Heat conduction in a three-dimensional momentum-conserving fluid

TL;DR

This study investigates heat conduction in a 3D momentum-conserving fluid, revealing a finite thermal conductivity in bulk but a crossover to abnormal 1D-like behavior in elongated systems, confirming Fourier's law and theories for 3D fluids.

Contribution

The paper demonstrates the transition from normal to abnormal heat transport in 3D fluids with varying aspect ratios, providing insights into size-dependent thermal conductivity behaviors.

Findings

Bulk 3D fluid exhibits finite, non-diverging thermal conductivity.

Crossover from 3D to 1D abnormal behavior occurs at large aspect ratios.

Abnormal heat transport persists in nearly 1D fluids over large sizes.

Abstract

Size-dependence of energy transport and the effects of reduced dimensionality on transport coefficients are of key importance for understanding nonequilibrium properties of matter on the nanoscale. Here, we perform nonequilibrium and equilibrium simulations of heat conduction in a 3D fluid with the multiparticle collision dynamics, interacting with two thermal-walls. We find that the bulk 3D momentum-conserving fluid has a finite non-diverging thermal conductivity. However, for large aspect-ratios of the simulation box, a crossover from 3D to one-dimensional (1D) abnormal behavior of the thermal conductivity occurs. In this case, we demonstrate a transition from normal to abnormal transport by a suitable decomposition of the energy current. These results not only provide a direct verification of Fourier's law but also further confirm the validity of existing theories for 3D fluids. Moreover, they indicate that abnormal heat transport persists also for almost 1D fluids over a large range of sizes.