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Engineering Science and Technology, an International Journal xxx (2015) 1e7

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CFD modeling of heat transfer performance of MgO-water nanofluid under turbulent flow Reza Davarnejad*, Maryam Jamshidzadeh Department of Chemical Engineering, Faculty of Engineering, Arak University, Arak 38156-8-8349, Iran

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info

Article history: Received 6 January 2015 Received in revised form 27 February 2015 Accepted 9 March 2015 Available online xxx Keywords: CFD Nanofluid MgO-water Friction factor Nusselt number

abstract In this paper, Computational fluid dynamics (CFD) modeling of turbulent heat transfer behavior of Magnesium Oxide-water nanofluid in a circular tube was studied. The modeling was two dimensional under keε turbulence model. The base fluid was pure water and the volume fraction of nanoparticles in the base fluid was 0.0625%, 0.125%, 0.25%, 0.5% and 1%. The applied Reynolds number range was 3000 e19000. Three individual models including single phase, Volume of Fluid (VOF) and mixture were used. The results showed that the simulated data were in good agreement with the experimental ones available in the literature. According to the experimental work (literature) and simulation (this research), Nusselt number (Nu) increased with increasing the volume fraction of nanofluid. However friction factor of nanofluid increased but its effect was ignorable compared with the Nu on heat transfer increment. It was concluded that two phase models were more accurate than the others for heat transfer prediction particularly in the higher volume fractions of nanoparticle. The average deviation from experimental data for single phase model was about 11% whereas it was around 2% for two phase models.

Copyright © 2015, Karabuk University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction Nowadays, the range of metal oxide nanoparticles is greatly expanding [1]. There are many industrial processes with water and ethylene glycol. Thermal properties of these fluids control the thermal efficiency and the size of the equipments. Addition of milli or micro size solid particles was one of the very old techniques for heat transfer enhancement. This technique was not attractive because of some inherent problems such as sedimentation. Furthermore, it increased pressure drop, fouling and erosion of the flow channel. Since the nanoparticles increased the thermal con-ductivity of the base fluid, the metallic and non-metallic nano-particles addition to a base fluid was initially considered by Choi [2].

The thermal conductivity of nanofluid depended on particles type, size and shape, and thermal properties of base fluid [3]. In-fluence of particle size and shape on turbulent heat transfer char-acteristics and pressure losses in water based nanofluids (Al2O3, SiO2, MgO) was investigated by Merilainen€ et al. [4]. They

* Corresponding author. Tel.: þ98 9188621773; fax: þ98 86 34173450. E-mail address: [email protected] (R. Davarnejad). Peer review under responsibility of Karabuk University.

concluded that the average convective heat transfer coefficients of nanofluids were typically increased up to 40% compared with the base fluids. They also found that small, spherical and smooth par-ticles (less than 10 nm in size) dramatically enhanced heat transfer and kept the pressure losses moderately. Utomo et al. experimen-tally and theoretically considered thermal conductivity, viscosity and heat transfer coefficient of Titania and Alumina nanofluids [5]. They investigated that the measured heat transfer coefficients for nanofluids in the straight pipes were in a very good agreement with the heat transfer coefficients predicted by the classical correlation developed for simple fluids. The numerical modeling of nanofluids heat transfer was studied in the literature [6e8]. It was found that the two-phase models are more precise than the single-phase model. They showed that heat transfer coefficient clearly increased with particle concentration enhancement. The average relative error between experimental data and CFD results based on the single-phase model was 16% while it was around 8% for the two-phase model for Cu/water nanofluid with 0.2% concentration.

There are a lot of researches on the effects of tube geometry on the heat transfer properties [9e11]. Akhavan-Behabadi et al. showed that the heat transfer properties changed when tube ge-ometry varied from plain tube to helically tube [12]. Yarmand et al. numerically studied nanofluid flow heat transfer characteristics in a rectangular tube [13]. They also used various types of nanofluids

http://dx.doi.org/10.1016/j.jestch.2015.03.011 2215-0986/Copyright © 2015, Karabuk University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/bync-nd/4.0/).

