Empowering the boiling condition of Argon flow inside a rectangular microchannel with suspending Silver nanoparticles by using of molecular dynamics simulation

Journal Pre-proof Empowering the boiling condition of Argon flow inside a rectangular microchannel with suspending Silver nanoparticles by using of molecular dynamics simulation

Yeping Peng, Majid Zarringhalam, Mehdi Hajian, Davood Toghraie, Shahrzad Jafari Tadi, Masoud Afrand PII:

S0167-7322(19)34577-5

DOI:

https://doi.org/10.1016/j.molliq.2019.111721

Reference:

MOLLIQ 111721

To appear in:

Journal of Molecular Liquids

Received date:

14 August 2019

Revised date:

4 September 2019

Accepted date:

7 September 2019

Please cite this article as: Y. Peng, M. Zarringhalam, M. Hajian, et al., Empowering the boiling condition of Argon flow inside a rectangular microchannel with suspending Silver nanoparticles by using of molecular dynamics simulation, Journal of Molecular Liquids(2018), https://doi.org/10.1016/j.molliq.2019.111721

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© 2018 Published by Elsevier.

Journal Pre-proof

Empowering the boiling condition of Argon flow inside a rectangular microchannel with suspending Silver nanoparticles by using of molecular dynamics simulation Yeping Peng1, Majid Zarringhalam2, Mehdi Hajian3, Davood Toghraie4, Shahrzad Jafari Tadi5,

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Masoud Afrand6,7*

1

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Shenzhen Key Laboratory of Electromagnetic Control, College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen 518060, China

2

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Young Researchers and Elite Club, South Tehran Branch, Islamic Azad University, Tehran, Iran

3

Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, 84156-83111,

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Iran

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Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran

5

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Department of Petroleum Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran

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Laboratory of Magnetism and Magnetic Materials, Advanced Institute of Materials Science, Ton Duc

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Thang University, Ho Chi Minh City, Vietnam

7

Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam

*Corresponding author: Email: [email protected]

Corresponding author at: Ton Duc Thang University, Ho Chi Minh City, Vietnam

Abstract This paper presents influences of suspending a different number of Silver nanoparticles on the flow parameters of Argon base fluid, which is under boiling condition inside a cubic microchannel. Argon flow is enforced by an external force of 0.002 eV/ A°. Also, a constant temperature of 108K is applied to the walls of the microchannel to prepare boiling flow condition. Presence of Silver nanoparticles empowers heat transfer rate and brings stronger phase change. It is the reason of sooner translocation of base fluid atoms from the vicinity of microchannel walls to the center of the microchannel in z1

Journal Pre-proof direction. This phenomenon enhances fluid temperature whereas; it is not in favor of external driving force, which supports the velocity of fluid flow inside microchannel in x-direction. Despite fluctuation in density profiles, it is indicated that Silver nanoparticles are never attached together. Also, the influence of nanoparticles on the density fluctuation is significant at lower time steps. Afterward, the statistical approach is employed to present accurate results. It was found that presence of two, four and six nanoparticles into Argon base fluid increases summation of density as much as 20%, 37% and 67%, Whereas; they bring enhancement in summation of temperatures as much as 20%, 49%, and 84% respectively. Finally, it is concluded that investment on preparing nanofluid by suspending two nanoparticles into Argon base fluid is not economical for practical application; while, suspending four and six numbers of Silver nanoparticles is applicable for practical application.

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Keywords: Microchannel; Molecular dynamics simulation; Ag-Argon nanofluid; Boiling condition.

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1- Introduction

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Investigations on the micro and nanoscale flows have attracted strong importance due to the

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essential applications in the micro and nanofluidic system in equipment. Because micro and nano flow characteristics can be completely different from flow characteristics at the

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macroscale. Also, in the present situation, experimental probes are still complicated in very

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small micro, and nano sizes flow. Because continuum approaches is broken down, so, molecular dynamics simulation (MDS) is employed as a reliable computational system in the prementioned scale. Nowadays, many researchers present their studies on the fluid flows inside the different microchannel. Also, suspending nanoparticles into base fluids has been an innovative way to empower thermophysical properties of working fluids to increase the heat transfer. Moreover, many numerical and experimental studies have investigated the behavior of the nanofluid flows and the effect of nanoparticles under different conditions which have been published as references [1-9]. But, the domain of their applications is not still in small scale of channels. Moreover, in the small microchannels, due to the limited channel widths, the fluid can be inhomogeneous on the channel surfaces which causes Navier-Stokes

