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Entropy generation of boehmite alumina nanofluid flow through a minichannel heat exchanger considering nanoparticle shape effect
Accepted Manuscript Entropy generation of boehmite alumina nanofluid flow through a minichannel heat exchanger considering nanoparticle shape effect Abdullah A.A.A. Al-Rashed, Ramin Ranjbarzadeh, Saeed Aghakhani, Mehdi Soltanimehr, Masoud Afrand, Truong Khang Nguyen
PII: DOI: Reference:
S0378-4371(19)30112-8 https://doi.org/10.1016/j.physa.2019.01.106 PHYSA 20537
To appear in:
Physica A
Received date : 19 September 2018 Revised date : 29 December 2018 Please cite this article as: A.A.A.A. Al-Rashed, R. Ranjbarzadeh, S. Aghakhani et al., Entropy generation of boehmite alumina nanofluid flow through a minichannel heat exchanger considering nanoparticle shape effect, Physica A (2019), https://doi.org/10.1016/j.physa.2019.01.106 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Entropy generation of boehmite alumina nanofluid flow through a minichannel heat exchanger considering nanoparticle shape effect Abdullah A. A. A. Al-Rashed1, Ramin Ranjbarzadeh2,3, Saeed Aghakhani2, Mehdi Soltanimehr2, Masoud Afrand2,*, Truong Khang Nguyen 4,5,*
1-Department of Automotive and Marine Engineering Technology, College of Technological Studies, The Public Authority for Applied Education and Training, Kuwait 2-Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran 3- Modern Manufacturing Technologies Research Center, Najafabad Branch, Islamic Azad University, Najafabad, Iran 4-Division of Computational Physics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam 5-Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam * Corresponding author Email: [email protected] (M. Afrand) [email protected] (T. K. Nguyen)
*Corresponding Author at: Division of Computational Physics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam (T. K. Nguyen)
Abstract This paper aims to study the effect of nanoparticle shape on the entropy generation characteristics of boehmite alumina nanofluid flowing through a horizontal double-pipe minichannel heat exchanger. Boehmite alumina (γ-AlOOH) nanoparticles of different shapes (cylindrical, brick, blade, platelet, and spherical) are dispersed in a mixture of water/ethylene glycol as the nanofluid. The nanofluid and water flow in the tube side and annulus side of the 1
heat exchanger, respectively. The effects of the Reynolds number and nanoparticle concentration on the frictional entropy generation rate, thermal entropy generation rate, total entropy generation rate and Bejan number are numerically analyzed for different nanoparticle shapes. The obtained results demonstrated that the nanofluids containing platelet shape and spherical shape nanoparticles have the highest and lowest rates of thermal, frictional, and total entropy generation, respectively. Additionally, it was found that the rates of thermal, frictional, and total entropy generation increase with an increase in the Reynolds number, while the opposite is true for the Bejan number. Furthermore, it was inferred from the obtained results that the increase of nanoparticle concentration results in higher frictional and total entropy generation rates and lower Bejan number.
Keywords: Minichannel heat exchanger; Nanoparticle shape effect; Boehmite alumina nanofluid; Entropy generation; Second law of thermodynamics.
Nomenclature Bejan number
specific heat capacity (J kg-1 K-1) thermal conductivity (W m−1 K−1) pressure (Pa) temperature (K) velocity (m s-1)
,
local frictional entropy generation rate (W m-3 K-1)
2
,
local thermal entropy generation rate (W m-3 K-1)
,
local total entropy generation rate (W m-3 K-1)
,
global frictional entropy generation rate (W m-3 K-1)
,
global thermal entropy generation rate (W m-3 K-1)
,
global total entropy generation rate (W m-3 K-1)
Greek symbols viscosity (kg m-1 s-1) density (kg m-3) volume concentration (%) Subscripts base fluid
nanofluid Particle
1. Introduction Heat-exchangers are appliances used to transfer thermal energy from one fluid to another with different temperatures without direct contact of the fluids. They form a vital part of almost all the processes, including the oil and gas industry, fossil and nuclear power generation, refrigeration, desalination, and so on. They have always been important in various industries, but the rapid increase in energy demand over the past decades has led to an increase in their importance. 3
Therefore, it is essential to improve the efficiency of the heat exchangers. So far, several methods are proposed by researchers to augment the performance of heat exchangers such as using various fins and turbulators. However, several disadvantages, like increase in pressure drop, weight and volume of heat exchangers, are associated with these improvements that limit their usage. Another recently proposed method to enhance the heat exchanger performance involves the use of working fluids with higher thermal conductivity than the conventional heat transfer fluids such as water, oil, and ethylene glycol [1-15]. This goal can be achieved through the use of nanofluids, which are synthesized by dispersing nanometer-scale solid particles into base liquids such as water, oil, ethylene glycol, etc [16-25]. Ebrahimnia-Bajestan et al. [26] experimentally and numerically investigated the heat transfer characteristics of water-TiO2 nanofluid for use in solar heat exchangers. The experimental results demonstrated that the presence of 2.3% volume concentration increases the average heat transfer coefficient by 21%. Additionally, the numerical results revealed that the convective heat transfer coefficient augments with increase of nanoparticle concentration and Reynolds number, while it reduces with increase of particle size. Shahrul et al. [27] experimentally investigated the overall performance of a shell and tube heat exchanger filled with water-Al2O3, water-SiO2, and water-ZnO nanofluids. The results indicated that the use of water-ZnO and water-SiO2 nanofluids leads to the highest and lowest convective heat transfer coefficient and overall heat transfer coefficient, respectively. Kumar et al. [28] carried out experiments to reveal the effect of symmetric ( ~30°/30° and 60°/60°) and mixed ( ~30°/60°) chevron angles on the heat transfer performance in plate heat exchangers operated with water-ZnO nanofluid. The results demonstrated that the maximum increase in heat transfer performance is achieved at
~30°/60° for nanofluid with volume concentration of 1%. The 4
performance of thermoelectric cooling of electronic devices with water-Al2O3 nanofluid in a multiport minichannel heat exchanger was experimentally evaluated by Ahammed et al. [29]. Their study indicated about 40% enhancement in coefficient of performance of thermoelectric module using 0.2% nanofluid. Moreover, they reported a 9.15% reduction in the thermoelectric temperature difference between the hot and cold side using 0.2% nanofluid. Fsadni et al. [30] performed a numerical study to investigate the turbulent heat transfer and pressure drop characteristics of a helically coiled hybrid rectangular-circular tube heat exchanger with waterAl2O3 nanofluid. The results revealed that both the heat transfer coefficient and pressure drop augment with the nanoparticle concentration and curvature. Besides, they used a thermohydrodynamic performance index to evaluate the overall impact and found that the use of nanofluid can lead to an increase in the overall system performance. Literature survey shows that most research studies on the performance of heat exchangers operated with nanofluids are based on the first law of thermodynamics. Considering the fact that heat cannot be converted completely into work, it can be concluded that the quality of thermal energy should be taken into account. To this end, the second law of thermodynamics can be utilized to calculate the lost work arising from friction and heat transfer. Therefore, entropy production can be employed as a criterion to evaluate the performance of engineering devices. Up to now only very few attempts have been made to assess the second law performance of heat exchangers operated with nanofluids. Entropy generation analysis of graphene–alumina hybrid nanofluid in a multiport minichannel heat exchanger coupled with a thermoelectric cooler was experimentally performed by Ahammed et al. [31]. The results revealed that by increasing the Reynolds number from 200 to 1000, the total entropy generation reduces by 96.2%. Bahiraei et al. [32] numerically studied the thermal and frictional entropy generation rates during laminar 5
forced convective flow of carbon nanotube (CNT)-Fe3O4 hybrid nanofluid in a double-pipe minichannel heat exchanger. They reported that heat transfer and friction are the main reason of entropy generation at low and high concentrations, respectively. Shahsavar et al. [33] numerically assessed the effect of nanoparticle concentration and Reynolds number on the frictional, thermal and total entropy generation rates during flow of a new hybrid nanofluid containing CNTs decorated with Fe3O4 nanoparticles through a double-pipe minichannel heat exchanger. The results demonstrated that the total entropy generation rate increases with increasing the CNT concentration, Fe3O4 concentration, and Reynolds number. Several scholars have reported that the shape of nanoparticles has a significant impact on the thermophysical properties of nanofluids [34-36], and, consequently, their cooling performance. Investigating the studies conducted on the impact of using nanofluids on the hydrothermal and entropy generation characteristics of heat exchangers shows that the effect of nanoparticle shape has rarely been studied so far. The influence of different nanoparticle shapes (such as cylindrical, brick, blade, platelet, and spherical) on the hydrothermal and entropy generation characteristics of water based nanofluid containing boehmite alumina nanoparticles inside a shell and tube heat exchanger was investigated by Elias et al. [37]. It was found that, among the five nanoparticle shapes, cylindrical shape demonstrates better heat transfer performance. In another study, Elias et al. [38] analyzed the effect of different baffle angles and segmental baffle on the heat transfer and entropy generation characteristics of a shell and tube heat exchanger operated with boehmite alumina nanofluid containing five different nanoparticle shape (i.e. cylindrical, brick, blade, platelet, and spherical). The results depicted that the nanofluid having cylindrical shape nanoparticles has better overall heat transfer coefficient and entropy minimization rate at 20° baffle angle. Sheikholeslami and Bhatti [39] reported the impact of a uniform magnetic field on 6
water-CuO nanofluid flow inside a porous semi-annulus considering shape effects of nanoparticles (such as cylindrical, brick, platelet, and spherical). They observed that the platelet shape has the greatest heat transfer rate. The influence of different shapes of boehmite alumina nanoparticles on the thermoeconomic improvement of a shell and tube heat exchanger was determined by Hajabdollahi and Hajabdollahi [40]. The authors found that the nanofluid containing brick shape nanoparticles has the highest heat exchanger thermoeconomic parameters. To the best of author’s knowledge, there is not any study which investigate the effect of particle shape on the entropy generation characteristics of a nanofluid flowing through a double-pipe heat exchanger. Therefore, the present investigation is expected to fulfil this important research gap. The considered nanofluid is a suspension of boehmite alumina nanoparticles with different shapes (cylindrical, brick, blade, platelet, and spherical) in a mixture of ethylene glycol and water (50:50). The influence of nanoparticle concentration and the Reynolds number on the frictional entropy generation rate, thermal entropy generation rate, total entropy generation rate, and Bejan number are also evaluated.
