Applied Mathematical Modelling 40 (2016) 6437–6450
Contents lists available at ScienceDirect
Applied Mathematical Modelling
journal homepage: www.elsevier.com/locate/apm
Numerical resizing study of Al2 O3 and CuO nanofluids in the
flat tubes of a radiator
M. Elsebay, I. Elbadawy∗, M.H. Shedid, M. Fatouh
Department of Mechanical Power Engineering, Faculty of Engineering at El-Mattaria, Helwan University, Masaken El-Helmia P.O., Cairo
11718, Egypt
a r t i c l e
i n f o
Article history:
Received 10 February 2015
Revised 20 December 2015
Accepted 13 January 2016
Available online 5 February 2016
Keywords:
Numerical
Heat transfer
Flat tube
Radiator
Nanofluid
a b s t r a c t
Heat transfer of coolant flow through the automobile radiators is significant for the optimization of fuel consumption and radiator sizing. Using of nanofluids as a coolant in the
car radiators is a crucial topic in the vehicles industry due to the expected enhancement
of cooling process. In this study, resizing process for a radiator is performed due to the
use of nanofluid instead of water flow. Two nanofluids (Al2 O3 /water and CuO/water) flowing in a flat tube of radiator are investigated numerically to evaluate both thermal and
flow performance and accomplish the resizing process. Four volume concentrations of 1,
3, 5 and 7% are studied at Reynolds number ranges from 250 to 1750. The flattened tube
model is constructed, discretized, tested and validated with the available data from the literature and the well-known correlations. A significant reduction of the radiator volume is
achieved due to marked improvement in the heat transfer performance. On the contrary,
the required pumping power after the radiator volume reduction is increased over that
needed for base fluid.
© 2016 Elsevier Inc. All rights reserved.
1. Introduction
Active and passive methods can be used to improve convective heat transfer. Active methods, which provide better enhancement, require additional external forces and/or equipment which can increase the complexity, capital and operating
costs of the system. While passive heat transfer enhancement can be achieved by changing flow geometry or modifying
thermo-physical properties of working fluid [1].
The radiator is considered one of the most important components of the vehicle engine. Normally, it represents the
cooling system of the engine and generally water is heat transfer medium. The radiators are often louvered finned flat
tubes [2]. Flat tube has been recently introduced for use in automotive radiators. A flat tube has a high surface to-crosssectional flow area ratio, which enhances the heat transfer rate and increases the compactness of heat exchangers. Moreover,
it achieves small air pressure drop due to its aerodynamic shape [3]. More reductions in the radiator area can be achieved
by using nanofluids because of the relatively high thermal transport properties over pure water.
Therefore, a significant research effort has been committed for more understanding about the thermal transport properties of nanofluids. A brief literature survey is performed in this paper.
∗
Corresponding author. Tel.: +96551609016.
E-mail addresses: Ibrahim_Mohamed01@m-eng.helwan.edu.eg, I.m.elbadawy@gmail.com (I. Elbadawy), mohamed_shedid@m-eng.helwan.edu.eg (M.H.
Shedid).
http://dx.doi.org/10.1016/j.apm.2016.01.039
S0307-904X(16)30027-0/© 2016 Elsevier Inc. All rights reserved.
