INTRODUCTION
The idea of using combination of solids and fluids was to enhance the efficient
heat transfer properties of the fluid because the fluid in general was poor
in thermal properties while the metal had high thermal properties. Hence, this
idea was used to enhance thermal properties, but had a bad effect on the flow
properties, where the solid particles, in millimeter and micrometer size, behaved
as a twophase flow and increased the power needed to force the fluids. The
preparation of nanofluids was made through suspension of nanoparticles in a
base fluid (Zamzamian et al., 2011), which increases
the thermal properties of the nanofluid and makes it behaves as a onephase
flow. The liquidparticles are compounds consisting of solid nanoparticles with
sizes less than 100 nm, suspended in a liquid. In order to evaluate the heat
transfer characteristics of nanofluids there must be adequate data on the thermophysical
properties of such fluids (Zamzamian et al., 2011).
Eastman et al. (2001) found that there is an
increase of 40% in thermal conductivity for one nanofluid composition of copper
suspended in ethylene glycol at 0.3% volume concentration. Das
et al. (2003) have reported that the suspension of alumina with a
volume concentration of 14% in water will increase thermal conductivity until
1025%. Li and Xuan (2000) studied experimentally the
effect of volume concentration of 0.51.2% copperwater nanofluids on the enhancement
of heat transfer coefficient was 1.05 to 1.14% in a circular tube with constant
heat flux at the wall of the tube at the constant velocity inlet. Also, Xuan
and Li (2003) investigated experimentally the flow and convective heat transfer
of nanoparticles of Cu suspended in deionized water through straight horizontal
brass pipes with constant heat flux, where the concentrations of Cu in water
are in the range of 0.32%. The Nusselt equation was derived for the laminar
and turbulent range, i.e., 80025, 000, where in this range, the classical correlation
(Dittus and Boelter, 1930) is not applicable for nanofluids.
The enhancement of heat transfer compared with water based fluid for 2% concentration
is 60%.
Wen and Ding (2004) built an experimental system to
study the convective heat transfer enhancement at the entrance region using
a nanofluid of Al_{2}O_{3}deionized water for laminar flow
and the system includes the nanofluid flowing through the copper pipe under
constant heat flux at the wall for different concentrations of nanoparticles.
The Nusselt equation was calculated for the nanofluids ant temperature profile
along the test pipe and the results showed that the Reynolds number and volume
concentration are the primary effects in the heat transfer coefficient. Yang
et al. (2005) presented the experimental study to a laminar flow
and heat transfer enhancement in a horizontal tube heat exchanger for nanofluid.
The disc shape graphite nanoparticle with aspect ratio 0.02 was used to enhance
heat transfer nevertheless the highly increase in viscosity of nanofluid. Yang
et al. (2005) investigated a two series of nanofluids with different
base fluids were used with the flow rates were of 62507 cm^{3} min^{1},
the Reynolds number 5110 and the fluid temperature 5070°C. The experimental
results illustrated that the heat transfer coefficient increased with the Reynolds
number and the particle volume fraction, while the heat transfer coefficient
of the nanofluids moderately increased compared with the base fluid and its
temperature. Sundar et al. (2007) reported the
experimental investigation to study the Peclet and Nusselt number for different
volume fraction aluminawater flowing in a circular tube at constant wall temperature.
The enhancement of heat transfer was found from the experiment to be much higher
than the prediction of heat transfer correlations used with nanofluid properties
suggested by Anoop et al. (2009).
An experimental rig was used to study the effect of twisted tape inserted in
a circular tube on the heat transfer of nanofluids with different volume concentrations.
The further enhancement in heat transfer with twisted tape was achieved when
compared with a smooth tube under the same conditions by Gherasim
et al. (2009), where the pressure drop and convective heat transfer
coefficient of waterbased Al_{2}O_{3} nanofluids flowing through
a uniformlyheated circular tube in the fullydeveloped laminar flow regime
were measured. Gherasim et al. (2009) study the
experimental results show that Darcy’s equation for singlephase flow is
applicable for predictions of the friction factor for nanofluids, while the
convection heat transfer coefficient increases by up to 8% at a concentration
of 0.3 vol% compared with that of pure water for this enhancement which could
not be predicted by the Shah equation. The correlation of heat transfer in the
entrance region has suggested depending on the experimental results for the
flow of nanofluids in a tube with constant heat flux. The effect of size of
alumina nanoparticles suspended in water on convective heat transfer in the
entrance laminar region was studied. The smaller size of nanoparticles gives
better enhancement in heat transfer in the developing region by Maiga
et al. (2004) and Khoddamrezaee et al.
(2010) examined the exergy heat transfer rate of the ethylene glycolalumina
nanofluid in the circular duct with constant wall temperature laminar flow,
where the study focussed on pressure drop and turbulent convective heat transfer
performance for CuO nanoparticles suspended in water. The results yielded 20%
pressure drop and 25% average increase of the heat transfer coefficient, which
showed good agreement predictions for the Buongiorno correlation.
Hence, the purpose of this paper is to study the effect of volume concentrations of different oxide nanofluids flowing in circular pipes with constant heat flux on heat transfer and pressure losses.
MATERIALS AND METHODS
Thermophysical properties of nanofluids: The calculation of the convective heat transfer requires knowing the transport properties for the nanofluid which is density, heat capacity, thermal conductivity and viscosity. Each property of nanofluid depends on many factors such as volume fraction, material type of nanoparticles, base fluid and temperature of the base fluid.
Density: In the absence of experimental data for nanofluid densities, a constant temperatureindependent density ρ, based on volume fraction of the nanoparticles φ, are typically used:
