1
Free convection heat transfer and entropy generation analysis of water-
Fe
3
O
4
/CNT hybrid nanofluid in a concentric annulus
Abstract
Purpose- This work aims to numerically investigate the heat transfer and entropy generation
characteristics of water-based hybrid nanofluid in natural convection flow inside a concentric
horizontal annulus.
Design/Methodology/approach- The hybrid nanofluid is prepared by suspending
tetramethylammonium hydroxide (TMAH) coated Fe
3
O
4
(magnetite) nanoparticles and gum
arabic (GA) coated carbon nanotubes (CNTs) in water. The effects of nanoparticles volume
concentration and Rayleigh number on the streamlines, isotherms, average Nusselt number as
well as the thermal, frictional and total entropy generation rates are investigated
comprehensively.
Findings- Results show the advantageous effect of hybrid nanofluid on the average Nusselt
number. Furthermore, the study of entropy generation shows the increment of both frictional
and thermal entropy generation rates by increasing Fe
3
O
4
and CNTs concentrations at various
Rayleigh numbers. Increasing Rayleigh number from 10
3
to 10
5
, at Fe
3
O
4
concentration of
0.9% and CNT concentration of 1.35%, increases the average Nusselt number, thermal entropy
generation rate, and frictional entropy generation rate by 224.95%, 224.65%, and 155.25%,
respectively. Moreover, increasing the Fe3O4 concentration from 0.5 to 0.9%, at Rayleigh
number of 10
5
and CNT concentration of 1.35%, intensifies the average Nusselt number,
thermal entropy generation rate, and frictional entropy generation rate by 18.36%, 22.78%, and
72.7%, respectively.
2
Originality/Value- To the best knowledge of the authors, there are not any archival
publications considering the detailed behaviour of the natural convective heat transfer and
entropy generation of hybrid nanofluid in a concentric annulus.
Keywords: Hybrid nanofluid, Natural convection, Entropy generation, Fe
3
O
4
,
CNT, concentric
annulus
1. Introduction
The problem of natural convection heat transfer in concentric and eccentric cylindrical annulus
has been attracting lots of attention due to its wide applications including heat exchangers,
thermal storage systems, solar collectors, water distillation and underground electric
transmission cables (Garg and Szeri, 1992; Khanafer and Chamkha, 2003; Ghernoug et al.,
2016; Mahmoud Aly and Asai, 2016; Afrand et al., 2017, Alipour et al, 2017). However,
modifying the heat transfer characteristics in the natural convection flows in the annulus is
always sought out due to a large number of applications (Afrand, 2017; Abhilash and Lab,
2018; Zhao et al., 2018, Mashayekhi et al., 2017). As one of the first studies, Crawford and
Lemlich (Crawford and Lemlich, 1962) studied the laminar natural convection flow between
concentric circular annulus for several diameter ratios and Grashof numbers at a constant
Prandtl number. Kuehn and Goldstein (1976, 1978) performed an investigation on natural
convection within a horizontal annulus. Different fluids of water and air were examined for
various Rayleigh numbers considering constant thermophysical properties. They reported good
agreement between the numerical and experimental results. Dutta et al. (2018) investigated the
impacts of tilt angle and fluid yield stress on the natural convection from an isothermal square
bar in a square annulus. They considered the effects of Rayleigh number, Prandtl number,
Bingham number, aspect ratio, and angle of inclination. The results showed that the Nusselt
3
number increases with increasing the Rayleigh number and decreases with increasing Bingham
number. Imtiaz and Mahfouz (2018) studied the natural convection flow in an eccentric annulus
containing heat-generating fluid. They found that the average dimensionless temperature of the
fluid intensifies with the increase in the heat generation parameter. Besides, it was reported that
the rate of heat transfer reduces for a fixed Rayleigh number as the inner cylinder moves
upward from negative eccentricity to positive eccentricity.
Heat transfer enhancement, especially in natural convection systems, is important for energy
saving purposes in industries (Eckert et al., 1987, Pourfattah et al., 2017, Rezaei et al., 2017).