2. Thermophysical properties of nanofluids In this study, the ethylene glycol and water mixture (50:50)-boehmite alumina nanofluids containing different shapes of nanoparticles are considered. Table 1 shows the thermophysical properties of the base fluid and nanoparticles. The density and specific heat of the studied nanofluids are given by Eqs. (1) and (2), respectively, which are based on the mixture theory: 1
(1)
7
1
,
,
,
(2)
where φ is the voluume concenntration. Alsso, subscrippts f, nf andd p refer to base fluid, nanofluid and nannoparticle, reespectively. Some scientists [441,42] have studied thee effect of nanoparticlle shape onn the therm mophysical propertiies of variouus nanofluidds and obseerved that thhe thermal cconductivityy and viscossity of the studied nanofluids are a functiion of nanoparticle shaape. Five typpes of nanooparticles with shapes of cylinndrical, brickk, blade, plaatelet, and sppherical aree studied in the present work. Fig. 1 shows a schemattic of the m mentioned nnanoparticlee shapes. Thhe thermal conductivitty of nanofl fluids with differennt nanoparticcle shapes, eexcept spherical, is giveen by the foollowing equuation [26,228]: 1 where
(3)
is constannt coefficiennt for differeent nanoparrticle shapess which is prresented in Table 2.
Table 1. Thermophyysical propertiies of boehmitte alumina andd mixture of etthylene glycoll and water at T=300 K [41,42]. Properrties
Boehmite alumina
Ethhylene glycol and water 50//50 mixture (550:50)
Density ((kg/m3)
30550
1067.5
Specific heaat (J/kg K)
6188.3
3300
Thermal conducttivity (W/m K K)
300
0.3799
D Dynamic viscoosity (kg/m s)
-
0.00339
8
Cylindrical
Brick
Blade
Platelet
Spherical
Fig. 1. Diverse particle shapes.
The thermal conductivity of nanofluids with spherical shape nanoparticle is given by using Eq. (4) [43]: 2
2
(4)
2
The viscosity of nanofluids with different nanoparticle shapes, except spherical, is calculated by using Eq. (5) [37,38]: 1 where
and
(5) are constant coefficient for different nanoparticle shapes which are presented in
Table 2.
Table 2. Constant coefficients defined in Eqs. (3) and (5) for the effect of nanoparticle shape on the thermal conductivity and viscosity of the nanofluid [37,38]. Type Platelets
2.61
37.1
612.6
Blades
2.74
14.6
123.3
Cylindrical
3.95
13.5
904.4
Bricks
3.37
1.9
471.4
The viscosity of nanofluids with spherical shape nanoparticle is determined by using Eq. (6) [37,38]:
9
1
(6)
.
3. Modeel configuraation 3.1. Geoometry and d boundaryy conditionss The schhematic view w of the geoometry conssidered in thhis work is displayed Fig. F 2. It is a doublepipe couunter-currennt minichannnel heat excchanger connsisting of ttwo concenttric tubes w with length of 1 m, inner diameeter of 1 mm m, and outerr diameter oof 2 mm. Hoot water andd cold nanoofluid flow throughh the annular region aand inner ttube, respecctively. Besides, zero relative pressure is employeed at the ouutlets of bothh tube and aannulus sidees and the ouuter wall off the heat excchanger is assumedd to be adiabbatic. Besiddes, the walll thickness of o tubes are neglected.
Fig. 2. The minichhannel heat exxchanger underr study.
3.2. Govverning equ uations For nanofluids, it iss often assum med that baase fluid andd nanoparticcles move with w a similarr velocity, m exists bettween them m. This asssumption is consideredd because and also thermal equilibrium
10
particles employed in nanofluids are very fine and are of nanometer order. According to above mentioned assumptions, the governing equations are given as follows: Conservation of mass: .
0
(7)
Conservation of momentum: .
.
(8)
Conservation of energy: .
.
,
where
is the velocity,
(9) is the pressure, and
is the temperature.
3.3. Entropy generation The entropy generation in the flow field comprises of two main parts; (i) frictional factors, and (ii) thermal irreversibility. The local thermal and frictional entropy generation rates can be obtained as [44], (10)
,
2
,
(11)
Moreover, the total entropy generation rate ( ,
,
,
) is obtained by the following equation: (12)
,
The global entropy generation rates are calculated by the integration of the local entropy generation rates over the whole domain as follows: 11
,
,
,
,
,
,
,
,
(13)
The Bejan number is a dimensionless number defined as the entropy generation ratio of the thermal entropy generation rate over the total entropy generation rate. That is: ,
(14) ,
3.4. Numerical method and validation In this contribution, computational fluid dynamics (CFD) methods incorporated with a finite volume method is utilized to solve the governing equations (7)-(9) along with the above mentioned boundary conditions. The second order upwind method is used for solving the momentum and energy equations. Pressure and velocity are coupled using Semi Implicit Method for Pressure Linked Equations (SIMPLE) algorithm. For all parameters, the convergence criteria is set to 10-6. In this study, a structured mesh is generated in the entire domain. Owing to severe velocity and temperature gradients adjacent to the walls, smaller elements are applied there. Five different grids are considered to check grid independency of the numerical results. The results of this study are listed in Table 3. As Reported in Table 3, a grid with 45 nodes radially for both the tube side and the annulus side of the heat exchanger, and 1000 nodes in longitudinal direction is selected as the best one.
Table 3. Mesh independence study for nanofluid flow with platelet shape nanoparticles at
and
%. In this table, the mesh resolution is reported as number of longitudinal nodes number of radial nodes in central
12
tube number of radial nodes in annulus. mesh ∆
800 40 40
900 40 40
1000 40 40
1000 45 45
1000 55 55
35.55
38.18
40.32
41.42
41.92
2367.34
2488.12
2598.71
2686.25
2717.23
Validation of the numerical analysis is accomplished by comparing the obtained numerical data for the Nusselt number with the experimental results of Duangthongsuk and Wongwises [45] for flow of water-TiO2 nanofluid in a double-pipe heat exchanger. Table 4 presents the results of this comparison and as can be seen, there is a good agreement between the results. Therefore, it can be said that the numerical method is valid and can be utilized for simulation of nanofluid behavior through the double-pipe heat exchanger.
