Heat flux of a granular gas with homogeneous temperature

TL;DR

This paper investigates a steady state of a granular gas with homogeneous temperature and nonzero heat flux, created by external forces or confinement, combining theoretical solutions and molecular dynamics simulations.

Contribution

It provides exact solutions at the mesoscopic level and links them with macroscopic inelastic Navier-Stokes equations, supported by molecular dynamics simulations.

Findings

Theoretical solutions match molecular dynamics in the quasi-elastic limit.

External forces can sustain heat flux in a homogeneous granular gas.

A one-parametric family of solutions is identified at the mesoscopic level.

Abstract

A steady state of a granular gas with homogeneous granular temperature, no mass flow, and nonzero heat flux is studied. The state is created by applying an external position--dependent force or by enclosing the grains inside a curved two--dimensional silo. At a macroscopic level, the state is identified with one solution to the inelastic Navier--Stokes equations, due to the coupling between the heat flux induced by the density gradient and the external force. On the contrary, at the mesoscopic level, by exactly solving a BGK model or the inelastic Boltzmann equation in an approximate way, a one--parametric family of solutions is found. Molecular dynamics simulations of the system in the quasi--elastic limit are in agreement with the theoretical results.