The molecular dynamics simulation of thermal manner of Ar/Cu nanofluid flow

Journal of Molecular Liquids 319 (2020) 114183

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

The molecular dynamics simulation of thermal manner of Ar/Cu nanofluid flow: The effects of spherical barriers size Amirhosein Mosavi a,b, Maboud Hekmatifar c, As'ad Alizadeh d, Davood Toghraie c, Roozbeh Sabetvand e, Aliakbar Karimipour f,⁎ a

Environmental Quality, Atmospheric Science and Climate Change Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran d Department of Mechanical Engineering, College of Engineering, University of Zakho, Zakho, Iraq e Department of Energy Engineering and Physics, Faculty of Condensed Matter Physics, Amirkabir University of Technology, Tehran, Iran f Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam b c

a r t i c l e

i n f o

Article history: Received 8 July 2020 Received in revised form 26 August 2020 Accepted 28 August 2020 Available online 31 August 2020 Keywords: Molecular dynamics simulation Spherical barrier Nanofluid Argon Copper Phase transition Thermal conductivity Thermal behaviour

a b s t r a c t In this computational work, we focus on spherical barrier effects on the thermal behaviour of Ar/Cu nanofluid with molecular dynamics simulation. LAMMPS software is implemented in our study with Universal Force Field and Embedded Atom Model force field for various atomic structures in the simulation box. The thermal behaviour study of Ar/Cu nanofluid is done with physical parameters calculations such as atomic temperature, total energy, number of nanofluid atoms at gas phase, radial distribution function, and thermal conductivity of Ar/Cu nanofluid. By atomic barrier adding to our simulated plates, the atomic phase transition occurs in fewer time steps. Numerically, phase transition in the simulated nanofluid occurs in 610,000-time steps by Pt spherical barriers simulation (with 15 Å radius). By increasing the atomic barrier size, the number of nanofluid atoms in which phase transition occur in them is increased. From these simulations results, we conclude that, heat flux in Ar/Cu nanofluid increases but thermal conductivity of the foremost constant. Numerically, the thermal conductivity of Ar/Cu nanofluid reaches to 0.016 W/m.K by atomic barrier radius increasing to 15 Å. © 2020 Elsevier B.V. All rights reserved.

1. Introduction Nanotechnology is one of the promising areas of science. The concepts that seeded nanotechnology were first discussed in 1959 by renowned physicist Richard Feynman in his talk There's Plenty of Room at the Bottom, in which he described the possibility of synthesis via direct manipulation of atoms [1]. Today, this method used in various areas such as electronic [2–6], heat transfer [7–11], etc. In addition to the above, one of the achievements of nanotechnology is nanofluid. Nanofluids are suspensions of nanoparticles in common base-liquids such as water, argon, etc. Several works in recent decades showed that the addition of an optimized rate of nanoparticles in cooling base-fluids optimized the thermal conductivity of these structures significantly.

Further, nanofluids convective heat transfer coefficients show a similar thermal manner, and this physical parameter increases by ⁎ Corresponding author.

E-mail addresses: amirhosein.mosavi@tdtu.edu.vn (A. Mosavi), aliakbarkarimipour@duytan.edu.vn (A. Karimipour).

https://doi.org/10.1016/j.molliq.2020.114183 0167-7322/© 2020 Elsevier B.V. All rights reserved.

optimization of the nanoparticles rates in base-fluid [12,13]. Numerically, experimental research calculated thermal conductivity enhancements in base-fluids were in the range 10–50%. Other experiment works showed enhancement values of the thermal conductivity coefficient in some nanofluids more than 100% [14]. To the efficient application of nanofluids thermal manner, the understanding of the heat transfer mechanism in these nanostructures was essential. Physically, Nanofluids are a promising type of heat transfer fluids, containing particles with 1 nm to 100 nm atomic size, which dispersed in a common base-fluids [15–18]. The nanostructures (nanoparticles), which dispersed in base-fluid, commonly made of metal or metal oxide materials.

This thermal manner of nanofluids allowing for heat energy transfer in various systems in industrial applications. Nanofluid structures have been assumed for applications as heat transfer fluids optimization.