Table 4. Comparison between results obtained from current study and experimental results [45]. Re 8900 10450 11820 13200 14500
Nu (experimental) 90.38 98.44 105.82 114.56 120.60
Nu (numerical) 85.82 98.90 106.50 114.66 123.51
Error (%) 5.05 0.47 0.64 0.09 2.41
4. Results and discussion Investigations are carried out to find the effect of various shapes of boehmite alumina nanoparticles (cylindrical, brick, blade, platelet, and spherical) on the entropy generation due to fluid flow and heat transfer inside a double-tube minichannel heat exchanger. The numerical simulations are performed at nanoparticle concentrations of 0.5 to 2.0%, Reynolds numbers of
13
500 and 2000 for the tube side, and constant Reynolds number of 1000 for the annulus side. Besides, the inlet temperature of the nanofluid and water is set at 298 K and 308 K, respectively. Fig. 3 shows the effect of nanoparticle shape on the thermal conductivity of boehmite alumina nanofluid at various concentrations. As is observed, the nanofluid containing cylindrical shape nanoparticles has the highest and the nanofluid containing platelet shape nanoparticles has the lowest amount of thermal conductivity. The results indicate that the thermal conductivity of the nanofluid containing cylindrical shape nanoparticles at concentrations of 0.5 and 2% is respectively 0.66 and 2.55% higher than the thermal conductivity of the nanofluid with platelet shape nanoparticles at similar concentrations. The findings also show that the thermal conductivity of nanofluids increases with the increase of nanoparticle concentration. For example, by increasing the nanoparticle concentration from 0.5 to 2%, the thermal conductivity of the nanofluid containing cylindrical shape nanoparticles increases by 5.81%, while this increase is 3.87% for the nanofluid with platelet shape nanoparticles.
0.42
Platelets Cylindrical Blades Bricks Spherical
k (W/mK)
0.41 0.4 0.39 0.38 0.37 0
0.5
1 φ (%)
1.5
2
Fig. 3. Effect of various particle shapes on thermal conductivity of boehmite alumina nanofluid.
14
Fig. 4 illustrates the effect of nanoparticle shape on the viscosity of boehmite alumina nanofluid at various concentrations. Clearly, the nanofluid with platelet shape nanoparticles has the highest viscosity, while the nanofluid containing spherical shape nanoparticles has the lowest viscosity. According to the results, at nanoparticle concentrations of 0.5 and 2%, the viscosity of the nanofluid containing platelet shape nanoparticles is respectively 18.59 and 88.92% higher than that of the nanofluid containing spherical shape nanoparticles. The results also show that the viscosity of the examined nanofluids increases with the increase of nanoparticle concentration from 0.5 to 2%; so that this increase of viscosity is 65.47% for nanofluids with platelet shape nanoparticles and 3.87% for nanofluids with spherical nanoparticles.
0.007
Platelets Cylindrical Blades Bricks Spherical
μ (kg/ms)
0.006
0.005
0.004
0.003 0
0.5
1 φ (%)
1.5
2
Fig. 4. Effect of various particle shapes on viscosity of boehmite alumina nanofluid.
The frictional entropy generation rate for various particle shapes at different nanoparticle concentrations has been displayed in Figs. 5(a) and 5(b) for Reynolds numbers of 500 and 2000, 15
respectively. As is observed, the highest frictional entropy generation rate belongs to the nanofluids with platelet shape nanoparticles and the lowest rate belongs to the nanofluids containing spherical shape nanoparticles. The results indicate that at the Reynolds number of 500, the frictional entropy generation rate for nanofluids with platelet shape nanoparticles at the concentration range of 0.5-2% is 66.94-576.71% greater than the frictional entropy generation rate for nanofluids containing spherical shape nanoparticles; while at the Reynolds number of 2000, the increase in the frictional entropy generation rate is in the range of 66.88-575.89%. In view of the constant diameter of the internal tube and the equal densities of nanofluids containing nanoparticles of various shapes, the inlet velocity of these nanofluids is directly related to the nanofluid viscosity at the same Reynolds number. Since, at the same Reynolds number, nanofluids with platelet shape nanoparticles have a greater viscosity than the other nanofluids, they also have a higher inlet velocity than the other nanofluids. This leads to the reduction of the velocity boundary layer thickness and, consequently, the increase of velocity gradient. On the other hand, the thermal boundary layer thickness diminishes with the reduction of velocity boundary layer thickness. This causes the interior layers of nanofluid to be affected more slowly by tube wall temperature; as a result of which, the average temperature of nanofluid diminishes. Based on Eq. (12), the frictional entropy generation rate is a function of viscosity, average fluid temperature and velocity gradient. Therefore, the higher frictional entropy generation rate of nanofluids containing platelet shape nanoparticles can be attributed to their higher viscosity and velocity gradient and the lower average temperature of this type of nanofluids. Moreover, the results show that the frictional entropy generation rate increases with the increase of nanoparticle concentration and Reynolds number, and that the amount of this increase differs for nanofluids containing nanoparticles of various shapes. For example, at the 16
Reynolds number of 500, by increasing the nanoparticle concentration from 0.5 to 2%, the frictional entropy generation rate of nanofluids with platelet shape nanoparticles and nanofluids containing spherical shape nanoparticles is increased by 330.23 and 6.13%, respectively. Also, at nanoparticle concentration of 2%, by increasing the Reynolds number from 500 to 2000, the frictional entropy generation rate of nanofluids with platelet shape nanoparticles and nanofluids containing spherical shape nanoparticles is increased by 1518.87 and 1520.86%, respectively. The increase of frictional entropy generation rate with the increase of nanoparticle concentration is due to the increase of both the viscosity and nanofluid velocity; whereas the increase of frictional entropy generation rate with the increase of Reynolds number only arises from the increase of nanofluid velocity. The increase of nanoparticle concentration at a fixed Reynolds number leads to the simultaneous increase of density and viscosity; however, the amount of viscosity increase is greater than that of density, and consequently, nanofluid velocity increases in order to keep the Reynolds number constant. Also, with regards to the constant values of density, viscosity and tube diameter, the increase of Reynolds number at a fixed nanoparticle concentration leads to the increase of flow velocity.
17
Frictional entropy generation rate (W/K)
0.0055
Platelets Cylindrical Blades Bricks Spherical
0.0045
0.0035
0.0025
0.0015
0.0005 0
0.5 1 1.5 Volume concentration (%)
2
(a)
Frictional entropy generation rate (W/K)
0.10
Platelets Cylindrical Blades Bricks Spherical
0.08
0.06
0.04
0.02
0.00 0
0.5 1 1.5 Volume concentration (%)
2
(b) Fig. 5. Effect of various particle shapes on global frictional entropy generation rate at (a) 2000.