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Journal Pre-proof equations fail to predict the flow parameters such as density, velocity, viscosity, temperature and so on. During the last decade, many papers were presented results of studies on the fluid flows within different nanochannels using molecular dynamics simulation. But, most of them have focused in the study of fluid flows with a limited number of atoms in nanochannels with the very small scale of nano and under single-phase condition of fluids. Therefore, in this work, Molecular dynamics simulation method (MDS) is used to aid statistical approach to

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investigate influences of suspending Silver nanoparticles on the flow behavior of Argon base

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fluid under phase change condition within a cubic microchannel.

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Minli et al. [10] using molecular dynamics simulation, probed the flow behavior of Argon-

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Copper nanofluid with cylindrical nanoparticles inside the nanochannel. In this research, the lower wall of nanochannel was fixed, and the upper walls were moved at speeds of 30 to 100

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m/s. They presented the density of nanofluids in 125 layers of fluid and observed that the

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nanofluid density in the flow center was higher than the other points. Also, the nanofluid velocity was also in nonlinear trend, while it was linear in the base fluid. Therefore, they

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concluded that the velocities values of nanoparticles into nanofluid are relatively higher than the velocity values of the base fluid. The angular and transient velocities of nanoparticles were investigated in the three directions of the coordinate system. Finally, it was found that these velocities are increased with shear velocity enhancement, which also affects the heat transfer and momentum exchange rate. Razmara et al. [11] employing the MDS method showed that the presence of roughness on the surfaces of nanochannel brings turbulences into nanofluid flow inside a channel, which leads to energy dissipation. Because it increases contact surface between solid and liquid. Also, it increases the thickness of the fluid layer adjacent to the nanochannel wall, which is the reason for fluid particles around the nanoparticles to move toward the wall and reduces

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Journal Pre-proof the thickness of the fluid layer around the metal nanoparticles. Consequently, nanoparticles can agglomerate together. Therefore, it was concluded that in order to prevent from nanoparticles clustering, the nanochannel surfaces should be as smooth as possible. Aminfar et al. [12] employing the MDS method, probed the effect of different types of Copper and Platinum solid particles into Argon base fluid in a nanochannel with different parameters of the Lennard-Jones potential. They concluded that the effect of external applied forces on the Platinum nanoparticles is more effective than that on the Copper nanoparticles.

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These researchers concluded that increasing cut off radius causes to delay in clustering

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phenomenon of nanoparticles. They also reported that the force of gravity (attractive force)

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between metal particles is stronger than the forces between that of the fluid particles which

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cause the nanoparticles of neighboring layers to attach together by Brownian motions. It means the stronger bond of molecular forces between metal nanoparticles, (compared with

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the bond of forces between nanoparticles with base fluid particles in the adjacent layer),

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results in the reduction of fluid particles between nanoparticles and eventually nanoparticles stick together. Obviously, metal nanoparticles are intended for each other. It is the reason of

nanofluid flow.

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emerging oscillation and non-uniform distribution of covalence interactions inside the

Also, in another study, Aminfar et al. [13] observed that suspending nanoparticles into Argon base fluid reduces fluid adherence to the nanochannel solid wall, which leads to increase in the length of fluid slip on the solid wall. It results in the reduction of boundary layer thickness on the wall and improves heat transfer efficiency in solid walls. These results were in accordance with the results of experimental research by Zarringhalam et al. [14]. They reported that applying different external forces can destroy the structure of the nanofluid, which increases the flow rate at the center of the nanochannel. Also, the enhancement of external force can decrease enthalpy and total energy of the system.

