The effects of suspending Copper nanoparticles into Argon base fluid inside a microchannel under boiling flow condition by using of molecular dynamic simulation

Journal of Molecular Liquids 293 (2019) 111474

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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq

The effects of suspending Copper nanoparticles into Argon base fluid inside a microchannel under boiling flow condition by using of molecular dynamic simulation Majid Zarringhalam a, Hossein Ahmadi-Danesh-Ashtiani b, Davood Toghraie c,⁎, Reza Fazaeli d a

Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran Department of Energy and Mechanical Engineering, Faculty of Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran c Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran d Department of Chemistry, South Tehran Branch, Islamic Azad University, Tehran, Iran b

a r t i c l e

i n f o

Article history: Received 4 June 2019 Received in revised form 6 July 2019 Accepted 28 July 2019 Available online 30 July 2019 Keywords: Microchannel Molecular dynamic simulation Boiling flow condition Nanofluid

a b s t r a c t Present paper employs Molecular Dynamic Simulation (MDS) Method to study the effects of suspending 2, 4 and 6 Copper nanoparticles into Argon base fluid, flowing inside microchannel with square cross section under boiling flow condition. Fluid flow is supported by an external driving force of 0.002 eV/Å at the inlet section of microchannel and boiling process is supported by boundary wall temperature of 108 K. Afterward, statistical approach is employed as new insight for data analysis of present MDS method. Finally, it is indicated that increasing number of suspended nanoparticles into Argon base fluid flow, expands density profiles of Argon base fluid as much as 20%, 35% and 55% in order of addition of 2, 4 and 6 Copper nanoparticles, while; they brings velocity enhancement as much as 17.8%, 32.6% and 52.8%. Also, temperature augmentation is reported as much as 30.7%, 50.45 and 69.5% respectively. It is analyzed that suspended nanoparticles empowers boiling condition and thermal driving force which is perpendicular direction with power of external driving force to move atoms. Therefore, it is concluded that due to disproportionation of statistical results, employing high fraction of suspended nanoparticles into base fluid is not always economical for practical application. © 2019 Elsevier B.V. All rights reserved.

1. Introduction With the passage over last decade, development in computers ability for data processing and storage capacities have prepared condition for different computational methods which have been employed to studies inside small size of micro and nano flow. Molecular dynamics simulation (MDS) method is introduced as a computer simulation method for studying the physical movements of atoms and molecules. It is one of the most applicable ways to investigate microscopic mechanisms of nano and micro flow characteristics, using Newton equations of atoms or molecules motion regarding effects of interaction potential between them. Also, this method determines the trajectories of atoms and molecules to be employed to probe in nanoscale phenomena and analyses particle interactions at the atomic scale. Nanofluids are one of the fluid types which can be analyzed by this method. Nowadays, nanofluids have gathered much interest to be used in practical application due to their influences in improvement of thermal conductivity and heat transfer efficiency, compared to their own base conventional fluids. Many papers presented behavior of nanofluids flows and effect of nanoparticles by numerical and experimental method in different ⁎ Corresponding author. E-mail address: [email protected] (D. Toghraie).

https://doi.org/10.1016/j.molliq.2019.111474 0167-7322/© 2019 Elsevier B.V. All rights reserved.