18
500 and (b)
Figs. 6(a) and 6(b) show the thermal entropy generation rates for nanoparticles of various shapes at different concentrations and for Reynolds numbers of 500 and 2000, respectively. As is observed, the highest thermal entropy generation rate belongs to the nanofluid with platelet shape nanoparticles and the lowest rate belongs to the nanofluid containing spherical shape nanoparticles. According to the results, at the Reynolds number of 500, the thermal entropy generation rate for nanofluids with platelet shape nanoparticles at the concentration range of 0.52% is respectively 7.41-23.79% higher than the thermal entropy generation rate for nanofluids containing spherical shape nanoparticles; while at the Reynolds number of 2000, the increase in the thermal entropy generation rate is in the range of 1.03-1.68%. As was mentioned, the thickness of the thermal boundary layer for nanofluids with platelet shape nanoparticles is less than that for other nanofluids, causing the temperature gradient in this type of nanofluids to be greater than that in other nanofluids. It was also stated that the average temperature and the thermal conductivity coefficient of nanofluids with platelet shape nanoparticles are respectively more than and less than those of other nanofluids. Since, according to Eq. (11), the thermal entropy generation rate is a function of thermal conductivity coefficient, average temperature of fluid, and temperature gradient, it can be concluded from Fig. 6 that in nanofluids with platelet shape nanoparticles, as compared to other nanofluids, the effects of higher temperature gradient and lower average temperature overcome the effect of lower thermal conductivity coefficient; so among all the nanofluids examined in the present research, the one with platelet shape nanoparticles has the highest thermal entropy generation rate. Moreover, the results indicate that the thermal entropy generation rate increases with the increase of Reynolds number, and that the amount of this increase is different for nanofluids containing nanoparticles of various shapes. For example, at the Reynolds number of 500, by increasing the nanoparticle concentration from 0.5 19
to 2%, the frictional entropy generation rate of nanofluids containing spherical, brick, blade, cylindrical and platelet shape nanoparticles is increased by 37%, 29.39%, 25.53%, 18.19% and 12.53%, respectively. The increase of Reynolds number leads to the reduction of the thermal boundary layer thickness and, thus, the increase of temperature gradient and the reduction of average nanofluid temperature; which results in the increase of thermal entropy generation rate. The findings also show that except for the nanofluid containing spherical shape nanoparticles at both Reynolds numbers of 500 and 2000 and the nanofluid with platelet shape nanoparticles at 2% concentration and Reynolds number of 2000, the increase of nanoparticle concentration at a fixed Reynolds number leads to the increase of thermal entropy generation rate. The increase of nanoparticle concentration at a fixed Reynolds number leads to the increase of thermal conductivity and thus the increase of heat transfer; as a result, the temperature gradient is reduced and the average temperature of nanofluid is increased. On the other hand, the increase of nanoparticle concentration leads to the increase of nanofluid velocity and, consequently, the reduction of average nanofluid temperature. According to the results, the effect of nanofluid velocity increase on average nanofluid temperature overcomes the effect of thermal conductivity increase; and the average temperature of nanofluid reduces with the increase of nanoparticle concentration. Therefore, the increase of nanoparticle concentration leads to the increase of thermal entropy generation rate (by increasing the thermal conductivity coefficient and reducing the average nanofluid temperature) and to the reduction of thermal entropy generation rate (by reducing the temperature gradient). Hence, the results presented in Fig. 6 indicate that in most cases, except for the nanofluid containing spherical shape nanoparticles at both Reynolds numbers of 500 and 2000 and the nanofluid with platelet shape nanoparticles at 2% concentration and Reynolds number of 2000, the effects of thermal conductivity coefficient 20
increase and nanofluid average temperature reduction overcome the effect of temperature gradient reduction, and the thermal entropy generation rate increases with the increase of nanoparticle concentration.
Thermal entropy generation rate (W/K)
0.0013
Platelets Cylindrical Blades Bricks Spherical
0.0012
0.0011
0.0010
0.0009 0
0.5 1 1.5 Volume concentration (%)
2
(a)
Thermal entropy generation rate (W/K)
0.00140
Platelets Blades Spherical
0.00139
Cylindrical Bricks
0.00138
0.00137
0.00136 0
0.5 1 1.5 Volume concentration (%) (b)
21
2
Fig. 6. Effect of various particle shapes on global thermal entropy generation rate at (a)
500 and (b)
2000.
Figs. 7(a) and 7(b) illustrate the total entropy generation rates for nanoparticles of various shapes at different concentrations and for Reynolds numbers of 500 and 2000, respectively. As is observed, the highest total entropy generation rate belongs to the nanofluid with platelet shape nanoparticles and the lowest rate belongs to the nanofluid containing spherical shape nanoparticles. The results show that at the Reynolds number of 500, the total entropy generation rate for nanofluids with platelet shape nanoparticles at the concentration range of 0.5-2% is respectively 32.42-264.52% higher than the total entropy generation rate for nanofluids containing spherical shape nanoparticles; while at the Reynolds number of 2000, the increase in the total entropy generation rate is in the range of 60.01-519.16%. The results also indicate that the total entropy generation rate increases with the increase of Reynolds number and nanoparticle concentration; which is due to the increase of the thermal and frictional entropy generation rates. For example, at the Reynolds number of 500, by increasing the nanoparticle concentration from 0.5 to 2%, the total entropy generation rate of nanofluids with platelet shape nanoparticles and nanofluids containing spherical shape nanoparticles is increased by 181.92% and 2.42%, respectively. Also, at nanoparticle concentration of 2%, by increasing the Reynolds number from 500 to 2000, the total entropy generation rate of nanofluids with platelet shape nanoparticles and nanofluids containing spherical shape nanoparticles is increased by 1230.04% and 683.04%, respectively. In view of Fig. 7, if a designer wants to select the right shape of boehmite alumina nanoparticles, based on the second law of thermodynamics, spherical
22
nanoparticles will be the best choice, and platelet shape nanoparticles will be the worst possible option.
Total entropy generation rate (W/K)
0.007
Platelets Cylindrical Blades Bricks Spherical
0.006 0.005 0.004 0.003 0.002 0.001 0
0.5 1 1.5 Volume concentration (%)
2
(a)
Total entropy generation rate (W/K)
0.10
Platelets Cylindrical Blades Bricks Spherical
0.08
0.06
0.04
0.02
0.00 0
0.5 1 1.5 Volume concentration (%) (b)
23
2
500 and (b)
Fig. 7. Effect of various particle shapes on global total entropy generation rate at (a) 2000.
Finally, the effects of nanoparticle shape on Bejan number at different nanoparticle concentrations have been displayed in Figs. 8(a) and 8(b) for Reynolds numbers of 500 and 2000, respectively. According to these figures, nanofluids with platelet shape nanoparticles have a higher Bejan number than the other kinds of nanofluids. The results also show that the increase of nanoparticle concentration and Reynolds number leads to the reduction of Bejan number; this means that the share of thermal entropy in total entropy is reduced and the share of frictional entropy is increased.
0.6
Bejan number
0.5
0.4
0.3
Platelets Cylindrical Blades Bricks Spherical
0.2
0.1 0
0.5 1 1.5 Volume concentration (%) (a)
24
2
0.12
Bejan number
0.09
0.06
Platelets Cylindrical Blades Bricks Spherical
0.03
0 0
0.5 1 1.5 Volume concentration (%)
2
(b) Fig. 8. Effect of various particle shapes on Bejan number at (a)
500 and (b)
2000.
7. Conclusion The aim of the present research is to numerically investigate the effects of nanoparticle shape on the entropy generation characteristics of a double-pipe heat exchanger containing boehmite alumina nanoparticles. For this purpose, five different shapes of boehmite alumina nanoparticle (i.e. cylindrical, brick, blade, platelet, and spherical) have been considered and the variations of frictional entropy generation rate, thermal entropy generation rate, total entropy generation rate and Bejan number versus nanofluid concentration and Reynolds number have been explored for each of these nanoparticle shapes. The most important findings of this research are as follows:
Nanofluids containing cylindrical shape nanoparticles and nanofluids with platelet shape nanoparticles have the highest and lowest thermal conductivities, respectively; while the
25
highest and lowest values of viscosity belong to nanofluids with platelet shape nanoparticle and nanofluids containing spherical shape nanoparticles, respectively.
The increase of nanoparticle concentration leads to the increase of thermal conductivity and viscosity.
Nanofluids containing platelet shape nanoparticles have the highest values of frictional entropy generation rate, thermal entropy generation rate and total entropy generation rate; while the least values of these parameters belong to nanofluids containing spherical shape nanoparticles.
The increase of Reynolds number leads to the increase of frictional entropy generation rate, thermal entropy generation rate and total entropy generation rate and the reduction of Bejan number.
The increase of nanoparticle concentration leads to the increase of frictional entropy generation rate and total entropy generation rate and the reduction of Bejan number. Also, except for the nanofluid containing spherical shape nanoparticles at both Reynolds of 500 and 2000 and the nanofluid with platelet shape nanoparticles at 2% concentration and Reynolds number of 2000, thermal entropy generation rate increases with the increase of nanoparticle concentration.
8. Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.
References
26
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31
Highlights (for review)
Highlights
Investigating a horizontal double-pipe minichannel heat exchanger containing boehmite alumina nanofluid
Nanofluid containing platelet shape nanoparticles had the highest rate of thermal, frictional, and total entropy generation.