Please cite this article in press as: R. Davarnejad, M. Jamshidzadeh, CFD modeling of heat transfer performance of MgO-water nanofluid under turbulent flow, Engineering Science and Technology, an International Journal (2015), http://dx.doi.org/10.1016/j.jestch.2015.03.011

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R. Davarnejad, M. Jamshidzadeh / Engineering Science and Technology, an International Journal xxx (2015) 1e7

such as Al2O3, ZnO, CuO and SiO2 with different concentrations. They showed that SiO2-water nanofluid had maximum Nu compared with the other nanofluids. Togun et al. numerically investigated the turbulent heat transfer of nanofluid flow over double forward-facing steps [14]. They showed that the step height increment amplifies the heat transfer rate due to the recirculation flow regions enhancement. Recently, some researchers found that carbon-base nano-particles can improve the heat transfer properties of fluids. Sade-ghinezhad et al. considered the effects of graphene nanoplatelets (GNP with carbon-base nanofluid) concentration and heat flux on the heat transfer turbulent flow conditions [15]. They discovered that the GNP nanofluids had the best heat transfer properties. In this research, turbulent forced convective heat transfer of MgO-water nanofluids inside a vertical tube with constant tem-perature boundary condition was investigated. MgO nanoparticles were assumed to be spherical with the mean diameter of 40 nm. Single phase, mixture and VOF models were implemented for the thermal behavior of nanofluids. keε turbulence model which is an usual model in this type of simulation [16] was chosen in the software. The simulation was carried out in the fully developed region of pipe. The results of numerical method were compared with the experimental ones obtained from the literature [17].

According to this table, nanoparticles addition regularly increased the nanofluid physical properties although a regular reduction was not observed in the specific heat for various nano-fluid concentrations. Furthermore, the viscosity slightly changed in various concentrations. It may be due to low concentration of nanoparticles in the base solution (which were less than 1%). Moreover, the viscosity is a temperature function while the tem-perature was fixed at 40 C for all of experiments as boundary condition.

3. CFD theory and equations The CFD approach uses a numerical technique for solving the governing equations for a given flow geometry and boundary conditions. In this paper flow pattern and temperature distribution through a circular pipe were simulated using the FLUENT software (version: 6.3.26). Three types of model involving single-phase, VOF and mixture models (as two-phase model) were fed into the software.

3.1. Single-phase flow equations Steady state simulations were carried out by solving mass, momentum and energy conservation equations, which are expressed as [19]:

2. Physical properties of the nanofuids The density of nanofluid is calculated using the mixing theory as [18]:

- Continuity equation:

rnf ¼ 4rp þ (1 4)rf

(1)

The specific heat capacity of MgO-water nanofluid can be calculated according to the thermal equilibrium model: cp;nf ¼

4r

þr

cp p

(2)

nf

ð1 4Þ rcp

nf

(4)

- Momentum equation:

f

The thermal conductivities were directly extracted from the literature [17]. According to the literature, an experimental corre-lation was proposed for the dynamic viscosity of MgO (with 40 nm) [17]:

m ¼

vr vt þ V$ðrUÞ ¼ 0:

2

1 þ 11:614 þ 1094 mf

(3)

Table 1 compares physical properties of pure MgO and H2O with various concentrations of nanofluid obtained from the experi-mental work.

v vt ðrUÞ þ V$ðrUUÞ ¼ VP þ Vt þ B:

(5)

where, P, t and B are pressure (hydrodynamic pressure force of nanofluid in our case), stress term (viscous forces related to the nanofluid viscosity in our case), and the sum of the body forces (weight of nanofluid in our case), respectively. - Energy equation:

v Table 1 Physical properties of MgO, H2O and various concentrations of nanofluid.

vt ðrhÞ þ V$ rUcpT ¼ V$ðkVTÞ:

(6)

MgO

3.2. Volume of Fluid (VOF) model

r (kg/m3)

Cp (j/kg.K)

k (W/m.K)

3560

955

45

H2O

r (kg/m3)

m (kg/m.s)

Cp (j/kg.K)

k (W/m.K)

998.2

0.001003

4182

0.6

Nanofluid properties MgO volume fraction%

rnf (j/kg.K)

mnf (kg/m.s)

Cpnf (j/kg.K)

knf (W/m.K)

0.000625 0.00125 0.0025 0.005 0.01

999.8011 1001.402 1004.605 1011.009 1023.818

0.001013 0.001013 0.001023 0.001043 0.001083

4174.818 4167.66 4153.411 4125.185 4069.791

0.642 0.654 0.666 0.69 0.714

The VOF model is a surface-tracking technique applied to a fixed Eulerian mesh. It is designed for two or more immiscible fluids where the position of the interface between the fluids is of interest. In the VOF model, a single set of momentum equation is shared by the fluids, and the volume fraction of each fluid in each computa-tional cell is tracked throughout the domain. Application of the VOF model includes in the stratified flows, free-surface flows, filling, sloshing, the motion of large bubble in a liquid, the motion of liquid after a dam break, the prediction of jet breakup (surface tension), and the steady or transient tracking of any liquidegas interface [20]. The tracking of the interfaces between the phases is accom-plished by the solution of a Continuity equation for the volume