However, due to the variety of these nanostructures, no agreement has been reported on the rate of benefits of using nanoparticles in common base-fluids for heat transfer mechanisms. For the first time, Choi introduced a promising class of fluids that depends on suspending nanostructures [19,20]. Choi et al. [21] calculated the thermal conductivity of carbon nanotube (CNT) structures which inserted in oil fluid,

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A. Mosavi et al. / Journal of Molecular Liquids 319 (2020) 114183

Nomenclature Fij Vij Fext m rc rij t T v Natom

interparticle force on particle i by particle j (eV/Å) interparticle potential (eV) external applied force (eV/Å) particle mass (u) cut-off distance (Å) distance between particle i and j (Å) time step (ps) temperature (K) velocity of particle (Å/ps) number of particles

Greek symbols ε energy parameter in Lennard-Jones (LJ) potential σ length parameter of LJ potential ϕ interaction potential θ0 Equilibrium angle

this research group conclude that the thermal conductivity of the studied oil increased significantly. Ahammed et al. [22] reported the thermal conductivity of the H2O base fluid at various temperatures. They showed that the thermal conductivity of nanofluid improves with increasing the optimized atomic rate of graphene nanoparticles. Numerically, the thermal behaviour of base fluid improves to 37.2% for 0.15% concentration of graphene nanosheets when compared with H2O base-fluid. Selvam et al. [23] prepared the promising nanofluid with ethylene glycol and H2O as based-fluid. They said that the thermal conductivity of nanofluids enhances with inserting nanoparticles to basefluid significantly. Ding et al. [24] researched about the thermal manner of H2O/CNT nanofluid with an experimental approach. This research group reported the optimization of the thermal behaviour approximately reach to 350% by adding CNT nanoparticles with a 0.5% atomic ratio.

Akhavan et al. [25] showed the transport coefficients of H2O basefluid increases by graphene nanoparticle, adding to base-fluid. They conclude the thermal conductivity of H2 O molecules can be optimized by adding nanostructures to them. Witharana et al. and Chen et al. [26,27] expressed that the science of the atomic manner and effect of nanofluids is a significant physical factor in planning their thermal behaviour for the heat transfer process. In various experimental studies, nanoparticles adding to common base-fluids cause phase transition to occur in base-fluid in shorter times. So we can conclude by inserting nanostructures to common base-fluids, the heat transfer rate in these structures improved. Today, theoretical methods like Molecular Dynamics (MD) simulation method can be used to the atomic study of various substances [28–30]. This computational approach is used in this study of nanostructures thermal, membranes and mechanical behaviours [31–41]. Li et al. in their simulation work which similar our research, studied the phase transition process of argon fluid in confined non-ideal Pt plates [42]. The simulation outcomes were that the molecular dynamics simulation approach accuracy on phase transition phenomena prediction in base-fluid, such as argon atoms. Further, Hekmatifar et al. studied the cone barriers effect on nanofluid phase transition phenomena.

The results of this computational work showed the significant impact of atomic barriers in the thermal manner of Ar/Cu nanofluid and the nanofluid phase transition phenomena [43]. In this work, we simulate Ar base-fluid thermal manner in a confined space which made of Pt plates by adding Cu nanoparticles. Pt plate in the upper region of our simulation box has a non-ideal surface with 9 spherical barriers in which the atomic size of these spherical structures affected to nanofluid thermal manner. For the study of thermal

behaviour in simulated structures, we report physical parameters such as temperature, total energy, the temperature of Ar/Cu nanofluid atoms, radial distribution function, number of nanofluid atoms in the gas phase, and thermal conductivity of nanofluid structure. We expected our MD simulation results could be used in the optimization of heat transfer procedures in industrial usages.