Nanofluid containing spherical shape nanoparticles had the lowest rate of thermal, frictional, and total entropy generation.
PII: DOI: Reference:
S0378-4371(19)30112-8 https://doi.org/10.1016/j.physa.2019.01.106 PHYSA 20537
To appear in:
Physica A
Received date : 19 September 2018 Revised date : 29 December 2018 Please cite this article as: A.A.A.A. Al-Rashed, R. Ranjbarzadeh, S. Aghakhani et al., Entropy generation of boehmite alumina nanofluid flow through a minichannel heat exchanger considering nanoparticle shape effect, Physica A (2019), https://doi.org/10.1016/j.physa.2019.01.106 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Entropy generation of boehmite alumina nanofluid flow through a minichannel heat exchanger considering nanoparticle shape effect Abdullah A. A. A. Al-Rashed1, Ramin Ranjbarzadeh2,3, Saeed Aghakhani2, Mehdi Soltanimehr2, Masoud Afrand2,*, Truong Khang Nguyen 4,5,*
1-Department of Automotive and Marine Engineering Technology, College of Technological Studies, The Public Authority for Applied Education and Training, Kuwait 2-Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran 3- Modern Manufacturing Technologies Research Center, Najafabad Branch, Islamic Azad University, Najafabad, Iran 4-Division of Computational Physics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam 5-Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam * Corresponding author Email: [email protected] (M. Afrand) [email protected] (T. K. Nguyen)
*Corresponding Author at: Division of Computational Physics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam (T. K. Nguyen)
Abstract This paper aims to study the effect of nanoparticle shape on the entropy generation characteristics of boehmite alumina nanofluid flowing through a horizontal double-pipe minichannel heat exchanger. Boehmite alumina (γ-AlOOH) nanoparticles of different shapes (cylindrical, brick, blade, platelet, and spherical) are dispersed in a mixture of water/ethylene glycol as the nanofluid. The nanofluid and water flow in the tube side and annulus side of the 1
heat exchanger, respectively. The effects of the Reynolds number and nanoparticle concentration on the frictional entropy generation rate, thermal entropy generation rate, total entropy generation rate and Bejan number are numerically analyzed for different nanoparticle shapes. The obtained results demonstrated that the nanofluids containing platelet shape and spherical shape nanoparticles have the highest and lowest rates of thermal, frictional, and total entropy generation, respectively. Additionally, it was found that the rates of thermal, frictional, and total entropy generation increase with an increase in the Reynolds number, while the opposite is true for the Bejan number. Furthermore, it was inferred from the obtained results that the increase of nanoparticle concentration results in higher frictional and total entropy generation rates and lower Bejan number.
Keywords: Minichannel heat exchanger; Nanoparticle shape effect; Boehmite alumina nanofluid; Entropy generation; Second law of thermodynamics.
Nomenclature Bejan number
specific heat capacity (J kg-1 K-1) thermal conductivity (W m−1 K−1) pressure (Pa) temperature (K) velocity (m s-1)
,
local frictional entropy generation rate (W m-3 K-1)
2
,
local thermal entropy generation rate (W m-3 K-1)
,
local total entropy generation rate (W m-3 K-1)
,
global frictional entropy generation rate (W m-3 K-1)
,
global thermal entropy generation rate (W m-3 K-1)
,
global total entropy generation rate (W m-3 K-1)
Greek symbols viscosity (kg m-1 s-1) density (kg m-3) volume concentration (%) Subscripts base fluid
nanofluid Particle
1. Introduction Heat-exchangers are appliances used to transfer thermal energy from one fluid to another with different temperatures without direct contact of the fluids. They form a vital part of almost all the processes, including the oil and gas industry, fossil and nuclear power generation, refrigeration, desalination, and so on. They have always been important in various industries, but the rapid increase in energy demand over the past decades has led to an increase in their importance. 3
Therefore, it is essential to improve the efficiency of the heat exchangers. So far, several methods are proposed by researchers to augment the performance of heat exchangers such as using various fins and turbulators. However, several disadvantages, like increase in pressure drop, weight and volume of heat exchangers, are associated with these improvements that limit their usage. Another recently proposed method to enhance the heat exchanger performance involves the use of working fluids with higher thermal conductivity than the conventional heat transfer fluids such as water, oil, and ethylene glycol [1-15]. This goal can be achieved through the use of nanofluids, which are synthesized by dispersing nanometer-scale solid particles into base liquids such as water, oil, ethylene glycol, etc [16-25]. Ebrahimnia-Bajestan et al. [26] experimentally and numerically investigated the heat transfer characteristics of water-TiO2 nanofluid for use in solar heat exchangers. The experimental results demonstrated that the presence of 2.3% volume concentration increases the average heat transfer coefficient by 21%. Additionally, the numerical results revealed that the convective heat transfer coefficient augments with increase of nanoparticle concentration and Reynolds number, while it reduces with increase of particle size. Shahrul et al. [27] experimentally investigated the overall performance of a shell and tube heat exchanger filled with water-Al2O3, water-SiO2, and water-ZnO nanofluids. The results indicated that the use of water-ZnO and water-SiO2 nanofluids leads to the highest and lowest convective heat transfer coefficient and overall heat transfer coefficient, respectively. Kumar et al. [28] carried out experiments to reveal the effect of symmetric ( ~30°/30° and 60°/60°) and mixed ( ~30°/60°) chevron angles on the heat transfer performance in plate heat exchangers operated with water-ZnO nanofluid. The results demonstrated that the maximum increase in heat transfer performance is achieved at
~30°/60° for nanofluid with volume concentration of 1%. The 4
performance of thermoelectric cooling of electronic devices with water-Al2O3 nanofluid in a multiport minichannel heat exchanger was experimentally evaluated by Ahammed et al. [29]. Their study indicated about 40% enhancement in coefficient of performance of thermoelectric module using 0.2% nanofluid. Moreover, they reported a 9.15% reduction in the thermoelectric temperature difference between the hot and cold side using 0.2% nanofluid. Fsadni et al. [30] performed a numerical study to investigate the turbulent heat transfer and pressure drop characteristics of a helically coiled hybrid rectangular-circular tube heat exchanger with waterAl2O3 nanofluid. The results revealed that both the heat transfer coefficient and pressure drop augment with the nanoparticle concentration and curvature. Besides, they used a thermohydrodynamic performance index to evaluate the overall impact and found that the use of nanofluid can lead to an increase in the overall system performance. Literature survey shows that most research studies on the performance of heat exchangers operated with nanofluids are based on the first law of thermodynamics. Considering the fact that heat cannot be converted completely into work, it can be concluded that the quality of thermal energy should be taken into account. To this end, the second law of thermodynamics can be utilized to calculate the lost work arising from friction and heat transfer. Therefore, entropy production can be employed as a criterion to evaluate the performance of engineering devices. Up to now only very few attempts have been made to assess the second law performance of heat exchangers operated with nanofluids. Entropy generation analysis of graphene–alumina hybrid nanofluid in a multiport minichannel heat exchanger coupled with a thermoelectric cooler was experimentally performed by Ahammed et al. [31]. The results revealed that by increasing the Reynolds number from 200 to 1000, the total entropy generation reduces by 96.2%. Bahiraei et al. [32] numerically studied the thermal and frictional entropy generation rates during laminar 5
forced convective flow of carbon nanotube (CNT)-Fe3O4 hybrid nanofluid in a double-pipe minichannel heat exchanger. They reported that heat transfer and friction are the main reason of entropy generation at low and high concentrations, respectively. Shahsavar et al. [33] numerically assessed the effect of nanoparticle concentration and Reynolds number on the frictional, thermal and total entropy generation rates during flow of a new hybrid nanofluid containing CNTs decorated with Fe3O4 nanoparticles through a double-pipe minichannel heat exchanger. The results demonstrated that the total entropy generation rate increases with increasing the CNT concentration, Fe3O4 concentration, and Reynolds number. Several scholars have reported that the shape of nanoparticles has a significant impact on the thermophysical properties of nanofluids [34-36], and, consequently, their cooling performance. Investigating the studies conducted on the impact of using nanofluids on the hydrothermal and entropy generation characteristics of heat exchangers shows that the effect of nanoparticle shape has rarely been studied so far. The influence of different nanoparticle shapes (such as cylindrical, brick, blade, platelet, and spherical) on the hydrothermal and entropy generation characteristics of water based nanofluid containing boehmite alumina nanoparticles inside a shell and tube heat exchanger was investigated by Elias et al. [37]. It was found that, among the five nanoparticle shapes, cylindrical shape demonstrates better heat transfer performance. In another study, Elias et al. [38] analyzed the effect of different baffle angles and segmental baffle on the heat transfer and entropy generation characteristics of a shell and tube heat exchanger operated with boehmite alumina nanofluid containing five different nanoparticle shape (i.e. cylindrical, brick, blade, platelet, and spherical). The results depicted that the nanofluid having cylindrical shape nanoparticles has better overall heat transfer coefficient and entropy minimization rate at 20° baffle angle. Sheikholeslami and Bhatti [39] reported the impact of a uniform magnetic field on 6
water-CuO nanofluid flow inside a porous semi-annulus considering shape effects of nanoparticles (such as cylindrical, brick, platelet, and spherical). They observed that the platelet shape has the greatest heat transfer rate. The influence of different shapes of boehmite alumina nanoparticles on the thermoeconomic improvement of a shell and tube heat exchanger was determined by Hajabdollahi and Hajabdollahi [40]. The authors found that the nanofluid containing brick shape nanoparticles has the highest heat exchanger thermoeconomic parameters. To the best of author’s knowledge, there is not any study which investigate the effect of particle shape on the entropy generation characteristics of a nanofluid flowing through a double-pipe heat exchanger. Therefore, the present investigation is expected to fulfil this important research gap. The considered nanofluid is a suspension of boehmite alumina nanoparticles with different shapes (cylindrical, brick, blade, platelet, and spherical) in a mixture of ethylene glycol and water (50:50). The influence of nanoparticle concentration and the Reynolds number on the frictional entropy generation rate, thermal entropy generation rate, total entropy generation rate, and Bejan number are also evaluated.