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M. Elsebay et al. / Applied Mathematical Modelling 40 (2016) 6437–6450
Nomenclature
A
Cf
CP
Dh
h
ho
K
L
Nu
p
Pm
P
Pr
Q
q
Re
T
U
Z
tube cross sectional area, [m2 ]
skin friction coefficient, [-]
specific heat, [J/kg.K]
hydraulic diameter, [m]
heat transfer coefficient, [W/m2 .K]
outside heat transfer coefficient, [W/m2 .K]
thermal conductivity, [W/m.K]
tube length
Nusselt number, [-]
pressure, [Pa]
perimeter, [m]
pumping power, [W]
Prandtl number, [-]
heat transfer rate, [W]
heat flux, [W/m2 ]
Reynolds number, [-]
temperature, [K]
velocity vector, [m/s]
axial distance from inlet, [m]
Greek symbols
β
ratio of the nanolayer thickness to the original particle radius, β = 0.1
ϕ
nanoparticle volumetric concentration, [%]
μ
dynamic viscosity, [kg/m.s]
ρ
density, [kg/m3 ]
τ
shear stress, [N/m2 ]
Subscripts
amb
avg
b
bf
in
nf
out
p
s
z
ambient
average
bulk
base fluid
inlet
nanofluid
outlet
particle
surface
local axial position
Park and Pak [2] presented a computational study of laminar flow in flat tubes of different shape and dimension using
a mixture of ethylene glycol and water. They implemented their computations in the range of Reynolds number from 10 to
200, which covers the fluid flow rate in the radiator from 18 to 75 l/min for an engine with a volume displacement of 1800
cc. Vajjha et al. [4] performed a numerical study to examine the thermal performance of Al2 O3 and CuO nanoparticles in a
mixture of ethylene glycol and water under laminar flow conditions using flat tubes of an automobile radiator. The results
demonstrated a significant enhancement of the convective heat transfer coefficient along the flat tubes for the nanofluid
over the base fluid. The average heat transfer coefficient of Al2 O3 nanofluid with a volume concentration of 10% is greater
than that of the base fluid by about 91%. Also, both the local and the average friction factor and convective heat transfer
coefficient increase with nanoparticles volume concentration. For example, the predicted local skin friction coefficient at 6%
CuO is 2.75 times that of the base fluid in the fully developed region.
Huminic and Huminic [5] investigated the effect of CuO/ethylene glycol nanofluids using different cross sectional tube
on the performance of convective heat transfer coefficient. The results show that the convective heat transfer coefficient
of nanofluids is higher than those of the base fluid. For example, at a Reynolds number of 10 and 4% CuO nanoparticles
volume concentration produces a heat transfer coefficient about 19% larger than that of the base fluid. Also, it was found
that enhancement of heat transfer are directly proportional to the particle concentration level and Reynolds number. A
high heat transfer coefficient enhancement of 82% is achieved by the flattened tube at Reynolds number of 125 and 4%
concentration level in comparison to circular and elliptic tubes.
An experimental and numerical study of nanofluids (SiO2 /water) heat transfer characteristics in the automotive cooling
system have been performed by Hussein et al. [6]. The results indicated a significant increase in the friction factor and
M. Elsebay et al. / Applied Mathematical Modelling 40 (2016) 6437–6450
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heat transfer coefficient with the nanoparticles volume concentration. While Qiang and Yimin [7] studied experimentally
the convective heat transfer and flow characteristics of CuO/water nanofluid. In this study, the suspended nanoparticles
achieved a remarkable augmentation of heat transfer performance compared with pure water under the same Reynolds
numbers. Also, it was observed that the friction factors of the nanofluids coincide well with those of the pure water in the
pressure drop test. That is because the nanofluids, in which the nanoparticles are so small, behave like a pure fluid.
Myers et al. [8] developed and analyzed a theoretical model for nanofluid flow, including Brownian motion and thermophoresis. The most significant result of this analysis is the clear decrease in the heat transfer coefficient as the particle
concentration increases.
According to the above discussion, it can be concluded that the emphasis of heat transfer enhancements due to use of
nanofluids however, it is misleading how these improvements reflected in the design process for the radiators and if this
new design is always beneficial. The current research adopts nanofluids (AL2 O3 /water and CuO/water) to computationally
examine the thermal performance of flat tube used in a vehicle radiator. This study aims to assess the change of the radiator
heat transfer area and the pumping power due to nanofluid usage. Heat transfer and pressure drop are studied for different
nanoparticles volume concentrations, particle type and Reynolds number.