2. Computational method In this computational work, we use molecular dynamics simulations to research the dynamical behaviour of Ar/Cu nanofluid between nonideal Pt plates. Non-ideal plates in our simulations made of spherical atomic barriers with various radiuses. Theoretically, in MD simulations time evolution of particles over time steps and all simulation time. For estimation of the displacement of the atoms in the simulated time interval, Newton's second law used as below equation [30], 2

F i ¼ ∑F ij ¼ mi i≠j

d ri dv ¼ mi i dt dt 2

ð1Þ

where mi is the atomic mass, ri is the atom position, and finally, vi is the atom velocity. Further, Gaussian formalism used to particles temperature definition, which can be calculated by below equation [30]: 3 1 N 1 kB T ¼ ∑ mv2i 2 Natom i¼1 2

ð2Þ

Computationally, these computational equations calculated by the velocity-Verlet algorithm as [30]: r ðt þ Δt Þ ¼ r ðt Þ þ vðt Þ Δt þ vðt þ Δt Þ ¼ vðt Þ þ

1 aðt Þ Δt 2 2

1 ½aðt Þ þ aðt þ Δt Þ Δt 2

ð3Þ ð4Þ

In Eqs. (3) and (4), the r(t + Δt), v(t + Δt), and a(t + Δt) are final position, velocity, and acceleration of particles. Further, r(t), v(t), and a(t) are the initial rate of these parameters. In the initial step of our MD simulations, we use periodic boundary conditions in y and x directions and fix one implemented in the z-direction which these conditions commonly used in the MD approach [30]. The MD simulation box length set to 100 Å, 100 Å, and 130 Å in x, y, and z directions. Further, the 1 fs rate chooses for the simulation time steps in all MD simulation steps. Theoretically, to get correct calculations in MD based simulations, one should choose the atomic force-field based on the physical phenomena which studied. The force-field for nanofluid and metal structures (Pt non-ideal plates and Cu nanoparticle) in our simulations was based on a universal force field (UFF), and Embedded Atom Model (EAM) potentials, respectively [44,45]. In the UFF force field, the interaction between particles was stated by the Lennard-Jones (LJ) potential as [45]: " 6 # σ 12 σ U ðr Þ ¼ 4ε − ð5Þ r ≪ rc r ij r ij In Eq. (5), rij is the distance between j and j atoms, rc is the cutoff radius, and σ and ε parameters are the energy and length scales—these computational constants selected from force-field references. Further, in our MD simulations, metal structures simulated by EAM potential.

EAM potential represented by the below equation [46]: !

1 Ei ¼ F α ∑ρβ r ij þ ∑ϕαβ r ij ð6Þ 2 i≠j i≠j where rij is the distance between j and i atoms, ϕαβ is a pair-wise potential function, ραβ is the contribution to the electron charge density from

A. Mosavi et al. / Journal of Molecular Liquids 319 (2020) 114183

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Fig. 1. Schematic of Pt plates and Ar fluid modelled in our MD simulation study.

atom j of type β at the location of atom i, and Fα is an embedding function that represents the energy required to place atom i of type α into the electron cloud. After the force-field definition for various atomic structures, atom's time evolution described by Newton's law. For this, we use the Large Scale Molecular/Atomic Massively Simulator (LAMMPS) package. This simulation package released by Sandia National Laboratories in 1995 for the first time [47–50]. To use this stimulation package to describe Ar/Cu nanofluid thermal behaviour and phase transition phenomena, Pt non-ideal plates and H2O/Cu nanofluid structures simulated as depicted in Fig. 1. This schematic of the atomic system visualized by the Open Visualization Tool (OVITO) is shown in

Fig. 1 [51]. In this structure, the temperature of heat source and heat sink defined with below equations: T HeatSource ¼ 107:5−Δt

ð7Þ

T HeatSink ¼ T 4 ¼ 107:5 þ Δt

ð8Þ

In these two equations, the Δt is 22.50 K. Simulation box in perspective view. These temperature setting in the simulated structure implemented by Nose-Hoover thermostat [30].

Fig. 2. Temperature variation of Ar/Cu nanofluid and non-ideal Pt plates as a function of simulation time steps.