2. Thermophysical properties of nanofluids In this study, the ethylene glycol and water mixture (50:50)-boehmite alumina nanofluids containing different shapes of nanoparticles are considered. Table 1 shows the thermophysical properties of the base fluid and nanoparticles. The density and specific heat of the studied nanofluids are given by Eqs. (1) and (2), respectively, which are based on the mixture theory: 1
(1)
7
1
,
,
,
(2)
where φ is the voluume concenntration. Alsso, subscrippts f, nf andd p refer to base fluid, nanofluid and nannoparticle, reespectively. Some scientists [441,42] have studied thee effect of nanoparticlle shape onn the therm mophysical propertiies of variouus nanofluidds and obseerved that thhe thermal cconductivityy and viscossity of the studied nanofluids are a functiion of nanoparticle shaape. Five typpes of nanooparticles with shapes of cylinndrical, brickk, blade, plaatelet, and sppherical aree studied in the present work. Fig. 1 shows a schemattic of the m mentioned nnanoparticlee shapes. Thhe thermal conductivitty of nanofl fluids with differennt nanoparticcle shapes, eexcept spherical, is giveen by the foollowing equuation [26,228]: 1 where
(3)
is constannt coefficiennt for differeent nanoparrticle shapess which is prresented in Table 2.
Table 1. Thermophyysical propertiies of boehmitte alumina andd mixture of etthylene glycoll and water at T=300 K [41,42]. Properrties
Boehmite alumina
Ethhylene glycol and water 50//50 mixture (550:50)
Density ((kg/m3)
30550
1067.5
Specific heaat (J/kg K)
6188.3
3300
Thermal conducttivity (W/m K K)
300
0.3799
D Dynamic viscoosity (kg/m s)
-
0.00339
8
Cylindrical
Brick
Blade
Platelet
Spherical
Fig. 1. Diverse particle shapes.
The thermal conductivity of nanofluids with spherical shape nanoparticle is given by using Eq. (4) [43]: 2
2
(4)
2
The viscosity of nanofluids with different nanoparticle shapes, except spherical, is calculated by using Eq. (5) [37,38]: 1 where
and
(5) are constant coefficient for different nanoparticle shapes which are presented in
Table 2.
Table 2. Constant coefficients defined in Eqs. (3) and (5) for the effect of nanoparticle shape on the thermal conductivity and viscosity of the nanofluid [37,38]. Type Platelets
2.61
37.1
612.6
Blades
2.74
14.6
123.3
Cylindrical
3.95
13.5
904.4
Bricks
3.37
1.9
471.4
The viscosity of nanofluids with spherical shape nanoparticle is determined by using Eq. (6) [37,38]:
9
1
(6)
.
3. Modeel configuraation 3.1. Geoometry and d boundaryy conditionss The schhematic view w of the geoometry conssidered in thhis work is displayed Fig. F 2. It is a doublepipe couunter-currennt minichannnel heat excchanger connsisting of ttwo concenttric tubes w with length of 1 m, inner diameeter of 1 mm m, and outerr diameter oof 2 mm. Hoot water andd cold nanoofluid flow throughh the annular region aand inner ttube, respecctively. Besides, zero relative pressure is employeed at the ouutlets of bothh tube and aannulus sidees and the ouuter wall off the heat excchanger is assumedd to be adiabbatic. Besiddes, the walll thickness of o tubes are neglected.
Fig. 2. The minichhannel heat exxchanger underr study.
3.2. Govverning equ uations For nanofluids, it iss often assum med that baase fluid andd nanoparticcles move with w a similarr velocity, m exists bettween them m. This asssumption is consideredd because and also thermal equilibrium
10
particles employed in nanofluids are very fine and are of nanometer order. According to above mentioned assumptions, the governing equations are given as follows: Conservation of mass: .
0
(7)
Conservation of momentum: .
.
(8)
Conservation of energy: .
.
,
where
is the velocity,
(9) is the pressure, and
is the temperature.
3.3. Entropy generation The entropy generation in the flow field comprises of two main parts; (i) frictional factors, and (ii) thermal irreversibility. The local thermal and frictional entropy generation rates can be obtained as [44], (10)
,
2
,
(11)
Moreover, the total entropy generation rate ( ,
,
,
) is obtained by the following equation: (12)
,
The global entropy generation rates are calculated by the integration of the local entropy generation rates over the whole domain as follows: 11
,
,
,
,
,
,
,
,
(13)
The Bejan number is a dimensionless number defined as the entropy generation ratio of the thermal entropy generation rate over the total entropy generation rate. That is: ,
(14) ,
3.4. Numerical method and validation In this contribution, computational fluid dynamics (CFD) methods incorporated with a finite volume method is utilized to solve the governing equations (7)-(9) along with the above mentioned boundary conditions. The second order upwind method is used for solving the momentum and energy equations. Pressure and velocity are coupled using Semi Implicit Method for Pressure Linked Equations (SIMPLE) algorithm. For all parameters, the convergence criteria is set to 10-6. In this study, a structured mesh is generated in the entire domain. Owing to severe velocity and temperature gradients adjacent to the walls, smaller elements are applied there. Five different grids are considered to check grid independency of the numerical results. The results of this study are listed in Table 3. As Reported in Table 3, a grid with 45 nodes radially for both the tube side and the annulus side of the heat exchanger, and 1000 nodes in longitudinal direction is selected as the best one.
Table 3. Mesh independence study for nanofluid flow with platelet shape nanoparticles at
and
%. In this table, the mesh resolution is reported as number of longitudinal nodes number of radial nodes in central
12
tube number of radial nodes in annulus. mesh ∆
800 40 40
900 40 40
1000 40 40
1000 45 45
1000 55 55
35.55
38.18
40.32
41.42
41.92
2367.34
2488.12
2598.71
2686.25
2717.23
Validation of the numerical analysis is accomplished by comparing the obtained numerical data for the Nusselt number with the experimental results of Duangthongsuk and Wongwises [45] for flow of water-TiO2 nanofluid in a double-pipe heat exchanger. Table 4 presents the results of this comparison and as can be seen, there is a good agreement between the results. Therefore, it can be said that the numerical method is valid and can be utilized for simulation of nanofluid behavior through the double-pipe heat exchanger.