Please cite this article in press as: R. Davarnejad, M. Jamshidzadeh, CFD modeling of heat transfer performance of MgO-water nanofluid under turbulent flow, Engineering Science and Technology, an International Journal (2015), http://dx.doi.org/10.1016/j.jestch.2015.03.011

R. Davarnejad, M. Jamshidzadeh / Engineering Science and Technology, an International Journal xxx (2015) 1e7

v

p

fraction of one (or more) of the phases. For the qth phase, the

3

2 k

Ek ¼ hk

equation has the following form: vaq

n$

t þ

Saq

a

(7)

q¼ r

!V

v

q

Momentum equation for VOF model:

ð !Þ þ V ð!!Þ ¼ V vt

v

rn

þV h

$nn

V!

$m

p

n

n

Ek ¼ hk for incompressible phase. 3.4. keε turbulence model

i

þ V!

(18)

rk þ 2

þ

!þ

T

rg

!

The keε turbulence model is used to simulate turbulent flow. Turbulent kinetic energy equation [14]:

F (8)

v vxj

rkuj

v

mt

"

¼ vxj

vk #

m þ sk

vxj

vui

vuj

þ mt vxj

þ vx i

! vui rε vx i

Energy is also shared among the phases as:

v r

vt

$ n r

ð

$keff VT þ Sh

!

EÞ þ V

(19)

(9)

E þ pÞÞ ¼ V

ðð

Rate of turbulent kinetic energy dissipation equation: Sh (source term) is contributions from radiation and any other volumetric heat sources. E for each phase (q) is based on the spe-cific heat of that phase and the shared temperature and can be obtained by the following equation:

"

v rεuj

#

v ¼

j

vx

mt

mþ

j

vx

ε

s

vε

ε

rC2

j

vx

2

(20)

p

K þ yε

ffiffiffiffiffi Pn

arE q¼1

E¼

Where, sk and sε are the turbulent Prandtl numbers for the tur-

q

Pn

q

(10)

q

bulent kinetic energy and its dissipation. Turbulent kinetic energy

(K) and its dissipation rate (ε) are coupled to the governing equa-tions via the 2 turbulent viscosity relation ðmt ¼ rCmk =εÞ$Cm is not a constant value as in the

ar

q¼1 q q

standard keε model. The empirical con-stants are C2 ¼ 1.9, sk ¼ 1:0 and sε ¼ 1:2 [16].

3.3. Mixture model

The mixture model is designed for two or more phases (fluid or particulate). 4. Modeling procedure In the Eulerian model, the phases are treated as interpenetrating continua. The mixture model solves the mixture momentum equation and prescribes relative The first step is to represent a two dimensional geometry of pipe that is velocities to the dispersed phases. Applications of the mixture model include ingenerated by GAMBIT software (version: 2.2.30). It is also divided in several particle-laden flows with low loading, bubbly flows, sedimentation, andcells. Fig. 1 shows the pipe scheme. cyclone separators. The mixture model can also be used without relative Fig. 2 shows the optimum grid of pipe. It is 15 cm in radial di-rection (R) velocities for the dispersed phases [21,22]. and 252 cmin pipe length direction (x). It needs 15 cm length of tube to Continuity equation for the mixture model is [22]:

(11)

v r $ n vt ð mÞ þ Vðrm! mÞ ¼ m They can be obtained by [22]: !m ¼

P

created fully developed turbulent flow [23]. So, the tube was divided to two parts. Part 2 of tube wall temperature was maintained at the constant temperature about 313.15 K. All of parameters were found for part 2 of pipe (fully developed flow region). The range of Reynolds and velocity of inlet flow was extracted from the experiment [17]. So:

(12) Vz

n

¼ ;

0 Vy

¼ ;

0 Vx

¼ rm

k

n

n

!