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A. Mosavi et al. / Journal of Molecular Liquids 319 (2020) 114183

3. Discussion and results 3.1. Equilibration process of simulated structures In the first step of this computational study to validate our MD simulation method, we equilibrated the Ar/Cu nanofluid and Pt non-ideal plates atomic structures. This atomic behaviour was similar to previous research and showed the appropriate choice for MD simulation setting [43]. In this section, the temperature and total energy of structures are calculated. Our result shows that 1,000,000-time steps are sufficient for thermodynamic equilibration of Ar/Cu nanofluid and Pt non-ideal plates. Figs. 2 and 3 show the temperature and total energy deference of these atomic structures. Numerically, from these figs. We conclude the temperature of simulated structures reaches to 85 K after 1,000,000-time steps. Further, the total energy of atomic structures shows that this physical parameter reaches to −381 eV. The negative magnitude of total energy shows that we choose the force field and atomic structures appropriately, and these structures have thermal stability. Computationally, the thermal stability of simulated structures arises from the atomic position and interatomic force-field mathematically adapting. These atomic manners show the initial atomic positions for various structures and interatomic force between them, defined with the appropriate way. After total energy and temperature equilibration process, we report the temperature, number of nanofluid atoms in the gas phase, Radial Distribution Function (RDF), and thermal conductivity of simulated nanofluid.

3.2. Average temperature of Ar fluid and Ar/Cu nanofluid structures In the second step of this molecular dynamics study, we simulated spherical barriers with the various radius as depicted in Fig. 4. After this atomic simulation, we calculated the average temperature of simulated nanofluid to predict the phase transition phenomena in Ar/Cu nanofluid. MD simulation results show by simulation time passing the heat flux movement in atomic structures rises and so the average temperature of Aar/Cu nanofluid increases. This atomic manner arises from the contact surface area between Ar/Cu nanofluid and Pt plate atoms increasing. This atomic contact increasing cause improves the atomic interaction and finally, the nanofluid particles mobility and temperature increases, too. Physically, by Ar/Cu nanofluid temperature increasing the phase transition in this atomic structure occur. Fig. 5 shows the nanofluid temperature variation in the middle region of the simulation package as a function of time. Our simulations show that the temperature of nanofluid atoms changes from 90 K to 113 K after 1,000,000time steps. Numerically, the phase transition phenomena detectable

Fig. 4. Atomic modelling of Pt spherical barrier with a) 5 Å, b) 7.5 Å, and c) 10 Å radius.

Fig. 3. Total energy difference of Ar/Cu nanofluid and non-ideal Pt plates as a function of MD simulation time.

A. Mosavi et al. / Journal of Molecular Liquids 319 (2020) 114183

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Fig. 5. Temperature variation of Ar/Cu nanofluid as a function of spherical barrier radius and simulation time steps.

after 1,000,000-time steps. By increasing of spherical barriers radius from 5 Å to 10 Å in non-ideal Pt plate, the average temperature of nanofluid reach to 126 K. Further, the phase transition in simulated nanofluid detectable after 425,000-time steps. Time evolution of Ar/Cu nanofluid temperature and phase transition time of nanofluid atomic structure reported in Table 1 as a function of barrier radius.

Table 1 Average temperature and phase transition time in Ar/Cu nanofluid as a function of spherical barrier radius and simulation time steps.

Barrier radius (Å)

The temperature in final time step (K)

Phase transition time (ns)

5 7.5 10

113 120 126

771,000 510,000 425,000

3.3. Number of nanofluid atoms in gas atomic phase The number of nanofluid atoms in various atomic phase is an important parameter for heat transfer applications. We report the number of Ar/Cu nanofluid atoms in the gas phase after the phase transition process in our MD simulations. Our results show that the number of nanofluid atoms in the gas phase increases to 3136 from 2562 after 1,000,000-time steps. By radius of spherical barrier enlarging from 5 Å to 10 Å, the number of nanofluid atoms in the gas phase reaches to 3214. Previous computational work shows a similar atomic manner [42]. Li et al. show that atomic barriers have a direct effect on the number of atoms in the phase transition process, and by adding this atomic parameter to simulated structures, phase transition phenomena occur effectively. Physically, this atomic improvement arises from increasing of atomic contact between plates and nanofluid particles which cause the heat flux increasing in the simulated structures. By heat flux increasing between the plate and nanofluid particles, the acceleration of nanofluid particles rises, and displacement of these particles get harder.

By this mechanical parameter changes, the atomic distance between nanofluid particles increases and the gas phase in this structure

Fig. 6. Number of gas atoms in Ar/Cu nanofluid as a function of the molecule dynamics simulation time step and Pt barriers radius.

