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


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.

http://iaeme.com/Home/issue/IJMET?Volume=9&Issue=13

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

Nabil Jamil Yasin and Kadhum Audaa Jehhef


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.


Helical Duct


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)



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:


Helical Duct


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.



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


Helical Duct


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)



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]


Helical Duct


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



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


Helical Duct


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



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


Helical Duct


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



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


Helical Duct


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



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%


Helical Duct


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 %



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%


Helical Duct


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



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


Helical Duct


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



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


Helical Duct


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 %



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 %


Helical Duct


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.



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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numerical investigation of laminar heat ......dean number of 590 and particle concentration of 3.0%...

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