Table 4. Comparison between results obtained from current study and experimental results [45]. Re 8900 10450 11820 13200 14500
Nu (experimental) 90.38 98.44 105.82 114.56 120.60
Nu (numerical) 85.82 98.90 106.50 114.66 123.51
Error (%) 5.05 0.47 0.64 0.09 2.41
4. Results and discussion Investigations are carried out to find the effect of various shapes of boehmite alumina nanoparticles (cylindrical, brick, blade, platelet, and spherical) on the entropy generation due to fluid flow and heat transfer inside a double-tube minichannel heat exchanger. The numerical simulations are performed at nanoparticle concentrations of 0.5 to 2.0%, Reynolds numbers of
13
500 and 2000 for the tube side, and constant Reynolds number of 1000 for the annulus side. Besides, the inlet temperature of the nanofluid and water is set at 298 K and 308 K, respectively. Fig. 3 shows the effect of nanoparticle shape on the thermal conductivity of boehmite alumina nanofluid at various concentrations. As is observed, the nanofluid containing cylindrical shape nanoparticles has the highest and the nanofluid containing platelet shape nanoparticles has the lowest amount of thermal conductivity. The results indicate that the thermal conductivity of the nanofluid containing cylindrical shape nanoparticles at concentrations of 0.5 and 2% is respectively 0.66 and 2.55% higher than the thermal conductivity of the nanofluid with platelet shape nanoparticles at similar concentrations. The findings also show that the thermal conductivity of nanofluids increases with the increase of nanoparticle concentration. For example, by increasing the nanoparticle concentration from 0.5 to 2%, the thermal conductivity of the nanofluid containing cylindrical shape nanoparticles increases by 5.81%, while this increase is 3.87% for the nanofluid with platelet shape nanoparticles.
0.42
Platelets Cylindrical Blades Bricks Spherical
k (W/mK)
0.41 0.4 0.39 0.38 0.37 0
0.5
1 φ (%)
1.5
2
Fig. 3. Effect of various particle shapes on thermal conductivity of boehmite alumina nanofluid.
14
Fig. 4 illustrates the effect of nanoparticle shape on the viscosity of boehmite alumina nanofluid at various concentrations. Clearly, the nanofluid with platelet shape nanoparticles has the highest viscosity, while the nanofluid containing spherical shape nanoparticles has the lowest viscosity. According to the results, at nanoparticle concentrations of 0.5 and 2%, the viscosity of the nanofluid containing platelet shape nanoparticles is respectively 18.59 and 88.92% higher than that of the nanofluid containing spherical shape nanoparticles. The results also show that the viscosity of the examined nanofluids increases with the increase of nanoparticle concentration from 0.5 to 2%; so that this increase of viscosity is 65.47% for nanofluids with platelet shape nanoparticles and 3.87% for nanofluids with spherical nanoparticles.
0.007
Platelets Cylindrical Blades Bricks Spherical
μ (kg/ms)
0.006
0.005
0.004
0.003 0
0.5
1 φ (%)
1.5
2
Fig. 4. Effect of various particle shapes on viscosity of boehmite alumina nanofluid.
The frictional entropy generation rate for various particle shapes at different nanoparticle concentrations has been displayed in Figs. 5(a) and 5(b) for Reynolds numbers of 500 and 2000, 15
respectively. As is observed, the highest frictional entropy generation rate belongs to the nanofluids with platelet shape nanoparticles and the lowest rate belongs to the nanofluids containing spherical shape nanoparticles. The results indicate that at the Reynolds number of 500, the frictional entropy generation rate for nanofluids with platelet shape nanoparticles at the concentration range of 0.5-2% is 66.94-576.71% greater than the frictional entropy generation rate for nanofluids containing spherical shape nanoparticles; while at the Reynolds number of 2000, the increase in the frictional entropy generation rate is in the range of 66.88-575.89%. In view of the constant diameter of the internal tube and the equal densities of nanofluids containing nanoparticles of various shapes, the inlet velocity of these nanofluids is directly related to the nanofluid viscosity at the same Reynolds number. Since, at the same Reynolds number, nanofluids with platelet shape nanoparticles have a greater viscosity than the other nanofluids, they also have a higher inlet velocity than the other nanofluids. This leads to the reduction of the velocity boundary layer thickness and, consequently, the increase of velocity gradient. On the other hand, the thermal boundary layer thickness diminishes with the reduction of velocity boundary layer thickness. This causes the interior layers of nanofluid to be affected more slowly by tube wall temperature; as a result of which, the average temperature of nanofluid diminishes. Based on Eq. (12), the frictional entropy generation rate is a function of viscosity, average fluid temperature and velocity gradient. Therefore, the higher frictional entropy generation rate of nanofluids containing platelet shape nanoparticles can be attributed to their higher viscosity and velocity gradient and the lower average temperature of this type of nanofluids. Moreover, the results show that the frictional entropy generation rate increases with the increase of nanoparticle concentration and Reynolds number, and that the amount of this increase differs for nanofluids containing nanoparticles of various shapes. For example, at the 16
Reynolds number of 500, by increasing the nanoparticle concentration from 0.5 to 2%, the frictional entropy generation rate of nanofluids with platelet shape nanoparticles and nanofluids containing spherical shape nanoparticles is increased by 330.23 and 6.13%, respectively. Also, at nanoparticle concentration of 2%, by increasing the Reynolds number from 500 to 2000, the frictional entropy generation rate of nanofluids with platelet shape nanoparticles and nanofluids containing spherical shape nanoparticles is increased by 1518.87 and 1520.86%, respectively. The increase of frictional entropy generation rate with the increase of nanoparticle concentration is due to the increase of both the viscosity and nanofluid velocity; whereas the increase of frictional entropy generation rate with the increase of Reynolds number only arises from the increase of nanofluid velocity. The increase of nanoparticle concentration at a fixed Reynolds number leads to the simultaneous increase of density and viscosity; however, the amount of viscosity increase is greater than that of density, and consequently, nanofluid velocity increases in order to keep the Reynolds number constant. Also, with regards to the constant values of density, viscosity and tube diameter, the increase of Reynolds number at a fixed nanoparticle concentration leads to the increase of flow velocity.
17
Frictional entropy generation rate (W/K)
0.0055
Platelets Cylindrical Blades Bricks Spherical
0.0045
0.0035
0.0025
0.0015
0.0005 0
0.5 1 1.5 Volume concentration (%)
2
(a)
Frictional entropy generation rate (W/K)
0.10
Platelets Cylindrical Blades Bricks Spherical
0.08
0.06
0.04
0.02
0.00 0
0.5 1 1.5 Volume concentration (%)
2
(b) Fig. 5. Effect of various particle shapes on global frictional entropy generation rate at (a) 2000.
