CC BY
13
AZERBAIJAN CHEMICAL JOURNAL № 3 2023 ISSN 2522-1841 (Online)
ISSN 0005-2531 (Print)
UDC 544.3
NUMERICAL ANALYSIS OF THE HEAT TRANSFER AND THE ENTROPY
GENERATION FOR A CuO-AhO3-WATER HYBRID NANOFLUID FLOW THROUGH
AN EXTENDED CURVED DUCT
11 2 Djamila Derbal , Mohamed Bouzit , Abderrahim Mokhefi
1 Laboratory of Maritime Sciences and Engineering LSIM Faculty of Mechanical Engineering, University of Science and Technology of Oran, Mohamed Boudiaf, El Mnaouar, B.P.1505, 31000,
Oran, Algeria
djamila.derbal@yahoo.com Mechanics, Modeling and Experimentation Laboratory L2ME, Faculty of Sciences and Technology, Bechar University B.P.417, 08000, Bechar, Algeria abderahimmokhefi@yahoo.fr
Received 17.03.2023 Accepted 12.04.2023
The present paper focus on the theoretical analysis of the convective heat transfer and the irreversibility state of a laminar flow of a hybrid nanofluid inside a extended curved duct of circular cross section. This nanofluid is obtained from the suspension of the Al2O3 and CuO nanoparticles in the pure water. The flow of the nanofluid start from a narrowed part of a curved duct of a semi-circular shape, its enlarged part is subjected to a uniform hot temperature. The present analysis deals with highlighting the impact of some parameters namely: Dean number (13.83 < De < 55.33), Richardson number (0 < Ri < 0.1) as well as the effect of the hybrid nanoparticles on the heat transfer rate and the generated entropy. The resolution of the governing equations that include mass, momentum and energy has been performed by the use of the finite element method. The results have shown that the rate of the heat exchange rise according to the augmentation of the Dean number and the hybrid nanofluid volume fraction. However, the flow system irreversibility is more important in the case of the highest Dean number and volume fraction. Moreover, a comparison between different simple and hybrid nanofluids has demonstrated that the latter is more efficient especially for technological and economic reasons.
Keywords: hybrid nanofluid, heat transfer, entropy generation, curved duct, laminar flow.
doi.org/10.32737/0005-2531-2023-3-26-38
Introduction
Fluid flow in curved pipes and ducts is considered one of the most fascinating and complex transport phenomena that attract the attention of researchers in different study fields. Indeed, it is uncommon to find an industrial application that is not hardly devoid of curved pipes, especially in the chemical, petrochemical, aeronautical, thermal industries... etc. [1, 2]. In the chemical and petrochemical industry, curved pipes and ducts are often used as a means of mass transport and also as a cooling or heating process [3]. Given the centrifugal force that the flow undergoes in the curved parts of these systems, co-rotating loops called Dean vortices develop at the level of the transverse planes of these ducts [4-6]. As a means of thermal application, curved pipes and ducts are
considered as important equipment due to their existence in serpentines and spirals pipes intended for heating or cooling processes [7-9]. In these applications, nanofluids are nanosus-pensions in which metallic or oxidometallic nanoparticles are suspended in a base fluid, in particular pure water. Thanks to their chemical and thermal characteristics, they are of enormous importance for improving heat transfer, especially in cooling processes [10, 11]. For technological and economic motivations, researchers in this field have introduced another type of nanofluids called hybrids [12, 13]. It requires a suspension of several metallic or oxidometallic types of nanoparticles in the same base fluid. This technique allows to benefit from the chemical and thermal advantages of each nanoparticle and is placed in the framework of an optimization of heat transfer efficiency.
Several studies by theoretical or experimental ways have been conducted in the literature in the aim of highlighting the thermal and hydrodynamic effects of nanofluids on the flow within curved pipes and ducts. Indeed, most of these studies have shown that the use of this type of suspensions is thermally efficient [14-18].
The present study deals with a theoretical contribution to the study of a hybrid nanofluid behavior (Al2O3-CuO-water) flowing in a curved duct of a circular cross-section. Similar to the case of straight ducts where enlargements causing the flow connection are equipped [19, 20], the present curved duct is equipped with an abrupt extended cross-section. The purpose of this investigation is to highlight the effect of this hybrid nanosuspension on the heat transfer enhancement and on the irreversibility of this thermo-hydrodynamic system. In view of the existence of several parameters controlling the study, the impact of curvature, buoyancy and nanoparticles hybridization are examined at the hydrodynamic, thermal and entropic levels.