2. Mathematical modeling
The schematic diagram for typical automobile radiator geometry is shown in Fig. 1(a) [5]. The radiator is an arrangement
of flat tubes equipped with plate fins for liquid-to-air cooling. Each tube has dimensions of height (H), width (W) and
length (L) of 3, 9 and 345 mm, respectively. These dimensions are considered typical ones that were used in a car radiator
as reported by Hussein et al. [6].
2.1. Governing equations
The following three conservation equations [5,9] are solved using the computational fluid dynamics (CFD) commercial
code, Fluent 14.0 [10].
Continuity:
∂
( ρ U ) = 0,
∂ xi nf i
(1)
where Ui is a component of the velocity vector (m/s),
Momentum:
∂U j
∂
∂p
∂
μnf
(ρnfU jUi ) = −
+
,
∂ xi
∂ x j ∂ xi
∂ xi
(2)
where ρ nf is the density of nanofluid (kg/m3 ), p is the pressure (Pa), μnf is nanofluid viscosity (kg/m.s) and i, j ∈ {1, 2, 3}.
Energy:
∂
∂
∂T
.(ρnfCp nfUi T ) =
K
,
∂ xi
∂ xi nf ∂ xi
(3)
where Cp nf is the specific heat of the nanofluid (J/kg.K), T is the flow temperature (K) and Knf is the nanofluid thermal
conductivity (W/m.K).
The following assumptions are used in solving the model (Eqs. (1–3));
•
•
•
The nanofluid inside the tube can be considered as incompressible [4],
The flow is laminar; hence the viscous dissipation term can be neglected [11],
The single-phase fluid approach will be applied. Although the nanofluid is actually a two-phase fluid in nature, the
results of [12–14] show that the nanofluid behaves more like a pure fluid than a liquid–solid mixture.
The investigation is carried out at laminar flow condition using two nanofluids with different volume concentrations.
Table 1 lists the conditions of the nanofluid flow. At the flat tube inlet, uniform inlet velocity boundary condition is adopted
while the outlet boundary condition depends on the flow characteristics. For example, in the cases of the thermal entrance
length (Xth = 0.05 Re.Pr.Dh ) is less than the tube length, the outflow boundary condition is used, while the pressure outlet
is adopted in other cases. Following Park and Pak [2], air side heat transfer coefficient and temperature are selected by
ho = 50 W/m2 K and T = 303 K, respectively at a mean vehicle speed with maximum velocity 72 (km/hr). No slip condition is
used to prescribe the tube wall.
The governing equations in Section 2.1 are solved by the control volume approach using FLUENT 14.0 [10]. The double
precision option is adopted for all computations. A second-order upwind scheme is employed to discretize the convection
terms, diffusion terms, and other quantities resulting from the governing equations. A staggered grid scheme is used, in
which the velocity components are evaluated at the control volume faces, while the rest of the variables governing the
flow field are stored at the central node of the control volume. The pressure–velocity coupling is handled with the SIMPLE
scheme for pressure linked equations given by Patankar [15]. Fluent solves the linear systems resulting from discretization
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M. Elsebay et al. / Applied Mathematical Modelling 40 (2016) 6437–6450
Fig. 1. Schematic of (a) the flat tube of atypical radiator [5] and (b) grid layout.
Table 1
Flow conditions considered.
Parameter
Value
Reynolds number, Re = ρ VDh /μ (-)
Nanoparticles
Nanoparticles volume concentration (%)
Inlet temperature (K)
Outside heat transfer coefficient, ho (W/m2 K)
Air temperature (K)
250–1750 [step = 250] (laminar)
Al2 O3 and CuO
1, 3, 5, 7
353
50
303
M. Elsebay et al. / Applied Mathematical Modelling 40 (2016) 6437–6450
6441
schemes using a point implicit (Gauss–Seidel) linear equation solver, in conjunction with an algebraic multi-grid method. For
all simulations performed in the present study, converged solutions are considered when the normalized residuals resulting
from an iterative process for all governing Eqs. (1–3) are lower than 10−3 . The three velocity components “VX , VY , VZ ”, the
pressure “p”, and the temperature “T” throughout the interior computational domain of the flat tube are solved. In data
post-processing, the flow outlet temperature, center plane temperature, surface heat flux, surface temperature, centerline
pressure and flow outlet pressure are recorded.