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Journal Pre-proof Davood Toghraie et al. [15] simulated Poiseuille flow of Argon inside nanochannel, containing different cases of two, three and four Copper and Platinum nanoparticles exerted in Argon base fluid using molecular dynamics simulation method. They observed that the suspending more number of nanoparticles, reduce the required time for agglomeration of the nanoparticles. Moreover, they reported that the agglutination time in a nanochannel with Copper particles is faster than in Platinum nanoparticles. Furthermore, according to their results, the existence of nanoparticle leads to increase the thermal conductivity of Argon base

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fluid.

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Frank et al. [16] employing molecular dynamics simulation probed the flow properties of

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Argon-Copper nanofluid inside the nanochannel. They observed that increasing the

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nanoparticle volume fraction increases the thermal conductivity of the nanofluid. These researchers also found that the nanochannel width was effective on thermal conductivity.

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They also reported that increasing nanochannel width causes to decrease the density of

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nanolayers around the particles, which reduce the thermal conductivity. On the other side, decreasing the nanochannel width increases the contact surface of the fluid particles

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exponentially. So, nanolayers occupy more space of system which brings thermal conductivity enhancement.

Also, the other published papers in references [17–27] present the molecular dynamics studies on the boiling and phase change condition behavior of Argon flow within different nanochannels with a limited number of particles. Moreover, references [33- 45] present studies in nanofluid flow by Eulerian and Lagrangian systems, which indicate the need for research in the nanofluid studies. Above review shows that molecular dynamics simulation studies on the nanofluids flows have been limited to the limited number of atoms. Also, there is a gap between theoretical studies and practical applications due to the difference between sizes of theoretical studies

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Journal Pre-proof and practical applications. Furthermore, the previous study in boiling flow condition and phase change is also limited to a few works are in very small nanoscales. Therefore, present molecular dynamics simulations are concentrated to study on the effect of suspending nanoparticles into a large number of Argon base fluid particles which are under boiling condition within a cubic microchannel by a statistical approach.

2- Simulation method

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Present simulations were performed by MDS method. Molecular dynamics simulation (MDS)

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is a computer simulation method to research the physical translocation of particles. The

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particles are allowed to interact for an appropriated period of time, to present a view of

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the dynamic evolution of the system. In this method, the motion of atoms and molecules are traced numerically by solving Newton's equations of motion for a system contains particles

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are interacting together, where forces between the particles and their potential energies are

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often determined to employ interatomic potentials or molecular mechanics force fields. Also, present MDS are simulated by LAMMPS software. LAMMPS is free and open-source

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software, distributed under the terms of the GNU General Public License. Present work is done as the below procedure.

First Platinum microchannel is simulated in size of 10000*5000*5000 A°3 in order of x, y and z Axes. Then Argon fluid atoms are put in the lateral region of the microchannel, and middle section of the microchannel is empty. Afterward, Silver particles are suspended inside Argon base atoms in diameter size of 25nm. Therefore, computational running is performed for 4 cases of study. First, Argon fluid contains no nanoparticle, and then Ag-Argon nanofluid is simulated in order of two, four, and six suspended nanoparticle, respectively. Fig. 1 shows front and perspective views of Ag-Argon nanofluid with six nanoparticles flowing inside cubic microchannel schematically. Microchannel height is divided into 1800

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Journal Pre-proof bins in Z direction. Structure of atoms is Face Center Cubic (FCC) with a lattice constant of 5.26 A°. Then, to prepare boiling flow condition in the z-direction, boundary temperature of 108K is applied on the Argon atoms through walls of microchannel. Also, an external propulsion force of 0.002 eV/ A° is compelled on the fluid flow at the entrance of

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microchannel in the x- direction.

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

equation:    (rij )  4   rij 

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The interatomic force between fluid atoms is accounted by LJ potential function as below

12 6            rij  

rij  rc

(1)

where rij , defines the interatomic space from atom i to atom j. Next, energy factor is introduced by Ԑ as the depth of the potential well, next cut-off distance is shown with rc which is as much as 8.5125 A°. The atomic mass, diameter, and potential depth of Argon fluid atoms are accounted respectively as much as mAr=39.95 grams/mole, σAr=3.405A° and -21

ԐAr=1.67*10

J. For the microchannel Platinum atoms, parameters are accounted as values

of: atomic mass mpt=195.08 grams/mole, diameter σpt= 2.475A°, and potential depth Ԑpt=8.35*10-20J.