Problem description
In this study, the hybrid nanofluid [21] composed of alumina nanoparticles (Al2O3) and copper oxide nanoparticles (CuO) flows inside a duct system containing a curved part with a brusquely enlarged cross section as shown in Figure 1. The percentage of the two oxidome-tallic types of nanoparticles in the amount suspended in pure water are equal (50%-50%). Moreover, in order to compare the thermal and entropic performance of this hybrid type of
nanofluid, it was considered useful in this investigation to examine nanofluids with Al2O3 and CuO nanoparticles suspended independently in pure water as well as pure water as reference case.
Let us consider a volume fraction p of hybrid nanoparticles suspended in pure water. If we consider that Vo presents the volume of different substances, p denotes nanoparticles and f denotes the base fluid (pure water), hence, it can be seen that the volume fraction of the nanoparticles is calculated by [21]:
Vo
9 =
Vo +Vo.
p f
, H> = <-Pe
+ H>
CuO
(1)
I/o,
Vo„
% =
Vo +Vof
=
Vo + VoT
p f
(2)
According to the laws of standard and nanometric suspension, the different thermos-physical properties of the hybrid nanofluid are functions of the volume fraction as well as of the particular volume fraction of each oxido-metallic type of the nanoparticles. Based on the overall volume fraction of the nanoparticles, the effective density (pnf), dynamic viscosity (unf), thermal conductivity (&nf), specific heat (Cpnf) and thermal expansion (ffnf) of the hybrid nanofluid are respectively given by [22, 23]:
Heated wall
(a) Extended curved duct
2ai
y
/ /yRc
x j
: e(N, x
2a2
(b) Longitudinale section
(c) Cross-section
Fig. 1. Geometry of the studied extended curved duct.
p
Л, f = + (1 - 4>)p<
^nf = »fi - V)
-2.5
к
nf
k{ fc+2 k{+cp(k{-kp)
{рСр)ы=фСр)+{1-^){рСр\
(3)
(4)
(5)
(6)
(7)
The thermophysical properties of Al2O3 and CuO hybrid nanoparticles are calculated based on each particular fraction as follows [13]:
^p = ^ai2o/ai2o3 + "PcuoPcuo
= VaIA/VO. + ^CuO^CuO
3 2 3
^K = ^оД^ + ^CucAuO
CuO
^p = ^Al2oAlA + ^CucAuO
(8) (9) (10)
(11) (12)
The thermophysical properties of the nanoparticles (Al2O3 and CuO) and the base fluid (pure water) are mentioned in Table 1.
Inside the curved part of the duct system the hybrid nanofluid flows from the narrowed to the extended part with an initial uniform inlet velocity u0 and a cold temperature (Tc). In addition, the duct extended part boundary is maintained at a uniform hot temperature (Th).
However, the other walls are assumed to be adiabatic, see Figure 1. The curvature radius of the investigated duct is Rc. In fact, it presents a medium value between the duct inner (Rin) and outer (Rout) radiuses. The diameters of the narrowed and the extended sections are D and 2D, see Figure 1.
Governing equations
Within the curved duct, the flow of the hybrid nanofluid takes place in a laminar regime which corresponds to a Reynolds number generally less than 200. The operating fluid was taken Newtonian and incompressible whereas flowing in a steady regime. Therefore, the numerical simulation is effectuated based on the conservation balances of the fluid mass, its momentum and its thermal energy. It should be noted that the flow has: no chemical reactions, negligible external forces, dilute mixture, negligible viscous dissipation, negligible radiative heat transfer, and local thermal equilibrium between nanoparticles and base fluid. Moreover, the thermophysical proprieties of the nanofluid are assumed all constants with except to the density which vary as a function of the temperature in the buoyancy term according to Boussinesq approximation [24]. If v = (u, v, w) presents the nanofluid velocity vector in a Cartesian referential (Oxyz), T its temperature and p its pressure at in any position (x, y, z) of the duct, the above balances are respectively given by:
V.(pnfv) = 0 (13)
(v.V)v = - — V.(p + ^nfVv)
Pat (14)
-g fUT~TJ
(рСр)ъ.УТ = кЪ2Т (15)
Table 1. Thermophysical properties the nanoparticles and the base fluid
Properties Density [kg/m3] Thermal capacity [J/(kg.K)] Thermal conductivity [W/(m.K)] Dynamic viscosity [kg/(m.s)] Thermal expansion [10-5.1/K]
Water (f) 997.1 4179 0.613 0.001003 21.0
M2O3 (p) 3970 765.0 40.00 0.85
CuO (p) 6500 540.0 18.00 0.85