2.2. Thermophysical properties of nanofluids
By assuming that the nanoparticles are well dispersed within the base fluid, thus the nanoparticles concentration can be
considered uniform throughout the system. Therefore, the effective thermo-physical properties of the mixtures can be evaluated using some classical formulae as usually used for two phase flow. These properties might include density, viscosity,
thermal conductivity and heat capacitance depending on what form the governing equations are written.
Duangthongsuk and Wongwises [16] conducted a comparison of the effects of measured and computed thermo-physical
properties of nanofluids on heat transfer performance. The results of the comparison show that the use of the Yu and Choi’s
model [17] for thermal conductivity, Eq. (4) and the Wang et al. [18] for viscosity, Eq. (5) to describe the Nusselt number
of the nanofluids give good agreement with the use of the measured data. As a result, these models will be considered in
the present study. The following correlations have been used to predict nanofluids thermal conductivity [17], viscosity [18],
specific heat and density, respectively,
ϕ
Kbf ,
3
K p + 2Kbf − (K p − Kbf )(1 + β ) ϕ
μnf = 1 + 7.3ϕ + 123ϕ 2 μbf ,
Knf =
Cpnf =
K p + 2Kbf + 2(K p − Kbf )(1 + β )
3
(4)
(5)
ϕ ρ p Cpp + (1 − ϕ )ρbfCpbf
,
ρnf
(6)
ρnf = (1 − ϕ )ρbf + ϕ ρ p ,
(7)
where β is the ratio of the nanolayer thickness to the original particle radius (β = 0.1), ϕ is the nanoparticles volume concentration and the subscripts “nf”, “bf” and “p” refer to nanofluid, base fluid and particle, respectively. The properties used
in this study are listed in Table 2.
2.2.1. Local heat transfer coefficient “hz ”and local Nusselt number “Nuz ”
The local heat transfer coefficient and corresponding Nusselt number can be calculated along the flat tube length using
the Newton’s law of cooling as follows:
qz = hz Tz = hz T f − Ts ,
(8)
z
where qz is surface heat flux (W/m2 ), Tf and Ts are the local fluid and surface temperatures (K), respectively and hz is the
local heat transfer coefficient (W/m2 .K). From the post processing of the computations, values for qz , Tf and Ts along the
tube length can be computed. Tf is calculated as the mean fluid temperature of the middle xy-plane along z-axis. Therefore,
the local heat transfer coefficient can be calculated by:
hz =
qz
(T f − Ts )z
.
(9)
The local Nusselt number can be calculated by:
N uz =
hz Dh
,
K
(10)
where Dh is the flat tube hydraulic diameter which is given by:
Dh =
4.A
,
Pm
(11)
Table 2
Thermal properties of nanoparticles and base fluid [6,19].
Material
Specific heat
(J/kg.K)
Thermal conductivity
(W/m.K)
Density
(kg/m3 )
Viscosity
(kg/m.s)
Al2 O3
CuO
Pure water
773
551
4195
40
33
0.668
3960
60 0 0
973.7
–
–
0.0 0 0365
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where A and Pm are the flat tube cross sectional flow area and perimeter, respectively. According to Eq. (11) and the flat
tube layout, shown in Fig. 1 (a), the hydraulic diameter is given by:
Dh =
4 π4 H 2 + (W − H )H
π H + 2(W − H )
.
(12)
By substituting in Eq. (12) by height (H), width (W) and length (L) of 3, 9 and 345 mm, respectively, it gives Dh = 4.68 mm.