condition as references [1–10]. Also, different studies have focused to probe single phase of nanoflows inside small nanochannels with limited number of atoms using MDS method. Therefore, nature of previous MDS works is theoretical and far from practical application. Therefore, in this work MDS is employed to support statistical approach to analyses results of Cu-Argon nanofluid with 2, 4 and 6 number of Copper nanoparticles are suspended into numerous number of Argon base atoms under boiling flow condition inside microchannel with cubic cross section. Minli et al. [11] investigated the microscopic mechanism for local flow enhancement in nanofluids by MDS method. Their report revealed that the microscopic mechanism for local flow enhancement in nanofluids is mainly due to irregular nanoparticles motions, including rotational and translational motions which causes extra momentum exchange between fluid molecules, consequently, disturbance of base fluid. Also, nanofluids flow would be more active, to improve heat transfer. Razmara et al. [12] carried out aggregation phenomena of nanofluid flow in a rough nanochannel by MDS. Nanochannel consists of spherical Copper nanoparticles dispersed in Argon as base fluid. They compared the results of smooth and roughened nanochannel and concluded that existence of surface roughness can induces extra energy losses and contributes to the reduction of aggregation time in nanochannel. So, to prolong in the aggregation of nanoparticles in nanofluid flow, nanochannels walls need to be manufactured very smooth.

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Aminfar et al. [13] studied Cu-Argon and Pt-Argon nanofluids flows inside nanochannel by MDS method and reported that agglomeration of nanoparticles decreases energy degradation and enthalpy of the system. They showed that increasing applied external force is the reason of sticking nanoparticles together and emerging clustering and increasing total entropy of system. Wenzheng et al. [14] using MDS method investigated the behavior of the Argon-Copper nanofluid within nanochannel and reported that the nanofluid density was higher than that of the base fluid, due to the presence of suspended Copper nanoparticles. Also, the shear rate of flow causes rotational speed of suspended nanoparticles, which results in the non-linearization of the nanoparticles velocity profile. Moreover, increasing rotational speed increases shear velocity. Therefore, it was concluded that the nonlinearity of the velocity, rotation and displacement of nanoparticles is related to the shear rate. Cui et al. [15] observed that Argon base fluid particles in the vicinity of suspended Copper nanoparticles are in higher level of thermal conductivity than that of other regions of which result in improvement of heat transfer. Hence, they reported that enhancement of conductive properties of fluid flow by adding Copper nanoparticles. On the other hand, these researchers reported that a nanoparticle in different directions produces relative velocities than direction of shear rate of Argon fluid. This phenomenon brings rotation, angular velocities, turbulence and changes in the local continuity in the fluid particles of Argon fluid flow which enhances energy transfer. Sheng et al. [16] using MDS method simulated a Copper-Ethylene glycol nanofluid. Diameters of Copper nanoparticles were between 6 and 14 Å. These researchers focused on the molecular mechanisms are effective on thermal conductivity and nano layer structure around nanoparticles employing Reduced Density Distribution (RDF) function. They reported that increasing the diameter of nanoparticles in the range of 6–10 A°, thermal conductivity increases significantly in the adjacent layer of nanoparticles. Also, the maximum thermal conductivity was reported with nanoparticles diameter of 9 A°. Chengzhen et al. [17] studied the thermal conductivity of ArgonCopper nanofluid under shear flow using MDS method. In this study, the Green-Kubo equations and the periodic boundary conditions were used. It was reported that the nanoparticles have a velocity gradient that causes them to rotate which results in increasing micro convection and linear conductivity enhancement. This enhancement is higher in nanofluid with lower volume fraction of nanoparticles than that of in nanofluid with higher volume fraction of their research. Mahian et al. [35,36] reviewed recent progress in nanofluid flow 3D simulation with different methods of Eulerian, Lagrangian in single and multi-phase models. These researchers also presented lack of researches in nanofluid studies. Also, researches in references [18–28] published MDS to investigate on boiling nano flow and phase change condition behavior of Argon fluid flow into very small nanochannels with limited number of particles. In this study, molecular dynamic simulation of CuArgon nanofluid inside microchannel under boiling flow condition was performed. Afterward, statistical approach is employed as new insight for data analysis of present MDS method. Finally, it is indicated that increasing number of suspended nanoparticles into Argon base fluid flow, expands density profiles of Argon base fluid as much as 20%, 35% and 55% in order of addition of 2, 4 and 6 Copper nanoparticles, while.