Where g is the gravity vector: g = (0, 0, -g). In order to generalize the governing equation, they are transformed to a dimension-less form introducing a set of dependent and the independent dimensionless variables defined as follow:
e =
t-Tc
Th-Tc
D (16)
P ,K
' nf o
The dimensionless form of the governing equation is:
V.v = 0
v 1 -, (V.V)V = -V.P + — V V
7/, Re
g (Pß\
■ me
9 P.A
a , 1 9
v.(ve) = -v2e
a. Re. Pr
(17)
(18)
(19)
Where a and v present respectively the fluids thermal diffusivity and the cinematic viscosity. The dimensionless number Re, Pr and Ri appearing in the dimensionless form of the governing equation are respectively: Reynolds number, Prandtl number and Richardson number. They are respectively given by:
Ri =
9ßt(Th-TB]
k
(20)
Another dimensionless number called Dean number characterizes the influence of the duct curvature radius. This number gives more information about the formation of two corotating vortices at the transverse planes. As a function of Reynolds number, the Dean number is defined by:
De = Re. — (21)
V
R
Boundary conditions
Let us consider that n presents the normal vector, hence, the system of dimen-
sionless balance equations has the following boundary conditions:
Inlet: V.n = 1 and 0 = 0 (22)
Outlet: P = 0 and (VB).n = 0 (23)
Adiabatic boundary: V.n = (VB).n = 0, (24) Enlarged duct boundary: V.n = 0 , 8 = 1 (25)
Heat exchange rate
The calculation of the dimensionless Nusselt number allows to quantify the heat transfer rate within the curved duct for different operating conditions. Indeed, it identifies the efficiency of the convective heat transfer mode compared to the conductive mode for different types of nanoparticles, different flow velocity and different thermal differences. At any arc 0 < $ < 2n of the circumference of the curved duct cross section, it is determined by the flowing expression:
k.
Nu = -^(V6).n
k.
(26)
The average value of the Nusselt number on the hot wall provides a global overview of the thermal efficiency at the enlarged curved duct, where A presents the area of this wall:
Nu =--
ave
J Nu d A with A =
71 R
_c_
2D2
(27)
Entropy generation
In the present study, the system irreversibility is presented through heat transfer and fluid friction. Thus, the total entropy sgen generation is the sum of the entropies due to the heat transfer sHT, and to the fluid friction sFF [25, 26]. For an average temperature T0, it is given by:
(28)
Sgen ~ SHT + SFF
k ß ,
o 0
(29)
The dimensionless generated entropy Sgen is consequently given by:
= (V0)2 + *(VV : VV)
u
0
2
U
0
with x presents a dimensionless factor that characterizes the entropy generated by the fluid friction:
X =
Kr^Tf
(31)
The Bejan number [26] gives a view on the dominance of the reversibility of the implemented flow system. Indeed, it allows to specify the entropy rate generated by the heat transfer with respect to the global entropy generation. It is given by:
Be =
Sr.
sr
(32)
Numerical steps
The governing equations including boundary conditions have been numerically solved using the finite element method based on the Garlkin discretization. After having chosen a suitable mesh of globally tetrahedral shape and effected a test of independence of the theoretical results from the chosen grid, we opted for a mesh containing 1234560 elements and 1254892 boundary elements. In addition, to ensure the fluidity of the flow in the vicinity of the curved duct boundaries, a boundary layer of prismatic shape was introduced in this area, see Figure 2. The criterion of convergence relates to the absolute error strictly less than 10-6 of each
dependent variable, namely the velocity components, temperature and pressure.
In order to ascertain the numerical results, a validation with the results of the literature has been carried out. Indeed, comparing the values of the nanofluid velocity along a radial line of the longitudinal plane of the curved duct with circular section obtained from the present study with those obtained from the reference [8], an excellent agreement has been noted, see Table 2.
Discussion of the results
The results obtained from the numerical simulation of the thermal, hydrodynamic and entropic behavior of the hybrid nanofluid are presented in this section. They take the form of velocity contours and streamlines, isotherms as well as isentropic at the level of the transverse plane corresponding to the 1350 angle.
