Drop, ΔP, pa
De
ϕ=0 %
ϕ=0.5 %
ϕ=1.0 %
ϕ=2.0 %
ϕ=3.0 %
0
5
10
15
20
25
30
0 100 200 300 400 500 600 700 800
Nusselt
Number, Nu
De
ϕ=0 %
ϕ=0.5 %
ϕ=1.0 %
ϕ=2.0 %
ϕ=3.0 %
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3.8. Performance Evaluation Criterion (PEC)
In order to evaluation the thermal performance of any system of fluid flowing, it can be used
the PEC as defined below [24]:
PEC =mwCpwTin−Tout
Pp
(21)
A Performance Evaluation Criterion (PEC) is adopted in order to compare the thermal and
fluid-dynamic performance of the triangular-corrugated channels with different design
factors. The variation of performance evaluation criteria (PEC) versus Reynolds number is
shown in Figure. 21 for different nanoparticles concentrations. It is seen that the PEC value
increases with the increase of Reynolds number, and then it decreases with further increase of
the Reynolds number. The maximum value of PEC was 3.4 in the case of using volume
fraction of 3% vol. and at Re=1000. It is clearly seen that when the Reynolds number is small,
a better thermo-hydraulic performance can be achieved. Thus, to achieve a relatively good
thermo-hydraulic performance over the tested Reynolds number range, the best parameter
combination should be Re=1000 and φ=3 % vol.
Figure. 21: variation of PEC of the water and nanofluid against Reynolds number ratio with various
nanoparticle volume fractions.
4. CONCLUSIONS
In this study the laminar flow of the Al2O3-water nanofluid with various nanoparticles volume
fraction flows in the vertical helical coiled duct with various aspect ratio for constant heat flux
applied on the walls of the duct has been investigated numerically. The parameters was
studied in this work incluies volume fraction of nanoparticles, Reynolds number, Dean
number, aspect ratio, and radius ratio. The results showed that the pressure drop increases
with increasing the aspect and coil radius ratios but it decreases with increasing pitch ratio.
Also, there is a significant enhancement in the Nusselt number when increasing the duct
aspect ratio and coil radius ratio as well as with increasing the Reynolds and Dean number for
water and nanofluid. Finally, the results concluded that the Nusselt number get a maximum
enhancement by (68 %) was obtained at Dean number of 590 and particle concentration of 3.0
%but, the minimum enhancement in Nusselt number by (31 %) was obtained at Dean number
of 65 and particle concentration of 0.5 %.
0
0.5
1
1.5
2
2.5
3
3.5
4
140 340 540 740 940 1140 1340 1540
Performance
Evaluation
Criterion
(PEC)
Re
ϕ=0 % (water)
ϕ=0.5 %
ϕ=1.0 %
ϕ=2.0 %
ϕ=3.0 %
Numerical Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in Coiled
Helical Duct
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ACKNOWLEDGEMENTS
The authors would like to thank to the Institute of Technology, Middle Technical University
for their support to accomplish this work in the computer center of the Institute.
NOMENCLATURES
a coiled duct width, m
b coiled duct higth, m
p coil pitch, m
R coil Radius , m
n number of turns, -
L coil length, m
Re Reynolds number, -
De Dean number, -
Pr Prandtl number,-
xi axial distance in x-direction, m
xj axial distance in y-direction, m
ui velocity in x-direction, m/s
uj velocity in y-direction, m/s
u' fluctuated velocity, m/s
p fluid static pressure, Pa
T temperature, K
Uav average inlet velocity, m/s
Dh hydraulic diameter, m
P cross section perimeter, m
Ac duct cross section area, m2
As heat transfer area, m2
Cp Specific heat, J/kg.K
h heat transfer coefficient, [W/m2.K]
k thermal conductivity, [W/m.K)
m mass flow rate, kg/s
V' volumetric flow rate, m3/s
Tin inlet temperatures, K
Tout outlet temperatures, K
Tw local wall temperature, K
Tf bulk fluid wall temperature, K
ΔP pressure drop, Pa
f friction factor, -
Greek letters
μ dynamic viscosity, Pa.s
δ internal tube radius di/mean coil radius D.
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φ Particle Volume Fraction, %
ρ fluid density, kg/m3
υ kinematic viscosity, m2/s
Subscript
nf nanofluid
in inlet
out outlet
p particle
f base fluid
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