2.2.2. Average heat transfer coefficient “havg ” and average Nusselt number “Nuavg ”
According to Newton’s cooling law the total heat transfer rate is given by:
Q = havg As T = havg As (Tb − Ts ),
(13)
where As is the tube surface area and Tb is the fluid bulk temperature, Eq. (14):
Tb =
Tin + Tout
,
2
(14)
where Tin and Tout are inlet and outlet fluid temperatures calculated as the facet average temperature over the inlet and
outlet faces, respectively and Ts is the average tube wall temperature computed from the computations post processing
data. The total rate of heat loss can be expressed as:
Q = ρ AV Cp (Tin − Tout ).
(15)
From Eqs. (13) and (15) the average heat transfer coefficient can be calculated by:
havg =
ρ AV Cp (Tin − Tout )
,
As (Tb − Ts )
(16)
and the corresponding average Nusselt number can be calculated as:
N uavg =
havg Dh
.
K
(17)
3. Results and discussion
The influence of mesh density is investigated first for the case of pure water with Re = 1750 and the center line temperature is a key parameter. The effect of mesh density on the prediction of this quantity using three different levels of
refinement based on the mesh accounting number, shown in Fig. 1(b). Solutions are obtained with grid of Nx × Ny × Nz
= 10 × 12 × 345 (grid 1), 15 × 18 × 345 (grid 2) and 20 × 24 × 345 (grid 3). Fig. 2(a) shows that predictions of center line
temperature, Tc , are effectively grid-independent (typically center line temperature obtained for grid 1 is far from those obtained with grid 2 and grid 3). Note that the predicted quantities such as heat transfer coefficient, skin friction coefficient
and pressure drop are found to be grid insensitive to the particular choice of grid 3 with maximum difference of 3%. On the
bases of these findings, all results reported subsequently have been obtained using grid 3 to get good solution accuracy.
A comparison between the present model and Hussein et al. [6] is made as shown in Fig. 2(b). It is clear that the results
are found to be in a good agreement with an average error 2.5%. In addition, Fig. 2(c) shows the predictions of local Nusselt
number, Eq. (10), along the flat tube and data obtained by the experimental correlation of Shah and London [20] which
correlated for the local Nusselt number for rectangular cross-section ducts with semicircular ends under fully developed
laminar flows, which is given by:
N uz = 1.953 ReP r
Dh
Z
1
3
for
N uz = 4.364 + 0.0722 ReP r
Dh
Z
ReP r
Dh
Z
for
≥ 33.33,
ReP r
Dh
Z
< 33.33.
(18)
The results are obtained for pure water at Re = 1750. Fig. 2(c) reveals a reasonable good agreement with the above correlation with an average error of 9% that may due to different cross sectional shapes.
M. Elsebay et al. / Applied Mathematical Modelling 40 (2016) 6437–6450
6443
Fig. 2. (a) Effect of mesh density on the center line temperature, (b) predicted average heat transfer coefficient and Hussein et al.’s data [6] and (c)
validation with Shah and London [20].
Fig. 3 shows the effect of AL2 O3 and CuO volume concentration, ϕ , change on the local heat transfer coefficient along the
axis (z-direction) at Re = 1750. In general, for the tube length z/L < 0.6 the local heat transfer coefficient decreased while for
z/L > 0.6, hz attains a nearly constant values independent of tube length (fully developed region). These constant values are
function of ϕ only.
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M. Elsebay et al. / Applied Mathematical Modelling 40 (2016) 6437–6450
Fig. 3. The effect of nanoparticles volume concentration for (a) AL2 O3 and (b) CuO on local heat transfer coefficient at Re = 1750.
The effect of AL2 O3 and CuO volume concentration on the predicted average heat transfer coefficient “havg ” at different
Reynolds numbers are shown in Fig. 4(a) and (b), respectively. It is clear that the average heat transfer coefficient increased
with both nanofluids concentration and Reynolds number. For example for Al2 O3 at Re = 10 0 0, the values of havg enhancement for ϕ = 1, 3, 5 and 7% are approximately 5, 16, 30 and 47%, respectively larger than this for the pure water; for CuO
the corresponding enhancements are 3, 13, 24 and 38%.