The influence of different parameters is analyzed on these behaviors namely: the influence of curvature or even inertia (23.83 < De < 55.33), buoyancy (0 < Ri <0.1) and hybridization compared to the mono-nanoparticle case. Furthermore, for further analysis, the heat transfer rate is investigated for different volume fractions (0 < p <0.1) and Dean numbers of the hybrid nanoparticles compared to using pure water.
Fig. 2. Mesh of the curved duct with enlarged cross section.
Table 2. Comparison of the velocity obtained from the present work with the literature data
Dimensionless diameter 00.00 00.20 00.40 00.60 00.80 01.00
Velocity from Present work 00.00 0.728 1.098 1.340 1.651 0.132
Velocity from Reference [8] 00.00 0.712 1.073 1.378 1.666 0.145
It should be noted that the basic parameters used in this simulation are respectively: De = 41.5 (Re =150), Ri = 0, ф = 0.04 (ФА1203 = фсио = 0.02) and Pr = 6.8. The calculation of the Bejan number for all simulation cases took a value close to Be = 0.99 which means the predominance of entropic generation due to heat transfers over the friction of the nanofluid in our curved duct system.
Influence of curvature
The influence of the curvature actually corresponds to the influence of the duct curvature radius (Rc) on the formation of vortices in the transverse planes. In dimensionless sense,
it is represented by the influence of the Dean (or Reynolds) number.
From Figure 3, the hydrodynamic, thermal and isentropic structures are illustrated for various Dean number. It appears that in addition to the development of the Dean vortices, the increase of this number up to 55.33 leads to the formation of two relatively weak co-rotating vortices accompanied by a significant increase in the nanofluid velocity especially in the vicinity of the outer curvature radius. In this zone, the thermal boundary layer becomes weaker where the temperature decreases significantly according to the Dean number.
Fig. 3. Velocity, streamlines, temperature and global entropy generated for different Dean number.
(a) Nuselt number
0 1 2 3 4 5 6
♦
(b) Average entropy
Fig. 4. Local Nusselt number and local generated entropy along the section circumference for different Dean number.
15
10
J 1 2 3 4 5 6
Ф
In this case, the overall entropy generation is more important in the vicinity of the outer radius zone and almost absent in the middle of the measurement section. Indeed, the maximum dimensionless entropy increases from 2.3 to 19.1 for an increase of the Dean number from 23.83 to 55.33, however, it remains almost null in the middle of the section. This indicates that the present thermo-hydrodynamic system becomes more and more irreversible when the duct curvature radius decreases.
The local Nusselt number along the cross-section circumference (1350) shown in Figure 4 (a) indicates that the heat exchange rate between the hot curved wall and the cold fluid increases explicitly according to the Dean number. Moreover, regardless the Dean number, it decreases symmetrically from the outer radius to the inner radius of the curved duct. Indeed, the decrease of the thermal boundary layer thickness in the vicinity of the outer radius due to the effect of inertia favors the forced convection rate in this zone, which improves the heat transfer. This is consistent with a significant cooling situation. As for the variation of the local entropy along the measurement circumference, it is in agreement with the variation of the Nusselt number. In fact, a reversible situation corresponds to more homogeneous temperature distribution and consequently low thermal gradients. This thermal gradient can be observed in the vicinity of the inner radius, especially in the case of small curvature radius, see Figure 4 (b).
The determination of the average heat exchange rate through the average Nusselt number at the extended hot wall allows to identify the percentage of cooling improvement as a function of the Dean number. Indeed, an improvement of almost 124% accompanied with an entropic increase of almost 160% has been recorded by increasing the Dean number from
the value of 23.83 to the value of 55.33. This indicates, that a thermal enhancement due to curvature or inertia effects is accompanied with an important irreversibility, see Table 3.
Influence of buoyancy
The buoyancy force or simply the natural convection schematizes the movement of hybrid nanofluid within the curved duct widened according to the direction of gravity. Indeed, the hot fluid moves upwards while the cold fluid moves downwards which causes the formation of a vertical loop which unites with Dean vortices as well as with the vortex due to the extension of the duct.
The Richardson number puts forward the impact of buoyancy through the increase of the difference between the fluid cold temperature and the wall hot temperature.
Figure 5 highlights the radical changes in the behavior that the hybrid nanofluid flow is subjected to at the measurement plane with increasing buoyancy force. The two diametrically symmetrical Dean vortices (with respect to the horizontal plane) appearing in the case of a purely forced convection (Ri = 0) change shape by uniting with the vertical streamlines due to buoyancy. Indeed, the symmetrical shape is totally lost with the increase of the Richardson number. Moreover, the maximum velocity of the nanofluid increases especially in the low side of the outer radius neighborhood. In fact, the thermal profile and the centrifugal force are the factors causing this kinetics. Due to the increase of the temperature in the section upper part cause the reduction of the thermal boundary layer thickness in the fourth quadrant of the measuring section.