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Journal Pre-proof Also, for the Silver nanoparticles atoms, parameters are accounted as following values: atomic mass mAg=107.87 grams/mole, diameter σAg= 2.664A°, and potential depth ԐAg=5.52*10-20J.

Then, for the interatomic force between Argon-Platinum, Silver-Platinum

and Argon- Silver interactions, the modified Lennard-Jones potential function was employed [28, 29],   12   6  w (rij )  412  12    12    r    rij   ij   

(2)

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1   2 2

(3)

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 12 

 sf  1 2

rij  rc

𝑖≠𝑗

𝜌𝛽 (𝑟𝑖𝑗 ) ) +

1 ∑ 𝜙𝛼𝛽 (𝑟𝑖𝑗 ) 2 𝑖≠𝑗

(4)

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𝐸𝑖 = 𝐹𝛼 (∑

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particles as following equation [30-31]:

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Also, the interatomic potential of embedded-atom method (EAM) was used for Silver-Silver

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where rij is the interval length between atoms i & 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

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i, and 𝐹 is an embedding function. Detail coefficients of embedded atom model potential function are presented in reference [32]. To propagate the system's motion with time, Newton’s second law is introduced in below equation.

d 2 ri dv i Fi   Fij  m i  mi 2 dt dt ij

(5)

Then, flow temperatures are determined using Gaussian distribution as following equation:

1 N atm

N atm

1

2m v i 1

i

2

3  k BT 2

(6)

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Journal Pre-proof Association of previous formulations is done by velocity Verlet method to integrate the Newton law as below equations,

v(t   t )  v(t )  a(t ) t

(7)

r (t   t )  r (t )  v(t ) t

(8)

Fig. 2 presents the energy stability state per time step. According to Fig. 2, total energy reached to equilibrium state before 20000 time step, but computational running is performed

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until 1000000 time step. As can be seen from Fig. 2, after equilibrium energy state, total energy was constant, and no noticeable energy drop was found for all cases of study.

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Therefore, the phenomenon of agglomeration does not happen for the nanoparticles. -48200

-48600

-48600 -48800

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-48800 -49000 -49200

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-49400 -49600 -49800

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Total Energy (eV)

-48400

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-48400

-48200

-50000 -50200

-49000 -49200 -49400 -49600

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

-49800 -50000 -50200

-50400

-50400

-50600

-50600

0

20000

40000

60000

80000

100000

Time Step

Fig. 2: Energy stability per time step.

3- Results and discussion Present work investigates effects of suspending different numbers of Silver particles into Argon fluid flowing inside a cubic microchannel under propulsion force of 0.002 eV/ A°. Argon atoms were under boiling condition by boundary wall temperature of 108 K. Results were as following. 9

Journal Pre-proof Figs. 3 to 6 present density profiles of Argon fluid flow inside microchannel under the boiling condition at time steps of 250000, 500000, 750000 and 1000000, respectively. Each figure contains 4 profiles which are related to 4 cases of study. First, the density graph of base fluid (without Silver nanoparticle) was drawn in different time steps. Afterward, other density profiles were reported for suspending nanoparticles into Argon base fluid in order of two, four, and six. As can be seen from Fig. 3, middle section of the microchannel is completely empty at time

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step 250000. According to Fig. 4 in time step 500000, despite increasing density values in the

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middle section; there are still some empty layers in this time step, while; no empty layer is

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seen at time steps 750000 and 1000000. Therefore, increasing time steps causes Argon atoms

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to move from lateral sections to the middle of microchannel under the boiling process. It means that evolution of the boiling process can be completed with increasing time steps.