particles and their potential energies are often computed employing interatomic potentials. Design and simulation size in molecular dynamics simulations shall account for the available computational power of computers. Therefore, this method is computationally expensive. Nevertheless, tool of present molecular dynamics simulations is LAMMPS software. LAMMPS is abbreviated from Large-scale Atomic/Molecular Massively Parallel Simulator. It is a molecular dynamics program which is developed every biweekly by Sandia National Laboratories. Therefore, LAMMPS software is free and open-source which is distributed under the terms of the GNU General Public License. This software is also supported by Message Passing Interface (MPI) for parallel communication. This software was selected due to simplicity and ease of operation. Simulations of this work are done as following sequences. Platinum microchannel is simulated with dimension of 10000*5000*5000 A°3 in order of X, Y and Z direction vector. Argon atoms were arranged as much as 1,000,000 numbers in 2 lateral regions of microchannel, while; central region of microchannel is completely empty in accordance to Fig. 1. Afterward, an external driving force of 0.002 eV/ A° is exerted on the Argon atoms at the inlet section of microchannel to push atoms to flow through microchannel in X direction vector. Simultaneously, constant boundary wall temperature of 108 K is applied on the Argon atoms to prepare phase change and boiling condition. Then, system reaches to equilibrium energy state, but computational running is continued to observe evolution of boiling process. Next, sampling data of density is done at 4 time steps of 250,000, 500,000, 750,000 and 1,000,000, whereas, sampling data of velocity and temperature are performed at time step 1,000,000. Afterward, Copper nanoparticles with diameter of 25 nm are suspended into Argon base fluid in order of 2, 4 and 6 nanoparticles. Running process and sampling data are repeated separately for 3 cases of simulated nanofluids to be comparable with results of Argon base fluid. The interatomic force between fluids atoms are accounted by LJ potential function as following formula:
 ϕ r ij ¼ 4ε

r ij ≤r c

ð1Þ

where rij, introduces the interatomic distance between atom i to atom j and energy parameter is known by ε as the depth of the potential well, then, cut-off radius is shown with rc which is accounted as much as 8.5125 A°. The atomic mass, diameter, and potential depth of Argon fluid atoms are accounted orderly as much as mAr = 39.95 g/mol, σAr = 3.405 A° and ԐAr = 1.67*10−21 J. For the microchannel Platinum atoms, parameters are indicated following values: atomic mass mpt = 195.08 g/mol, diameter σpt = 2.475A°, and potential depth Ԑpt = 8.35*10−20 J. Also, for the Copper nanoparticles atoms, parameters are accounted as following values: atomic mass mCu = 63.546 g/mol, diameter σCu = 2.338A°, and potential depth ԐCu = 6.5536*10−20 J. On the one side, the modified Lennard-Jones potential function coupling with mixing rules of Lorentz–Berthelot as following equations [29,30] is employed for the interatomic force between Argon-Platinum, CopperPlatinum and Argon- Copper atoms.
 ϕw rij ¼ 4ε12

2. Simulation method Present work uses MDS method to simulate boiling flow condition of nanofluids inside microchannel. MDS method is a computer simulation method for tracing the physical and location of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving an insight of the dynamic evolution of the system. In the most common version, the trajectories of particles (atoms and molecules) are determined by numerically solving Newton's equations of motion for a system of interacting particles, where forces between the

"   6 # σ 12 σ − r ij r ij

ε 12 ¼

pffiffiffiffiffiffiffiffiffiffi ε1 ε2

"    # σ 12 12 σ 12 6 − r ij r ij σ 12 ¼

σ1 þ σ2 2

r ij ≤r c

ð2Þ

ð3Þ

On the other side, for Copper-Copper atoms interactions, the interatomic potential of embedded atom model, embedded-atom method or EAM is employed as following formulation [31,32]: 
 1 X
 Ei ¼ F α ∑i≠ j ρβ r ij ϕ r þ 2 i≠ j αβ ij