On the other hand, the generated entropy increases with the increase of the Richardson number especially in the vicinity of the borders.
Table 3. Average Nusselt number for different Dean number
Dean number 13.83 27.67 41.50 55.33
Average Nusselt number 1.386 2.105 2.653 3.111
%Heat rate 51.42 91.30 124.3
Average generated entropy 1.586 2.627 3.440 4.129
% Entropy variation 102.5 116.8 160.3
Whatever the Richardson number, along a direct turn, the heat transfer rate decreases in the measurement section going up from the outer radius and then decreases. In addition, the Richardson number disfavors the heat transfer rate along the first quadrant, see Figure 6 (a). Nevertheless, from the data of the Table 4, the overall heat transfer rate is favored by the buoyancy force with a rate of almost 14% in the case of Ri = 0.1 compared to the case of no buoyancy force (Ri = 0). In addition, the irreversibility of the system follows the thermal
behavior Figure 6 (b). Indeed, an increase of the entropy average value of almost 12% has been noted with the increase of the Richardson number to 0.1, see Table 4.
Influence of nanoparticles
In this section, we intend to study the influence of alumina (Al2O3), copper oxide (CuO) and hybrid nanoparticles (Al2O3- CuO) suspended in pure water. A volume fraction of 0.04 is used for the different suspensions with an equal percentage in the hybrid case.
Fig. 5. Velocity, streamlines, temperature and global generated entropy for different Richardson number.
—■- Ri = —A- Ri = —T- Ri = —•- Ri = .025 .075 Ss A
^ t 2
\f
0 1 2 3 4 5 6
♦
(a) Nuselt number
2 4
♦
(b) Average entropy
Fig. 6. Local Nusselt number and global generated entropy along the section circumference for different Richardson number.
4.5
3.5
Z 2.5
1.5
Figure 7 presents the profiles of velocity, of temperature as well as of the entropy generated by the thermo-hydrodynamic system of the curved duct for the different mentioned nano-suspensions, namely pure water. Overall, the addition of the different types nanoparticles does not affect the shapes of the presented profiles except for a relative increase of the velocity in the case suspension especially when using CuO nanoparticles. Moreover, the thermo-hydrodynamic system of the curved duct shows a relatively higher irreversibility in this case compared to the other nano-suspensions (Al2O3-water and hybrid nanofluid). However, pure water presents the least irreversible system compared to the other systems corresponding to the lower entropic generation.
For a more in-depth analysis, in Figure 8, the local Nusselt number and the generated entropy are presented along the circumference of the measurement section in the direct direction for the different suspensions, namely pure water. It has been observed that the heat transfer rate increases relatively with the addition of nanoparticles especially in the vicinity of the outer radius. The CuO nanoparticles show the best heat transfer rate followed by the CuO-Al2O3 hybrid nanoparticles. However, the low heat transfer rate has been noted in the case of using pure water. As for the entropy generation along the measurement direction adopted for the Nusselt
number, it is found that the thermo-hydrodynamic system tends to be more irreversible in the case of CuO-water suspension keeping the same order as that of the discussed heat transfer enhancement, see also Table 5.
At a Dean number of 41.5, the overall heat transfer rate with respect to pure water presented by the average Nusselt number in the expanded part of the duct increases in the case of using CuO nanoparticles with a percentage of 6.75% and in the case of using Al2O3 nanoparticles with a percentage of 5.95%, see Table 5. However, a percentage of 6.49% has been recorded in the case of use of hybrid nanoparticles. This rate is close to 67.5% of the thermal improvement rate obtained by using CuO nanoparticles.
Based on this result, the consideration of hybrid nanofluids yields an acceptable efficiency, especially on the economic level where CuO nanoparticles are the costliest.
Indeed, half (50%) of the cost can be recovered with a thermal reduction of 32.5%. A further analysis is to compare the heat transfer rate in the hybrid nanofluid use case against pure water and against single nanoparticle suspensions for different flow velocities and nanoparticle volume fractions. Hence, we found it useful to compare the heat transfer rate in terms of the average Nusselt number for different Dean numbers (13.83 < De < 55.33) and different volume fractions (0 < 9 < 0.1).