¼

Vinlet

;

Tinlet ¼ 298:15 K

1akrk k

n

X

(13)

rm ¼ k¼1akrp

The momentum equation for the mixture can be obtained by summing the individual momentum equations for all phases [22]:

v r n $r n n ! V h ! ! m mÞ ¼ Vp þ V vt ð m mÞ þ ð m

$m

n V!m þ V!m

m

r g þ

!þ

m $

þV

n

T

i

F n

a k¼1

r k k

n

n

The pressure outlet was chosen for the tube outlet boundary condition. This pressure was assumed to be in atmosphere pressure in outlet flow. The wall was in stationary state and no slip was applied to shear condition. Wall temperature of developed region (part 2) was fixed at 313.15 K. The pressure-based solver was used for the calculations. Second-order upwind interpolation scheme was applied for the momentum and energy calculations. The SIMPLE algorithm was

! dr;k! dr;k

chos en for the pres s ureevelocity coup ling. The keε tu rbulence

X

(14)

They can be calculated by [22]:

model was used during the calculations. Furthermore, the enhanced wall treatment was chosen for near-wall treatment. Convergence of the numerical solution was assured by monitoring

n

6

X

(15) (16)

mm ¼ k¼1akmk

!

v

v

!

v

¼ k

dr;k

!

v

n

k¼1 ð

X

ar k

E

for each variable.

4.1. Grid independency

m

Energy equation for the mixture is [22]:

vt

the scaled residuals to a constant level below 10

n

V$

k kÞ þ

k¼1 ð

X

For compersible phase [22]:

a v

r E

! k kð k k

þp

ÞÞ ¼

V$

k eff

VT

S

þ E (17)

The grid independence examination was performed for each model at several concentrations. For example, the results of mixture model were reported in Fig. 3 at concentration of 0.0625. According to this figure, the Nu number data were very close to each other. 15 252 meshes were chosen due to the time reduction and experimental data reproduction.

Please cite this article in press as: R. Davarnejad, M. Jamshidzadeh, CFD modeling of heat transfer performance of MgO-water nanofluid under turbulent flow, Engineering Science and Technology, an International Journal (2015), http://dx.doi.org/10.1016/j.jestch.2015.03.011

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Fig. 1. Pipe scheme.

Fig. 2. Mesh layout.

5. Results and discussion The predicted Nusselt number data for MgO nanofluid inside a tube with constant wall temperature were compared with the experimental ones. In this study, five different volume fractions of nanofluid (involving 0.0625%, 0.125%, 0.25%, 0.5% and 1%) were studied. keε turbulence model was chosen in this work. It gave more reasonable data than the other models such as keu. Furthermore, they were in good agreement with the excremental data.

Since the experiment was performed in the fully developed flow condition, the applied tube was divided into two regions. The first 15 cm of tube length was used to reach the fully develop region [20] whereas the calculations were done on the remaining length of the tube. Finally, the relative errors were reduced and reasonable re-sults were obtained. Friction factor and Nu number were investigated under various Reynolds numbers to consider nanoparticles addition effect on the heat transfer properties. According to the experimental work [17], the friction factor and Nu number were numerically studied with the inlet flow Reynolds number increment. Figs. 4e6 show the friction factor of nanofluid according to three models (Fig. 4 based on VOF, Fig. 5 based on mixture and Fig. 6

Fig. 3. Grid independency (for mixture model at volume fraction of 0.0625%).

based on single phase model). According to these figures, the fric-tion factors at various concentrations of nanoparticles were very close to the experimental data in Re > 7000. The average errors for VOF, mixture and single phase model were around 4.43%, 4.43% and 5.45%, respectively. VOF and mixture (two phase models) data had lower deviation compared with the single phase model. Figs. 7e9 show the Nu number data according to VOF, mixture and single phase model, respectively. As shown in these figures, VOF and mixture models data were in very good agree-ment with the experimental ones for all of the volume fractions although the single phase model deviation increased with the volume fractions increment. Furthermore, the heat transfer increased with the nanoparticles concentration enhancement [17]. In fact, the nanoparticle concentrations were less than 1% in this study. It may cause the negligible changes in Nu number for the single phase model. The data were close to each other in the lower Reynolds numbers for various nanoparticles concentra-tions while they were sharply located in the higher Reynolds numbers.

Fig. 10 shows friction factors for the nanofluid volume fraction of 1% (as an example) according to three models. The friction factors were properly matched on the experimental ones for Reynolds numbers higher than 5000. Similar trend was also observed in the

Fig. 4. Friction factors for various volume fractions of nanoparticle based on the VOF model.