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Generally, it is clear from Fig. 3 to 6 that adding nanoparticles increases density. Also, an

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increasing number of suspended nanoparticles enhance density profiles. It is logic due to the increasing number of atoms. However, a comparison of these figures shows that the role of

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nanoparticles has higher importance at lower time steps. Because the difference between density profiles is maximum in time steps 250000, and this difference is reduced with increasing time steps to 500000, 750000 and 1000000. orderly. This phenomenon can be convinced by the role of nanoparticles in empowering boiling process at lower time steps, which cause to occur sooner phase change in Argon atoms. Hence, adding more Silver particles into Argon can result in reduction of required time to complete boiling process of the base fluid. On the other side, density oscillation of profiles is maximum at time step 250000, and it is declined with rising up time steps. Also, maximum density fluctuation belongs to the case of study with six Silver particles, and it is reduced by reducing the number of suspended nanoparticles. Therefore, despite of positive role of nanoparticles in

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Journal Pre-proof improvement of boiling process, they bring so instability in normal distribution of Argon fluid atoms that density values alter between 0.01 gram/cm3 and 0.04 gram/cm3 in time step 250000 with 6 suspended nanoparticles, whereas, this difference is reduced averagely to range of 0.01 gram/cm3 to 0.03 gram/cm3 at time step 500000. Also, maximum and minimum of density profiles of nanofluids are approximately between 0.012 gram/cm3 to 0.03 gram/cm3 at time steps of 750000 and 0.01 gram/cm3 to 0.025 gram/cm3 at time steps 1000000 respectively.

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Therefore, the negative role of nanoparticle in the distribution of fluid atoms is noticeable at

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lower time steps, and rising up time steps can diminish this phenomenon. Thus, it is

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concluded that the presence of Silver nanoparticles empower boiling flow condition and heat

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transfer rate from boundary wall temperature. It is the reason for stronger phase change,

0.05

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

Density at 250000 Time Step

0.04

0.03

0.02

0.02

0.01

0.01

500

1000

1500

0.05

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

0.04

0.04

0.03

0

0.05

0.05

Density at 500000 Time Step

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fluctuation in lower time steps.

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which increases translocation of atoms between different layers that augmentates density

0

0.03

0.03

0.02

0.02

0.01

0.01

0

Bin Number

0.04

500

1000

1500

Bin Number

Fig. 3: Density profiles at 250000 time step

Fig. 4: Density profiles at 500000 time step

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0

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

0.02

0.02

0.01

0.01

500

1000

1500

Density at 750000 Time Step

0.03

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

0.04

0.04

0.03

0.05

0.04

0.03

0.03

0.02

0.02

0.01

0.01

0

0

500

1000

1500

Bin Number

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Bin Number

Fig. 6: Density profiles at 1000000 time step

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Fig. 5: Density profiles at 750000 time step

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Figs. 7 and 8 present velocity and temperature profiles of fluid flow at 1000000 time step. These profiles were drawn by velocity and temperature values in 1800 bins of Argon and

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nanofluid flow, which contains nanoparticles in order of two, four, and six respectively. Velocity profiles are supported by force of 0.002 eV/ A° at the entrance region, whereas; boiling is reinforced by temperature of 108 K. Taking into consideration in overall view of

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Density at 750000 Time Step

0.04

0

0.05

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density distribution, velocity and temperature profiles in figures 2 to 7, it is demonstrated that normal condition of nanoparticles distribution does not change strongly which is in contrast with results of previous studies by Aminfar [12] and Razmara [13]. Therefore, result of increasing dimension of channel and flow from nanoscale to micro scale shows that initial arrangement of Argon atoms and Silver nanoparticles is kept in normal condition, and no agglomeration is occurred throughout 1000000 time step, while; previous researchers [12, 13] had reported sticking of nanoparticles and reducing nano layer thickness which causes flow parameters to be weakened. Nevertheless, the general view of Figs. 7 and 8 shows that suspending Silver particles increases velocity and temperature values. Moreover, an

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Journal Pre-proof increasing number of suspended nanoparticles increases velocity and temperature values. Because, as is clear in density analysis, adding Silver nanoparticles increases the general number of atoms into 1800 bins inside microchannel, so that summation of density values in 1800 layers are enhanced as much as 20%, 37% and 67% in order of adding two, four and six nanoparticles. But, the summation of density values in 1800 layers indicated velocity enhancement as much as 19%, 32% and 64% in order of adding two, four, and six nanoparticles. In fact, augmentation in percentage values of velocity is less than enhancement

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in percentage values of density. Therefore, the statistical approach demonstrates that despite

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previous imagination from Fig. 7, effect of suspending two nanoparticles does not strongly

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affect the velocity. Also, suspending four and six nanoparticles can bring augmentation in

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summation of velocity profiles. It means, in case of replacing four and six nanoparticles with Argon base fluid equally, enhancement values of velocity shall be more than 32% and 64%.