Table 4. Average Nusselt number for different Richardson number
Richardson number 00.00 0.025 0.075 00.10
Average Nusselt number 2.653 2.733 2.960 3.050
% Heat rate 3.010 9.370 14.96
Average generated entropy 3.440 3.527 3.758 3.844
% Entropy variation 2.550 9.260 11.76
Table 5. Average Nusselt number for different nanoparticles
Nanofluids H2O Al2O3-H2O CuO-H2O Al2Os-CuO-H2O
Average Nusselt number 2.491 2.639 2.659 2.653
% Heat rate -— 5.950 6.750 6.490
Average generated entropy 3.352 3.416 3.462 3.440
% Entropy variation ---- 1.879 3.281 2.625
Fig. 7. Velocity, streamlines, temperature and global entropy generated for different nanoparticles.
0123456 0123456
♦ ♦
(a) Nuselt number (b) Average entropy
Fig. 8. Local Nusselt number and global generated entropy along the section circumference for different nanoparticles.
Figure 9 shows the histograms of the average Nusselt number as a function of different natures of nanoparticles: CuO, Al2O3 and hybrid nanoparticles for various volume fractions and various Dean numbers. As the Dean number can show the effect of inertia (see equation (21)), we considered that the change of Dean number reflects Reynolds number and thus the flow inlet velocity.
At low nanofluid flow velocities (Re = 50) the heat transfer rate appears almost identical especially in the case of CuO-water and hybrid nanofluid. Therefore, the use of hybrid nanofluid
at low flow velocity regardless of the volume fraction is very beneficial in economic terms due to the cost reduction and keeping the same heat transfer rate. As the inlet flow velocity increases (Reynolds increases) the difference between the efficiency of CuO-water nanofluid and hybrid nanofluid increases especially at higher volume fractions. Consequently, laminar flow at moderate velocities and moderate volume fractions of the hybrid nanofluid can present cases of near-equality in terms of thermal efficiency between the different nanofluids.
De = 41.5 (Re = 150) De = 55.33 (Re = 200)
Fig. 9. Average Nusselt number for different Reynolds number and nanoparticles volume fraction.
Conclusion
The present study concerns a contribution to the numerical study of the thermal, hydrodynamic and entropic behavior of a hybrid nanofluid (Al2O3-CuO-water) flowing in a curved duct with an abruptly enlarged section. It deals with highlighting the effect of the curvature (still of the inertia), of the buoyancy as well as of the nanoparticles namely: Al2O3, CuO and Al2O3-CuO on the flow stream, isothermal and isentropic distributions. The essential points of the present study can be summarized as follows: • Through the Dean number expressing the radius of curvature effect of the duct, it has
been found that the heat transfer rate as well as that of entropy generation increases. In other words, the thermo-hydrodynamic system of the curved duct is characterized with a good heat transfer accompanied by a significant irreversibility that increases in the centrifugal force direction. The thermal buoyancy strongly affects the hybrid nanofluid behavior, especially in terms of flow and vortex formation. Indeed, the Dean vortexes existing at the transverse planes unite with the buoyancy stream and form a more complex vortex. On the other hand, the overall heat transfer and entropy is
found to be more important as the Richardson number increases.
• The best heat transfer rate has been obtained in the case of CuO nanoparticle suspension with a rate of 6.75% followed by Al2O3-CuO suspension with a rate of 6.49% compared to pure water. Here, the thermo-hydrodynamic irreversibility is directly proportional to the heat transfer rate.
• At a Dean number of 41.5, the hybrid nanofluid shows a percentage improvement of 67% over the Al2O3-water nanofluid. This percentage tends to become similar to that obtained by the CuO-water nanofluid as the inlet velocity of the nanofluid increases on the one hand and the volume fraction of the nanoparticles decreases on the other hand.
• Given that CuO nanoparticles are the costliest, the use of the hybrid nanofluid presents an economical case. Indeed, at moderate flow velocities and volume fractions, a very satisfactory thermal efficiency can be achieved with a reduction of half the cost of CuO nanoparticles.
References
1. Rudolf P., Desova M. Flow characteristics of curved ducts. Applied and Computational Mechanics. V. 5. No 1. P. 255-264.
2. Xiaoyun W., Sangding L., Kyoji Y., Shinichiro Y. Vortex Patterns of the Flow in a Curved Duct. Energy Procedia. 2011. V. 12. P. 920 - 927
3. Mokeddem M., Laidoudi H., Bouzit M. 3D Simulation of Dean Vortices at 30° Position of 180° Curved Duct of Square Cross-Section under Opposing Buoyancy. Defect and diffusion forum. 2018. V. 389. P. 153 - 63.
