Atomistic-Continuum Hybrid Simulation of Heat Transfer between Argon Flow and Copper Plates

📝 Abstract

A simulation work aiming to study heat transfer coefficient between argon fluid flow and copper plate is carried out based on atomistic-continuum hybrid method. Navier-Stokes equations for continuum domain are solved through the Pressure Implicit with Splitting of Operators (PISO) algorithm, and the atom evolution in molecular domain is solved through the Verlet algorithm. The solver is validated by solving Couette flow and heat conduction problems. With both momentum and energy coupling method applied, simulations on convection of argon flows between two parallel plates are performed. The top plate is kept as a constant velocity and has higher temperature, while the lower one, which is modeled with FCC copper lattices, is also fixed but has lower temperature. It is found that, heat transfer between argon fluid flow and copper plate in this situation is much higher than that at macroscopic when the flow is fully developed.

💡 Analysis

A simulation work aiming to study heat transfer coefficient between argon fluid flow and copper plate is carried out based on atomistic-continuum hybrid method. Navier-Stokes equations for continuum domain are solved through the Pressure Implicit with Splitting of Operators (PISO) algorithm, and the atom evolution in molecular domain is solved through the Verlet algorithm. The solver is validated by solving Couette flow and heat conduction problems. With both momentum and energy coupling method applied, simulations on convection of argon flows between two parallel plates are performed. The top plate is kept as a constant velocity and has higher temperature, while the lower one, which is modeled with FCC copper lattices, is also fixed but has lower temperature. It is found that, heat transfer between argon fluid flow and copper plate in this situation is much higher than that at macroscopic when the flow is fully developed.

📄 Content

1    Atomistic-Continuum Hybrid Simulation of Heat Transfer between Argon Flow and Copper Plates

Yijin Mao, Yuwen Zhang and C.L. Chen

Department of Mechanical and Aerospace Engineering University of Missouri Columbia, Missouri, 65211 Email: zhangyu@missouri.edu

Abstract A simulation work aiming to study heat transfer coefficient between argon fluid flow and copper plate is carried out based on atomistic-continuum hybrid method. Navier-Stokes equations for continuum domain are solved through the Pressure Implicit with Splitting of Operators (PISO) algorithm, and the atom evolution in molecular domain is solved through the Verlet algorithm. The solver is validated by solving Couette flow and heat conduction problems. With both momentum and energy coupling method applied, simulations on convection of argon flows between two parallel plates are performed. The top plate is kept as a constant velocity and has higher temperature, while the lower one, which is modeled with FCC copper lattices, is also fixed but has lower temperature. It is found that, heat transfer between argon fluid flow and copper plate in this situation is much higher than that at macroscopic when the flow is fully developed.

Keywords: heat transfer, multiscale modeling, molecular dynamics, LAMMPS, OpenFOAM.

Nomenclature A surface area expose to argon flow, m2 C volumetric heat capacity, J/m3 K cp specific heat, J/kg-K D characteristic length, m e internal energy, J fi force acting on ith atom, N h heat transfer coefficient, W/m2K k thermal conductivity, W/m K kB Boltzmann constant, 1.38×10-23 J/K mi mass of atom i, kg MJ mass of liquid argon of Jth control volume, kg n coupling interval N number of atoms Nu Nusselt number p pressure, Pa rij vector from pointing from atom j to i rc cutoff distance, m ri position vector of atom i t time, s T temperature, K u average velocity of total atoms in one control volume, m/s 2    U velocity, m/s UJ velocity of liquid argon of Jth control volume, m/s vi velocity of atom i, m/s V potential energy (or Volume of simulation box), J Q Total energy passes through the copper wall, J Greek Symbols α damping factor δtP time-step in molecular dynamics simulation ε minimum potential energy ρ density σ depth of potential well υ viscosity 

Introduction Fluid dynamics and heat transfer behaviors in micro fluidics have drawn intensive attentions in the last two decades due to the rapid development of MEMS/NEMS and many other micromechanics applications [1-3]. A better scientific understanding on fundamental mechanism at such small scale will definitely bring a favorable impact on in the foreseeable future. For example, an improved understanding of thermal conductivity from atomic point of view reveal the causes leading to thermal damage of the computer chip which is supposed to be thermally safe under the conventional Fourier law. It is often found that some experimentally measured parameters under micro- spatial/temporal scale, such as heat transfer coefficient at solid-fluid interface and thermal conductivity at solid-solid interface, dramatically disagree with the ones predicted through conventional theory for macro-scale, due to size effect [4]. In order to better understanding the heat transfer mechanism in micro-/nano-scale, numerical simulation is an effective and promising alternative approach. It is well known that the widely applied three conservation laws can resolve problems for macroscopic scale. However, due to the break-down of continuum assumption, it is also understood that an advanced theory should be developed to remedy the subsistent disadvantage of current conservation laws based simulation tools. Thus, classical molecular dynamics simulations are emerging as another powerful tool to provide detailed information on phonon scattering, which further can be used to calculate corresponding thermal properties through certain formula, such as Green-Kubo formulism. A faithful representation of dynamic system should be spatially and temporally large and long enough [4]. As a result, such level of simulation is far beyond the most advanced super computer simulation capability.
As a compromise and meanwhile to take full advantages of both sides, a hybrid simulation scheme that solve three conservation equations in larger domain while resolve atomic trajectory in smaller domain could be a promising approach at the present time. In fact, several effective hybrid simulation methods have been developed to study these particular phenomena caused by the size effect; these methods include atomic finite element method (AFEM) [5], atomistic-smooth particle method [6], and atomistic-finite volume method[7]. The AFEM has advantage of high computational efficiency for solid state problems, and the smooth-particle method is a simulation technique that is still under development [8], which also

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