ð4Þ

M. Zarringhalam et al. / Journal of Molecular Liquids 293 (2019) 111474

3

Fig. 1. Schematic of microchannel in front and perspective views.

where rij is introduced for the distance between atoms i and j, ϕαβ is a pair-wise potential function, ρβ is the contribution to the electron charge density from atom j of type β at the location of atom i, and F is an embedding function that represents the energy required to place atom i of type α into the electron cloud. Coefficients values of EAM potential function is detailed in reference as [33]. For computations of the system's motion through time, Newton's second law at the atomic level is used as the gradient of the potential function in following equation. ! 2! ! X d r dv Fi ¼ F ij ¼ mi 2i ¼ mi i dt dt i≠ j

ð5Þ

Then, temperature is calculated by Gaussian distribution as below formula: N atm 1 X 1 2 3 m v1 ¼ kB T Natm i¼1 2 2

ð6Þ

Association of previous formulations is done by velocity Verlet method to integrate the Newton law as following equations. vðt þ δt Þ ¼ vðt Þ þ aðt Þδt

ð7Þ

r ðt þ δt Þ ¼ r ðt Þ þ vðt Þδt

ð8Þ

To set thermodynamic state of system, atomic oscillations in the vicinity of the walls were adjusted with initial temperatures of 108 degrees of Kelvin. Also, initial fluid velocity was equilibrated with constant wall temperature. Then, external driving force was exerted at the entrance region of channel. Therefore, Argon fluid velocity and temperature can be increased logically with time step progress due to constant boundary wall temperature.

The nanoparticles are simulated spherically. This work was carried out within the framework of the simulation code, using the definition of the region as a sphere and filling the region by copper atoms. The gridding of this region depends on the crystalline structure of the materials for which the crystalline structure of the copper nanoparticle is FCC with a Lattice constant of 3.61 Angstrom [34]. Also for platinum microchannel walls, the grid structure is FCC and with a grid constant of 3.92 Angstrom. Despite equilibrium energy state is at around 150,000 time step, computational running is carried out until 1,000,000 time step to exhibit evolution of boiling process and distribution of atoms. 3. Results and discussion Present work studied influences of suspending of Copper nanoparticles into Argon base fluid in different cases of 2, 4 and 6 numbers of nanoparticles. Argon base fluid and nanofluids were flowing inside microchannel with square cross section. All cases of studied flows were enforced under external driving force of 0.002 eV/ A° at the entrance region of microchannel. Also, Argon atoms were under boiling condition by boundary wall temperature of 108 K. Results are reported respectively in density, velocity and temperature profiles. Figs. 2, 3, 4 and 5 presents density profiles of fluid and nanofluids flows inside microchannel at time steps of 250,000, 500,000, 750,000, and 1,000,000 regularly. Nanofluids are produced by suspending 2, 4 and 6 Copper nanoparticles into Argon base fluid flow orderly. As can be seen from these figures, addition of Copper nanoparticles increases density profile of fluid flow. Also, detail calculations showed that increasing number of suspended nanoparticles expands density profile of Argon base fluid as much as 20%, 35% and 55% in order of addition of 2, 4 and 6 Copper nanoparticles respectively. Moreover, it is clear from Figs. 2 to 5 that minimum density in the middle section of microchannel in belonged to time step 250,000 and its maximum is related to time

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0.05

0.04

Density at 250000 Time Step

0.05

Argon Argon + 2 Nanoparticles Argon + 4 Nanoparticles Argon + 6 Nanoparticles

0.04

0.03

0.03

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0.02

0.01

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0

500

1000

Bin Number

1500

0

Fig. 2. Density profile versus bin number at time step 250,000.

0.05

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Argon Argon + 2 Nanoparticles Argon + 4 Nanoparticles Argon + 6 Nanoparticles

Density at 500000 Time Step

0.04

0.04

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Bin Number

Fig. 3. Density profile versus bin number at time step 500,000.