4. Dean W. R. XVI. Note on the motion of fluid in a curved pipe. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 1927 V. 20. No 4. P. 208 - 223.
5. Dean W.R. Fluid motion in a curved channel. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 1928. V. 121. No 787. P. 402-420.
6. Dean, W. R., Hurst J. M. Note on the motion of fluid in a curved pipe. Mathematica. 1959. V. 6. No 1. P. 77-85.
7. Ahadi M., Abbassi A. Exergy analysis of laminar forced convection of nanofluids through a helical coiled tube with uniform wall heat flux. International J. Exergy. 2013. V. 13. P. 21 - 35.
8. Akbarinia A., Behzadmehr A. Numerical study of laminar mixed convection of a nanofluid in
horizontal curved tubes, Applied Thermal Engineering. 2007. V. 27. P. 1327 - 1337.
9. Khairul M.A., Saidur R., Rahman M.M., Alim M.A., Hossain A., Abdin Z. Heat transfer and thermodynamic analyses of a helically coiled heat exchanger using different types of nanofluids. International Journal of Heat and Mass Transfer. 2013. V. 67. P. 398 - 403.
10. Choi S.U.S., Eastman J. A. Enhancing thermal conductivity of fluids with nanoparticles. International mechanical engineering congress and exhibition, San Francisco. 1995. CA (United States). P. 99-105.
11. Bianco V., Manca O., Nardini S., Vafai K. Heat Transfer Enhancement with Nanofluids. 2015. 1e ed. New York: CRC Press Taylor & Francis Group.
12. Madhesh D., Parameshwaran R., Kalaiselvam S. Experimental investigation on convective heat transfer and rheological characteristics of Cu-TiO2 hybrid nanofluids. Experimental Thermal and Fluid Science. 2014. V. 52. P. 104 - 115.
13. Hesam M., Ehsan A., Hamid S., Milad M., Armin E. Numerical analysis on laminar forced convection improvement of hybrid nanofluid within a U-bend pipe in porous media. International J. Mechanical Sciences. 2020. V. 179. P. 105659.
14. Aieel R. K., Sopian K., Zulkifli R., Fayyadh S. N., Hilo A. K. Assessment and analysis of binary hybrid nanofluid impact on new configurations for curved-corrugated channel. Advanced Powder Technology. 2021. V. 32. No 10. P. 3869 - 3884.
15. Hayat T., Aslam N., Alsaedi A., & Rafiq M. Numerical study for MHD peristaltic transport of Sisko nanofluid in a curved channel. International Journal of Heat and Mass Transfer. 2017. V. 109. P. 1281 - 1288.
16. Hayat T., Tanveer A., & Alsaedi A. Numerical analysis of partial slip on peristalsis of MHD Jeffery nanofluid in curved channel with porous space. Journal of Molecular Liquids. 2016. V. 224. P. 944-953.
17. Wenqian L., Ruifang S., Jianzhong L. Heat Transfer and Pressure Drop of Nanofluid with Rod-like Particles in Turbulent Flows through a Curved Pipe. Entropy. 2022. V. 24. P. 416.
18. Saba K., Abbasi F.M. Hall current and Joule heating effects on peristalsis of TiO2-Ag/EG hybrid nanofluids via a curved channel with heat transfer. Waves in Random and Complex Media. 2022.
19. Hussain S., Ahmed S. E. Unsteady MHD forced convection over a backward facing step including a rotating cylinder utilizing Fe3O4-water ferrofluid. J of Magnetism and Magnetic Materials. 2019. V. 484. P. 356 - 366.
20. Toumi M., Bouzit M., Bouzit F., Mokhefi A. MHD forced convection using ferrofluid over a backward facing step containing a finned cylinder. acta mechanica et automatica. 2022. V. 16 No 1. P. 70 - 81.
21. Ranga Babu J.A., Kiran Kumar K., Srinivasa Rao S., State-of-art review on hybrid nanofluids. Renewable and Sustainable Energy Reviews. 2017. V. 77. P. 551 - 565.