The effect of nanoparticles volume concentration on local skin friction coefficient “Cf ” along the tube length is illustrated
in Fig. 5 for Al2 O3 and CuO at Re = 1750. It is observed that the local skin friction coefficient near to the tube inlet reduces
rapidly with the tube length, particularly for z/L < 0.1 and is much more constant for the rest length of the tube. At z/L
> 0.1, a larger Al2 O3 and CuO concentration resulted to a larger skin friction coefficient. For example at z/L = 0.5 and ϕ = 0,
3 and 7%, Cf equals 0.01, 0.017 and 0.039 for Al2 O3 and 0.01, 0.015 and 0.035 for CuO, respectively.
Fig. 6(a) and (b) show the variation of the average skin friction coefficient, Cf,avg , with Reynolds number and different
volume concentrations of Al2 O3 and CuO nanoparticles, respectively. It is observed that Cf,avg is increasing with Re as well
M. Elsebay et al. / Applied Mathematical Modelling 40 (2016) 6437–6450
6445
Fig. 4. Variation of the average heat transfer coefficient with Reynolds number for different nanoparticles volume concentrations of (a) Al2 O3 (b) CuO.
as the volume concentration. At Re = 10 0 0 and ϕ = 7%, the average friction coefficient increases by 268% and 260% than that
of pure water for Al2 O3 and CuO/water, respectively.
Fig. 7 shows the variation of the pressure drop between the inlet and outlet with Reynolds number for both Al2 O3 /water
and CuO/water nanofluids. Generally, the pressure drop is increasing with Reynolds number as well as volume concentration increase. However, the increase in pressure drop due to volume concentrations is more pronounced at high Reynolds
number. For instance at Re = 250 and ϕ =7%, the pressure drop increases by 268% for Al2 O3 /water and 223% for CuO/water
while at Re = 1750, these ratios reach to 267% and 226% for Al2 O3 and CuO/water, respectively.
As discussed above, the heat transfer coefficient is enhanced due to use of the nanofluid over the base fluid. Consequently, the required heat transfer area will be reduced for the same cooling load and the new radiator size can be redesigned for the same cooling rate. This might help in decreasing the weight of material, the cost and the fuel consumption
of the vehicle. For this purpose, a resizing investigation is performed in the present study to evaluate the effect of a particle
volume concentration on the tube length. This study is carried out by calculating the new tube length for different particle
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M. Elsebay et al. / Applied Mathematical Modelling 40 (2016) 6437–6450
Fig. 5. Variation of the local skin coefficient along the tube length with different nanoparticles volume concentrations of (a) Al2 O3 (b) CuO at Re = 1750.
concentrations that achieved the same inlet and outlet temperature difference of base fluid as indicated in Eq. (19):
Lnew =
ρnf AV CPnf (Tin − Tout )bf
,
hnf Pm (Tb − Ts )
(19)
where Lnew is the new tube length.
Fig. 8 shows the percentage reduction in the radiator tube length depending on nanoparticles volumetric concentration
of Al2 O3 /water and CuO/water nanofluids. It is clear that the radiator tube length reduces due to using nanofluid rather
than pure water at the same cooling rate and flow temperatures. This reduction significantly increases with increasing the
nanoparticles concentration. Also, it can be observed that Al2 O3 /water nanofluid is more pronounced effect on the tube
length reduction than CuO/water nanofluid.
M. Elsebay et al. / Applied Mathematical Modelling 40 (2016) 6437–6450
6447
Fig. 6. Variation of the average skin friction coefficient with Reynolds number for different nanoparticles volume concentrations of (a) Al2 O3 (b) CuO.
Table 3
Resizing of radiator tubes by using Al2 O3 /water nanofluid.