1500

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M. Zarringhalam et al. / Journal of Molecular Liquids 293 (2019) 111474

0.05

0.05

Argon Argon + 2 Nanoparticles Argon + 4 Nanoparticles Argon + 6 Nanoparticles

0.04

Density at 750000 Time Step

5

0.04

0.03

0.03

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1000

Bin Number

1500

0

Fig. 4. Density profile versus bin number at time step 750,000.

0.05

0.05

Argon Argon + 2 Nanoparticles Argon + 4 Nanoparticles Argon + 6 Nanoparticles

Density at 750000 Time Step

0.04

0.04

0.03

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500

1000

Bin Number

1500

Fig. 5. Density profile versus bin number at time step 1,000,000.

0

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M. Zarringhalam et al. / Journal of Molecular Liquids 293 (2019) 111474

transfer rate, without turbulences, instability in density profiles and annoyance in normal distribution of atoms between neighboring layers. But, influences of nanoparticles are reduced at time step 1,000,000 due to completion of evaporation of Argon atoms. Figs. 6 and 7 present velocity and temperature profiles of fluid and nanofluids flowing inside microchannel. Both figures were drawn by sampling data from 1800 bins at time step 1,000,000. Each figure contains 4 profiles which are related to Argon base fluid with no nanoparticle and 3 nanofluids as shown in symbol boxes inside Figs. 6 and 7. Velocity profiles are supported by external driving force of 0.002 eV/Å, exerted on the fluid atoms at the entrance region of microchannel, whereas; boiling process is supported by boundary temperature of 108 K, applied into walls of microchannel. Overview from Fig. 6 shows that adding Copper nanoparticles into Argon base fluid upgrade velocity profile. Also, amount of this variation depends to number of suspended nanoparticles into base fluid. But important factor behind analysis of negative and positive influences is behind ratio of density and velocity variation. Because, summation of velocity and density values of 1800 bins indicated that addition of Copper nanoparticles in order of 2, 4 and 6 brings velocity enhancement as much as 17.8%, 32.6% and 52.8%, while; order of density enhancement were 20%, 35% and 55% respectively. Therefore, it can be found that ratio of velocity enhancement is less than ratio of density enhancement. The reason behind this phenomenon is related to role of suspended nanoparticle in increasing power of boiling process and increasing thermal driving force which is supported by boundary wall temperatures of 108 K. In fact, force of boiling process is not parallel with external driving force direction. Therefore, effects of suspending Copper nanoparticles with large number of atoms in empowering boiling process are perpendicular with external force. Thus, it cannot increase velocity and density proportionally. As can be seen from Fig. 7, temperature profiles are increasing with increasing number of nanoparticles. It is logic due to higher conductivity of Copper atoms than that of Argon atoms. Also, Argon nano layer structures around Copper nanoparticles are in higher conductivity level than that

Velocity (angstroms/picoseconds)