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This phenomenon is related to influences of nanoparticles in empowering of energy transfer

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and phase change, which reduces the velocity of Argon atom. Moreover, statistical analysis of temperature results from the summation of temperature

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values in 1800 layers demonstrates temperature augmentation as much as 20%, 49% and 84% in order of adding two, four and six nanoparticles. It means that except the case of suspending two nanoparticles, adding nanoparticles into base fluid causes to increase the temperature of fluid flow despite of their role in the reduction of velocity. Therefore, there is no doubt in emphasizing their effects in completion of the boiling process of Argon atoms and preparing sooner phase change in Argon base fluid. Consequently, the thermal driving force of boiling flow is enhanced in z-direction. Therefore, immigration of Argon atoms from lateral regions to the central region of the microchannel is accelerated. This occurrence is not in favor of external driving force, which supports velocity of fluid flow inside microchannel in the xdirection. Thus, velocity is reduced in the exposure of contradiction between empowered

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Journal Pre-proof thermal driving force of boiling (powered by a wall temperature of 108K) and constant external force of 0.002 eV/ A°.

5.5

5.5

5

1000

4.5

4

3.5

Temprature (degree of Kelvin)

4

3.5

3

3

2.5

2.5

2

1.5

1.5

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

0.5

500

1000

1

0.5

1500

600

600

400

400

200

0

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Bin Number

0

800

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1

800

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2

1000

500

1000

1500

4- Conclusion

Fig. 8: Temperature profiles at 1000000 time step

Present work studied the effect of Silver nanoparticles on the boiling of Argon within the cubic microchannel. First, the Argon base fluid was simulated. Then, Silver nanoparticles were suspended into Argon base fluid in order of two, four, and six separately. Finally, results of density, velocity, and temperature were analyzed as following: 1) Generally, despite deceptive results by velocity and temperature profiles, statistical results demonstrated that using two suspended Silver nanoparticles does not change flow behavior. Therefore, investment in this case, is not economical for practical application. 2) Presence of nanoparticles into Argon base fluid brings stronger boiling condition, which is noticeable at lower time steps. Also, an increasing number of suspended nanoparticles reduces the required time for the evolution of the boiling process. 14

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Bin Number

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Fig. 7: Velocity profiles at 1000000 time step

200

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Velocity (angstroms/picoseconds)

4.5

0

1200

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

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Journal Pre-proof 3) Statistical results showed that presence of four and six nanoparticles into Argon base fluid increases summation of density as much as 37% and 67%, whereas; they bring enhancement in summation of temperatures as much as 49% and 84% respectively. Therefore, these cases shall be applicable for practical application.

5- Acknowledgments This research is supported by the NSFC (51905351), Natural Science Foundation of

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Guangdong Province, China (2018A030310522), Shenzhen Science and Technology

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Planning Project, China (JCYJ20170818100522101) and Natural Science Foundation of

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Shenzhen University (2017032).

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Alnaqi, M Goodarzi, D Toghraie, Investigating the effect of nanoparticles diameter on turbulent flow and heat transfer properties of non-Newtonian Carboxy Methyl Cellulose/CuO fluid in a microtube, International Journal of Numerical Methods for Heat & Fluid Flow, https://doi.org/10.1108/HFF-07-2018-0368 [10] M Bai, W Cui, J Lv, G Li, X Li, Molecular dynamics simulation on motion behaviors of nanofluids with cylindrical nanoparticles in nanochannel, Proceedings of the

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Journal Pre-proof ASME 2012 Summer Heat Transfer Conference HT2012, July 8-12, 2012, Rio Grande, Puerto Rico [11] N Razmara, M Tavvakol Aghaii, S Jafarmadar, Effect of surface roughness on the microstructure of nanofluid flow inside nanochannels, 3rd International Conference on Nanotechnology (ICN2015), 27-28 August 2015, Istanbul, Turkey [12] H Aminfar, MA Jafarizadeh, N Razmara, Nanoparticles aggregation in nanofluid flow through nanochannels: Insights from molecular dynamic study" International Journal

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of Modern Physics C, 25 (2014) 1450066

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[13] H Aminfar, N Razmara, M Mohammadpourfard, On flow characteristics of liquid-

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solid mixed-phase nanofluid inside nanochannels, Appl. Math. Mech., 35(2014) 1541–

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1554.