where, ρ_{f}, ρ_{p} and ρ_{nf} represent densities of the base fluid, the nanoparticle and the nanofluid, respectively.
Specific heat: Similarly, in the absence of experimental data relative
to nanofluids, it has been suggested by Li and Xuan (2000)
that the effective specific heat C_{pnf} can be calculated using the
following equation:
where, C_{p} and C_{nf} is specific heats of the nanoparticle and the nanofluid, respectively. This is the standard equation for nanofluid specific heat C_{nf} and the effective specific heat determined through energy balances during the experiments in this study was found to be within 1% of the calculation.
Thermal conductivity: To determine the thermal conductivity of nanofluids,
the following model appears appropriate for nanofluids (Xuan
and Roetzel, 2000; Akbarinia and Behzadmehr, 2007;
Rezaee and Tayebi, 2010).
where, K_{f}, K_{p} and K_{nf} is thermal conductivity coefficients of the base fluid, the nanoparticle and the nanofluid, respectively. Where K_{f} it’s a function to the temperature.
Viscosity: To calculate the effective dynamic viscosity of nanofluid can be calculated using Einstein’s equation for a viscous fluid containing a dilute suspension (Ø<0.2) of rigid, small and spherical particles which is written as follows:
where, μ_{nf} is the viscosity of nanofluid and μ_{f}
is the viscosity of base fluid and it’s a function to the temperature.
However, experimental work to establish the viscosity of nanofluids showed that
the measured viscosity it is have accepted variance with the existing theoretical
predictions (Drew and Passman, 1999; Wen
and Ding, 2004). The equation used to predict the viscosity of Al_{2}O_{3}water,
CuOwater and TiO_{2}water nanofluids, respectively.
Governing equations
Geometrical: The case set for this investigation
is the threedimensional steady state incompressible flow with forced laminar
convection of nanofluids flowing inside a circular tube having a diameter of
0.01 m and a length of 2 m with the thickness of the tube being 0.001 m. The
flow enters the tube with a constant temperature and a uniform velocity. The
relevant governing equations used can be written as follows:
The governing equations of the fluid flow are nonlinear and coupled partial differential equations, subjected to the following boundary conditions. At the tube inlet section, uniform axial velocity V_{in} and temperature T_{in}, turbulent intensity and hydraulic diameter were specified. At the outlet section, the flow and temperature fields were assumed to be fullydeveloped and the flow and temperature fields were also assumed as fullydeveloped (x/D>10). Outflow boundary conditions were enforced for the outlet section. This boundary condition implies zero normal gradients for all flow variables except pressure. On the upper wall of the tube, the noslip boundary condition was imposed. The wall is subjected to a uniform heat flux of 5000 W m^{2} as shown in Fig. 1.
Numerical procedures: To solve the present problem, the CFD module in
the COMSOL Multiphysics software was employed, which utilizes the governing
Eq. 57 to generate the pressure, velocity
and temperature fields. The solution was obtained based on the spatial integration
of the conservation equations using the finite element method, converting the
governing equations into a set of algebraic equations. The algebraic “linear
equations”, resulting from this spatial integration process, are sequentially
solved throughout the physical domain considered. COMSOL solves the systems
resulting from linearization, schemes using a numerical method. The residuals
resulting from the integration of the governing Eq. 46
are considered as convergence indicators and uniform. In order to ensure the
accuracy as well as the consistency of numerical results, several nonuniform
grids were subjected to an extensive testing procedure for each of the cases
considered.
The results obtained for the particular test case showed that, for the tube
flow problem under consideration, the 757, 817 elements appears to be satisfactory
to ensure the precision of numerical results as well as their independency with
respect to the number of nodes used. Such a grid has 315,157 elements along
the tube. The computer model has been successfully validated with correlations
reported by Pak and Cho (1998) for thermally and hydraulically
developing flow, showing an average error less than 2%, as reported in Fig.
2 and 3 where the local Nusselt number is calculated according
to the following definition:
where, D is the diameter of the circular duct and h(z) is defined as:
From the previous equation, h_{avg} is calculated as:
and the average Nusselt number becomes:
RESULTS AND DISCUSSION
Validation of the results: The halftube was used to reduce the calculation
time as a result of a symmetry approach of modeling. The tube had a diameter
of 0.01 m and a length of 1 m and the nanofluid flowed with a constant velocity
and a temperature of 300 K. Constant heat flux 5000 W m^{2} was applied
to the outer wall of the tube as shown in Fig. 1. The Reynolds
(Re) number varied from 100 to 1,000. The comparison of the numerical results
with the theoretical data validated the numerical model for conventional fluid.
The Darcy friction factor f was given by Blasius which can be derived from Eq.
7 and 8, i.e.:
Figure 2 shows the comparison of pressure drop for water
in copper pipe estimated from Blasius Eq. 13 and the numerical
results in the present study; a good agreement is observed with maximum deviation
of 3% from the theoretical equation over the range of Reynolds numbers. The
Nusselt number for fullydeveloped laminar flow for water and 2% Al_{2}O_{3}
nanofluid is compared with the empirical correlation given by Shah
(2006) is presented in Fig. 3. The results give a good
agreement with this correlation for water. The figure shows the enhancement
in heat transfer for 2% Al_{2}O_{3 }nanofluid comparing to pure
water. The enhancement in heat transfer as a result to the enhance in thermal
conductivity of base fluid.
Effect of nanoparticle volume fraction concentration on heat transfer coefficient:
Figure 4, 5 and 6 show
the variation of the heat transfer coefficient for different volume concentrations
for three different nanofluids at a range of x/D. It shows that the heat transfer
coefficient increases with the rise of the volume concentration as well as the
heat transfer coefficient decrease with an increase in x/D at the Reynolds number
700. This is due to the increase of the Prandtl number of the nanofluid and
to an increase in volume concentration.