22. Maxwell J.C. A Treatise on Electricity and Magnetism. V. II, Oxford University Press, Cambridge, UK, 1873. P. 54.
23. Brinkman H.C. The viscosity of concentrated suspensions and solutions. J. Chem. Phys. 1952. V. 20. P. 571 - 581.
24. Huminic G., Huminic A., A numerical approach on hybrid nanofluid behavior in laminar duct flow
with various cross sections, Journal of Thermal Analysis and Calorimetry. 2020. V. 140 No 5.
25. Magherbi M., Abbassi H., Hidouri N., Ben Brahim A. Second law analysis in convective heat and mass transfer. entropy. 2006. V. 8. No 1. P. 1-17.
26. Sheremet M. A., Oztop H. F., Pop I., Abu-Hamdeh N. Analysis of Entropy Generation in Natural Convection of Nanofluid inside a Square Cavity Having Hot Solid Block: Tiwari and Das' Model. Entropy. 2016. V. 18. No 9.
GENÍSLONMÍS OYRÍ BORU VASÍTOSÍ ÍLO CuO-Al2O3-SU HÍBRÍD NANO-MAYE AXINI Ü£ÜN ÍSTÍLÍK MÜBADÍLOSÍ VO entropíya yaranmasinin roqomsal tohlílí
Camila Derbal, Mohammed Buzit, Abderahim Mohefi
Bu i§ konvektiv istilik otürülmasinin va dairavi en kasiyinin uzunsov ayilmi§ kanali daxilinda hibrid nanomayenin laminar axininin donmazlik vaziyyatinin nazari tahlilina hasr edilmi§dir. Bu nano maye tamiz suda AI2O3 va CuO nanohissaciklarinin suspenziyasindan alda edilmi§dir. Nano maye axini yarimdairavi ayri kanalin daralmi§ hissasindan ba§layir va onun geni§lanmi§ hissasi barabar isti temperatura maruz qalir. Bu tahlil bazi parametrlarin tasirini nazara alir, yani: Din adadi (13.83 < De < 55.33), Rigardson adadi (0 < Ri < 0.1), hamginin hibrid nanohissaciklarin istilik otürma süratina va yaranan entropiyaya tasiri. Kütla, impuls va enerji daxil olmaqla idaraedici tanliklarin halli sonlu elementlar metodundan istifada etmakla yerina yetirilmi§dir. Naticalar gostardi ki, istilik otürma sürati Din adadinin artmasi va hibrid nano mayenin hacm hissasindan asili olaraq artir. Bununla bela, axin sisteminin donmazliyi an boyük Din adadi va hacm fraksiyasinda daha vacibdir. Üstalik, müxtalif sada va hibrid nanomayelarin müqayisasi gostardi ki, sonuncular xüsusila texnoloji va iqtisadi sabablardan daha samaralidir.
Agar sozlar: hibrid nano-maye, istilik mübadibsi, entropiya yaranmasi, 3yri boru, laminar axin.
ЧИСЛЕННЫЙ АНАЛИЗ ТЕПЛООБМЕНА И ГЕНЕРАЦИИ ЭНТРОПИИ ДЛЯ ПОТОКА ГИБРИДНОГО НАНОФЛЮИДА Cu0-Al203-В0ДА ЧЕРЕЗ РАСШИРЕННУЮ ИЗОГНУТУЮ ТРУБКУ
Джамила Дербал, Мохамед Бузит, Абдеррахим Мохефи
Настоящая работа посвящена теоретическому анализу конвективного теплообмена и состояния необратимости ламинарного потока гибридной наножидкости внутри вытянутого изогнутого канала круглого сечения. Эта наножидкость получена из суспензии наночастиц Л120з и СиО в чистой воде. Поток наножидкости начинается из суженной части изогнутого канала полукруглой формы, а его расширенная часть подвергается равномерному воздействию горячей температуры. В данном анализе рассматривается влияние некоторых параметров, а именно: Число Дина (13.83 < De < 55.33), Число Ричардсона (0 < Ш < 0.1), а также влияние гибридных наночастиц на скорость теплопередачи и создаваемую энтропию. Решение управляющих уравнений, включающих массу, импульс и энергию, было выполнено с помощью метода конечных элементов. Результаты показали, что скорость теплообмена возрастает в зависимости от увеличения числа Дина и объемной доли гибридной наножидкости. Однако необратимость системы течения более важна в случае наибольшего числа Дина и объемной доли. Более того, сравнение между различными простыми и гибридными наножидкостями показало, что последние более эффективны, особенно по технологическим и экономическим причинам.
Ключевые слова: гибридная наножидкость, теплообмен, генерация энтропии, изогнутая трубка, ламинарный поток.