ϕ
2
havg (W/m .K)
Re
LNew (mm)
(Power)New (Watt)
Power (%)
0%
1%
3%
5%
7%
2154.34
1750
345
0.0 0 0135
0
2190
1666.36
339.38
0.0 0 0145
7.21
2280
1448.73
325.98
0.0 0 0166
22.24
2370
1223.013
313.60
0.0 0 0197
45.38
2440
1024.67
304.60
0.0 0 0237
74.52
The corresponding effect of nanoparticles concentration on pumping power for the redesigned radiator is investigated.
The pumping power is computed as the following:
P = AV p,
(20)
where p is the pressure drop along the new tube length, Lnew .
A comparison between the required pumping power for nanofluid and that of pure water at the same cooling rate and
inlet and outlet temperature difference is performed.
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M. Elsebay et al. / Applied Mathematical Modelling 40 (2016) 6437–6450
Fig. 7. Variation of pressure drop with Reynolds number at different nanoparticles volume concentration of (a) Al2 O3 and (b) CuO.
Table 4
Resizing of radiator tubes by using CuO/water nanofluid.
ϕ
0%
1%
3%
5%
7%
havg (W/m2 /K)
Re
LNew (mm)
(Power)New (Watt)
Power (%)
2154.34
1750
345
0.0 0 013
0
2200
1703.76
337.84
0.0 0 014
6.63
2260
1540.44
328.87
0.0 0 016
24
2330
1344.6
318.99
0.0 0 02
47.25
2390
1159.5
310.98
0.0 0 0244
79.48
M. Elsebay et al. / Applied Mathematical Modelling 40 (2016) 6437–6450
6449
Fig. 8. Percentage reduction in tube length against nanoparticles volume concentration for both Al2 O3 and CuO.
Fig. 9. Percentage power increase against nanoparticles volume concentration for both Al2 O3 and CuO.
The results are summarized in Tables 3 and 4 for Al2 O3 /Water and CuO/Water nanofluids, respectively and indicated in
Fig. 9. A significant increase in the pumping power is observed with increasing nanoparticles concentration. As shown in
Figs. 8 and 9, Al2 O3 /water nanofluid achieves more radiator compact size and less required pumping power than CuO/water
nanofluid. Therefore, Al2 O3 will be more efficient than CuO in the vehicle radiator.
4. Conclusion
In this paper, the flow characteristics and heat transfer performance in a flat tube of automobile radiator have been investigated computationally with three distinct working fluids: pure water and two water based nanofluids (small amount
of Al2 O3 and CuO nanoparticles in water) at different concentrations. This research addresses explicitly the benefits of enhanced heat transfer rate and drawbacks of high pumping power due to using nanofluids. Most previous studies in this field
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M. Elsebay et al. / Applied Mathematical Modelling 40 (2016) 6437–6450
used non-dimensional parameters that do not highlight about the nanofluids that are not cost free. The following conclusions are made:
1. Addition of Al2 O3 and CuO nanoparticles in water can enhance the heat transfer rate of the automobile radiator. The
enhancement degree of average heat transfer coefficient depends on the amount of nanoparticles added to pure water,
2. The increase in heat transfer coefficient reached 45 and 38% for Al2 O3 /water and CuO, respectively compared to the
values of the pure water,
3. Friction coefficient and pressure drop increase with using nanofluids. At Re = 1750 and ϕ = 0.07, they increased by 271
and 267% for Al2 O3 /water and 266 and 226% for CuO/water, respectively,
4. Al2 O3 /water nanofluid achieves a higher length reduction than CuO/water nanofluid. Estimated 11.7% and 9.8% reduction of tube length are achieved by adding 7% Al2 O3 and CuO nanoparticles, respectively for the same cooling rate and
temperature difference,
5. Using of nanofluids is not always beneficial where additional 75% and 80% of the pumping power is needed for a radiator using a flat tube with reduced length by 11.7% and 9.8 % for flowing nanofluid of 7% Al2 O3 and CuO, respectively
compared to the radiator using pure water flowing in the original tube length and removes the same amount of heat.
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