[14] M Zarringhalam, A Karimipour, D Toghraie, Experimental study of the effect of

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solid volume fraction and Reynolds number on heat transfer coefficient and pressure drop

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of CuO–water nanofluid, Exp. Therm. Fluid Sci. 76 (2016) 342–351. [15] D Toghraie, M Mokhtari, M Afrand, Molecular dynamics simulation of Copper and

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Platinum nanoparticles Poiseuille flow in a nanochannels, Physica E, 84(2016)152–161 [16] M Frank, D Drikakis, N Asproulis, Thermal conductivity of nanofluid in nanochannels, Microfluid Nanofluid, 19 (2015) 1011–1017 [17] A Liakopoulos, F Sofos, TE Karakasidis, Darcy-Weisbach friction factor at the nanoscale: From atomistic calculations to continuum models, Physics of Fluids, 29(2017) 052003 [18] A Liakopoulos, F Sofos, TE Karakasidis, Friction factor in nanochannel flows, Microfluid Nanofluid, 2 (2016) 20-24

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Journal Pre-proof [19] D Toghraie Semiromi, AR Azimian, Molecular dynamics simulation of annular flow boiling with the modified Lennard-Jones potential function, Heat Mass Transfer, 48 (2012) 141–152. [20] S Zhang, F Hao, H Chen, W Yuan, Y Tang, X Chen, Molecular dynamics simulation on explosive boiling of liquid Argon film on Copper nanochannels, Applied Thermal Engineering, 113 (2017) 208–214. [21] L Li, P Ji, Y Zhang, Molecular Dynamics Simulation of Condensation on

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Nanostructured Surface in a Confined Space, Applied Physics A, 122 (2016) 496-504

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[22] CY Ji, YY Yan, A molecular dynamics simulation of liquid– vapor–solid system

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near triple-phase contact line of flow boiling in a microchannel, Applied Thermal

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Engineering, 28 (2008) 195–202

[23] D Toghraie, AR Azimian, Molecular Dynamics Simulation of Annular Flow Boiling

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Sciences, 5(2011)

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in a Microchannel with 70000 Atoms, International Journal of Physical and Mathematical

[24] T. Fu, Y Mao, Y Tang, Y Zhang, W Yuan, Effect of nanostructure on rapid boiling

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of water on a hot Copper plate: a molecular dynamics study, Heat Mass Transfer, 015(2015)1668-1672

[25] BY Cao, M Chen, ZY Guo, Liquid flow in surface nanostructured channels studied by molecular dynamics simulation, Physical Review E, 74(2006) 066311 [26] F Sofos, TE Karakasidis, A Liakopoulos, Non-Equilibrium Molecular Dynamics Investigation of Parameters Affecting Planar Nanochannel Flows, Contemporary Engineering Sciences, 2 (2009) 283 – 298 [27] L Chao, L Binwu, study of Molecular dynamics simulation of poiseuille flow in a microchannel, Micro/Nanoscale Heat Transfer International Conference January 6-9, 2008, Tainan, Taiwan

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Journal Pre-proof [28] EM Yezdimer, AA Chialvo, PT Cummings, Examination of chain length effects on the solubility of alkanes in near-critical and supercritical aqueous solutions, J. Phys. Chem. B, 105 (2001) 841–847. [29] DP Millie, Inadequacy of the Lorentz–Berthelot combing rules for accurate predictions of equilibrium properties by molecular simulation, Mol. Phys., 99 (2001) 619–625.

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[30] D Murray, M Baskes, Embedded-atom method: Derivation and application to

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impurities, surfaces, and other defects in metals, Physical Review B. American Physical

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[31] D Murray, S Foiles, The embedded-atom method: a review of theory and applications, Mat. Sci. And Engr. Rep., 9 (1993) 7–8.