Fig. 1: 
Schematic representation of the test section used in the present
analysis 

Fig. 2: 
The comparison of pressure drop by Blasius’ equation
and numerical model results for water 

Fig. 3: 
Comparison of the numerical local Nusselt number with empirical
Shah equation for water and 2% Al_{2}O_{3} nanofluid under
the constant heat flux at Re 1000 
Here, the results are similar to that observed by He
et al. (2009) and Bianco et al. (2009).
Material effect on heat transfer coefficient: Figure 7 shows the effect of the material types of nanoparticles where the CuOwater nanofluids has the best enhancement over the TiO_{2} and Al_{2}O_{3} nanofluids for the same volume fraction and the Reynolds number.

Fig. 4: 
The influence of the Al_{2}O_{3} nanoparticle
volume concentration on the heat transfer coefficient along the tube at
Reynolds number 700 

Fig. 5: 
The influence of the TiO_{2} nanoparticle volume concentration
on the heat transfer coefficient along the tube at Reynolds number 700 

Fig. 6: 
The influence of the CuO nanoparticle volume concentration
on the heat transfer coefficient along the tube at Reynolds number 700 

Fig. 7: 
The comparisons of heat transfer coefficient for Al_{2}O_{3},
TiO_{2} and CuO nanofluids along the tube at Reynolds number 700 
CONCLUSIONS
In this study, the hydrodynamic and thermal behaviors of waterAl_{2}O_{3}, waterCuO and waterTiO_{2} nanofluids flowing inside a uniformlyheated tube were numerically investigated in stationary condition and for laminar flow for a range of Reynolds numbers from 100 to 1000 with a range of volume concentrations from 0 to 4%. The results show that both the Nusselt number and the heat transfer coefficient of nanofluids are strongly dependent on nanoparticles and increase with the increasing of the volume concentration of nanoparticles. Also for each investigated concentration value, the heat transfer enhancement is higher for the highest Reynolds number. The results illustrate that by increasing the volume concentration, the pressure losses increase. These results are in good agreement with other wellestablished correlations. So, these correlations could be used to predict the heat transfer behavior of these kinds of fluids.
ABBREVIATIONS
K 
= 
Thermal conductivity (W/m K) 
h 
= 
Heat transfer coefficient (W/m^{2} K) 
p 
= 
Pressure of the tube 
q 
= 
Constant heat flux at the wall of the tube 
Re 
= 
Reynolds number 
Nu 
= 
Average Nusselt number 
C_{p} 
= 
Specific heat capacity 
V 
= 
Velocity vector 
Greek letters:
ρ 
= 
Density 
μ 
= 
Dynamic viscosity 
φ 
= 
Volume fraction 
Subscripts:
nf 
= 
nanofluid 
p 
= 
Nanoparticles 
f 
= 
Base fluids 