## 2 Simulation Detail  
To achieve the objectives of the present work, MD simulations were performed. For thermodynamic properties, equilibrium MD simulation is conducted for various diameters under the canonical ensemble (NVT). Non-equilibrium MD simulation is conducted to investigate a proper location of solid/fluid boundary. The metallic materials (Ag, Cu) are considered as a channel. For the fluid molecules, inert species (Ar, He) were considered. By testing the two solid models and two fluid models, the effect of the potential parameters was investigated. We assumed that there is no chemical reaction as we utilized classical MD simulation. The interatomic potentials are modeled by 12-6 Lennard-Jones (LJ) potential. The potential parameter used in this work is summarized in Table 1. Lorentz-Berthelot  
Figure 1: A pictorial representation of solid/fluid boundary at (a) the macroscopic scale; (b) the molecular scale.  
combining rules are utilized for the LJ parameters between different atoms. All MD simulations were conducted using LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) [32] with GPU (Graphics Processing Unit) package [33], while OVITO (Open Visualization Tool) [34] was used for the visualization.  
Figure 2 shows the detailed simulation setup for the MD simulation with heat transfer used in this study. This heat transfer MD setup has extensively studied for interfacial thermal resistance [37; 38; 39]. In this work, three different channel widths were considered. The periodic boundary condition is applied to the x and y directions, and the fixed boundary condition is utilized to the z-direction. The number of fluid molecules is determined so that it can reproduce a proper bulk density at the center of the fluid block (bulk region). An ideal flat solid surface is considered. The outmost second to fourth layers were locally thermostated. The thermostat generates and removes the same amount of heat by manipulating the velocity magnitude conserving the net momentum. Hence, no heat accumulation is allowed during the simulation and a constant temperature gradient can be achieved. Therefore, 0.01 eV/ps z-directional heat flux is maintained during the steady state. To reaches the desired temperature, the system is first integrated under the canonical ensemble (NVT) for 0.5 ns - 1.0 ns without the local thermostats. Then, micro-canonical ensemble (NVE) is used and the two local thermostats are activated. The heat flux data is collected during long time spans (200 ns \(\sim\) 400 ns) to ensure reliable statistics. For the equilibrium MD simulation, the simulated system is the same as the heat transfer MD, but it is only integrated under NVT ensemble at 100 K without the local thermostats during 10 ns.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Atom** & **\(\epsilon\) (eV)** & **\(\sigma\) (Å)** & **Reference** \\ \hline Cu & 0.20470 & 2.3306 & [35] \\ Ag & 0.19774 & 2.6326 & [35] \\ He & 0.00094 & 2.6400 & [36] \\ Ar & 0.01030 & 3.4050 & [36] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Pair potential parameter (12-6 Lennard-Jones).  
Figure 2: A systematic detail of heat transfer molecular dynamics (MD) simulation. The fluid molecules are confined between two solid blocks. The black atoms at the outmost solid layer are fixed. The second to forth outmost solid layer marked with red and blue color represent thermostated atoms. \(H_{\text{cc}}\) is center-to-center distance. The solid blocks have a width of seven lattice constants except for the thermostated layers and nine lattice constants along x and y directions.