# Microscopic molecular dynamics characterization of the second-order non-Navier-Fourier constitutive laws in the Poiseuille gas flow

## Abstract

The second-order non-Navier-Fourier constitutive laws, expressed in a compact algebraic mathematical form, were validated for the force-driven Poiseuille gas flow by the deterministic atomic-level microscopic molecular dynamics (MD). Emphasis is placed on how completely different methods (a second-order continuum macroscopic theory based on the kinetic Boltzmann equation, the probabilistic mesoscopic direct simulation Monte Carlo, and, in particular, the deterministic microscopic MD) describe the non-classical physics, and whether the second-order non-Navier-Fourier constitutive laws derived from the continuum theory can be validated using MD solutions for the viscous stress and heat flux calculated directly from the molecular data using the statistical method. Peculiar behaviors (non-uniform tangent pressure profile and exotic instantaneous heat conduction from cold to hot [R. S. Myong, “A full analytical solution for the force-driven compressible Poiseuille gas flow based on a nonlinear coupled constitutive relation,” Phys. Fluids 23(1), 012002 (2011)]) were re-examined using atomic-level MD results. It was shown that all three results were in strong qualitative agreement with each other, implying that the second-order non-Navier-Fourier laws are indeed physically legitimate in the transition regime. Furthermore, it was shown that the non-Navier-Fourier constitutive laws are essential for describing non-zero normal stress and tangential heat flux, while the classical andmore »

- Authors:

- School of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju, Gyeongnam 52828 (Korea, Republic of)
- (Korea, Republic of)

- Publication Date:

- OSTI Identifier:
- 22598912

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Fluids; Journal Volume: 28; Journal Issue: 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 42 ENGINEERING; ANALYTICAL SOLUTION; BOLTZMANN EQUATION; COMPUTERIZED SIMULATION; FLOW MODELS; FLUIDS; GAS FLOW; HEAT; HEAT FLUX; MOLECULAR DYNAMICS METHOD; MONTE CARLO METHOD; NAVIER-STOKES EQUATIONS; NONLINEAR PROBLEMS; PROBABILISTIC ESTIMATION; SHEAR; STRESSES; THERMAL CONDUCTION

### Citation Formats

```
Rana, A., Ravichandran, R., Park, J. H., Myong, R. S., E-mail: myong@gnu.ac.kr, and Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju, Gyeongnam 52828.
```*Microscopic molecular dynamics characterization of the second-order non-Navier-Fourier constitutive laws in the Poiseuille gas flow*. United States: N. p., 2016.
Web. doi:10.1063/1.4959202.

```
Rana, A., Ravichandran, R., Park, J. H., Myong, R. S., E-mail: myong@gnu.ac.kr, & Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju, Gyeongnam 52828.
```*Microscopic molecular dynamics characterization of the second-order non-Navier-Fourier constitutive laws in the Poiseuille gas flow*. United States. doi:10.1063/1.4959202.

```
Rana, A., Ravichandran, R., Park, J. H., Myong, R. S., E-mail: myong@gnu.ac.kr, and Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju, Gyeongnam 52828. Mon .
"Microscopic molecular dynamics characterization of the second-order non-Navier-Fourier constitutive laws in the Poiseuille gas flow". United States.
doi:10.1063/1.4959202.
```

```
@article{osti_22598912,
```

title = {Microscopic molecular dynamics characterization of the second-order non-Navier-Fourier constitutive laws in the Poiseuille gas flow},

author = {Rana, A. and Ravichandran, R. and Park, J. H. and Myong, R. S., E-mail: myong@gnu.ac.kr and Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju, Gyeongnam 52828},

abstractNote = {The second-order non-Navier-Fourier constitutive laws, expressed in a compact algebraic mathematical form, were validated for the force-driven Poiseuille gas flow by the deterministic atomic-level microscopic molecular dynamics (MD). Emphasis is placed on how completely different methods (a second-order continuum macroscopic theory based on the kinetic Boltzmann equation, the probabilistic mesoscopic direct simulation Monte Carlo, and, in particular, the deterministic microscopic MD) describe the non-classical physics, and whether the second-order non-Navier-Fourier constitutive laws derived from the continuum theory can be validated using MD solutions for the viscous stress and heat flux calculated directly from the molecular data using the statistical method. Peculiar behaviors (non-uniform tangent pressure profile and exotic instantaneous heat conduction from cold to hot [R. S. Myong, “A full analytical solution for the force-driven compressible Poiseuille gas flow based on a nonlinear coupled constitutive relation,” Phys. Fluids 23(1), 012002 (2011)]) were re-examined using atomic-level MD results. It was shown that all three results were in strong qualitative agreement with each other, implying that the second-order non-Navier-Fourier laws are indeed physically legitimate in the transition regime. Furthermore, it was shown that the non-Navier-Fourier constitutive laws are essential for describing non-zero normal stress and tangential heat flux, while the classical and non-classical laws remain similar for shear stress and normal heat flux.},

doi = {10.1063/1.4959202},

journal = {Physics of Fluids},

number = 8,

volume = 28,

place = {United States},

year = {Mon Aug 15 00:00:00 EDT 2016},

month = {Mon Aug 15 00:00:00 EDT 2016}

}