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Table 2 Number of gas atoms in Ar/Cu nanofluid and needed MD simulation time step for atomic phase transition to occur.

Barrier radius (Å)

Number of nanofluid atoms in gas phase (atoms)

Time step of maximum rate of phase transition

5 7.5 10

3136 3189 3214

780,000 670,000 610,000

detectable. Fig. 6 shows the number of nanofluid atoms in the gas phase as a function of spherical barrier radius and MD simulation time steps.

Further, our MD simulations show that by atomic barriers enlarging, the time step of MD simulations to reach a maximum rate of atoms in the gas phase decreases from 780,000 to 610,000-time steps, as reported in Table 2.

3.4. Phase transition process of simulated Nanofluid The radial distribution function (RDF) is one of the physical parameter in common molecular dynamics simulation. In our study, RDF reported shows the probability of fluid atom finding at a distance r from other fluid atoms. This physical parameter presented by this Eq. (9) [30]: dnr g ðr Þ ¼ 4π dr ρ

3.5. Thermal conductivity of simulated nanofluid In industrial applications of nanostructures as a heat transfer apparatus, the thermal conductivity of them is an important parameter. In the last step of this MD simulations, we compute the thermal conductivity of Ar/Cu nanofluid with 2 simulation methods: equilibrium and nonequilibrium methods. In equilibrium calculations, we use the GreenKubo (GK) method [53,54]. In this computational method, thermal coefficient calculated by integrating time autocorrelation functions of heat flux with the equation below [54]: λ¼

In this equation, ρ is the density, dnr is a function that calculates the number of fluid atoms within a shell of thickness dr. RDF analyze result difference in this simulations show the phase transition phenomena and convert liquid phase to gas one in Ar/Cu nanofluid structure.

Based on Fig. 7, we can express that the Ar atomic structure in 0-time step has liquid phase, by MD simulation time evolution, RDF curve of Ar fluid show the phase transition process after 450,000-time steps. Further, this calculated RDF curve for liquid phase of Ar fluid is similar to earlier reports, which shows the correctness of this molecular dynamic simulations settings and validation of our simulation procedure [52].

Further, the phase transition process and attraction of fluid atoms to up non-ideal Pt plate as a function of simulation time steps, depicted in Fig. 8. As depicted in this Fig. By simulation time passing the number of fluid atoms in the gas phase increases, and we conclude the phase transition process occurs in the simulated structure.

Z∞

T 2 kB V

<J ðt Þ:J ð0Þ >

ð10Þ

0

In this formula, V is the volume of the atomic system, J(t) is the heat flux and T is the temperature of structure, and finally, kB is the Boltzmann constant. GK approach predicted the thermal conductivity of Ar/Cu nanofluid is 0.016 W/m.K. Further, the Fourier approach used for non-equilibrium method simulation of nanofluid thermal conductivity. According to the heat conduction, that indicates that the heat flow per unit area in unit time is proportional to the temperature variation at the cross-section of structures. In this method, we can write [54]: λ¼

ð9Þ

1

Q=AΔt dT=dz

ð11Þ

In Eq. (11), Q is the heat flow of the structure, and A is the crosssection, Δt is the time difference and, dT/dz. is the temperature gradient in the atomic system. By estimating the temperature and heat flow difference in MD simulations, the thermal conductivity calculated by Eq. (11). To thermal conductivity calculation from the nonequilibrium approach, the simulation package is divided into 100 slabs with 100 D thickness, where D is the length of the simulation box. The temperature of the heat source region is fixed at 157.5 K, and the temperature of heat sink temperature is equilibrated at 57.5 K. For temperature equilibration in our MD simulations, we use the NPT ensemble with 0.01 and 0.1 values for pressure and temperature damping rates.

After this equilibrium process, we implement the NVE ensemble for 1,000,000-time steps to reach constant heat flow in a simulated nanofluid. After this computational process, MD simulations run continued for 1,000,000-time steps later and finally, the thermal conductivity of simulated nanofluid reported. This computational procedure

Fig. 7. RDF curve of Ar\ \Ar in nanofluid structure as a function of the MD simulation time step.