18
500 and (b)
Figs. 6(a) and 6(b) show the thermal entropy generation rates for nanoparticles of various shapes at different concentrations and for Reynolds numbers of 500 and 2000, respectively. As is observed, the highest thermal entropy generation rate belongs to the nanofluid with platelet shape nanoparticles and the lowest rate belongs to the nanofluid containing spherical shape nanoparticles. According to the results, at the Reynolds number of 500, the thermal entropy generation rate for nanofluids with platelet shape nanoparticles at the concentration range of 0.52% is respectively 7.41-23.79% higher than the thermal entropy generation rate for nanofluids containing spherical shape nanoparticles; while at the Reynolds number of 2000, the increase in the thermal entropy generation rate is in the range of 1.03-1.68%. As was mentioned, the thickness of the thermal boundary layer for nanofluids with platelet shape nanoparticles is less than that for other nanofluids, causing the temperature gradient in this type of nanofluids to be greater than that in other nanofluids. It was also stated that the average temperature and the thermal conductivity coefficient of nanofluids with platelet shape nanoparticles are respectively more than and less than those of other nanofluids. Since, according to Eq. (11), the thermal entropy generation rate is a function of thermal conductivity coefficient, average temperature of fluid, and temperature gradient, it can be concluded from Fig. 6 that in nanofluids with platelet shape nanoparticles, as compared to other nanofluids, the effects of higher temperature gradient and lower average temperature overcome the effect of lower thermal conductivity coefficient; so among all the nanofluids examined in the present research, the one with platelet shape nanoparticles has the highest thermal entropy generation rate. Moreover, the results indicate that the thermal entropy generation rate increases with the increase of Reynolds number, and that the amount of this increase is different for nanofluids containing nanoparticles of various shapes. For example, at the Reynolds number of 500, by increasing the nanoparticle concentration from 0.5 19
to 2%, the frictional entropy generation rate of nanofluids containing spherical, brick, blade, cylindrical and platelet shape nanoparticles is increased by 37%, 29.39%, 25.53%, 18.19% and 12.53%, respectively. The increase of Reynolds number leads to the reduction of the thermal boundary layer thickness and, thus, the increase of temperature gradient and the reduction of average nanofluid temperature; which results in the increase of thermal entropy generation rate. The findings also show that except for the nanofluid containing spherical shape nanoparticles at both Reynolds numbers of 500 and 2000 and the nanofluid with platelet shape nanoparticles at 2% concentration and Reynolds number of 2000, the increase of nanoparticle concentration at a fixed Reynolds number leads to the increase of thermal entropy generation rate. The increase of nanoparticle concentration at a fixed Reynolds number leads to the increase of thermal conductivity and thus the increase of heat transfer; as a result, the temperature gradient is reduced and the average temperature of nanofluid is increased. On the other hand, the increase of nanoparticle concentration leads to the increase of nanofluid velocity and, consequently, the reduction of average nanofluid temperature. According to the results, the effect of nanofluid velocity increase on average nanofluid temperature overcomes the effect of thermal conductivity increase; and the average temperature of nanofluid reduces with the increase of nanoparticle concentration. Therefore, the increase of nanoparticle concentration leads to the increase of thermal entropy generation rate (by increasing the thermal conductivity coefficient and reducing the average nanofluid temperature) and to the reduction of thermal entropy generation rate (by reducing the temperature gradient). Hence, the results presented in Fig. 6 indicate that in most cases, except for the nanofluid containing spherical shape nanoparticles at both Reynolds numbers of 500 and 2000 and the nanofluid with platelet shape nanoparticles at 2% concentration and Reynolds number of 2000, the effects of thermal conductivity coefficient 20
increase and nanofluid average temperature reduction overcome the effect of temperature gradient reduction, and the thermal entropy generation rate increases with the increase of nanoparticle concentration.
Thermal entropy generation rate (W/K)
0.0013
Platelets Cylindrical Blades Bricks Spherical
0.0012
0.0011
0.0010
0.0009 0
0.5 1 1.5 Volume concentration (%)
2
(a)
Thermal entropy generation rate (W/K)
0.00140
Platelets Blades Spherical
0.00139
Cylindrical Bricks
0.00138
0.00137
0.00136 0
0.5 1 1.5 Volume concentration (%) (b)
21
2
Fig. 6. Effect of various particle shapes on global thermal entropy generation rate at (a)
500 and (b)
2000.
Figs. 7(a) and 7(b) illustrate the total entropy generation rates for nanoparticles of various shapes at different concentrations and for Reynolds numbers of 500 and 2000, respectively. As is observed, the highest total entropy generation rate belongs to the nanofluid with platelet shape nanoparticles and the lowest rate belongs to the nanofluid containing spherical shape nanoparticles. The results show that at the Reynolds number of 500, the total entropy generation rate for nanofluids with platelet shape nanoparticles at the concentration range of 0.5-2% is respectively 32.42-264.52% higher than the total entropy generation rate for nanofluids containing spherical shape nanoparticles; while at the Reynolds number of 2000, the increase in the total entropy generation rate is in the range of 60.01-519.16%. The results also indicate that the total entropy generation rate increases with the increase of Reynolds number and nanoparticle concentration; which is due to the increase of the thermal and frictional entropy generation rates. For example, at the Reynolds number of 500, by increasing the nanoparticle concentration from 0.5 to 2%, the total entropy generation rate of nanofluids with platelet shape nanoparticles and nanofluids containing spherical shape nanoparticles is increased by 181.92% and 2.42%, respectively. Also, at nanoparticle concentration of 2%, by increasing the Reynolds number from 500 to 2000, the total entropy generation rate of nanofluids with platelet shape nanoparticles and nanofluids containing spherical shape nanoparticles is increased by 1230.04% and 683.04%, respectively. In view of Fig. 7, if a designer wants to select the right shape of boehmite alumina nanoparticles, based on the second law of thermodynamics, spherical
22
nanoparticles will be the best choice, and platelet shape nanoparticles will be the worst possible option.
Total entropy generation rate (W/K)
0.007
Platelets Cylindrical Blades Bricks Spherical
0.006 0.005 0.004 0.003 0.002 0.001 0
0.5 1 1.5 Volume concentration (%)
2
(a)
Total entropy generation rate (W/K)
0.10
Platelets Cylindrical Blades Bricks Spherical
0.08
0.06
0.04
0.02
0.00 0
0.5 1 1.5 Volume concentration (%) (b)
23
2
500 and (b)
Fig. 7. Effect of various particle shapes on global total entropy generation rate at (a) 2000.
Finally, the effects of nanoparticle shape on Bejan number at different nanoparticle concentrations have been displayed in Figs. 8(a) and 8(b) for Reynolds numbers of 500 and 2000, respectively. According to these figures, nanofluids with platelet shape nanoparticles have a higher Bejan number than the other kinds of nanofluids. The results also show that the increase of nanoparticle concentration and Reynolds number leads to the reduction of Bejan number; this means that the share of thermal entropy in total entropy is reduced and the share of frictional entropy is increased.
0.6
Bejan number
0.5
0.4
0.3
Platelets Cylindrical Blades Bricks Spherical
0.2
0.1 0
0.5 1 1.5 Volume concentration (%) (a)
24
2
0.12
Bejan number
0.09
0.06
Platelets Cylindrical Blades Bricks Spherical
0.03
0 0
0.5 1 1.5 Volume concentration (%)
2
(b) Fig. 8. Effect of various particle shapes on Bejan number at (a)
500 and (b)
2000.
7. Conclusion The aim of the present research is to numerically investigate the effects of nanoparticle shape on the entropy generation characteristics of a double-pipe heat exchanger containing boehmite alumina nanoparticles. For this purpose, five different shapes of boehmite alumina nanoparticle (i.e. cylindrical, brick, blade, platelet, and spherical) have been considered and the variations of frictional entropy generation rate, thermal entropy generation rate, total entropy generation rate and Bejan number versus nanofluid concentration and Reynolds number have been explored for each of these nanoparticle shapes. The most important findings of this research are as follows:
Nanofluids containing cylindrical shape nanoparticles and nanofluids with platelet shape nanoparticles have the highest and lowest thermal conductivities, respectively; while the
25
highest and lowest values of viscosity belong to nanofluids with platelet shape nanoparticle and nanofluids containing spherical shape nanoparticles, respectively.
The increase of nanoparticle concentration leads to the increase of thermal conductivity and viscosity.
Nanofluids containing platelet shape nanoparticles have the highest values of frictional entropy generation rate, thermal entropy generation rate and total entropy generation rate; while the least values of these parameters belong to nanofluids containing spherical shape nanoparticles.
The increase of Reynolds number leads to the increase of frictional entropy generation rate, thermal entropy generation rate and total entropy generation rate and the reduction of Bejan number.
The increase of nanoparticle concentration leads to the increase of frictional entropy generation rate and total entropy generation rate and the reduction of Bejan number. Also, except for the nanofluid containing spherical shape nanoparticles at both Reynolds of 500 and 2000 and the nanofluid with platelet shape nanoparticles at 2% concentration and Reynolds number of 2000, thermal entropy generation rate increases with the increase of nanoparticle concentration.
8. Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.
References
26
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Highlights (for review)
Highlights
Investigating a horizontal double-pipe minichannel heat exchanger containing boehmite alumina nanofluid
Nanofluid containing platelet shape nanoparticles had the highest rate of thermal, frictional, and total entropy generation.
Nanofluid containing spherical shape nanoparticles had the lowest rate of thermal, frictional, and total entropy generation.