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[32] SM Foiles, MI Baskes, MS Daw, Embedded-atom-method functions for the fcc

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metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys, Phys Rev B, 33(1986) 7983

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[33] O Mahian, L Kolsi, L Amani L, P Estellé, G Ahmadi, C Kleinstreuer, JS Marshall, M Siavashi, RA Taylor, H Niazmand, S Wongwises, Recent advances in modeling and simulation of nanofluid flows-part I: fundamental and theory, Physics reports, 790 (2019) 1-48.

[34] O Mahian, L Kolsi, L Amani L, P Estellé, G Ahmadi, C Kleinstreuer, JS Marshall, M Siavashi, RA Taylor, H Niazmand, S Wongwises, Recent advances in modeling and simulation of nanofluid flows-part II: applications, Physics reports, 791(2019) 1-59

[35] Q Gravndyan, OA

Akbari, D Toghraie, A Marzban, R Mashayekhi, R Karimi, F

Pourfattah, The effect of aspect ratios of rib on the heat transfer and laminar water/TiO2

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Journal Pre-proof nanofluid flow in a two-dimensional rectangular microchannel, Journal of Molecular Liquids, 236 (2017) 254-265.

[36] MR Shamsi, OA Akbari, A Marzban, D Toghraie, R Mashayekhi, Increasing heat transfer of non-Newtonian nanofluid in rectangular microchannel with triangular ribs, Physica E: Low-Dimensional Systems and Nanostructures, 93 (2017) 167-178.

[37] O Rezaei, OA Akbari, A Marzban, D Toghraie, F Pourfattah, R Mashayekhi,The

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numerical investigation of heat transfer and pressure drop of turbulent flow in a triangular

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microchannel, Physica E: Low-Dimensional Systems and Nanostructures, 93 (2017) 179-

A Heydari, OA Akbari, MR Safaei, M Derakhshani, A Alrashed, R Mashayekhi,

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189.

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GR Ahmadi Sheikh Shabani, M Zarringhalam, TK Nguyen, The effect of attack angle of triangular ribs on heat transfer of nanofluids in a microchannel, Journal of Thermal

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Analysis and Calorimetry, 131 (2018) 2893-2912.

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[39] P Alipour, D Toghraie, A Karimipour, Investigation the atomic arrangement and stability of the fluid inside a rough nanochannel in both presence and absence of different roughness by using of accurate nano scale simulation, Physica A: Statistical Mechanics and its Applications, 524(2019) 639-660.

[40] P Alipour, D Toghraie, A Karimipour, M Hajian, Molecular dynamics simulation of fluid flow passing through a nanochannel: Effects of geometric shape of roughnesses, Journal of Molecular Liquids, 275(2019) 192-203.

[41] P Alipour, D Toghraie, A Karimipour, M Hajian, Modeling different structures in perturbed Poiseuille flow in a nanochannel by using of molecular dynamics simulation:

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Journal Pre-proof Study the equilibrium, Physica A: Statistical Mechanics and its Applications, 515(2019) 13-30

[42] M Rezaei, AR Azimian, D Toghraie, The surface charge density effect on the electro-osmotic flow in a nanochannel: a molecular dynamics study, Heat and Mass Transfer 51 (2015) 661-670

[43] H Noorian, D Toghraie, AR Azimian, Molecular dynamics simulation of Poiseuille

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flow in a rough nano channel with checker surface roughnesses geometry, Heat and mass

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transfer 50 (1), 105-113, 2014

[44] M Rezaei, AR Azimian, D Toghraie, Molecular dynamics study of an electro-kinetic

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fluid transport in a charged nanochannel based on the role of the stern layer, Physica A:

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Statistical Mechanics and its Applications 426, 25-34, 2015

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[45] D Toghraie, M Hekmatifar, Y Salehipour, M Afrand, Molecular dynamics simulation of Couette and Poiseuille Water-Copper nanofluid flows in rough and smooth

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nanochannels with different roughness configurations, Chemical Physics, Volume 527, 1,

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Journal Pre-proof Highlights: A statistical investigation

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Using of molecular dynamic simulation

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Effects of suspending different number of Silver nanoparticles on the flow behavior

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boiling condition inside a microchannel with square cross section

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