step 1,000,000 as validated by previous works [37,38]. Therefore, it is indicated that rising up time steps from 250,000 to 1,000,000, causes completion of boiling process and enhancement of density values in central layers in the middle section of microchannel. Because, Argon atoms are in phase change condition and high time steps increases kinetic energy of atoms while; total energy is unchanged. Therefore, intention of atoms to move from 2 lateral sections toward middle section of microchannnel is increasing with increasing time steps. On the other side, it is seen from Figs. 2 to 5 that density level in lateral regions of microchannel is maximum at time step 250,000, while its minimum is at time step 1,000,000. Hence, it is clear that domain of difference in density profiles, between Argon base fluid flow and nanofluids flow is reducing with increasing time step. Furthermore, Figs. 2 to 5 shows that difference of density values in the middle section of microchannel is noticeably lower than that of lateral region. Because, Argon atoms are in single gas phase in the central layers whereas; they can be in phase change condition in lateral regions under evolution of boiling process. Moreover, increasing time step to 750,000 and 1,000,000 shows that domain of between minimum and maximum values of density in profiles of Argon base fluid flow is lower than that of density profiles of nanofluids flows. Also, oscillation in density profiles of Argon base flow is lower than that of nanofluids. It is due to role of suspended nanoparticles in enhancement of heat transfer and empowering phase change and increasing atomic interaction which brings instability. In fact, thermal conductivity of Copper nanoparticles is higher than that of Argon fluid which is the reason of enhancement in conductivity of nanofluids. Therefore, it can be reported that suspending more number of Copper nanoparticles can result in acceleration of boiling process evolution which causes higher heat transfer rate. Also, it brings higher turbulences and fluctuations in distribution of atoms especially in the layers are in two symmetric regions in vicinity of microchannel walls. This phenomenon is obvious at time steps of 250,000, 500,000 and 750,000. Overview of Figs. 2 to 5 shows that presence of nanoparticles after time step 750,000 and before 1,000,000 is the best due to empowering boiling process and heat

Argon Argon + 2 Nanoparticles Argon + 4 Nanoparticles Argon + 6 Nanoparticles

Bin Number

Fig. 6. Velocity profile versus bin number at time step1000000.

M. Zarringhalam et al. / Journal of Molecular Liquids 293 (2019) 111474

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Temprature (degree of Kelvin)

Argon Argon + 2 Nanoparticles Argon + 4 Nanoparticles Argon + 6 Nanoparticles

Bin Number

Fig. 7. Temperature profile versus bin number at time step1000000.

of other regions of Argon base fluid. Hence, it results in augmentation of heat transfer rate and acceleration of boiling which leads to temperature enhancement of Argon atoms. Nevertheless, visual comparison between profiles of temperatures shows that difference between profiles of nanofluids with 4 and 6 nanoparticles is less that difference between profiles of base fluid and nanofluid with 2 nanoparticles. Also, difference between profiles of nanofluids with 2 and 4 nanoparticles is less than difference between profiles of base fluid and nanofluid with 2 nanoparticles. Therefore, it is revealed that first case of nanofluid with 2 nanoparticles can be more efficient in empowering boiling process and increasing flow temperature. On the other side, statistical approach indicated that effects of nanoparticles in increasing temperature values of 1800 bins are as much as 30.7%, 50.45 and 69.5% in order of 2, 4 and 6 suspended Copper nanoparticles into Argon base fluid respectively, whereas; densities enhancement were 20%, 35% and 55% respectively. Therefore, statistical approach shows that increasing number of suspending Copper nanoparticles into Argon base flow is not always economical. Because, percentage of flow temperature enhancement is not proportional with increasing number of nanoparticles, suspended into Argon base fluid. 4. Conclusion Present paper investigated effect of suspending 2, 4 and 6 Copper nanoparticles into Argon base fluid, flowing inside microchannel with square cross section under boiling condition. Argon atoms were enforced at the inlet section of microchanel with an external driving force of 0.002 eV/Å. Also to prepare required energy of boiling condition, microchannel walls were putted under boundary temperature of 108 K. Conclusions are as following: • Generally, addition of Copper nanoparticles increases density, velocity and temperature profile of fluid flow due to their role in empowering phase change condition and increasing number of atoms.

• Effect of suspended nanoparticles in oscillation of density profile and distribution of Argon base fluid atoms is stronger at lower time steps so that its maximum is seen at time step 250,000 and its minimum is related to time step 1,000,000. • Statistical approach showed that increasing number of Copper nanoparticles into Argon base fluid can accelerate phase change, heat transfer. It increases thermal driving force, turbulences and fluctuation in distribution of atoms which reduces power of external driving force to move Argon atoms forwardly. • Despite, role of suspending nanoparticle in upgrading density, velocity and temperature profiles, statistical approach showed that increasing number of nanoparticles is not always economical for practical application.

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