A. Mosavi et al. / Journal of Molecular Liquids 319 (2020) 114183

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estimated the thermal conductivity of nanofluid equal by 0.016 W/mK. Fig. 9 depicted the thermal conductivity changes of Ar/Cu nanofluid as a function of MD simulation time steps. From this Fig. We conclude as MD simulation running, the thermal conductivity of nanofluid decreases and then converged to a constant value. By atomic barrier enlarging, we expect the heat flux in simulated structures increases, but thermal conductivity of them remain consistent. The maximum rate of thermal conductivity reaches to converged rate after 355,000 and 493,000time steps for the smallest and most significant atomic barriers in equilibrium MD simulations. This atomic manner shows the thermal interaction between nanofluid particles and Pt atoms done in shorter time steps by atomic barrier size increasing. This MD simulation result can be used for thermal conductance structures designing to reach the optimal performance of them. Numerically, 0.018 W/m.K and 0.016 W/m.K rates for thermal conductivity of Ar/Cu nanofluid thermal conductivity calculated with non-equilibrium MD simulations as reported in Fig. 10 and Table 3. We can conclude that by atomic barriers increasing the atomic interaction between nanofluid and plate atoms increases and the amplitude of atomic fluctuations increases. These physical phenomena cause mobility increasing in simulated structures, and so the thermal coefficient of simulated nanofluid increases.

4. Conclusion In our computational study, the thermal behaviour of Ar/Cu nonfluid between the ideal and non-ideal Pt plates reported. In these MD simulations, the barriers size effect on Ar/Cu nanofluid phase transition procedure reported for the first time, and we expected these effects, optimize the thermal conductance procedures in industrial applications. Our results show that the presence of the atomic barrier is having an essential impact on the phase transition process of simulated nanofluid. Atomic barriers in our simulation are spherical shape. Physically, by spherical barrier's radius increasing, the total heat flux in atomic structures increases and thermal conductivity of Ar/Cu nanofluid converged in a shorter time. Numerically, we conclude that: • Spherical barrier radius increasing cause phase transition in Ar/Cu nanofluid occur in shorter time steps (T = 780,000 to T = 610,000).

• The average temperature of Ar/Cu nanofluid increases from 113 K to 126 K by spherical barrier radius enhancing from 5 Å to 10 Å.

• The number of Ar/Cu nanofluid atoms in the gas phase increases from 3136 to 3214, by spherical barriers radius increasing from 5 Å to 10 Å.

• Thermal conductivity of Ar/Cu nanofluid reach to 0.016 W/m.K by using molecular equilibrium dynamics, and non-equilibrium molecular dynamics approach.

These outcomes of our simulations from LAMMPS software can be used in difference industrial procedures like heat transfer mechanisms designing to increase their efficiency.

CRediT authorship contribution statement Amirhosein Mosavi: Writing - review & editing, Investigation.

Maboud Hekmatifar: Methodology, Software, Validation, Writing - review & editing, Investigation. As'ad Alizadeh: Methodology, Software, Validation, Investigation. Davood Toghraie: Methodology, Software, Validation, Writing - original draft, Investigation. Roozbeh Sabetvand: Methodology, Software, Validation, Writing - review & editing, Writing - original draft. Aliakbar Karimipour: Writing - review & editing, Writing - original draft.

Fig. 8. The Ar atoms arrangement in the simulation box as a function of the molecular dynamics simulation time step: a) T = 0, b) T = 500,000, and c) T = 1,000,000 time steps.

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A. Mosavi et al. / Journal of Molecular Liquids 319 (2020) 114183

Fig. 9. Thermal conductivity variation of Ar/Cu nanofluid as a function of the simulation time step and atomic barrier height (equilibrium MD simulations).

Fig. 10. Thermal conductivity variation of Ar/Cu nanofluid as a function of the simulation time step and atomic barrier height (non-equilibrium MD simulations).

References Table 3 Calculated thermal conductivity of Ar/Cu nanofluid by using equilibrium and non-equilibrium methods as a function of atomic barrier heights.

Barrier height (Å)

Equilibrium MD method (W/mK)

Non-equilibrium MD method (W/mK)

5 7.5 10

0.017 0.016 0.016

0.018 0.016 0.016

Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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