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Nonequilibrium versus equilibrium molecular dynamics for calculating the thermal conductivity of nanofluids

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Abstract

Both equilibrium and nonequilibrium molecular dynamics (EMD and NEMD, respectively) methods have been used to predict the thermal conductivity of nanofluids. However, there are considerable discrepancies among the results of these two methods. In this study, by estimating the effects of different mechanisms including the Brownian motion of nanoparticles, the micro-convection in the base fluid, the nanolayers around the nanoparticles, and the thermal boundary resistance at the surface of nanoparticle, we determine upper and lower physical limits for the thermal conductivity of a nanofluid with spherical nanoparticles. The prediction of the NEMD simulations is in the acceptable range, while the result of the EMD simulations is higher than the upper bound. Since the prediction of the EMD method is not physically justifiable, we conclude the inadequacy of the traditional EMD method in calculating the thermal conductivity of nanofluids. Consequently, we recommend the researchers to use a modified version of the EMD method or the NEMD method for new studies in this field. We also apply the NEMD method to investigate the effects of the shape of nanoparticles and the formation of percolation networks in enhancing the thermal conductivity of nanofluids. The interference of the effects of nanolayer and thermal boundary resistance on the thermal conductivity of nanofluids is a new phenomenon we introduce in this study.

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Data availability

The data that support the plots within this paper and other findings of the current study are available from the corresponding author upon reasonable request.

Abbreviations

\(A\) :

Area (\({\text{m}}^{2}\))

\(d\) :

Diameter (Å)

\(E\) :

Specific energy (\({\text{J}}\,{\text{kg}}^{ - 1}\))

\(e\) :

Energy (\({\text{J}}\))

\(\varvec{F}\) :

Force vector (\({\text{N}}\))

\(\varvec{f}\) :

Force vector (\({\text{N}}\))

\(h^{0}\) :

Time-averaged partial enthalpy (\({\text{J}}\,{\text{kg}}^{ - 1}\))

\(i\) :

Summation index

\(\varvec{J}\) :

Heat or energy flux vector (\({\text{Wm}}^{ - 2}\))

\(j\) :

Summation index

\({\text{Kn}}\) :

Knudsen number

\(k\) :

Thermal conductivity (\({\text{W}}\,{\text{m}}^{ - 1} {\text{K}}^{ - 1}\))

\({\text{ke}}\) :

Kinetic energy (\({\text{J}}\))

\(k_{\text{B}}\) :

Boltzmann constant

\(L\) :

Length (\({\text{m}}\))

\(L_{\text{c}}\) :

Characteristic length

\(M\) :

Molar mass (\({\text{gr}}\,{\text{mol}}^{ - 1}\))

\(m\) :

Mass (\({\text{kg}}\)); summation index

\(N\) :

Number of atoms; number of timesteps

\(N_{\text{Avo}}\) :

Avogadro number

\(P\) :

Pressure (\({\text{atm}}\))

\({\text{pe}}\) :

Potential energy (\({\text{J}}\))

\(\dot{Q}\) :

Rate of heat transfer (\({\text{W}}\))

\(q\) :

Heat flux (\({\text{W}}\,{\text{m}}^{ - 2}\))

\(R_{\text{b}}\) :

Interfacial thermal resistance (\({\text{m}}^{2} \,{\text{K}}\,{\text{W}}^{ - 1}\))

\(\varvec{r}\) :

Radial distance vector (\({\text{m}}\))

\(T\) :

Temperature (\({\text{K}}\))

\(t\) :

Time (\({\text{s}}\))

\(U\) :

Potential energy (\({\text{kcal}}\,{\text{mol}}^{ - 1}\))

\(V\) :

Volume (\({\text{m}}^{3}\))

\(\varvec{v}\) :

Velocity vector (\({\text{m}}\,{\text{s}}^{ - 1}\))

\(\epsilon\) :

Lennard–Jones interaction strength (\({\text{kcal}}\,{\text{mol}}^{ - 1}\))

\(\sigma\) :

Lennard–Jones length scale (Å)

\(\delta\) :

Thickness (\({\text{nm}}\))

\(\lambda\) :

Mean free path (\({\text{nm}}\))

\(\rho\) :

Density (\({\text{kg}}\,{\text{m}}^{ - 3}\))

\(\phi\) :

Volume fraction

\({\text{Ar}}\) :

Argon

\({\text{BF}}\) :

Base fluid

\({\text{Cu}}\) :

Copper

D:

Diameter direction

e:

Energy flux

\({\text{eff}}\) :

Effective

\({\text{ext}}\) :

External

h:

Enthalpy

L:

Length direction

\({\text{m}}\) :

Matrix index

NF:

Nanofluid

NL:

Nanolayer

NP:

Nanoparticle

q:

Heat

TOT:

Total

α:

Species

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Funding

The authors are grateful to Shiraz University for the computational resources and financial support.

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Authors and Affiliations

  1. School of Mechanical Engineering, Shiraz University, Shiraz, 71936-16548, Iran

    Mostafa Nejatolahi, Ali Akbar Golneshan & Reza Kamali

  2. Faculty of Advanced Technologies, Shiraz University, Shiraz, 7134851154, Iran

    Samad Sabbaghi

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  1. Mostafa Nejatolahi
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  3. Reza Kamali
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Correspondence to Ali Akbar Golneshan or Samad Sabbaghi.

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Nejatolahi, M., Golneshan, A.A., Kamali, R. et al. Nonequilibrium versus equilibrium molecular dynamics for calculating the thermal conductivity of nanofluids. J Therm Anal Calorim 144, 1467–1481 (2021). https://doi.org/10.1007/s10973-020-09595-x

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