The main limitation of conventional heat transfer fluids is their low thermal conductivity which
has a high effect in natural convection systems (Parvin et al., 2012, Akbari et al., 2016,
Sajadifar et al., 2017). Nanofluids have been used widely in the last two decades as one of the
advantageous methods to increase the heat transfer in different energy systems (Putra et al.,
2003, Akbari et al., 2015, Arabpour et al., 2018a, Shamsi et al., 2017). By using nanoparticles
in a base fluid, the heat transfer characteristics of the employed fluid can be modified (Vadasz
et al., 2005, Akbari et al., 2017, Arabpour et al., 2018b, Heydari et al,, 2017, Zadkhast et al.,
2017). There have been lots of studies on the heat transfer enhancement in natural convection
problems in the literature using nanofluids. Cadena-de la Peña et al. (2017) examined different
mineral oil-based nanofluids as a cooling fluid in an annulus between two cylinders and showed
heat transfer enhancement by the newly generated nanofluids. The inner cylinder acted as a
heat source while the outer one remained at a constant temperature. AIN and TiO
2
nanoparticles
were added to the oil-based fluid with various concentrations with and without oleic acid
treatment. They presented correlations for the Nusselt number in terms of Rayleigh number.
Selimefendigil and Oztop (2017) numerically assessed the natural convection heat transfer of
water-CuO nanofluid in a horizontally partitioned annulus in the presence of an inclined
magnetic field. They considered a conductive partition with different thickness and thermal
4
conductivity. The results demonstrated that the heat transfer enhances by increasing the
thickness of the conductive partition, Rayleigh number and inclination angle while reduces by
decreasing Hartmann number. Siavashi and Rostami (2017) numerically examined the natural
convection heat transfer of non-Newtonian water-Al
2
O
3
nanofluid within a cylindrical annulus
with a concentric circular heat source covered with a conductive porous layer. The results
revealed that the non-Newtonian nanofluid has a higher Nusselt number than the other studied
cases. Li et al. (2018) investigated the influence of radiative heat transfer on
magnetohydrodynamic free convection of a water-Fe3O4 nanofluid in a sinusoidal annulus.
They showed a decrease in the average Nusselt number with the increase of buoyancy force,
Hartmann number and numbers of undulations. Miroshnichenko et al. (2018) studies natural
convection in an open inclined cavity for cooling heat generation elements using a water-Al
2
O
3
nanofluid. They studied different effective parameters of the system in order to minimize the
average temperature of the heater and showed the advantageous effect of alumina nanoparticles
in the base fluid.
To the best knowledge of the authors, there are not any archival publications considering the
detailed behaviour of the natural convective heat transfer and entropy generation of hybrid
nanofluid in a concentric annulus. In this paper, the problem of two-dimensional natural
convection of water-Fe
3
O
4
/CNT hybrid nanofluid between two horizontal concentric cylinders
is investigated. The inner cylinder surface is kept at a constant temperature which is higher
than the outer cylinder temperature. The effects of nanoparticles volume concentration and
Rayleigh number on the streamlines, isotherms, average Nusselt number as well as the local
and global thermal entropy generation rate, frictional entropy generation rate and total entropy
generation rate are analysed.
2. Physical properties of nanofluid
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The water-based hybrid nanofluid containing TMAH coated Fe
3
O
4
nanoparticles and GA
coated CNTs is synthesized by mixing the required amount of water-Fe
3
O
4
nanofluid and
water-CNT nanofluid, followed by sonication of the mixture for 5 min. The water-Fe
3
O
4
nanofluid was prepared by utilizing the technique proposed by Berger et al. (1999) and the
water-based CNT nanofluid was synthesized via the method described by Garg et al. (2009).
The details of the preparation and characterization of the hybrid nanofluid can be found in the
author’s previous work (Shahsavar et al., 2016). The interaction between the TMAH and GA
molecules results in the physical attachment of the Fe
3
O
4
and CNT nanoparticles.
After careful preparation and characterization, a series of experiments were carried out to
obtain the thermophysical properties of the hybrid nanofluids containing different
concentrations of the Fe
3
O
4
and CNT nanoparticles. The volume concentration of the Fe
3
O
4
and CNT nanoparticles in the prepared nanofluid samples as well as the density (
), specific
heat (
), viscosity (
), thermal conductivity (
) and thermal expansion coefficient
(
) of these hybrid nanofluids are presented in Table 1.
Table 1. Characteristics of the studied nanofluid samples.
sample name
Fe
3
O
4
vol.%
CNT
vol.%
0.5%FF
0.5
0
1016.77
4093.83
0.001042
0.695
0.000256
0.7%FF
0.7
0
1024.67
4060.29
0.001300
0.728
0.000255
0.9%FF
0.9
0
1032.58
4027.27
0.001534
0.749
0.000254
0.9%FF+0.45%CNT
0.9
0.45
1037.54
3996.40
0.001755
0.839
0.000253
0.9%FF+0.9%CNT
0.9
0.9
1042.50
3965.83
0.001804
0.856
0.000252
0.9%FF+1.35%CNT
0.9
1.35
1047.47
3935.55
0.001855
0.887
0.000251
3. Model configuration
