Molecular dynamics study of the thermal conductivity in nanofluids

Nanofluids are a new kind of fluid which contain well-dispersed nano-sized solid particles. They tend to have higher thermal conductivity than the bulk fluid in which they are mixed. In this work, the thermal conductivity of the bulk Lennard-Jones fluid and nanofluids at various volume fractions of nanoparticles is computed thanks to equilibrium molecular dynamics (EMD) and non-equilibrium molecular dynamics (NEMD) simulations. The Green-Kubo formalism is used for the EMD simulations while a net heat flux is imposed on the system with a change of the boundary conditions for the NEMD simulations. The interactions inside the nanoparticles, between the fluid atoms, and between nanoparticles and fluid atoms are all taken as a Lennard-Jones potential. An empirical parameter, ζ , is added to the attractive part of the potential to control the hydrophilicity of the nanoparticles. Additionally, bonded atoms of nanoparticles interact with the Finitely Extensible Non-Linear Elastic (FENE) potential. The NVE ensemble is used in the simulations, for which the total number of atoms, the total volume and the total energy are constant. In order to improve the computational efficiency, we construct neighbor lists with the cell list algorithm. The equations of motion are then integrated with the Velocity Verlet algorithm with a time step of 0.001. The total energy E and the total momentum P are computed to check the validity of the code since they are both conserved quantities. Using the Lennard-Jones phase diagram from literature, we choose a phase point corresponding to a liquid state. The temperature and density are taken respectively as 1.1 and 0.7798 in dimensionless units throughout all the simulations. The initial condition of the bulk fluid has a total number of 5000 fluid atoms arranged in a regular FCC lattice. On the other hand, a spherical nanoparticle consisting of 58 atoms is generated and equilibrated in a separate molecular dynamics simulation. The bulk fluid and nanoparticles are mixed to obtain 4 simulation boxes with varying nanoparticle volume fractions of 2%, 3%, 6% and 10%. The hydrophobic parameter of the interaction potential between nanoparticles is fixed to ζ nn = 0.3 for all the simulations in order to prevent flocculation, and thus to have a well dispersed nanofluid. On the other hand, in order to study the effect of hydrophilicity on the thermal conductivity we use three different values of the hydrophilicity parameter of the fluid-nanoparticle interaction, namely ζ n f = 0.5, ζ n f = 1 and ζ n f = 1.5. In total 12 sets of simulations are initially run for 10 7 time steps of equilibration. The resulting coordinates are then used for the calculation of the average kinetic and potential energies of each atom of each species for a further 10 6 time steps. Finally, molecular dynamics simulations for collecting the heat current data are computed during 10 7 time steps. The time auto-correlation function of the heat current and its time integral are calculated in a post-processing program. The results show that the hydrophilicity of the nanoparticles did not have a measurable effect on the thermal conductivity of the nanofluid. Nanofluids with volume fractions of 2% and 3% showed an enhanced thermal conductivity with respect to the bulk fluid. The increase in the thermal conductivity is of approximately 10%. Surprisingly, nanofluids with higher volume fractions did not show any enhancement of the thermal conductivity. The numerical results obtained from EMD are then validated with NEMD simulations.