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Fig. 5. Friction factors for various volume fractions of nanoparticle based on the mixture model.

Fig. 7. Nu number for various volume fractions of nanoparticle based on the VOF

model.

Fig. 6. Friction factors for various volume fractions of nanoparticle based on the single phase model.

Fig. 8. Nu number for various volume fractions of nanoparticle based on the mixture model.

lower volume fractions of nanoparticle. In addition, single phase model deviation from experimental data increased when nano-particle volume fractions increased. This deviation was more than that of the VOF and mixture models, respectively. Fig. 11 shows the Nu numbers data obtained from the experi-ment, VOF, mixture and single phase in volume fraction of 0.25% (as an example). The average deviation for VOF, mixture and single phase models were around 5.9%, 6.1% and 7.8%, respectively. So, the single phase model was not able to predict heat transfer behavior, properly. The nanoparticle enhancement apparently caused Nu number (heat transfer) and friction factor increment. The nanofluid vis-cosity slightly increased with increasing nanoparticle amounts (because nanofluid concentrations were less than 1% in this research). Since the uniform inlet Re numbers in a set of experi-ments (various concentrations of nanofluid) were necessary, the pumping power (flow velocity) should be increased with nanofluid concentration enhancement. Furthermore, Nu number increased with Re number (flow velocity) increment in the same

Fig. 9. Nu number for various volume fractions of nanoparticle based on the single phase model.

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R. Davarnejad, M. Jamshidzadeh / Engineering Science and Technology, an International Journal xxx (2015) 1e7

Nomenclature B

Sum of body forces, e Model constant, e

C2 Cp

1

Cm E

Energy, j Friction factor, e

f ! F

g h

h

k

k

Km n Nu

Fig. 10. Friction factor versus Re number based on the experiment and various models for nanoparticle volume fraction of 1%.

1

Specific heat at constant pressure, j.kg K Model parameter, e

Body forces, N 2 Gravity acceleration, m s

2

1

Heat transfer coefficient, W m K Sensible 2 1 enthalpy for phase k, W m K Thermal 1 1 conductivity, W m K Turbulent kinetic energy, j Mass transfer due to cavitation, kg s Empirical shape factor, e

1

Average Nusselt number, e Pressure, Pa

P Re Tt

Reynolds number, e Temperature, K Time, s

U

Velocity, m s 1

V

Velocity, m s 1

Greek letters

Volume fraction of phase k, e Turbulent 2 3 1 dissipation rate, m s Viscosity, kg m 1 s

ak ε

m mt

Turbulent dynamic viscosity, kg m 1 s 1 Density, kg m3

r

Diffusion Prandtl number fork, e Diffusion Prandtl number for ε, e Volume fraction, e

sk sε

F n !

2 2

nm

!n

dr;k

t

concentrations. It is due to the pumping power (flow velocity) enhancement, as well [24]. 6. Conclusions The MgO-water nanofluid convective heat transfer in turbulent regime inside a tube was numerically investigated. Friction factor and Nusselt number were studied in various nanoparticles con-centrations and Reynolds numbers. Three models including single phase, mixture and VOF were applied to predict the modified heat transfer properties in the turbulent flow. The results indicated that nanofluid heat transfer and pressure drop (friction factor) increased with the nanoparticle volume fraction enhancement. This was in good agreement with the literature, as well. However the two phase models (VOF and mixture) could dramatically predict friction factor and Nu numbers but, some deviations obtained from the single phase model may be due to having low nanoparticles con-centrations in this study (less than 1%) particularly in the lower Reynolds numbers. Furthermore, Nu number and friction factor increased with the nanofluid concentration increment. It was due to pumping power [flow velocity (Re number)] enhancement. This output was properly supported with the literature.

Drift velocity for secondary phase k, m s 1

Particle sphericity, e 2 Stress, N m

j

Fig. 11. Nu number versus Re number based on the experiment and various models for nanoparticle volume fraction of 0.25%.

Kinetic viscosity, m s Mass1 averaged velocity, m s

Subscript b eff f

Bulk, e Effective, e Base fluid, e

nf m p

Nanofluid, e Mixture, e Solid particle, e

w

Wall, e

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Please cite this article in press as: R. Davarnejad, M. Jamshidzadeh, CFD modeling of heat transfer performance of MgO-water nanofluid under turbulent flow, Engineering Science and Technology, an International Journal (2015), http://dx.doi.org/10.1016/j.jestch.2015.03.011